Citation |

- Permanent Link:
- http://ufdc.ufl.edu/AA00004697/00001
## Material Information- Title:
- Derivatives and earnings management
- Creator:
- Nan, Lin
- Publication Date:
- 2004
- Language:
- English
- Physical Description:
- viii, 82 leaves : ill. ; 29 cm.
## Subjects- Subjects / Keywords:
- Accounting interpretations ( jstor )
Cost efficiency ( jstor ) Creative accounting ( jstor ) Derivative contracts ( jstor ) Financial accounting ( jstor ) Hedging ( jstor ) Investors ( jstor ) Management accounting ( jstor ) Net income ( jstor ) Signals ( jstor ) Business Administration-Accounting thesis, Ph. D ( lcsh ) Dissertations, Academic -- Business Administration-Accounting -- UF ( lcsh ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) non-fiction ( marcgt )
## Notes- Thesis:
- Thesis (Ph. D.)--University of Florida, 2004.
- Bibliography:
- Includes bibliographical references.
- General Note:
- Printout.
- General Note:
- Vita.
- Statement of Responsibility:
- by Lin Nan.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Resource Identifier:
- 3100802 ( ALEPH )
AA00004697_00001 ( sobekcm ) 759207867 ( OCLC )
## UFDC Membership |

Downloads |

## This item has the following downloads: |

Full Text |

DERIVATIVES AND EARNINGS MANAGEMENT By LIN NAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DERIVATIVES AND EARNINGS MANAGEMENT By Lin Nan August 2004 Chair: Joel S. Demski Major Department: Fisher School of Accounting Derivative instruments are popular hedging tools for firms to reduce risks. However, the complexity of derivatives brings earnings management concern and there are recent accounting rules trying to regulate the use of derivatives. This dissertation studies the joint effect of derivatives' hedging function and earnings management function, and explores how the recent rules influence firms' hedging behavior. The two-edged feature of derivatives is modeled by bundling a hedging option and a misreporting option. A mean preserving spread structure is employed to capture the risk-reduction theme of hedging. This dissertation shows a trade-off between the benefit from hedging and the dead weight loss from misreporting. It is shown that when the manager's misreporting cost declines with the effectiveness of hedging, the principal's preference for the hedge-misreport bundle does not change monotonically with the effectiveness of hedging. Specifically, when hedging is highly effective, the principal's preference for the bundle increases in the effectiveness, while when hedging's effectiveness is moderate, the principal's preference decreases in the effectiveness. When hedging is only slightly effective, whether the principal prefers the bundle is not influenced by the effectiveness. In addition, this dissertation shows that sometimes it is not efficient to take any measure to restrain earnings management. Recent regulations require firms to recognize the ineffective portion of hedges into earnings. This dissertation indicates that this early recognition may change the firms' hedging behavior. Since the early recognition increases the interim earnings' riskiness, hedging may become inefficient even though it still reduces the total risk. In this sense, the new regulations may not benefit investors, though their intention is to provide more information about the risk and value of derivatives to the investors. Copyright 2004 by Lin Nan To my parents Manping Wang and Weihan Nan, and to Laurence ACKNOWLEDGEMENTS I am very grateful to Joel S. Demski, my Chair, for his guidance and encouragement. I also thank David Sappington, Karl Hackenbrack, Froystein Gjesdal, and Doug Snowball for their helpful comments. TABLE OF CONTENT ACKNOWLEDGMENTS....................................................... .......... iv A B ST R A C T ........................................................................................ v CHAPTER 1 BACKGROUND AND LITERATURE REVIEW.............................. .............. B ackground............................................................................ ........................1. . Literature Review on Hedging................................................... ..................... 3 Review of Earnings Management and Information Content...............................9 Review of LEN Framework.......................................................................11 Summ ary. .................................................... ................. ... .......... ....... .14 2 BASIC MODEL........................................................... ........ 15 The M odel............................................................................. ...............15 Basic Setup..................................... .. ...... ............................ ..... 16 B enchm ark ........................................................................................................ 17 Hedging and Earnings Management Options..................................................... 19 Sum m ary................................................. ... .............................. ...................30 3 HEDGE-MISREPORT MODEL..................................................32 Bundled Hedging and Misreporting Options...................................................32 W whether to Take the Bundle................................................................... 34 Sum m ary.................................................. ........................................... ...37 4 MANIPULATION RESTRAINED BY HEDGE POSITION............................. 41 Cost of Earnings Management...................................................................41 "Strong Bundle" M odel..................................................................................41 Whether to Take the Strong Bundle.......................................................... ..... 43 Sum m ary................................................................. .... ......... 47 5 EARLY RECOGNITION MODEL ............ ... ............................ .... ..... ...... 51 Early Recognition of Hedging ...... .............................................................. 51 Centralized Case......................................... ....... ........ 53 Delegated Case...................................................................................54 Sum m ary.................... ...................... .........................................................59 6 OTHER RELATED TOPICS.......................................................................61 Riskiness and Agency....................................................................................... 61 Informative Earnings Management: Forecast Model........................................ 62 Sum m ary......................... ................................................................................ 64 7 CONCLUDING REMARKS...................................................................... 66 A P P E N D IX ............................................................................................................. 68 REFERENCE LIST........................................................................................................78 BIOGRAPHICAL SKETCH...................................................................................82 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DERIVATIVES AND EARNINGS MANAGEMENT By Lin Nan August 2004 Chair: Joel S. Demski Major Department: Fisher School of Accounting Derivative instruments are popular hedging tools for firms to reduce risks. However, the complexity of derivatives brings earnings management concern and there are recent accounting rules trying to regulate the use of derivatives. This dissertation studies the joint effect of derivatives' hedging function and earnings management function, and explores how the recent rules influence firms' hedging behavior. The two-edged feature of derivatives is modeled by bundling a hedging option and a misreporting option. A mean preserving spread structure is employed to capture the risk-reduction theme of hedging. This dissertation shows a trade-off between the benefit from hedging and the dead weight loss from misreporting. It is shown that when the manager's misreporting cost declines with the effectiveness of hedging, the principal's preference for the hedge-misreport bundle does not change monotonically with the effectiveness of hedging. Specifically, when hedging is highly effective, the principal's preference for the bundle increases in the effectiveness, while when hedging's effectiveness is moderate, the principal's preference decreases in the effectiveness. When hedging is only slightly effective, whether the principal prefers the bundle is not influenced by the effectiveness. In addition, this dissertation shows that sometimes it is not efficient to take any measure to restrain earnings management. Recent regulations require firms to recognize the ineffective portion of hedges into earnings. This dissertation indicates that this early recognition may change the firms' hedging behavior. Since the early recognition increases the interim earnings' riskiness, hedging may become inefficient even though it still reduces the total risk. In this sense, the new regulations may not benefit investors, though their intention is to provide more information about the risk and value of derivatives to the investors. CHAPTER 1 BACKGROUND AND LITERATURE REVIEW Background Derivatives include "a wide variety of financial and commodity instruments whose value depends on or is derived from the value of an underlying asset/liability, reference rate, or index" (Linsmeier 2003). Financial derivatives have been developed rapidly and employed widely since the early 1990s. Alan Greenspan, the Chairman of the Federal Reserve Board, said in a speech before the Futures Industry Association in 1999 that "by far the most significant event in finance during the past decade has been the extraordinary development and expansion of financial derivatives." Financial derivatives are very popular tools for risk-reduction in many firms and the global derivatives market has grown rapidly. At the end of June 2003, the Bank for International Settlements estimated that the total estimated notional amount of over-the-counter (OTC) derivatives contracts stood at US$169.7 trillion with a gross market value of $7.9 trillion.1 The derivatives have played an important role in the firms' risk management activities. On the other hand, the complexity of financial derivatives raises investors' concern about how the derivatives change the firms' performance, and suspicion about whether the derivatives are abused in the interest of the management. During the past ten years, there are numerous scandals involving the use of derivatives. For example, in March 2001, a Japanese court fined Credit Suisse First Boston 40 million Yen for using complex derivatives transactions to conceal losses. Also in 2001, Enron, the seventh largest company in the United States and the largest energy trader in 'Notional amount is the market value of the hedged items whose risk is hedged by the use of derivatives. It is different from the market value of the derivatives. the world, collapsed. Investigations revealed that it had made extensive use of energy and credit derivatives to bolster revenues. Responding to the investors' concern, the Financial Accounting Standards Board (FASB) recently issued several new statements on the measurement and disclosure of derivatives, including SFAS 133, 137, 138 and 149. There are also tons of detailed implementation guidance from the Emerging Issues Task Force (EITF). As of the November 12-13, 2003, EITF meeting, there are at least 38 issues directly addressing the accounting for derivative instruments. Although the FASB makes all these new regulations, it is unlikely that the new regulations will eliminate earnings management through derivatives. In addition, some new rules may even provide new avenues for earnings management. For example, SFAS 133 requires firms recognize both derivatives and hedged items at their fair value, even before the settlement of the derivative contracts. When the increase/decrease in a derivative's fair value cannot offset the decrease/increase in its hedged item's fair value, the uncovered part is regarded as the ineffective portion of the hedge and is recorded immediately into earnings. However, evaluating the "fair value" of unsettled derivatives is often subjective. Managers can either estimate the fair value based on the current market price of other derivatives, or invoke "mark-to-model" techniques. With a subjective estimation of the fair value, the estimation of the ineffective portion is also discretionary. Derivative instruments, therefore, have a two-edged feature. They can be used as tools to reduce firms' risks (that is, tools of hedging), but they can also be used as tools of earnings management. This two-edged feature provides us an ideal setting to study the joint effect of hedging and earnings management, which is one of the focuses of this dissertation. Literature Review on Hedging Among the research on hedging activities, the incentives for hedging, how hedging activities influence contracting between the principal and the manager, and how the FASB regulations affect hedging behavior are most explored. Hedging Incentives First, for the research on hedging incentives, there are some finance studies on why firms hedge. Smith and Stulz (1985) analyze the determinants of firms' hedging policies from the perspective of firm value. They examine taxes, bankruptcy cost, and managers' wealth. Regarding hedging activities as a kind of insurance, Mayers and Smith (1982) use the theory of finance to analyze the corporate demand for insurance from the perspectives of taxes, contracting costs and the impact of financing policy on firms' investment decisions. Smith and Stulz (1985) conclude that hedging reduces a firm's tax liability if the post-tax firm value is a concave function of the pre-tax firm value. Nance, Smith, and Smithson (1993) provide the empirical evidence that firms with more of the range of their pretax income in the statutory progressive region of the tax schedule, or have more tax preference items, are more likely to hedge. This supports Smith and Stulz's statement on the corporate hedging incentive from tax liability. However, Graham and Rogers (2002) quantify the convexity-based benefits of hedging by calculating the tax savings that result from hedging and do not find evidence that firms hedge in response to tax convexity. Smith and Stulz (1985) also study hedging from the perspective of the manager's wealth. They indicate that the manager would like to hedge if his end-of-period wealth is a concave function of the end-of-period firm value, while the manager would not hedge if his end-of-period wealth is a convex function of firm value. Rogers (2002) considers both the manager's stock holdings and option holdings, and finds the risk-taking incentives from options are negatively associated with the use of derivatives. This evidence is consistent with Smith and Stulz's suggestion that the manager's wealth plays a role in hedging decision, and is also consistent with the notion that derivatives are to reduce firms' risks. Mayers and Smith (1982) argue that the corporation does not "need" insurance to reduce the stockholders' risk since the stockholders can eliminate insurable risk through diversification. Instead, insurance is optimally designed to shift the risk of managers and employees to stockholders, since the managers and other employees do not have enough ability to diversify claims on human capital. It then follows that the higher the employees' fraction of the claims to the firm's output, the higher the probability that the firm will purchase insurance. Smith and Stulz (1985) point out that hedging lowers the probability of incurring bankruptcy costs. Graham and Rogers (2002) show empirical evidence that firms with more expected financial distress hedge more, which is consistent with the idea that firms hedge to reduce risks. Nance, Smith and Smithson (1993) find that firms who have less coverage of fixed claims (a proxy for financial distress) hedge more, which is another piece of empirical evidence to support the risk reduction incentive. Contrary to works such as Smith and Stulz (1985) and Nance, Smith and Smithson (1993), Schrand and Unal (1998) emphasize that hedging is a means of allocating a firm's risk exposure among multiple sources of risk rather than reducing total risk. However, in some sense, their allocation theory is still consistent with the risk-reduction theory. In Schrand and Unal's paper, the total risk is reflected in the variability of a loan portfolio's cash flow. They further classify the risk into two types: core-business risk, from which the firm can earn economic rent for bearing since it has an information advantage in the activities related to this risk; and homogenous risk, where the firm does not have any information advantage and cannot earn rent. Schrand and Unal claim that the firms use hedging to increase core-business risk and reduce homogenous risk. In other words, the firms confidently play with core-business risk in which they have expertise and more "control," but reduce the uncontrollable homogenous risk by hedging. The uncontrollable homogenous risk is the real risk for the firms. Though there are a number of incentives for hedging activities, here in this paper I focus on the risk-reduction incentive. Risk reduction is the initial intention of the invention of various financial derivatives, and it is the main purpose of hedging activities. Hedging and Contracting Secondly, for the research on contracting, there are some, but not many, studies on how the hedging activities affect contracting. Campbell and Kracaw (1987) focus on optimal insurance through hedging by the manager. They show that under certain incentive contracts, shareholders will be hurt by the manager's hedging behavior since the manager will deviate from the optimal managerial effort level with the acquisition of insurance. However, if the contract anticipates the hedging, then the shareholders will benefit from that hedging. The reason is that the shareholders can reduce fixed payments to the manager to acquire the direct gain from hedging reaped by the manager and they can induce the manager to exert more effort by raising the manager's share of risky returns. Their result is consistent with this paper's conclusion that hedging reduces compensating wage differentials in a LEN framework. However, unlike the model in this paper, they assume the outputs are always public and their work does not consider earnings management. In addition, their analysis focuses on how hedging influences firm value, while in the current paper my focus is how hedging influences the information content of performance measures. Another related paper is DeMarzo and Duffie (1995), who also analyze hedging behavior from the perspective of information content. They show that financial hedging improves the informativeness of corporate earnings as a signal of managerial ability and project quality. However, in their model, the manager's action is given, so there is no need to motivate the manager to work diligently. Moreover, unlike the model in my work, their model does not consider manipulation of earnings by the managers. Recent Hedging Regulations Thirdly, recent new FASB regulations on hedging have triggered some research on how the new rules affect firms' hedging behavior. The recent rapid development of various financial derivatives and the complexity of derivatives raise the concern that the explosion in their use may endanger investors' interest, since it is difficult for investors to understand from the financial reports the magnitude, value and potential risk of the derivatives. Since 1994, the FASB has issued several new regulations on the disclosure of derivatives. Among these regulations, SFAS 119 (which was later superseded by SFAS 133) requires more disclosure on the use of derivatives, and SFAS 133 requires that an entity recognize all derivatives as either assets or liabilities in the statement of financial position and measure those instruments at fair value. These regulations are complex, to say the least, and have led to considerable debate. Responding to the controversy, the FASB issued SFAS 137 to defer the effective date for SFAS 133 from June 1999 to June 2000, and later also issued SFAS 138 and 149 as amendments of SFAS 133. Recent research provides both pros and cons of the hedging disclosure policy. Barth et al. (1995) respond to the FASB Discussion Document about hedge accounting and the FASB Exposure Draft. They argue that a mark-to-market accounting is the best approach to accounting for hedging activities and they support the disclosure policy. They claim that disclosures about management objectives in using derivatives for risk management are useful to financial statement users and are value relevant. Kanodia, Mukherji, Sapra, and Venugopalan (2000) examine the social benefits and costs under different hedge accounting methods from a macroeconomic view. They claim that hedge accounting provides information about firms' risk exposure to the market, thus helps make the futures price more efficient. Melumad, Weyns, and Ziv (1999) also compare different hedge accounting rules, but they focus on the managers' decision making process. They show that under comprehensive fair-value hedge accounting, investors can infer the necessary information from the reported earnings for the valuation of the firm, though the market does not directly observe intermediate output and hedge position. In this case the managers choose the same hedge position as in the public information case. In contrast, under the no-hedge accounting rules, the managers choose a lower hedge position than in the public information case. This is because the investors cannot infer new information from the earnings report to revise their evaluation and the market price at the interim date has less variance. Melumad, Weyns and Ziv support hedge accounting against no-hedge accounting, but they believe only comprehensive fair-value hedge accounting is efficient while recent accounting regulations, e.g., SFAS No. 133, only require limited fair-value hedge accounting or cash-flow hedge accounting. On the other side, DeMarzo and Duffie (1995) argue that it is optimal for the shareholders to request only the aggregate output instead of disclosure of hedging positions. The reason is that with nondisclosure of hedging positions, managers choose risk minimization (full hedging) since reduced output variability leads to a more stable wage. However, when the hedging positions are required to be disclosed, the managers deviate from optimal full hedging since disclosed hedging eliminates noise from the outputs and makes the outputs more sensitive signals of the managers' ability. Holding the variability of output fixed, this disclosure makes the managerial wage more variable. A related concern is that the recorded value for derivatives can be manipulated by managers. A derivative's "fair value" refers to the current market price of similar derivatives. However, it is often difficult to find "similar" derivatives. Managers then must estimate the "fair value" of the derivatives based on the current market price of other derivatives or invoke "mark-to-model" techniques. This leaves the "fair value" of the derivatives up to the managers' discretion. In this sense, the new accounting rules for derivatives provide a new field for earnings management, and the complexity of many derivatives is itself a choice variable. Therefore, derivatives can function both as tools for hedging and for earnings management. Even in Barth, Elliott et al. (1995) and Barth, Collins et al. (1995), they admit that the mark-to-market approach is arbitrary and creates opportunities for earnings management, though they insist that the "fair value" approach to report hedging activities is still the best option. Among empirical studies, Barton (2001) is probably the first to study the interaction between hedging and earnings management. He measures derivatives using notional amounts and discretionary accruals using the modified Jones model. Barton finds that firms with larger derivatives portfolios have lower levels of discretionary accruals. He suggests managers use discretionary accruals and derivatives as partial substitutes to smooth earnings so as to reduce agency costs, income taxes, and information asymmetry, and to increase personal wealth and utility. Since he believes that the earnings management through accruals and derivatives use are some kind of substitutes, his paper suggests that SFAS No. 133 may cause fewer hedging activities but more accrual management. Unlike the analysis of the current paper, Barton's study only considers the hedging function of derivatives and does not consider the earnings management function of derivatives. Focusing on the oil and gas industry, Pincus and Rajgopal (2002) also explore the interaction between accrual management and hedging. Their empirical result is partially consistent with Barton's result. However, they emphasize that their result suggests a sequential process whereby the managers first decide how much to hedge and manage the accruals only during the fourth quarter, which weakens Barton's substitution hypothesis. Review of Earnings Management and Information Content Literature on earnings management is as vast as the ocean. There are numerous studies attempting to document the existence of earnings management, and a lot of research on when and why the managers manage the earnings. I am not so ambitious as to review all related literature, not to say there are already some good reviews of the earnings management literature, such as Schipper (1989), Healy and Wahlen (1999), Beneish (2001), and Lev (2003). Here I focus on the literature on "efficient" earnings management. For empirical studies, researchers usually use the market reaction to an earnings announcement to measure the information content in the earnings. Abnormal discretionary accruals are usually regarded as proxies for managers' manipulation and many studies focus on whether the market can "see through" the managed earnings. The hypothesis is that if the market is efficient, then the investors will not be fooled by the manipulation. There are further studies on who is more easily fooled (unsophisticated investors). The unspoken words here are that the manipulation of earnings is "bad," and it is just a garbling of the information. This opinion about earnings manipulation is even stronger among investors and regulators after the scandals of Enron and WorldCom. The SEC has been taking measures to fight earnings management. Walter P. Schuetze, a former chief accountant in the SEC, even proposes mark-to-market accounting to eliminate the manipulation of earnings. However, recently researchers began to question whether it is worth eliminating managers' manipulation. First, the elimination of discretion will shut the doors of communicating managers' private information to investors. Taken to the extreme, if we totally eliminate any manipulation and return to a mark-to-market accounting, then the existence of accounting is meaningless. Financial statements should be sources of information and communication tunnels between management and investors. If financial statements were reduced to be just records of the investors' estimates about the firms' operating activities based on other information, then we did not "need" financial statements or accounting. Accrual accounting provides a tunnel for the managers to use their judgement and discretion to better communicate with the financial statements users. Beneish (2001) states that there are two perspectives on earnings management. One is the opportunistic perspective, which claims that managers seek to mislead investors. The other is the information perspective, which regards the managerial discretion as a means for managers to reveal to investors their private expectations about the firm's future cash flows. Similarly, Dechow and Skinner (2000) call for attention on how to distinguish misleading earnings management from appropriate discretion. They further indicate that it is hard to distinguish certain forms of earnings management from appropriate accrual accounting choices. Demski (1998) demonstrates that in a setting with blocked communication, when the manager's manipulation requires his high effort level, it may be efficient for the principal to motivate earnings management. If we eliminate discretion in order to put a stop to the "detrimental" earnings management, we may close the communication channel between the managers and the investors. Secondly, eliminating earnings management, even if earnings management merely garbles information, may be too costly. Liang (2003) analyzes equilibrium earnings management in a restricted contract setting and shows that the principal may reduce agency cost by tolerating some earnings management when the contract helps allocate the compensation risk efficiently. Arya, Glover and Sunder (2003) tell a story of "posturing," that when the commitment is limited and the information system is not transparent, allowing manipulation is more efficient than forbidding it. Demski, Frimor and Sappington (2004) show that assisting the manager to manipulate in an early period may help ease the incentive problem of a later period. In their model the principal's assistance reduces the manager's incentive to devote effort to further manipulation and induces the manager to devote more effort to production. As stated in Arya, Glover and Sunder (1998), when the Revelation Principle is broken down (that is, when communication is limited, the contract is restricted, or commitment is missing), earnings management may be efficient. In this paper, in most cases the existence of earnings management in equilibrium comes from the violation of the unrestricted contract assumption, since I assume a linear contract. I also suppose an uneven productivity setting to induce earnings management, following a design in Liang (2003). This paper shows that, even if earnings management merely destroys information, sometimes it is not only inefficient to motivate truth-telling but also inefficient to take any measure to restrain earnings management, since restraining manipulation may be too costly. In the last chapter of this paper, I also include an analysis of informative earnings management (the forecast model), in which earnings management conveys the manager's private information. Review of LEN Frameworks Most of my analysis in this paper is in a LEN framework. LEN (linear contract, negative exponential utility function, and normal distribution) is a helpful technology for research in agency and has been employed in more and more analytical research. Among the three assumptions of the LEN framework, exponential utility and normal distribution have been widely used and accepted, while the linear contract assumption is more controversial. Lambert (2001) gives a good review on LEN. He summarizes three common justifications for the linear contracting setting. The first is that according to Holmstrom and Milgrom (1987), a linear contract is optimal in a continuous time model where the agent's action affects a Brownian motion process. However, it is not easy to fit their model into multi-action settings. The second justification is that the contracts in practice are usually simple, instead of in the complicated form of the optimal contracts from agency models. The argument against this justification, however, is that even in practice, contracts are not strictly linear. The third justification is tractability. Linear contracts are usually not the optimal contracts, but they provide great tractability and help researchers explore some agency questions that were hard to analyze in the conventional agency models. For example, LEN is especially helpful in multi-action or multi-period agency problems. This is the most important reason that LEN has become more popular. However, as mentioned by Lambert, we achieve this tractability with a cost of restricting the generality. Nevertheless, except for some questions that cannot be addressed by linear assumptions such as the study on contract shapes, the LEN setting still provides plentiful insight. Feltham and Xie (1994) are among the first to employ LEN in analytical analysis. They focus on the congruity and precision of performance measures in a multidimensional effort setting, where the agent allocates his effort on more than one task. They show that with single measure, noncongruity of the measure causes a deviation from the optimal effort allocation among tasks, and noise in the measure makes the first-best action more costly. In their setting, the use of additional measures may reduce risk and noncongruity. There are some works on selecting performance measures for contracting purposes using LEN frameworks. Indjejikian and Nanda (1999) use a LEN framework to study the ratchet effect in a multi-period, multi-task contract. They show that in a two-period setting, when the performance measures are positively correlated through time, and when the principal cannot commit not to use the first period performance in the second period contracting, the agent is inclined to supply less effort in the first period, since a better first period performance increases the "standard" for the second period performance. To motivate the agent to work hard in the first period, the principal has to pay more for the first period. Indjejikian and Nanda also suggest that an aggregate performance measure may be better than a set of disaggregate measures, and consolidating multi-task responsibility to one agent may be better than specializing the responsibilities to avoid the ratchet effect. Autrey, Dikolli and Newman (2003) model career concerns in a multi-period LEN framework. In their model, there are both public performance measures and private measures that are only available to the principal. Their work shows that the public measures create career concerns and help the principal reduce the compensation to the agent, while the private measures enable the principal to reward the agent more efficiently. They suggest that it is better to use a combination of both public and private measures in contracting. LEN technology is also employed in the research on valuation and accrual accounting. Dutta and Reichelstein (1999) adopt a multi-period LEN framework in part of their analysis on asset valuation rules. In a setting where the agent's effort affects the cash flows from operating activities, they show that incentive schemes based only on realized cash flows are usually not optimal since it is difficult for the principal to eliminate the variability in cash flow from financing activities. Discretionary reporting and earnings management are also among the topics explored using LEN frameworks. Christensen and Demski (2003) use a covariance structure to model reporting schemes (either conservative or aggressive) under a linear contract in a two-period setting. They discuss when reporting discretion is preferred to inflexible reporting and when it is not, and further explore the role of an auditor in this setting. They use an asymmetric piece-rate to model the incentive for the exercise of reporting discretion. Similarly, Liang (2003) uses a time-varying production technology and therefore uneven bonus schemes through time to explore earnings management. He studies the equilibrium earnings management in a two-period, multi-player (managers, shareholders, and regulators) setting. His work shows that a zero-tolerance policy to forbid earnings management may not be economically desirable. In this paper, LEN provides great tractability, and also induces earnings management. Summary Prior research on derivatives explores the incentives for hedging, how hedging influences contracting, and the pros and cons of the recent derivatives disclosure regulations. Derivatives are popular instruments for hedging. However, the complexity of derivatives also makes them handy tools for managers to manipulate earnings. Up to now there is little theoretical research on the joint effect of the hedging function and the earnings management function of derivatives, though there is a lot of research on either hedging or earnings management. In addition, this chapter also provides a review of the LEN framework, which is a component of my following models to study the joint effect of hedging and manipulation. CHAPTER 2 BASIC MODEL To study the joint effect of hedging and earnings management through the use of derivatives, I use a two-period LEN model. A no-hedging, no-misreporting case is employed as the benchmark. The hedging option and the misreporting option then will be introduced into the benchmark to study the influence of hedging and manipulation. The Model The main model in this paper is a two-period model in a LEN framework. There is a risk neutral principal and a risk averse agent (manager). The principal tries to minimize her expected payment to the manager while motivating the manager to choose high as opposed to low actions in both periods. The manager's preference for total (net) compensation is characterized by constant absolute risk aversion, implying a utility function of u(S c) = -e-r(-), where S is the payment to the agent, c is the manager's cost for his actions, and r is the Arrow-Pratt measure of risk aversion. Without loss of generality, the manager's reservation payment is set at 0. In other words, his reservation utility is -e-r(). Performance signals (outputs) are stochastic, and their probability is affected by two factors: the manager's action and some exogenous factor. The manager's action is binary. In each period, the manager either supplies low action, L, or high action, H, H > L. Without loss of generality, L is normalized to zero. The manager's personal cost for low action is zero. His personal cost for high action is C > 0 in each period. The principal cannot observe the manager's actions. An exogenous factor also affects realized output. The effect of this exogenous factor on the output can be hedged at least partially by using derivatives. Neither the principal nor the manager can foresee the realization of the exogenous factor. Here, "output" represents a noisy performance measurement of the manager's action levels (e.g., earnings); "output" does not narrowly refer to production and can be negative. I use x1 to represent the output for the first period, and x2 to represent the output for the second period. Basic Setup Assume x1 = klal + ei and x2 = k2a2 + E2, with ai E {H, 0}, i E {1, 2}. ai represents the action level for period i. k1, k2 are positive constants and represent the productivity in the first and the second periods, respectively. Suppose k, > k2. The uneven productivity follows a design in Liang (2003). The different productivity induces different bonus rates through time and is important for the ensuing of earnings management. (The assumption ki > k2 is relaxed in Chapter 5.) The vector [e, e2] follows a joint normal distribution with a mean of (0, 0]. There is no carryover effect of action, and the outputs of each period are independent of each other.' If the outputs are not hedged, the covariance matrix of [E, 2] is E = o2 0 S If the second period output is hedged (as I discuss in a later section, 0 22 o any such hedge is confined to the second period), the matrix is Ed = 0 O a2 < a2. The hedging process is stylized with a mean preserving spread structure: assuming the same action level, the hedged production plan has a lower variance, aO, than that of the unhedged one, a2, though they share the same mean. Thus the unhedged production plan is a mean preserving spread of its hedged counterpart. In this way, hedging lowers the variance of output due to the uncontrollable exogenous factor and reduces the noisy output risk. This structure captures the risk reduction theme of Rothschild and Stiglitz (1970), and also offers tractability. SThe conclusions in this paper persist when the outputs have a non-zero covariance. The manager's contract or compensation function is assumed to be "linear" in the noted output statistics. Specifically, S = S(xl, X2) = W + axl + /32, where W is a fixed wage, and a and 3 are the bonus rates respectively assigned to the first period output, xl, and the second period output, x2. Benchmark The benchmark is a public-output, no-hedge-option model. There is no option to hedge in this benchmark, and earnings management (misreporting actual outputs) is impossible since the output for each period is observed publicly. To solve the principal's design program in this benchmark, I start from the second period. To motivate the manager's high action in the second period, the principal sets the contract so that the manager's certainty equivalent, when he chooses high action, is at least as high as that when he chooses low action, for each realization of xi. Denote the manager's certainty equivalent when he chooses a2 given x, at the beginning of the second period as CE2(a2; xl), the incentive compatibility constraint for the second period is CE2(H; xl) CE2(0; x), V x (IC2) With x1 known and x2 a normal random variable with mean k2a2 and variance a2, it is well known that CE2(a2; l) = W + ax + Ok2a2 c(al, a2) 23a2. (c(al, a2) represents the manager's cost for his actions.) Thus, (IC2) can be expressed as W + ax + k2H C 32a2 > W + axI j2a2, which reduces to > j, regardless of xl. Denote the manager's certainty equivalent at the beginning of the first period when he chooses al followed by a2 regardless of xl as CE (al; a2). To motivate al = H given high action in the second period, the incentive compatibility constraint for the first period is CEI(H; H) 2 CE(0; H) (IC1) If a2 = H, regardless of x1, (IC2) is satisfied, then S(zx, X2) is a normal random variable with mean W + akcial +,3k2H and variance a2c2 + /322. Thus (IC1) implies W+akiH+ 3k2H- 2C- !(a 2 +2 +22) > V W+ k2H -C- (2a22 + 2a2), which reduces to a > C kiH The individual rationality constraint requires the manager's certainty equivalent when he chooses high actions in both periods is not lower than his reservation wage, normalized to 0. The individual rationality constraint therefore is CE (H; H) > 0 (IR) Expanding (IR), we get W + aklH + fk2H 2C --(cT2a2 + /2U2) > 0. The principal minimizes her expected payment to the manager, E[W + a(kiH + e1) + f(k2H + E2)] = W + oakH + 3k2H. Her design program in this benchmark model is min W +akiH+3k2H Program[A] s. t. W + akH + k2H 2C -(a2 2q2) > 0 (IR) a> (IC1) i kiH (IC2) The individual rationality constraint must be binding, as otherwise the principal can always lower W. Thus, the optimal fixed wage must be -akiH - Ok2H+2C+ (a2a2+/ 32u2), and the principal's expected cost is 2C+((2a2 a2+f2a2). Therefore, the principal's design program reduces to the minimization of (a (2a2 + 02a2) subject to the two incentive constraints.2 The optimal fixed wage is chosen to ensure that the individual rationality constraint binds. I therefore focus on the bonus rates in the optimal contracts in our analysis. Denote a* as the optimal first period bonus rate and /3 the optimal second period bonus rate, we now have 2This result has been shown in, for example, Feltham and Xie (1994). Lemma 2.1: The optimal contract in the benchmark model exhibits a* = -- and P* C A k2H Proof: See the Appendix. In a full-information setting the principal only needs to pay for the reservation wage and the personal cost of high actions, 0 + 2C. In the present benchmark setting, the principal needs to pay 0 + 2C + (aoU2 + f32U2). The principal pays more since the manager bears compensation risk with a risk premium or compensating wage differential of (a*2a2 + 0322). Next I introduce the hedging and earnings management options. Hedging and Earnings Management Options Hedging Option Initially suppose the second period output can be hedged, but no possibility of managing earnings is present. In practice, a hedging decision is usually made to reduce the risk in the future output. To capture this feature, assume that the hedging decision is made at the beginning of the first period, but the hedge is for the second period output only and doesn't influence the first period output. Recent FASB regulations on derivatives, e.g. SFAS No. 133, require that firms recognize the ineffective portion of hedges into earnings even before the settlement of the derivatives." In this chapter I do not consider the recognition in earnings from unsettled derivatives. (That is, I assume hedging only influences the output of the second period, when the hedge is settled.) The estimation of the hedge's ineffectiveness involves earnings management, and I will address the manipulation associated with the use of derivatives later. 3Consider a fair value hedge as an example. At the date of financial reporting, if the increase/decrease in the fair value of the derivative doesn't completely offset the decrease/increase in the fair value of the hedged item, the uncovered portion is regarded as the ineffective portion of the hedge, and is recognized into earnings immediately. However, this gain or loss from unsettled derivatives is not actually realized, and the estimation of the hedge's ineffectiveness is usually subjective (for the evaluation of derivatives' fair value is usually subjective). Centralized-hedge case First, consider a centralized-hedge case, where the principal has unilateral hedging authority. (Later in this chapter I will delegate the hedging option to the manager.) Notice that the benchmark is identical to the case here if the principal decides not to hedge. If the principal hedges, the principal's design program changes slightly from the one in the benchmark. The expected payment is still IV + aklH + f3k2H. The incentive constraints for the manager remain the same, since the hedging decision is not made by the manager and the action choice incentives are unaffected by hedging activities. However, the individual rationality constraint changes to be W + akH + /3k2H 2C -!(a2.2 + 32 o) > 0. The principal's design program in the centralized-hedge model when she hedges is min W + aklH + /k2H Program [B] W,a,3 s. t. W + akH +3k2H- 2C --a(L22 + /32) > 0 (IR) a > c (IC1) kjH S> !H( (IC2) I use a*, 0* to denote respectively the optimal bonus rates in the first and the second periods in Program [B]. Paralleling Lemma 2.1, I immediately conclude Lemma 2.2: The optimal contract in the centralized-hedge model exhibits a* = kiH and /B = k2H Proof: See the Appendix. The optimal contract shares the same bonus rates with that in the benchmark, because the manager's action affects the output mean, while hedging only affects the output risk. As implied by the (IR) constraint, when there is no hedging option or when the principal does not hedge, the principal's expected payment is 2C+ (Oa*2a2+ /2a2), while its counterpart with hedging is 2C + (~o2 + Af dj). With hedging, her expected cost is reduced by ~2 (a2 -oU). Obviously, the principal prefers hedging to no hedging. Using d = 0 to represent the strategy of no hedging, and d = 1 to represent the strategy of hedging, we have Lemma 2.3: The principal prefers d = 1 in the centralized-hedge model. Proof: See the above analysis. The principal's expected cost is lower when she hedges, because hedging reduces the noise in using output to infer the manager's input, and thus provides a more efficient information source for contracting. Therefore, the compensating wage differential is reduced. Delegated-hedge case Next, I change the setting into a delegated one. In practice, managers, not shareholders, typically decide on the use of derivative instruments, since the managers usually have expertise in financial engineering. To capture this fact, I change the model so the manager, rather than the principal, makes the hedging decision. This decision is made by the manager at the beginning of the first period, but hedges the second period's output. The time line of this delegated-hedge model is shown in Figure 2-1. It has been shown that when the principal makes the hedging decision, she prefers hedging since hedging reduces the compensating wage differential. The question now, is whether hedging is still preferred when the hedging decision is delegated to the manager. With the hedging decision delegated to the manager, although the manager has the option not to hedge, the manager will always choose to hedge. This is because hedging reduces the output variance and therefore reduces the manager's compensation risk derived from noisy output signals. To illustrate this conclusion, I use CE (al, d; a2) to denote the manager's certainty equivalent at the beginning of the first period when he chooses al and d in the first period and chooses a2 in the second period. By hedging, CE,(al, 1; a2) = W + akla, + 3k2a2 c(ai, a2) r(a2 2 + 020 2). If the manager doesn't hedge. CE (ai, 0; a2) = W + aklal + 3k2a2 c(al, a2) (au2 + 02a2). Since a, 3 > 0, CE, (al, 1; a2) > CE1(al, 0; a2) for o2 < (2. Therefore d = 1 is always preferred. Lemma 2.4: For any action choice, the manager always prefers d = 1. Proof: See the above analysis. As with the centralized model, allowing the manager to hedge the output is efficient. The manager gladly exercises this option and in equilibrium the compensating wage differential is reduced. Proposition 2.1: Hedging is efficient regardless of whether the manager or the principal is endowed with unilateral hedging authority. Proof: See the analysis in this section. In the LEN framework, hedging lowers the output variance but has no effect on the output mean, while the manager's action affects the output mean but not the variance. Therefore, there is separability between the action choices and the hedging choice. The optimal bonus rates are not affected by the hedging choice. Misreporting Option To this point, I have focused on settings where the realized output is observed publicly. Here I introduce the option to manipulate performance signals. I presume hedging is not possible in this subsection, but will combine both hedging and earnings management options later in the next chapter. Suppose the output for each period is only observable to the manager. The manager chooses the first period action level, al e {H, 0}, at the beginning of the first period. At the end of the first period the manager observes privately the first-period output xl. He reports x 6E {xl, xz A} to the principal and chooses his action level for the second period, a2 E {H, 0}. At the end of the second period, again the manager observes privately the second-period output, 2, and reports x2 = Xz 21 + x2. The principal observes the aggregate output of the two periods at the end of the second period and pays the manager according to the contract. The linear contract here becomes S = W + ail + T2. The manager may have an option to misreport the output by moving A from the first to the second period. (A can be negative. Negative A implies that the manager moves some output from the second to the first period.) Assume the manager manipulates at a personal cost of -A2, which is quadratic in the amount of manipulation.4 The manager faces the misreporting option with probability q, and he doesn't know whether he can misreport until the end of the first period.5 I use m = 1 to represent the event that the misreporting option is available, and m = 0 to represent its counterpart when the misreporting option is unavailable. The time line is shown in Figure 2-2. Notice in the benchmark case of Lemma 2.1 where there is no option to misreport, the bonus rates for the two periods are not equal, and a* = < 3* = __. If the outputs were observed privately by the manager, the manager would have a natural incentive to move some output from the first to the second period, since he receives greater compensation for each unit of output produced in the second period. If m = 1, the manager's certainty equivalent at the beginning of the second period becomes W + axi + 3k2a2 + ( a)A A2 c(a, a2) 322. Notice that with a linear contract, the manager's manipulation choice is separable from his action choices and the output risk. This separability implies that the optimal 4The quadratic personal cost follows a similar design in Liang (2003). It reflects the fact that earnings management becomes increasingly harder when the manager wants to manipulate more. 5The manager, even though determined to manipulate, may not know whether he can manipulate at the beginning, but has to wait for the chance to manipulate. "shifting" occurs where '[(l a)A _A2] = 0, or A*= 1 a. The only way to deter manipulation in this setting is to set a = 3. I again solve the principal's design program starting from the second period. Since the manager always chooses A* = / a as long as he gets the misreporting option, we use CE2(a2, A*; x1, m = 1) to denote the manager's certainty equivalent at the beginning of the second period when he gets the misreporting option and chooses a2 after privately observing the first period output xl. We use CE2(a2; X, m = 0) to denote the manager's certainty equivalent when he doesn't get the misreporting option. The incentive constraints for the second period are CE2(H, A*; xI, 1) > CE2(0, A*; xi, 1), and CE2(H; x1, 0) > CE2(0; x1, 0), Vxl. With the noted separability, it is readily apparent that both constraints collapse to 3 > C-, just as in the k2H' benchmark. I use CEl(al;a2) (to distinguish from CEl(al;a2) in the benchmark) to denote the manager's certainty equivalent at the beginning of the first period when he chooses al followed by a2 in the second period. At the beginning of the first period, since m is random, the manager's expected utility at the beginning of the first period is: (1 q)Eu[W +a(kial + fe) + 3(k2a2 + 62) c(a, a2)] +qEu[W + a(klal + e- A) +P(k2a2 + 2 A*) c(al, a2) 1A*2]. Therefore, CE1(al; a2) is the solution to u(CEl(a; a2)) = (1-q)Eu[W +a(klal +l)+3(k2a2+ 2) -c(al, a2)] +qEu[W + a(kial + eI A*) +f(k2a2 + E2 + A*) -c(a, a2) 2] = -(1 q)e-r[lW+aklal +k2a2-c(al,a2)- 1 (a2 +O2U2)J _qe-r[W+aklal+Ok2a2-c(a1,a2)- ~(a 2a+/02a2) -A*2+( -4 )A*j = _e-r[W+ak1ia1+k2a2-c(ai,a2)- (a2o+ 2a2)] [(1 -rq[( -)A* -A*2] = -e-r(CEl(al;a2)) Thus, -r(CE1(a(;a2)) = -r[W + akial + 3k2a2 c(a,) -(a2 2 + 032a2)] + ln[(l q) + qe-(-)2], and CE (al; a2) = W + akial + Ok2a2 c(al, a2) - 2(a2"2 + 32a2) 1ln[(1 q) + q- ]. Comparing CE (al; a2) with CE (aa; a2) in the benchmark, we have CE, (a,; a2) = CE (a,; a2) i ln[(l q) + qe- -)] Importantly, now, the agent's risk premium reflects the summation of the earlier risk premium, due to the variance terms, and an additional component due to the shifting mean effects introduced by earnings management. The additional component comes from the extra bonus from manipulation and the higher uncertainty of the compensation. Given a2 = H, the incentive compatibility constraint for the first period is CE1(H; H) > CE1(0; H). Again, thanks to the separability between the action choice and the manipulation amount choice, this constraint reduces to a > c just as in the benchmark case. The individual rationality constraint in this model is CEI(H; H) > 0, or W + aklH + fk2H 2C --(a22 + 32) ln[(l q) + qe-i(-)2]'] 2 0. The principal's expected payment to the manager, upon substituting the manager's A choice, is (1 q)E[W + a(k1H + Eq) + i(k2H + E2)] +qE[W + a(k1H + e1 (/ a)) + O3(k2H + Q2 + (3 a))] = (1 q)[W + akiH + Sk2H] +q[W + a(kiH (3 a)) + 1(k2H + (/ a))] = W + akH + pk2H + q(P a)2. Now the principal's design program in this misreporting model is: min W + ak1H + /k2H + q(3 a)2 Program [C] W,a, 3 s. t. W + akiH + k2H 2C -(22 + 2a2) ln[(l q) + qe- )2] 0 (IR) a> C (IC1) > k2H (IC2) Similar to the previous models, here the individual rationality constraint must bind, and the principal's expected cost can be expressed as 2C +!(a2ao2 +,32a2) +1 ln[(1 q) + qe- -)2] + -a)2. For later reference, the reduced program is written below. min (a22 + 12) + 1 ln[(l q) + qe-(-o)2] + q(_ a)2 Program [C] s. t. a > c (IC1) S> 2H (IC2) Define a*. 3* as the optimal bonus rates in Program [C'], we have the following results. Proposition 2.2: The optimal contract in the misreporting model exhibits C k1H -- ac k-- c* Corollary 2.1: When q is sufficiently low, the optimal contract in the misreporting model exhibits ac = and P H = - Corollary 2.2: When q is sufficiently high and ki is sufficiently large, the optimal contract in the misreporting model exhibits a* > C- and *c = cj. Proof: See the Appendix. Compare Program [C'] with the benchmark: when q = 0. we revert to our benchmark case; however, when q > 0, the misreporting option introduces a strict loss in efficiency. The principal must compensate for the manager's risk from the uncertain misreporting option. There is also a bonus payment effect for the manipulated amount of output. In addition, the principal may choose to raise the first period bonus rate, which increases the riskiness of the unmanaged compensation scheme. Note in this model we always have a* < 0*. Although the misreporting option merely garbles the information and does not benefit the principal, it is never efficient for the principal to motivate truth-telling and completely eliminate the manager's incentive to misreport by setting a = 3. Instead, it is efficient to tolerate some misreporting. This surprising fact is also shown in Liang (2003). Liang documents that the optimal contract exhibits a* $ P, while the analysis in the present paper provides more details on the optimal contact. More surprisingly, the principal not only tolerates some misreporting by setting ac < 3*, but sometimes she even maintains the bonus rates at the levels in the benchmark case where there is no misreporting option. Although an uneven bonus scheme leads to manipulation, it may not be efficient for the principal to adjust the bonus scheme to restrain manipulation. The reason for this conclusion is the following. Since the induced misreporting is given by A* = a a, the dead weight loss of misreporting can be reduced by lowering 3 a. To lower 3 a, the principal either lowers 8 or raises a. However, / has a binding lower bound at c, and the principal cannot reduce 3 below that bound. Thus the optimal 3 remains at its bound. By raising a, the principal reduces the dead weight loss of misreporting, but simultaneously increases the riskiness of the unmanaged compensation scheme ( (a2a2 +/2a2) goes up). Hence there is a trade-off. When the chance of misreporting is small (q is sufficiently low), the principal finds it inefficient to raise the bonus rate, since the corresponding reduction in the misreporting dead weight loss does not outweigh the increase in the riskiness of the unmanaged compensation scheme. On the other hand, when the probability of misreporting is sufficiently high, the losses from misreporting constitute a first order effect. In this case, the principal may find it optimal to raise the first period bonus rate. In addition, when the first period productivity k1 is high, the lower bound for the first period bonus is low, and the principal is more willing to raise the first period bonus above the lower bound to reduce the misreporting dead weight loss. Table 2-1 shows a numerical example to illustrate Proposition 2.2, and Corollaries 2.1 and 2.2. In this numerical example, I fix the values of the cost of high action C = 25, high action level H = 10, output variance a2 = 0.5, risk aversion r = 0.5, and the second period productivity k2 = 15. I focus on how the optimal contract changes with the misreporting probability q and the first period productivity kl. When q is very small (q = 0.01), the optimal contract has both a* and 3* at their lower bounds. However, when q is high (q = 0.9) and ki is large (ki = 200), the first period bonus rate a* in the optimal contract deviates from its lower bound c kiH' For simplicity, I use the case q = 1 to explore more details on the misreporting option. Ubiquitous misreporting opportunities (q = 1) When q = 1, Program [C] becomes min W + aklH +pk2H + (3 a)2 Program [C(q = 1)] W,a,B s. t. W + ak1H +/k2H -2C + I(/ a)2 (a22 + /2a2) > 0 (IR) a 2 (IC1) S> k1H (IC2) The situation when q = 1 is special, because there is no uncertainty about the misreporting option. The principal knows the manager will always shift 3 a to the second period to get additional bonus income of (/3-a)A* = (0-a)2. Responding to this, she can cut the fixed wage by (3 a)2 to remove the bonus payment effect. However, although the principal removes fully the certain bonus payment from her expected payment to the manager, she must compensate for the manager's dead weight personal cost of misreporting. Define a 1, I/3 as the optimal bonus rates for the misreporting model when q = 1. We have the following result. Proposition 2.3: When q = 1, the optimal contract in the misreporting model exhibits Ci = T and -c =k- if ki > k2(1 + ro2); a1 = and 3e = otherwise. kIH C k2H Proof: See the Appendix. If the productivity of the two periods is very different (that is, kl is much higher than k2), the naive bonus rates for the two periods are very different too, and the manager prefers to move a great amount of output between periods to take advantage of the uneven bonus scheme. In this case, the principal raises the first period bonus rate to make the bonus scheme more even to reduce the dead weight loss of misreporting. However, keep in mind that this brings a cost of higher risk premium for unmanaged noisy output. Unexpectedly, even when q = 1, in some cases the principal still maintains the bonus rates at the levels as in the setting where there is no misreporting option. The optimal contract may still exhibit (a*1, 0Z*) = (a*, ,3). In other words, even when the misreporting opportunities are ubiquitous, it may still be optimal not to restrain misreporting. With an attempt to restrain misreporting by raising a from its lower bound, the increase in the riskiness of the unmanaged compensation scheme may outweigh the reduction in the dead weight loss of misreporting. It is a general belief of investors and regulators that we must take measures to address detrimental earnings management. In September 1998, Arthur Levitt, Chairman of SEC, warned that earnings management is tarnishing investors' faith in the reliability of the financial system, and kicked off a major initiative against earnings management. From then on, the SEC has taken a variety of new and renewed measures to fight earnings management. However, according to our results in Propositions 2.2 and 2.3, in some cases it is optimal not to take any measure to restrain earnings management. Even when misreporting opportunities are ubiquitous, it may be better just to live with misreporting instead of taking any action to fight it. This conclusion may sound counter-intuitive and cowardly, but is in the best interest of investors. 30 Summary This chapter shows that in a LEN framework, hedging option reduces the compensating wage differential for the principal and reduces the compensation risk for the manager. On the other hand, the introduction of a misreporting option complicates the agency problem. Surprisingly, although manipulation is detrimental to the principal, sometimes it is not efficient to take any action to restrain earnings management. 2nd Period Manager chooses xl observed publicly. X2 observed publicly. al E {H, 0}, and Manager chooses Manager gets paid. dE {0,1}. a2 {H,0}. Figure 2-1: Time line for delegated-hedge model 1st Period 2nd Period Manager chooses Manager observes al E {H,0}. privately Xl and m. i1 reported. Manager chooses a2 E {H, 0}. Figure 2-2: Time line for misreporting model Manager observes privately X2. 22 reported. (Principal sees aggregate output.) Table 2-1: Numerical Example for Proposition 2.2, Corollaries 2.1 and 2.2 kC C a kl q kiH k2H C 20 0.01 0.125 0.1667 0.1250 0.1667 C = ji, C = H 200 0.9 0.125 0.1667 0.1304 0.1667 aC > C ,B = C= ...... .__ ...._ I_ __ II IIC___ C k2H 1st Period CHAPTER 3 HEDGE-MISREPORT BUNDLE MODEL The last chapter analyzes the hedging and misreporting options respectively. Now I bundle the delegated hedging option and the misreporting option. This bundling allows us to study the joint effect of the hedging function and manipulation function of derivatives. Bundled Hedging and Misreporting Options Suppose at the beginning of the first period, the manager chooses his action level al E {H, 0}, and has the option to hedge. Hedging again only affects the output in the second period but the hedging decision is made at the beginning of the first period. Further, suppose the hedging option is bundled with the misreporting option. If and only if the manager chooses hedging, with probability q can he later misreport the output by moving some amount of output between periods. This "hedge-misreport bundle" setting reflects the current concern that managers use derivatives to reduce risks but can also use the derivatives as tools of earnings management. At the end of the first period the manager observes privately the first-period output x1, and at this point he observes whether he can misreport (if he chose hedging). Similar to the misreporting model, if the manager gets the misreporting option, he shifts 3 a from the first to the second period. The time line of the hedge-misreport bundle model is shown in Figure 3-1. Similar to Lemma 2.4 in the last chapter, here, the manager always prefers to hedge. To illustrate this, I use CE1 (a, d; a2) to represent the manager's beginning certainty equivalent when he chooses al and d followed by a2. When the manager chooses to hedge, CE1 (a,, 1; a2) = W + aklat + /k2a2 c(al, a2)- (a2a + 2a) - Sln[(l q) + qe-i(-o)21]. When the manager does not hedge, CEi(al, 0; a2) = W + 32 akcia + /k2a2 c(al, a2) ~a2a2 + 222). It is easy to verify that CEi(al, 1; a2)> CE (al, 0; a2). That is, the manager always hedges in this bundled model. Therefore the bundled model is identical to the misreporting model with the second period output hedged (in other words, with the second period output variance reduced to O2). The principal's design program in this bundled model is min W + ak1H + fk2H + q(3 a)2 Program [D] w,a,3 s. t. W + aklH + Pk2H 2C -(a2 + 2) ln[(l q) + qe-(-2] >2 0 (IR) a > (IC1) k2 (IC2) Again, Program [D] can be reduced to the minimization of !(a(2 2+/32o"2)+ In[(1 q) + qe- (-~)2J+ q(0 a)2 subject to the incentive constraints. For the convenience of later analysis, I show the reduced program below. min (a2 r2 + 032),2 1 ln[(l q) + qe-(3-a)2]+ q(/ a)2 Program [D'] s. t. a > c (IC1) k2H (IC2) It is readily verified that the optimal bonus rates in the bundled model are identical to those in the misreporting model, since the manager's action choices do not depend on his hedging choice. However, compared with the misreporting model, the principal's expected cost is reduced by 2(,2 2- 2), thanks to the hedging option. The principal does not need to motivate the manager to hedge, since the manager always exercises the hedging option. Although the hedging option and the misreporting option both affect output signals, they affect the signals in different ways. The hedging option influences output signals through variances. The greater is the reduction in the noisy output's variance (a2 oa), the more beneficial is the hedging option. On the other hand, the misreporting option influences output signals through means. With the misreporting option, the manager shifts 3* OD from the mean of the first period output to the mean of the second period output. The amount of manipulation / aD and the increased compensating wage differential due to misreporting depend on a host of factors, including the misreporting probability q, the action productivity, and ra2. In addition, note that although we target earnings management associated with the use of derivatives, the analysis of the influence on performance signals from earnings management holds for general earnings management activities. Whether to Take the Bundle The hedge-misreport bundle is a mixture of "good" and "bad." As analyzed in the prior chapter, the hedging option alone, no matter whether centralized or delegated, is always preferred, since it lowers the output variance and reduces the compensating wage differential. However, the misreporting option complicates the agency problem. It is just a garbling of information and reduces the reliability of performance signals. In their classic article, Ijiri and Jaedicke (1966) define the reliability of accounting measurements as the degree of objectivity (which uses the variance of the given measurement as an indicator) plus a bias factor (the degree of "closeness to being right"). In their terms, we say that the hedging option improves the objectivity of performance signals, and therefore improves the reliability of the signals. On the other hand, the misreporting option increases the bias by shifting output between periods, and reduces the reliability of performance signals. If the principal faces a take-it-or-leave-it choice on the hedge-misreport bundle, she needs to see whether the increase in the reliability of performance signals from the hedging option exceeds the decrease in the reliability from the misreporting option. Lemma 3.1: When q is sufficiently low, the hedge-misreport bundle is preferred to the benchmark. Lemma 3.2: When q is sufficiently high and k1 is sufficiently large, the hedge-misreport bundle is preferred to the benchmark only if a2 o2 is sufficiently large. Proof: See the Appendix. Table 3-1 illustrates numerical examples for the above lemmas. I suppose the cost of high action C = 25, high action H = 10, risk aversion degree r = 0.5, and the second period productivity k2 = 1.5. From the numerical examples, we see when q is sufficiently low (q = .1), the principal prefers the bundle. While when q is sufficiently high (q = .8) and ki is sufficiently large (ki = 5), the principal does not prefer the bundle if a2 o2 is small (a2 a_ = .25). She prefers the bundle when o2 o2 is sufficiently large (a2 = 6). When the probability that the manager can misreport, q, is sufficiently low, misreporting is of limited concern. The increase in agency cost due to the misreporting option is outweighed by the reduction in agency cost due to hedging, and it is optimal for the principal to take the hedge-misreport bundle. With high probability of misreporting option and high first period productivity ki, however, the misreporting option in the bundle can impose severe damage and greatly increases the compensating wage differential. In this case, the principal admits the hedge-misreport bundle only when the benefit from hedging is sufficiently large. That is, only when the hedging option greatly reduces the noise in the output signals (a2 a2 is sufficiently large) does the principal take the bundle here. Now focus on the q = 1 case. From Program [D'], when q = 1, the program becomes min (a 2a2 + 3202) +(( a)2 Program [D'(q = 1)] s. t. a > (IC1) k2 (IC2) Define aD1, 3l as the optimal bonus rates in the bundled model when q = 1, we have Lemma 3.3: When q = 1, the optimal contract in the hedge-misreport bundle model exhibits aD1 2 = and D1i = -2 if k12 k2(1 rr2); aD =C and Xi" = otherwise. Proof: See the Appendix. As mentioned earlier, due to the separability between the manager's hedging choice and his action choices, the optimal bonus scheme in the bundled model is identical to that in the misreporting model. Proposition 3.1: When q = 1, (1) if ki > k2(1 + ro2), the hedge-misreport bundle is preferred to the benchmark when k2 _2-(i+ra2)(a2) 2 ) fc( > 1(I+ra2) (a) and (2) if kI < k2(1 + ra2), the bundle is preferred to the benchmark when (k-k2 (b) (kl -k2)2 > r7_,) Proof: See the Appendix. Proposition 3.1 provides a detailed analysis on the trade-off between the benefit from the hedging option and the cost from the misreporting option when q=1. First, for both the cases of kl > k2(1 + ra2) and ki < k2(1 + ra2), the hedge-misreport bundle is more likely to be preferred (in other words, condition (a) or (b) is more likely to be satisfied) when a2 is high.' Intuitively, when the unhedged output signals are very noisy, the principal has a strong preference for hedging to reduce the noise and is more likely to take the bundle, regardless of the accompanied cost of misreporting. af2-(l+ra2)(a2--a, -(1+ra2)2a2-ra2)2%2 'Define Q --~r(i+) in condition (a), we have = -0(l+r a)- < 0. It is easy to verify that in condition (b) also decreases in o2. Second, for both cases, it is readily verified that conditions (a) and (b) are more likely to be satisfied when the Arrow-Pratt degree of risk aversion, r, is high. When the manager is very risk averse, the principal must pay a high compensating wage differential to the manager for the noisy output signals. Thus, the principal would like to reduce the noise in output signals and so has a strong preference for hedging. Hence she is more likely to take the hedge-misreport bundle regardless of the accompanying cost of misreporting. Third, for both cases, the harm from misreporting behavior is smaller when ki and k2 are similar in magnitude. (ki and k2 are similar in magnitude implies the bonus rates can be set closer, and the potential damage from misreporting is small.) The more similar are ki and k2, the more likely is condition (a) or (b) to be satisfied, hence the more likely is the hedge-misreport bundle to be preferred. Fourth, for both cases, the benefit from hedging is higher when hedging greatly reduces the noise in output signals (that is, when a2 ao2 is large). The more the hedge can lower the second period output variance, the more likely is condition (a) or (b) to be satisfied, hence the more likely is the principal to prefer the bundle. The numerical examples in Table 3-2 illustrate these comparative static observations. We see from the examples that the principal is more likely to take the bundle when o2 od2 is large, a2 is high, r is high, or ki is close to k2. Summary A hedge-misreport bundle is used to model the two-edged feature of derivative instruments in this chapter. I analyze the trade-off between the improvement of performance signals' objectivity brought by hedging and the increase in the performance signals' bias due to earnings management. With a LEN framework, hedging makes it easier for the principal to infer the manager's action from output signals, and thus helps lower the compensating wage differential. In addition, hedging is efficient regardless of whether the manager or the principal is endowed with unilateral hedging 38 authority. On the other hand, earnings management merely garbles information. It is also shown that hedging and earnings management influence performance signals from different angles. and their net influence depends on various factors. 2nd Period Manager chooses a E {H, 0}, dE {0,1} Figure 3-1: Time Manager observes priv, xz and m (if chose d = x1 reported. Manager chooses a2 E {H, 0}. line for hedge-misreport lately x2 observed privately. 1). x2 reported. (Principal sees aggregate output.) bundle mode Table 3-1: Numerical Examples for Lemma 3.1, 3.2 parameters principal's expected cost benchmark ? bundle q=.1 ki = 3 50.4340 -< 50.2977 a2 a = .25 q =.8 ki = 5 50.3785 >- 50.4454 a2 a = .25 q=.8 k = 5 50.6056 -< 50.5239 a2 -- o=.6 1st Period Table 3-2: Numerical Examples for Proposition 3.1 parameters key parameters principal's expected cost benchmark ? bundle a2 = .75 r = .5 (U22 high; a2 a' high) 50.8138 50.5534 ki =2 k2I = 1.5 a2 = .30 50.3255 50.3548 9 = .25 (a2 low; a2 a low) kl =2 r = .9 (r high) 50.9766 -< 50.7509 k2 = 1.5 a2 =.5 r = .01 (r low) 50.0109 < 50.0104 ad = .25 ki = 1.6, k2 = 1.5 r = .5 (kl, k2 close) 50.6524 < 50.4842 a2 = .5 a] = .25 kl = 5, k2 = 1.5 50.3785 50.4514 (kl, k2 not close) CHAPTER 4 MANIPULATION RESTRAINED BY HEDGE POSITION In the hedge-misreport bundle model in Chapter 3, a hedging option is bundled with a misreporting option, but the influence on the outputs from misreporting is separable from the effect of hedging. In this chapter, a stronger bond is tied between hedging and misreporting. This stronger bond reflects the fact that greater use of derivatives can provide expanded opportunities for earnings management. Cost of Earnings Management Firms' risks involve many uncontrollable factors, such as interest rate changes, foreign exchange rate changes, credit defaults, and price changes. Reducing firms' risks more effectively requires more hedging, while the increase in the use of derivatives, in turn, makes it easier to manipulate earnings. When the manager reduces risks more effectively with more derivatives, he also obtains additional ways to manipulate. In other words, the cost of earnings management is lowered. To reflect the association between the cost of earnings management and the extent of hedging, I suppose the manager's personal cost of earnings management is ( -) A2. To simplify the notation, define D =- a2 a2, and express the manipulation cost as 2A2. The personal cost of manipulation is still quadratic in the amount of manipulation. In addition, now the marginal cost of manipulation is associated with the hedge position. I call this new setting the "strong bundle" model. As in the previous model, I suppose the manager can manipulate only if he hedges. Without hedging, there is no way to manipulate earnings, or it is extremely costly to manipulate. "Strong Bundle" Model With personal cost of manipulation A2, the manager's optimal manipulation amount will again occur when the marginal cost of manipulation equals the marginal benefit, that is, when = 2(0-). This implies A* = D(/ a). As in the previous hedge-misreport bundle model, suppose the manager gets the misreporting option with probability q given that he hedges, and he does not know whether he can misreport until the end of the first period. If he obtains the misreporting option, he will shift D(P a) from the first to the second period to capture additional bonus. Let CE (al; a2; d = 1) denote the manager's certainty equivalent at the beginning of the first period, given that he hedges. We readily find CE'(al; a2; d = 1) = W + akla + fk2a2 c(al, a2) Oa 22 +2) ln[(l q) + qe-D(-0)2. Now the manager's benefit from misreporting, -' ln[(l q) + qe-D(-)2]1, is associated with the hedging position, D. In addition, the larger the D, the more the benefit from misreporting for the manager, regardless of the additional increased riskiness from the misreporting option2. Compared to the previous model in Chapter 3, the manager benefits not only from hedging through reduced riskiness of outputs, but also from an increased marginal gain from manipulation. Therefore, it is easy to verify that the manager still always prefers hedging (d = 1), regardless of his action choices. Similar to the analysis in Chapter 3, the principal's design program to encourage the manager's high actions is: min W + ak1H + Ok2H + qD(f a)2 Program [E] W,a,1 s. t. CE(H; H; d= 1) > 0 (IR) a > C. (IC1) k1H (IC) C H (IC2) 'Notice that -In[(1 q) + qe-gD(e-a' ] is positive. It is the result of joint effects from increased riskiness of compensation and additional bonus from manipulated output net of personal manipulation cost. 2Define Q ln[(1 q) + qe-zD(-)2] We have a = 2 qe- -'2("- ) > 0. o 2 l--q(l--e-f D("-U')) As usual, the (IR) constraint must bind, so W* = -aklal /Sk2a2 + 2C + r(a22 + /2o.) + I ln[(l q) + qe-1D(-a)2], and the principal's objective function can be rewritten as (a2a2 + 2ao) + 1 ln[(l q) + qe-1D(,-~)2] + qD(3 a)2. Now the principal's design program reduces to min (a(22 + /32) + 1 ln[(1 q) + qe-D(-a")2] + qD(3 a)2 s. t. Program [E'] a > c (IC1) Sk2H (IC2) Define a), 0* as the optimal bonus rates in Program [E']. We have Proposition 4.1: The optimal contract in the strong bundle model has kiH E < k~H P Corollary 4.1: When q is sufficiently low, the optimal contract in the strong bundle model has a* = and 3* -. kH E k2H Corollary 4.2: When q is sufficiently high, D is sufficiently large, and the difference between ki and k2 is sufficiently large, the optimal contract in the strong bundle model has aE > and *E = Proof: See the Appendix. In contrast to the model in Chapter 3, the hedge position now plays a role in deciding whether to linit earnings management. When D is sufficiently large, the cost of misreporting (-A2) is low. If the probability of misreporting is not trivial, the potential misreporting damage is severe. With a severe misreporting threat, it is efficient for the principal to raise a to limit earnings management. Whether to Take the Strong Bundle In the hedge-misreport bundle model in Chapter 3, although hedging is a prerequisite for the manager to misreport, the benefit from hedging and the cost from misreporting are separable. Whether it is efficient to take the bundle depends on a clear-cut trade-off between the reduced output variance and the garbled output means. In the current strong bundle model, hedging is not only a prerequisite for earnings management, but also affects the manager's manipulation amount through its effect on the personal cost of earnings management. The trade-off between hedging and earnings management becomes more complex. Lemma 4.1: When q is sufficiently low, the strong bundle is preferred to the benchmark. Proof: See the Appendix. Obviously, if the probability of misreporting option is very low, misreporting is all second order effect, even though hedging reduces the misreporting cost. However, when q is high and k1 is significantly larger than k2, D plays a double role in the principal's view of the strong bundle. A highly effective hedge greatly reduces the noise in the output signals, but also greatly reduces the manager's personal cost of manipulation. This is most evident when q = 1. Ubiquitous Misreporting Opportunities When q = 1, that is, when the manager can always misreport, the principal's design program becomes mm (2(a2 + 2) + D( a)2 s. t. Program [El] a > (IC1) k2> H (IC2) Define a*, 31, as the optimal bonus rates for the strong bundle model when q = 1. We have the following result. Proposition 4.2: When q = 1, the optimal contract in the strong bundle model has E1 D n C ,r2 <,2 o and 371 = C if D > (or 2, < ( )); k2H kl/k2-1 r kl/k2-1 EI = Hand = -i otherwise. Proof: See the Appendix. We use Figure 4-1 to show how the first period optimal bonus rate, a*l, changes with the hedging position, D. Notice that ac, = 2C > C when D > r2. In other words, the +ra2k2H k-H ki/k2-1 principal raises a from its lower bound when D > 2 Intuitively, if D is large, earnings management is going to be a first order effect, and the optimal contract has to reduce the manipulation incentive by increasing a. More precisely, when D < ,r2 the optimal first period bonus rate is fixed at -, while when D > the optimal first period bonus rate increases gradually at a decreasing rate.3 Right after D exceeds ra2 /k2-1, as the hedge becomes more effective (D gets larger), the principal has to increase the first period bonus rate sharply to cope with the increased manipulation. However, when the hedge gets even more effective (D approaches oa2), the principal does not need to improve the first period bonus so much to deal with manipulation. Turning to the question at hand, we have the following characterization. Proposition 4.3: When q = 1 : Case (1): If -< 2(1_ k/k the strong bundle is preferred to the benchmark when k2 (2-2)(a2-ru2) ( k c 2(2_ +,ra2)2 (A') Case (2): If a > a2(1 2-1) the strong bundle is preferred to the benchmark when 1> 1- -Vr (B') Otherwise, it is not efficient for the principal to take the strong bundle. Proof: See the Appendix. Corollary 4.3: In Case (1) or (2) of Proposition 4.3, condition (A') or (B') is less stringent with higher risk aversion degree r;and condition (A') or (B') is less stringent when kl and k2 are similar in magnitude. Proof: See the Appendix. Condition (A') or (B') is less stringent means the condition is more likely to be satisfied. With a less stringent condition (A') or (B'), the principal is more likely 3Here -' r ra c (- ) ,= r-2 < 3Here -- TT= ^ k > 0, and o72 = 2 kT < O. ,H';fi7( T-D),k to prefer the strong bundle. Intuitively, a higher r indicates that the manager is more risk averse. When the manager is very risk averse, the principal must pay a high risk premium to the manager for the noisy output signals. Thus, the principal would like to reduce the noise and has a strong preference for hedging. Hence she is more likely to take the strong bundle. In addition, when productivity does not change much through time (kl and k2 are similar in magnitude), the bonus rates will not change much through time either. With little additional bonus gain from misreporting, even when the cost of misreporting is low, the manager's manipulation will not bring great damage. Thus the principal is more likely to take the strong bundle. In other words, the conditions for the strong bundle to be preferred are less stringent. Corollary 4.4: When a o- 2(1 k/k21) (a) if a(T2 < 2( 1 ), then the smaller the a2 the less stringent is condition (A'); (b) if a2( 1+) < ,2 < a2 k/-l), t then the larger the o2 the less stringent is condition (A'). Corollary 4.5: When o, > a2(1 )k,)), o does not influence the principal's decision on whether to take the strong bundle. Proof: See the Appendix. In the strong bundle, the "good" from hedging and the "bad" from manipulation are colinear, so a low ao in and of itself is not a cause for joy. The principal's preference for the bundle is not monotonic in a2. To explore the intuition behind these results, recall Figure 4-1: In Figure 4-1, when D is small (o- is large), the principal does not raise the first period bonus rate a from its lower bound, since it is not worth raising the bonus rate to restrain earnings management. Correspondingly, here in Corollary 4.5, when acr is sufficiently large, the effectiveness of hedging does not affect the principal's decision on whether to take the strong bundle. Since the hedge is poorly effective and the manipulation cost is high, neither hedging nor manipulation has significant influence. In Figure 4-1, when D gets larger and exceeds "'2 (od gets smaller than a2(1 r_)), the principal has to raise a greatly to deal with the increased manipulation, while when D approaches a2 (oa approaches zero), the principal raises the first period bonus rate only at a decreasing rate. In Corollary 4.4, we see when ad is intermediate, the marginal benefit from hedging's effectiveness cannot beat the marginal loss from manipulation, and the principal is more likely to take the bundle with a less effective hedge. When ad approaches zero, however, the marginal benefit from hedging's effectiveness beats the marginal loss from manipulation, and the principal is more likely to take the bundle with a more effective hedge. Figures 4-2A and 4-2B show how the principal's preference for the strong bundle changes with the effectiveness of the hedge (represented by ad). To further illustrate the tension between the benefit from the hedge's effectiveness and the loss from the more manipulation around a21r2~) in Figure 4-2A, we use a numerical example to show how the principal's preference for the effectiveness of the hedge changes. In this example we suppose r = .5, ki = 5, k2 = 1, a2 = .5 so that or2( r2) a2(1 l/r-1) is satisfied. The value of a2(`2j) here is .4165. The numerical example is presented in Table 4-1. Summary From the analysis in this chapter, we see when the manager's personal cost of manipulation decreases with the effectiveness of the hedge, there is more tension when the principal decides whether to take the hedge-misreport bundle. When the hedge is highly effective, the more effective the hedge, the more likely the principal prefers the bundle since the marginal benefit from hedging's effectiveness beats the marginal loss from lower manipulation cost. When the hedge is moderately effective, however, the principal is more likely to take the bundle with a less effective hedge, since the marginal loss from misreporting is more considerable compared with the marginal 48 benefit from the hedge's effectiveness. But when the hedge is poorly effective, the effectiveness plays no role in the principal's decision on whether to take the bundle, since both the hedging benefit and the loss from manipulation are insignificant. I C Ir1 H T - C k, 4-1: D and 0 k. Figure 4-1: D and a* ________ & 1k1 -I the smaller the ad, the more likely the bundle is preferred the larger the ad, the more likely the bundle is preferred ad has no influence 2(1 k/k2-1 the smaller the ad, the more likely the bundle is preferred Ca has no influence Sk1/k2-1 )+r Figure 4-2: oa and preference. A)When +2(- ) < k 2(1 /2- ). B)When a2( ) > o2(1 kl/k2-1) Table 4-1: Numerical Example for principal's preference and a2 principal's expected cost ad <- 2( +-) = .4165 benchmark strong bundle a = .25 50.8125 -< 50.7813 2 = .35 50.8125 > 50.8398 a > 2( 1) = .4165 o2 = .42 50.8125 50.8456 T = .4999 50.8125 ~ 50.8125 CHAPTER 5 EARLY RECOGNITION MODEL The FASB has recently issued several new regulations on the measurement and disclosure of derivatives. There is also substantial detailed implementation guidance from the Emerging Issues Task Force (EITF). The new regulations are intended to recognize the effect of a hedge on earnings and use "mark-to-market" techniques to evaluate the unsettled derivatives, presumably so investors understand the potential risk and value of the derivative contracts held by firms. However, the "mark-to-market" technique may be problematic. The prior chapters have discussed the case in which this technique is abused to manipulate earnings. In this chapter, I further explore its impact on the firms' risk management behavior. Early Recognition of Hedging In practice, over-the-counter derivative contracts are difficult to evaluate, for they are not traded on exchange markets. For OTC derivatives, their "fair value" is more easily manipulated. However, for derivative instruments that are frequently traded on exchange markets, such as futures and options, their market value is readily available. Manipulation may not be a major concern for these derivatives. However, the new regulation of evaluating unsettled derivatives may still influence the firms' risk management behavior. According to FASB Statement 133, the ineffectiveness of a hedge would result from "a difference between the basis of the hedging instrument and the hedged item or hedged transaction, to the extent that those bases do not move in tandem," or "differences in critical terms of the hedging instrument and hedged item or hedging transaction, such as differences in notional amounts, maturities, quantity, location, or delivery dates." In practice, the effectiveness of hedging refers to the degree to which the fair value changes in the derivatives offset the corresponding fair value changes in the hedged item. For this chapter, I assume the manager cannot manipulate the fair value of unsettled derivatives. There is no other option of earnings management either. Without hedging, xz = klal + cl and x2 = k2a2 + 62, where [1, 62] follow a joint a 2 0 normal distribution with zero means, and the covariance matrix is As 0 a2 in the previous models, suppose any hedge is for the second period only. If the firm does not recognize the hedging influence earlier, the second period output will be x2 = k2a2 + E2, where e2 ~ N(0, a2) with oa < a2. In this way, again we capture the risk reduction theme of hedging by a mean preserving spread structure. Since in this chapter I am not interested in earnings management, I relax the earlier assumption kI > k2, and allow kl and k2 to be any positive value. With hedging (but without early recognition), the second period output variance is reduced from a2 to oa. If firms have to recognize the ineffective portion of hedge before the settlement of derivative contracts, I suppose x1 = kial + e1 + pe' and x2 = k2a2 + (1 p)E, p E (0, 1). Due to the early recognition, part of the reduced variance is recognized in the first period and the remaining variance is recognized in the second period, when the derivative contract is settled. Centralized Case First consider the case in which the principal is endowed with the hedging authority and decides to hedge. Suppose the outputs are publicly observed. Paralleling earlier work, it is routine to verify that the incentive constraints collapse to the following two constraints: a > (IC1) SI3k (IC2) Moreover, the individual rationality constraint is W + aklH + 3k2H 2C -r2 (a2 + p2a2) z 2(1 P)2a2 > 0. Therefore, the principal's design program is min W + aklH + 3k2H Program[F] W,a43 s. t. W + akH + 3k2H 2C -:a2(a 2 + p2o ) /2(1 p)2o2 > 0 (IR) SkiH (IC1) Sk2H (IC2) Since, as usual, (IR) must bind, the reduced version of Program [F] is min !a2(a2 + p2ao) + !/32(1 p)2o02 Program[F'] s. t. a > C (IC1) 2 (IC2) Notice the only difference from the prior centralized case in Chapter 2 is that part of the second period output variance is moved to the first period. Denote the optimal bonus rates for Program [F] as a* and P.. It is readily verified that the optimal solution is a] = C and /3. = k. The optimal bonus rates here are identical to those in the benchmark case where either the principal does not hedge or there is no hedging option at all. This follows because hedging only influences the output variance and does not affect the incentive constraints. In this case, the principal's expected cost is B 2C + ac(2 + p2d) + 02(1 p)2a.d Compared to her expected cost if she does not hedge, A = 2C + ra2 + 2o2, hedging is efficient when A B > 0, or when < ~2-() Since S= and = --, this implies hedging is efficient when k2 ^20.2 2 [&2 kI > 2-(1-=)2Cr = 2^ I[Q] 2 a7 (' d -(1.p)2 Proposition 5.1: In the centralized case, hedging is efficient when condition [Q] is satisfied. Proof: See the above analysis. From condition [Q]. we see when hedging greatly reduces the output noise (when o2 is small), the principal prefers to hedge. In addition, when ki >> k2, the principal prefers to hedge. With ki >> k2, a* << *. When the first period bonus rate is low, the compensating wage differential for the increased risk in the first period output is not significant, and the principal is willing to hedge to obtain the benefit from hedging regardless of the increased risk in the first period output. Moreover, when p is small, there is only a small increase in the riskiness of the first period output since only a small portion of the ineffectiveness is recognized earlier, and the insignificant early recognition will not overturn the preference for hedging. Delegated Case Now consider the case in which the manager makes the hedging decision. As in the centralized case, suppose the outputs are publicly observed. When [Q] is satisfied, will hedging still be efficient in the delegated case? Since the manager makes the hedging decision, to motivate him to hedge, there are two more incentive constraints besides the constraints in Program [F]. Using CE1 (al, d; a2) to denote the manager's certainty equivalent at the beginning of the first period, these two constraints are: CE (H, d = 1; H) > CE (H, d = 0; H) CE(H, d = 1; H) > CE1(0, d = 0; H) Expanding the constraints, we get W + aklH +lk2H -2C- a2(2 + p2 2) :2(1 p)2oa W + aklH + k2H - 2C -a2 a2 W + akH + 3k2H 2C (a22 p2) 2 p)2 > W +k2H C - hr2 227 2 They reduce to 2[ (1 p)2oa] > a2p2aO (ICa) a -> C- { i "[-(-)_hp)2V(-C2p2a) a kH (IClb) The second constraint is redundant, for 32[u2 (1 p)2a2] > a2p2C2 and a> C kiH Now the new design program is: min Ia2(2 + p2o2) + 2(1 p)2 Program[G'j s.. t. > C (IC1) Sk2 (IC2) 2[a2 (1 p)201] 2 ap2D (IC1a) Plug the optimal bonus rates ac = and = into the IC constraints. For (ICla), we have 2[(2-(1- p)2 2]-)2 p2a = ( )2 2-(1 ) ] Condition u 2-(l-p)2,2 p 02 2 [Q] implies ( 2 2 0, thus (IC,) is satisfied. Therefore, the optimal bonus rates in Program [F] are also the optimal bonus rates in Program [G'J. In addition, (ICla) satisfied implies the manager will always hedge as long as [Q] holds, thus it is free for the principal to motivate hedging. No matter whether it is the principal or the manager who has the authority to hedge, hedging is efficient when condition [Q] is satisfied. Lemma 5.1: When [Q] holds and hedging is motivated, the optimal contract has a= and /* = Proof: See the above analysis. The intuition behind this proposition is the following: When [Q] is satisfied, under the benchmark bonus scheme a* = C and 3" = although the first period output is more risky with the hedge, the total risk premium for the two periods outputs, *2(02 +p22) +1./2(1 -p)2o2, is still lower than the risk premium without the hedge, a*2a2 + *2 2. However, when [Q] is not satisfied, a* = c and = are not the optimal rates for Program [G']. Define < ~2-- as condition [Q]. We have the following lemma. '2 7-(l-p)2 d Lemma 5.2: When [Q] holds and hedging is motivated, the optimal contract has a* = and 3* = /- p)2 kH V a 2-(1-p)2 kH' Proof: See the Appendix. From the above lemma, when [Q] holds, the principal has to set a higher second period bonus rate to motivate hedging. [Q] implies that ki is low. When ki is low, the lower bound of a, --, is high. With a high bonus rate in the first period, the induced increased risk in the first period will be high. Thus the manager is reluctant to hedge. To motivate hedging, the principal has to reduce the weight of the first period bonus in the manager's compensation, either by reducing a or by increasing p. Since a has its lower bound at --, the principal cannot reduce the first period rate below that bound. The only way is to increase the second period bonus rate, /. Here hedging is not so attractive as in the case when [Q]. The question now is what if the principal does not encourage hedging when [Q]. If the principal does not encourage hedging, the incentive constraints for the second period are the same as when the principal encourages hedging, since the hedging choice is already made at the beginning of the first period. Using CE (al, d; a2) to denote the manager's certainty equivalent at the beginning of the first period, the incentive constraints for the first period given a2 = H become CE (H,d = O;H) 2 CE'(H, d = 1;H) (ICl') CE'(H, d = 0; H) > CE(O, d = 1; H) CE (H, d = O; H) CE (O, d = 0; H) Rewrite the (IC1') constraints, we have 2[o2 (1 p)2_,] < a2p2a2 (IC12) >C+-51 {2-(1-p)2]-2p2o} (IC > kH (IC1,) a > C (ICl1) Here (IClb) is redundant, since 2[a2 (1 p)2a2] < a2p a2. The individual rationality constraint in this case is CE (H, d = 0; H) > 0, and it must bind. Therefore, the program can be rewritten as min 'aa2r2 + 22a2 Program[H'] s. t. a > (IC1:) k> H c 3 k2H (IC2') a2p2a > [a (1 p)22] (ICI:) Lemma 5.3: When [Q] holds, the optimal contract that precludes hedging has a* = k6H and 3* -= c Proof: See the Appendix. Now, when [Q] holds and hedging is discouraged, the principal's expected cost is 2C+6 ( C )222_ri C 2H22 (A') while when hedging is encouraged, her expected cost is 2C + ( )2(o2 + p2a2) + ( )2(1 p)22 (B') Comparing A' with B', we have B'-A'=r( C)2(2 + p2 )+ ( C)2 2 2 (1 22 C )22 ( r )202 2k- H d 2 k t2-(l-p)2a21 P) -d 2k -- -H) +r( c 2 _p_)2a2 =r- c 2 +2 .2 2 2 r(C)2,2[ 1 P2a 1 _r(@C202 I 1[Z /,2r -2-() O fjo,_-(i- _1 i] > 0 Therefore, with condition [Q] satisfied, B'-A'>0. Thus hedging is not efficient. In other words, the principal prefers not to hedge when < ( a =<2 k2a:P --(l--p)2 ' ad no matter whether the principal or the manager has the hedging authority. Proposition 5.2: If [Q] holds, encouraging hedging is efficient, and the optimal contract has a* = H and /* = ; If [Q] holds, discouraging hedging is efficient, and the optimal contact has a* = and 3* = k.H Proof: See the above analysis. Table 5-1 has a numerical example to illustrates the conclusion in Proposition 5.2. I assume r = 0.5, C = 25, and H = 10. I use d = 1 to denote the case that the principal encourages hedge, and use d = 0 to denote the case that hedge is discouraged. From the above proposition and the numerical example in Table 5-2, it is shown that the delegated case is similar to the centralized case in that hedging is k2 2 efficient only when 5 > -2 _P- In the delegated case, there is no moral hazard 2 -ay-(1-p) d problem on hedging. The principal still follows the rules in the centralized case to decide whether to encourage hedging. The principal need not motivate hedging when [Q], and need not forbid hedging when [Q]. This is because the principal and the manager share the same interest. The lower the induced output risk for the manager, the less the compensating wage differential the principal has to pay. More importantly, recall that in the previous chapters when there is no early recognition, hedging is always efficient since it reduces the compensating wage differential. However, with the early recognition of hedging's ineffective portion, in some cases hedging is not efficient any more, since it adds more risk to the first period output, though the risk in the second period output is reduced. When the first period output has a sufficiently great weight in deciding the manager's compensation, increased riskiness in the first period output greatly increases the manager's compensation risk. The principal has to pay a relatively large compensating wage differential, thus hedging becomes unattractive. In addition, the less effective is the hedge (that is, 2 is closer to 1), the less likely is hedging to be efficient. Moreover, d the larger the portion of the ineffectiveness is recognized earlier (that is, the higher the p), the less likely hedging is efficient. Summary In Chapters 2 and 3, hedging is efficient since it reduces the second period output variance, and therefore reduces both the manager's compensation risk and the principal's compensating wage differential. However, when I introduce the early recognition of a portion of the hedge's ineffectiveness, it is shown that sometimes hedging becomes undesirable. The reason is that the early recognition increases the riskiness of the first period output. When the first period output carries a great weight in the manager's compensation, or when a large percentage of the ineffectiveness has to be recognized early, the early recognition policy makes hedging unattractive. In addition, without the early recognition, as long as a2 > 4a, hedging is efficient; while with the early recognition, only when the effectiveness is sufficiently high will hedging be efficient. The analysis of this chapter sheds light on how some recent accounting regulations may influence the firms' risk management behavior. Recent accounting regulations require that firms recognize the ineffectiveness of hedge into earnings even before the settlement of derivatives contracts. Although the intention of the new rules is to provide investors with more information on the firms' use of derivatives, they may have a side effect of discouraging the firms' risk management activities. Table 5-1: Numerical Example for Proposition 5.2. a* kf" k _C principal's expected cost d = 1 1.250 1.667 50.2631 Q1 1.25 1.667 d = 0 4.410 1.667 52.7778 d = 1 2.500 .095 50.8929 2 22.50 .833 d = 0 2.500 .833 50.8681 'For the case with condition [Q], I assume kl = 2, k2 = 1.5,a2 = .5, a = .25, and p = .5. Therefore = 1.7 > -- = .142, which satisfies [Q]. 2For the case with condition [Q], I assume ki = 1, k2 = 3,u2 = .5, a' = .25, and p = .5. Therefore k2 2 satisfy - = 0.111 < = .142, which satisfies [Q]. ,4 -W CHAPTER 6 OTHER RELATED TOPICS In this chapter I briefly explore the relationship between riskiness and agency problems. In addition, I also analyze a model with "informative" earnings management, where manipulation is desirable. Riskiness and Agency For the main model in this paper I assume output follows a normal distribution, and show that hedging reduces the firms' risks and helps reduce the compensating wage differential. However, we need to be cautious not to take this result casually and conclude that "as long as hedging reduces the risk in output, it improves the agency problem." The normal distribution assumption may play an important role here. In a continuous setting, Kim and Suh (1991) illustrate that if there are two information systems whose distributions belong to the normal family, the system with the higher likelihood ratio variance is more efficient (costs less for the principal to induce the manager's certain action level). In a binary action setting, it is easy to verify that the hedged plan also has a higher likelihood ratio variance. A likelihood ratio distribution with a higher variance makes it easier for the principal to infer the manager's action from the output, and therefore helps reduce the compensating wage differential. Without the normal distribution assumption, reduction in riskiness may not improve an agency problem. Consider a finite support numerical example in which hedging drives up the compensating wage differential. For simplicity, assume a one-period, centralized-hedge case with three possible outputs, {1,2,3}. When the principal does not hedge (or when there is no hedging option), the probability distribution of {1,2,3} given the manager's high action is PH = (1, -, 1), and when the manager chooses low action the distribution is PL = (, 3, -). But when the principal hedges, the probability distribution given high action is PHd = (, i, ), and the distribution given low action is PLd = (, ). Also assume C = 25 and r = 0.01. Given the action, it is readily verified that PH is a mean preserving spread of PHd and PL is a mean preserving spread of PLd. In other words, the unhedged plan is more risky, according to Rothschild and Stiglitz (1970). However, in this example, the principal pays 54.1149 to encourage high action when she hedges, while she only pays 37.7216 when she does not hedge or when there is no hedging option. Risk reduction is usually believed to be beneficial to investors. However, as illustrated here there is no necessary connection between risk reduction and improvement in the agency problem. Counter-intuitively, risk-reducing activities may increase the compensating wage differential. In other words, even though hedging activities reduce firms' risks, in some cases they are detrimental to investors. Informative Earnings Management: Forecast Model To this point, the misreporting behavior is just garbling, and it merely destroys information. That is, the misreporting behavior is bad for the principal, although sometimes the principal tolerates some misreporting behavior because the elimination is too costly. However, when misreporting carries some private information, in some cases it is good for the principal to encourage earnings management. Consider an extreme case in which earnings management is not only encouraged but enforced by the principal for her interest. I will show that with some engineering, encouraging manipulation may lead to first best solution. As in the previous models, the agent chooses a first period action level and decides whether to hedge the second period's output at the beginning of the first period. Here I further assume the agent can hedge only when he chooses high action in the first period. That is, I assume the hedging activities need effort, and a slack manager will not be able to hedge. In addition, if the agent decides to hedge and chooses high action in the second period, he can also perfectly forecast the output of the second period at the beginning of the second period. The principal cannot observe the agent's choices or the outputs for each period, but can observe the actual aggregate output at the end of the second period. For simplicity, assume the cost of misreporting is zero and the agent can misreport freely, as long as the aggregate reported output, i1 + x2, is equal to the actual aggregate output, xz + x2. The time line for the forecast model is shown in Figure 6-1. In this model, although the principal cannot observe the output of each period and cannot know the agent's forecast, she can design a contract that achieves first best to encourage high actions and hedge. Think about the contract that pays the agent the first-best compensation if the agent reports equal outputs for period 1 and period 2, but pays the agent a penalty if the reported outputs for the two periods are not equal. Under this contract, the agent can forecast the second period's output only when he works hard and hedges, and only when he forecasts the second period's output is he able to manage the earnings so that the two periods' outputs are equivalent. With any other choice of actions, he cannot perfectly smooth the earnings to avoid the penalty, and the chance to get two equivalent outputs by accident is small. Therefore, the only choice for the agent to avoid the penalty is to supply high effort in both periods, hedge, and smooth the reported earnings. In this case, earnings management is not only encouraged but enforced. It helps the principal to reap the rent from the agent. Income smoothing here is desirable to the principal. The program for the principal in the forecast model is min J S1 fH(x )fHd(X2)dxldx2 Program [I] So,Si s.t. ff u(Si 2C)fH(xl)fHd(x2)dxldx2 > -U f fu(SI 2C) fH(Xl)fHd(x2)dxldx2 > E(u) for any choice other than e1,e2 H, hedge, and equal 21, 2, where S1 is the payment to equivalent reported outputs, and So is a penalty. Proposition 6.1: In the forecast model, first best can be achieved by S, = 2C - r In(-7) for equivalent reported outputs for the two periods and penalty So << 0 otherwise. Proof: See the Appendix. Summary In this chapter it is shown that there is no necessary connection between the reduction in riskiness and the improvement in agency problems. It is a general belief that risk reduction activities are beneficial to the investors, while this chapter illustrates that this may not be true in some cases. A model with informative earnings management is also included in this chapter. When earnings management conveys the manager's private information, manipulation may be efficient and desirable. It is shown that in a well-constructed model, encouraging manipulation can achieve the first best. 1st Period 2nd Period Agent chooses al E {H, L}. If al = H, can hedge for 2nd period output. Agent observes xl, report il. Choose a2 E {H, L}.Can forecast x2 if a2 = H and hedged Agent observes x2, reports x2. Principal observes x1 + 2. Figure 6-1: Time line for forecast model CHAPTER 7 CONCLUDING REMARKS Derivative instruments arouse mixed feelings. They are inexpensive hedging instruments that cost much less than real option hedging, while their complexity makes them harbors for earnings management. Investors and regulators are concerned and nervous about the potential damage from abusing derivatives, but cannot forgo the convenience and benefit from hedging through derivatives. Derivative instruments are like nuclear power stations, when they work well, they provide users with clean and cheap energy, while when anything goes wrong, their destructive power is dreadful. This has led to great effort aimed at restraining the abuse of derivatives. To help investors get more information about and more control of firms' use of derivatives, the FASB has issued various rules recently on the recognition and disclosure of derivatives, such as SFAS 133, 137, 138 and 149. There are also numerous detailed guidance from Emerging Issues Task Force (EITF) on how to implement these complicated new rules. The main strategy of the regulators to fight the abuse of derivatives is to require firms to disclose the fair value of both the derivatives and the hedged items. The regulators believe investors can understand better the value of the derivative contracts through the managers' estimates of the derivatives' fair value. However, to do this, discretionary evaluation of the fair value is necessary, since many unsettled derivatives' fair value is not available from the market. The more discretion for the managers may offer more earnings management opportunities, contrary to the initial intention of the new accounting rules. Moreover, another intention of the new regulations is to help the investors understand better the potential risk of derivatives through the managers' early disclosure of the ineffectiveness of hedging. However, the early recognition of the hedging's ineffectiveness raises the riskiness of interim earnings. With a higher risk in the interim earnings, the firms may be discouraged from risk reduction activities, which may not be a desirable consequence for investors and regulators. In addition, the discouragement of hedging may force the managers to look for other ways to secure their wealth. Unfortunately, more earnings management is a promising candidate. As shown in this dissertation, the current accounting regulations on derivative instruments may be inefficient. But shall we give up the effort to restrain the abuse of derivatives? Or shall we just discard derivative instruments? I would say no. It is not the purpose of this paper to criticize the current rules and claim the effort is totally in vain. Instead, the intention is to explore the complicated feature of derivatives so we get better ideas on how to keep the benefit of cheaper hedging while minimizing the potential destruction from derivatives abuse. An ancient Chinese saying says, "a thorough understanding of both yourself and your enemy guarantees a victory." I hope this research may shed some light on the feature of our enemy, the dark-side of derivatives, and help us find more efficient ways to regulate the use of derivatives. APPENDIX Chapter 2: Proof for Lemma 2.1: Proof. We use /t1, /2 to denote the Lagrangian multipliers for (IC1) and (IC2) respectively. With the reduced program, the first order conditions are -ra2a+pt1 = 0 and -ra23 + A2 = 0. Since a > > > 0 and 3 C > 0, we get p = ra22a > 0 and '2 = ra2 > 0. This implies both (IC1) and (IC2) bind, or a* = -, *1 = C Proof for Lemma 2.2: Proof. The principal's design program can be expressed as the minimization of 2(a2o2 + /2o2) subject to the incentive constraints. Again let D1, 2 denote the Lagrangian multipliers of (IC1) and (IC2) respectively, with the reduced program, we have the first order conditions -ra2a + ~ = 0 and -rad + p2 = 0. Hence /1P = ra2a > 0 and /2 = ra2d/ > 0. This implies both (IC1) and (IC2) are binding, and thus a* = Ci and 03 = c. n Proof for Proposition 2.2: Proof. Define it as the Lagrangian multiplier for (IC1) and p2 for (IC2). With the reduced Program [C'], the first order conditions are -ra2a q,-f)2(-2 + 2q(3 a) + Pi = 0 (FOC1) l-q+qe (8-) and -ra213 + q_- ) -2q( a) + p2 = 0. (FOC2) l-q+qe -5(0-)2 In the optimal solution, if neither constraint is binding, P1i = #2 = 0. Substitute Pi = 112 = 0 into the first order conditions and add the two conditions together, we get -ra2, ra2a = 0, which implies a = 0 = 0. This contradicts a > > 0 and S> ~2 > 0. Therefore, MP = /2 = 0 is not true in the optimal solution, and at least one of the constraints is binding. If /1 > 0, 12 = 0, then a = C and3 2 (FOC2) implies 3 = M Q, where M _= 2- 1-2 where M = 2- q+qe-7(- Rewriting M, we have M = 1M_( {(1- )(1- e-i(-)2) +[1-q(1-e-i(Pa))]} > 0. With M > 0, we get / = 2aa < a = - However, ki > k2 implies / does not satisfy the constraint /3 > Therefore, (a = iH, /3 ) -) cannot be true. Hence, regardless of IL, (IC2) always binds, implying/ k-T Thus, p2 > 0 and p, > 0. Moreover, if (IC1) binds, then a = -; if (IC1) is slack, then from (FOC1) a = SM 3 < 3. Hence we always have a* < /3. * Proof for Corollary 2.1: Proof. Using the first order conditions displayed in the proof of Proposition 2.2, we see when q is sufficiently near zero, (FOC1) reduces to -ra2a + e1 + p, = 0 and (FOC2) reduces to -rr2/3 + E2 + A2 = 0, where E1 and E2 are small. This implies Ii > 0 and 12 > 0. That is, when q is sufficiently small, both incentive constraints bind and aC = X = -7. Proof for Corollary 2.2: Proof. Using the first order condition (FOC1) in the proof of Proposition 2.2 again, if 1 > 0 and a = then A1 = ro72 -C (2q )ge ( O57) > 0. (i) k1H I-q +g e r )2 Clk (i) can be re-expressed as r (2 ()- 2 ( ) > 0. (ii) k ,1-q+qe 2 _-" k' 1l Now suppose q is sufficiently high and ki is sufficiently large. This implies the inequality in (ii) is reversed and a* > C Proof for Proposition 2.3: Proof. Define A1, A2 as the Lagrangian multipliers of the two constraints respectively. We get the following first order constraints: -ro2a + (/3 -a) + 1 =0 fociI') -ra2/ (3 a) + 12 = 0 (FOC2') From Proposition 2.2, we know p2 > 0, and z1 > 0. If /l = 0, [2 > 0, then 3= -, and from fociI') we get -r2a + ( a) 0, which implies a = 1/3 = 1 If 1 > then both incentive -ra 1+r-TH -2IH' = lfr2 k2H and are the optimal bonus constraints are satisfied, and ac = 12 and = are the optimal bonus rates. The condition 12 c > c reduces to ki > k2(1 + r2). l+ra2 k2H k-H Ifi1 C < C then a = C does not satisfy the constraint a > C, I1+r" k2 H kh 1+ra2 k2H -- k1H and the optimal contract must have abc = 7 and /i = ', as both incentive constraints bind. * Chapter 3: Proof for Lemma 3.1: Proof. From Chapter 2, when q is sufficiently low, the optimal contract in the misreporting model is (ab = C-, 3c = ). The misreporting model, Program [C'], is identical to the bundled model, Program [D'], except that the second period output variance decreases to ad in the bundled model. It is easy to verify that (a* = H, 0C* = rc) remains optimal in the bundled model when q is sufficiently near zero. The principal's expected cost in the bundled model therefore gets close to 2C + S(aga2 +/ or 3 ") when q is near zero. In the benchmark model where there is neither hedging nor misreporting option, her expected cost is 2C + -(oc2 + / 2), which is higher than 2C + j (o022 + 3*22d). The hedge-misreport bundle is preferred. m Proof for Lemma 3.2: Proof. From Corollary 2.2, when q is sufficiently high and k: is sufficiently large, the optimal contract exhibits a* > -H, 0 = C. We rewrite a' as ( + e, e > 0. In H C C addition, from Proposition 2.2, we know ab = C + e < /3 = . In the benchmark model where there is neither a hedging nor a misreporting option, the principal's expected cost is 2C +(a*o*22 + n*o2,2), while in the bundled model it is 2C + j(au72 + ,C ) + ln[(l e- -c2] q( a)2. If r(a*<2 2) {*22 ,+ R2 + ln[(1 q) + qe-(-V)~2+ q(o a)2} A A 2 C C 2r 2 2 =r(.C)2(2 2- u2) {(2[( +E)2 -( )2] k2Hc c 2 2 q c +- ln[(1 q) + qe-z2 2-H kH 2] + q H- k )2} > 0 (iii) then hedge-misreport bundle is preferred to no hedging, no misreporting. But (iii) is positive only when a2 car is sufficiently large. * Proof for Lemma 3.3: Proof. Refer to the proof for Proposition 2.3. Program [C'(q = 1)] is identical to Program [D'(q = 1)] except that in the bundled model program's objective function, the second period variance is a2 instead of a2. It is easy to verify these two programs share the same optimal bonus coefficients. (a*\D) Dl) = (a*l *c1)" u Proof for Proposition 3.1: Proof. In the benchmark model where there is neither a hedging nor a misreporting option, the principal's expected cost is 2C +-(a2a*2 + /2Ua2), while in the bundled model it is 2C +V(aa*2 2 + 2 + (,3 ca1)2. As long as (af*2a2 + *a2)- [j(a*2 a2 + *2 ,) + (31i aD1)2] > 0, the hedge-misreport bundle is preferred. (1). When kl > k2(l + ro2), the optimal contract exhibits (a*I 1+ k2H D = gC) Substitute ac, O and a*D(, 3 into rU 2 + 2a2) [r(a*22 DI3 2) + 2(/ D D1)2]. We have r(a*2,2 + Ia2) [(a.2 2 + / 2) + 1 1)2] 1 (2ra2 ra2 r(a2-a2) (ra2)2 T2TH) k"2 (l+rcr2)2k2jJ = =kl2 -L" -?. -(r -- SG)2 r2(1+r2)2k 2r 2k 2+r(2 -)(1+ 22 -(22)2k -"2H ]lr2 2 (l+ra2)2k k' -21H (1+ro2)2k;12 = )2(+r )2 r (1 ra2)2k2 k2[r2 r( a2)(1 + ra2)2 + (ra2)2]} Thus, we need ra2(1 + ra2)2k2 k2[ra2 r(a2 a2)( + ra2)2 + (ra2)2] > 0. This fes k2 -(1+r2)(a2-2) implies > r2(1+r:2) (2). When ki < k2(l+ra2), the optimal contract exhibits (a*o = = (aOD1, lD1) is identical to (aA, 0*). Substitute a, A* and a* into 1( a 0 2 +r -u2) [ D(l1"2 ) + 2d D 2 -1 D 1)2], we have S*22 2 0*2 2 \ *2 .*2 2 1 2 1 C2r 2) 1 1)2] r(a or (a a+a- a -aC*1)2] = 1(C)2 2 (1)2] Thus, we need r2 ( )2 > 0, which implies > 3 2 '(k-k2)d >" Chapter 4: Proof for Proposition 4.1: Proof. Define 1 as the Lagrangian multiplier for (ICl) and /2 for (IC2). The first order conditions are -ra2a -q+qe3-D(3_)2 + 2qD( a a) + 1 = 0 (FOC1) 1-q+qe- JD(3-.a 2 -ra2 + qe--D(-) ) -2qD( a) + /2 = 0. (FOC2) l-q+qe7D(3-)2 Suppose neither constraint is binding, implying /,, p2 = 0. Substitute l, /12 = 0 into the first order conditions and add the two conditions together, we get -ro-a - ra2a = 0, which implies a = 0 = 0. This contradicts a >_ c > 0 and > c > 0. Therefore, /1, A2 = 0 is not true and at least one of the constraints is binding. If #1 > 0, A2 = 0, then a = and/ > C (FOC2) implies a = Pa, where T- D(3-a)2 - T (2 +e-qi(3-)2 )D. Rewriting T, we have T = D_1-e-{(1 )(1 - 1 {(1 - e-D(- a)2) q( -D(2-a)2)]} > 0. With T > 0, we get 0 = -,a C However, kl > k2 implies 0 doesn't satisfy the constraint 3 > Therefore, (a = j, > C-) cannot be true. k1H k2H C Hence, regardless of [I, (IC2) always binds, implying *E -- k2i* Thus, A2 > 0 and Pli 2 0. Moreover, if (IC1) binds, then a = ; if (IC1) is slack, then from (FOC1) a = 2+Tq 3 < 3. Hence we always have aE < E. * Proof for Corollary 4.1: Proof. Using the first order conditions displayed in the proof of Proposition 4.1, we see when q is sufficiently near zero, (FOC1) reduces to -ra2c0 + E1 + 1 = 0 and (FOC2) reduces to -roa2$ + 62 + [2 = 0, where el and E2 are small. This implies A, > 0 and A2 > 0. 0 Proof for Corollary 4.2: Proof. Using the first order condition (FOC1) in the proof of Proposition 4.1 again, if 1i > 0 and a = ', then -JD(OE_ -F 2 02 C -k-7) A1 = 2 (2q qe- E )2 )D(E k7) > 0. (i) 1-q+qe 1 kl" (i) can be re-expressed as rr21 q(2 e )D( )> 0. (ii) T1q- -_JD(j )2(. __))D(k2 kT2 T .1 1-q+ge 2 2l Now suppose q is sufficiently high, kl and k2 are sufficiently different, and D is large. This implies the inequality in (ii) is reversed and ac > k-. e 2 1 In addition, define G = (2 e )D( ). We have 1-q+qe D( 2 Weh G 1 1 )2- e-D(-a2 e- JD(8-)2 ~ )2 )2(1-) D k2 ki 1-q+qe- D(-)2 (1-q+qe- D(0-)2 2 and a D[(2 e-(-a)2 e-~ ( D-a)2 D ()22( )2(1-q) a =+ 2 H k )2(l J2 JD ) -q+qe- D(O-)2 (I-) q+e- -D(-)- 2 D(O-a)2 From the proof for Proposition 4.1, we know T = (2- _e- a-o )D > 1-q+qe D(-a) ) 0.Therefore (2- e"-iD(BO .)2) > 0, and both 0 > 0 and G > 0.This implies 1-q+qe k2 k1 that the larger a2 da, the more likely (ii) is reversed and ac > k- ; Also, the larger (k -) (in other words, the greater the difference between kl and k2), the more likely (ii) is reversed and a* > C. Proof for Lemma 4.1: Proof. From Corollary 4.1, when q is sufficiently low, the optimal contract in the strong bundle model is a* = and /3 = ,2 as in the benchmark, where there is neither a hedging nor a misreporting option. The principal's expected cost in the bundled model therefore gets close to 2C + j[( T)2"2 + (kCT)2d2] when q is near zero. In the benchmark model where there is neither a hedging nor a misreporting option, her expected cost is 2C + '[('/)202 + (f)2 a2], which is higher than 2C + [(k )22 + C )2U]. The strong bundle is preferred. * Proof for Proposition 4.2: Proof. Define 1, /2 as the Lagrangian multipliers of the two constraints respectively. We get the following first order constraints: -ru2a + D(3 a) + p = 0 fociI') -rad D(3 a) + 12 = 0 (FOC2') From Proposition 4.1, we know 12 > 0, and y1 > 0. If p, = 0, P2 > 0, then / = c, and from fociI') we get -ra2a + D(/ a) = 0, which implies a = = D+- If > C then both incentive ,,7kD+ra2 k2H-Dr2 k1 = D C and X*i C are the optimal bonus constraints are satisfied, and a* = and E\ = are the optimal bonus rates. The condition D- kC- > C can be rewritten into D > r2 (or a < D+rorTH-- -- kl/k2-1 d a2(1 kl/I )). If D < r2 /k- then a D+= 2 does not satisfy IC1 and the optimal contract must have a 1 = and 3E = as both incentive constraints bind. n Proof for Proposition 4.3: Proof. In the benchmark model where there is neither a hedging nor a misreporting option, the principal's expected cost is A 2C +w[(-C-)2a2 + () i)202], while in the strong bundle model it is B 2C +(r (12 ,2 2 + *D(2 a )2. As long as El E1Vd) -- D(3E I As long as A B > 0, the strong bundle is preferred. (1). When a2 < ,2(1 k/2-), the optimal contract has ao1 = D- k- and E1 = Then B = (D ) ( 22 +)2 k)22-D + D ( )2( )2 We have A B = l 2f + I2 Iro2 rra22 A-B ){ 2 1k2 2 -D+ro2 2 r-D( D+r)2 = ( )2f I 2 ftl )22 + D( 2 rD)]} A B > 0 requires ra- r [( ) D 2r + D(D )2 D > 0, which implies k2 > ( D )2 ra2 D > (D+- ) + D 2 k Da2( D+ra2) (D+ra2)2 k > a2(D+ra2)2 kc2 (.2- u)(,2-ru2) 2 r the(optimal2)2r (2). When oa > a2(1 k/ ), the optimal contract exhibits a*l = and 3 = .2 Then A B ( )2D 1 )2( )2 C )2D[ 1 -- 1)2]. Al 2 > r 2( -) 2 > kic iml > H1 H U k2k A-B > requires -1 2 )2 > 0, which implies k' > 1 Vr. Proof for Corollary 4.3: Proof. In condition (A'), case (1), define Z ,2("2_ )2 = 2D(-2). (A') is rewritten as > Z. 1 Z D [(D+ra2)2(-a2)-2(D+ra2)2 (,2 -r22)] =r a2 (D+ro2)4 D[-(D+ro2)a-2a2 _-ra-2) (D+roa2)3 D(-(D+ra2)-2(or-ra2) (D+ra2)3 = (D+ro2)3 (02_-a)[-(1-r)ja2_ag (D+ra2)3 < 0 Since < 0 the higher the risk aversion degree r, the smaller the Z, and the more likely the condition (A') is satisfied. In other words, (A') is less stringent with higher r. In condition (B'), case (2), it is easy to verify that the higher the r, the smaller is 1 Vr, and more likely is condition (B') satisfied. In other words, (B') is less stringent with higher r. It is also easy to verify that in either case (1) or (2), the closer are ki and k2, the less stringent condition (A') or (B') is. * Proof for Corollary 4.4 and 4.5: Proof. In case (1), ad < a2(1 k7k-1), and the strong bundle is preferred when k2 (,22)( 2 ro) (u -2)(u2-r2) ff> 2(Lr2)2 Define Z = ,2,22 we have az 2 r(a2-& +r2)2{-a2d+r +(a 2- )}+2 (2-(a 2 + _)(a2 -)(a- 2) a? 2((2-oo2+r-2)2 2t 2 o2 12 ( 2 2 2 a 2 2 22a 2 d2 a 2(,2-a2+r` 2){((t 2-oZA+p`,)((g -2o2+ ` )+2(g2-%)(%-rg2)} ,a4(a-_,2+ra2)4 f 4-2 2,2+2ra 4--2, +2a --ra2a2+r `,+2a4 --2r4 --24d+2ra2a'2 -- 02(,2 _-_+r0`2)3 r o4-+22r-ra2a+ 224 -- 02(u2--.2+ru2)3 (l+r2)u2-(l+r),2 (o2-a'+o2)3 When (1+r2)2 (1+r)r2 > 0, that is, when a2 < a2( 1+), z > 0, the smaller the o2, the less constraining is > Z. When (1 + r2)U2 (1 + r)a < 0, that is, when a2 > o r(1r ), < 0, the larger ~1dd d =,9a 2k2 the a2, the less constraining is > Z. In case (2), from (B') we see cr does not play a role in the principal's decision on whether to take the bundle. * Chapter 5: Proof for Lemma 5.2: Proof. Denote the Lagrangian coefficients for (ICl), (IC2) and (ICla) in Program [G'] as A1, /2 and /3. The first order conditions are: -ra(a2 + p2a2) + p 2ap2a2 13 = 0 (FOC1) -rp(1l- p)2a+ + 2[a2 (1 p)2 2]3 = 0 (FOC2) From (FOC1), if p, = 0, then -ra(a2 + p22) 2ap2p3 = 0, which implies /13 < 0. Therefore we must have M1 > 0, that is, a* = C. From (FOC2), if /2 = 0, P3 = 0, then -r3(l p)2a2 = 0, which is not true. Therefore, we cannot have both /2 and p3 = 0. If A2 = 0,13 > 0, then 2[2 (1 p)2] a= 2p2o2, which implies = ___ c a* c th en P P2- O)_ 2 If this > then a* = C and 3* =- -, are S02-(j-p)~ kkH Va2-(1-p)2d kl o l *p2___ c_2_2 k2 optimal. = 2_ )2~2 > implies .(p) > which is condition 2--(1-- p)2 kIH a,-(' 'd [Q]. In other words, if condition [Q] is satisfied, the optimal contract has a* -= and 3* = p= $ c V2 -(1-p)2au ki H Proof for Lemma 5.3: Proof. Define the Lagrangian coefficients for (IC1C), (IC2') and (ICl') in Program [H'] as /i, /4 and p3. The first order conditions are: -raa2 + p + 2ap2a2,/, = 0 (FOCI') -r3a2 + pI 23p'[[a2d (1 p)2a] = 0 (FOC2') From (FOC2'), it is easy to verify we cannot have /4 = 0, since in that way /j < 0. Therefore, /Z > 0, and 0* = . If p/ > 0, = 0, then a* = and a*2p2 2 > 3*2[a2 (1 p)2a2], which k2 2 2 implies condition [Q, 4 < 2 __ 2 In other words, with condition [Q] satisfied, the optimal contract shows a* = C, and 3* = c Chapter 6: Proof for Proposition 6.1: Proof. The program for the principal is min f f S1 fH(l)fHd(X2)dxldX2 So,S1 s.t. ff u(S1 2C)fH(xl)fHd(X2)dXldx2 > U (IR) ff u(S1-2C)fH(xl)fHd(x2)dxIdx2 f ff u(So-C)fH(zl)fL(x2)dxldX2+ f f u(Si- X2Xl 52=Xl C)fH(l)fL(x2)dxldx2 (IC1) f f u(S-2C)fH(xl)fHd(Z2)dxldx2 f f u(So-C)fL(xl)fH(x2)dxldx2+ ff u(S1- X2*xl X2=XI C)fL(l)fH (x2)dxldx2 (IC2) f fu(S1 2C)fH(xl)fHd(x2)dxldx2 >2 f u(So)fL()fL(x2)dxldx2 + f f u(Sl)fL(xl)fL(X2)dxldx2 (IC3) ff u(Si 2C)fH(xl)fHd(x2)dxdx2 > f f u(So 2C)fH(xZ)fHd(x2)dxldx2 + f u(SI 2C)fH(x,)fHd(x2)dxldx2 (IC4) X2=X1 With a sufficiently low So, it is obvious that the IC constraints are not binding. (Think about So = -oo All the right hand sides of the IC constraints are equivalent to -oo then. Therefore none of the IC constraints is binding.) With none of the IC constraints binding, we reduce the program into a first-best one. Therefore we have, f f u(Si 2C) fH(x)fHd(Z2)dxidzx = U or u(S 2C) = U. That is, the optimal S1 = 2C In(-U). * r- REFERENCE LIST Autrey, R., S. Dikolli, and P. Newman, 2003, "The effect of career concerns on the contracting use of public and private performance measures," University of Texas at Austin working paper Arya, A., J. Glover, and S. Sunder, 1998, "Earnings management and the revelation principle," Review of Accounting Studies, 3, 7-34 --, 2003, "Are unmanaged earnings always better for shareholders?," Accounting Horizons, Vol. 17, Supplement, 117-128 Barth, M. E., J. A. Elliot, D. W. Collins, G. M. Crooch, T. J. Frecka, E. A. Imhoff, Jr., W. R. Landsman, and R. G. Stephens, 1995, "Response to the FASB discussion document 'Accounting for hedging and other risk-adjusting activities: questions for comment and discussion'," Accounting Horizons, Vol. 9. No.1 March, 87-91 Barth, M. E., D. W. Collins, G. M. Crooch, J. A. Elliot, T. J. Frecka, E. A. Imhoff, Jr., W. R. Landsman, and R. G. Stephens, 1995, "Response to the FASB exposure draft 'Disclosure about derivative financial instruments and fair value of financial instruments'," Accounting Horizons, Vol. 9. No.1 March, 92-95 Barton, J., 2001, "Does the use of financial derivatives affect earnings management decisions?", The Accounting Review, Volume 76, No.l, 1-26 Beneish, M. D., 2001, "Earnings management: A perspective," Managerial Finance, 27, 12, 3-17 Campbell T. S. and W. A. Kracaw, 1987, "Optimal managerial incentive contracts and the value of corporate insurance," Journal of Financial and Quantitative Analysis, Vol. 22, No. 3 September, 315-328 Christensen, P. O., J. S. Demski, and H. Frimor, 2002, "Accounting policies in agencies with moral hazard and renegotiation," Journal of Accounting Research, Vol. 40, No. 4 September, 1071-1090 Christensen, J. A. and J. S. Demski, 2003, "Endogenous reporting discretion and auditing," working paper Christensen, J. A. and J. S. Demski, 2003, Accounting theory: an information content perspective, Chapter 17, McGraw-Hill/Irwin, New York. NY Dadalt, P., G. D. Gay, and J. Nam, 2002, "Asymmetric information and corporate derivatives use," Journal of Futures Markets, Vol. 22, No. 3, 241-267 Dechow, P. M. and D. J. Skinner, 2000, "Earnings management: Reconciling the views of accounting academics, practitioners, and regulators," Accounting Horizons, Vol. 14 No. 2, June, 235-250 DeMarzo, P. M. and D. Duffie, 1995, "Corporate incentives for hedging and hedge accounting," The Review of Financial Studies, Fall 1995 Vol. 8, No. 3, 743-771 Demski, J. S., 1998, "Performance measure manipulation," Contemporary Accounting Research, Vol. 15 No.3, 261-285 Demski, J. S., and H. Frimor, 1999, "Performance measure garbling under renegotiation in multi-period agencies," Journal of Accounting Research, Vol. 37, supplement 1999, 187-214 Demski, J. S., H. Frimor, and D. Sappington, 2004, "Effective manipulation in a repeated setting," Journal of Accounting Research, Vol. 42, No. 1, March, 31-49 Dutta, S. and F. Gigler, 2002, "The effect of earnings forecasts on earnings management," Journal of Accounting Research, Vol. 40, No. 3 June, 631-655 Dutta, S. and S. Reichelstein, 1999, "Asset valuation and performance measurement in a dynamic agency setting," Review of Accounting Studies, 4, 235-258 Dye, R. A., 1988, "Earnings management in an overlapping generation model," Journal of Accounting Research, Vol. 26(2), 195-235 Financial Accounting Standards Board (FASB), 1994, "Disclosure about derivative financial instruments and fair value of financial instruments," Statement of Financial Accounting Standards No. 119 ---, 1998, "Accounting for derivative instruments and hedging activities," Statement of Financial Accounting Standards No. 133 -- 1999, "Accounting for derivative instruments and hedging activities--deferral of the effective date of FASB statement No. 133-an amendment of FASB Statement No. 133," Statement of Financial Accounting Standards No. 137 2000, "Accounting for certain derivative instruments and certain hedging activities, an amendment of FASB Statement No. 133," Statement of Financial Accounting Standards No. 138 2003, "Amendment of Statement 133 on derivative instruments and hedging activities," Statement of Financial Accounting Standards No. 149 Feltham, G. A. and J. Xie, 1994, "Performance measure congruity and diversity in multi-task principal/agent relations," The Accounting Review, Vol. 69, No. 3, July, 429-453 Graham, J. R. and D. A. Rogers, 2002, "Do Firms Hedge In Response To Tax Incentives?," Journal of Finance, Vol. 57(2, Apr), 815-839 Greenspan, A., 1999, "Financial derivatives", speech before the Futures Industry Association, Boca Raton, Florida, March 19 Healy, P. M. and J. M. Wahlen, 1999, "A review of the earnings management literature and its implications for standard setting," Accounting Horizons, Vol. 13 No. 4 December, 365-383 Holmstrom, B. and P. Milgrom, 1987, "Aggregation And Linearity In The Provision Of Intertemporal Incentives," Econometrica, Vol. 55(2), 303-328 Ijiri, Y. and R. K. Jaedicke, 1966, "Reliability and objectivity of accounting measurements," The Accounting Review, July, 474-483 Indjejikian, R. and D. Nanda, 1999, "Dynamic incentives and responsibility accounting," Journal of Accounting and Economics, 27, 177-201 Kanodia, C., A. Mukherji, H. Sapra, and R. Venugopalan, 2000, "Hedge disclosures, future prices, and production distortions," Journal of Accounting Research, Vol. 38 Supplement, 53-82 Kim, S. K., 1995, "Efficiency of an information system in an agency model," Econometrica, Vol. 63, No. 1, 89-102 Kim, S. K., and Y. S. Suh, 1991, "Ranking of accounting information systems for management control," Journal of Accounting Research, Vol. 29, No. 2 Autumn, 386-396 Lambert, R. A., 2001, "Contracting theory and accounting," Journal of Accounting and Economics, 32, 3-87 Lev, B, 2003, "Corporate earnings:facts and fiction," Journal of Economic Perspectives, Vol 17, No. 2, Spring, 27-50 Levitt, A., 1998, "The numbers game", remarks of Chairman at the N.Y.U. Center for Law and Business, New York, N.Y. Sept. 28 Liang, P. J., in press, "Equilibrium earnings management, incentive contracts, and accounting standards," Contemporary Accounting Research Linsmeier, T., 2003, "Accounting for Derivatives in Financial Statements," Financial Accounting AAA Annual Conference presentation, Orlando Mayers, D. and C. W. Smith, 1982, "On the corporate demand for insurance," Journal of Business, Vol. 55, No. 2, 281-296 Melumad, N. D., G. Weyns and A. Ziv, 1999, "Comparing alternative hedge accounting standards: shareholders' perspective," Review of Accounting Studies, Vol. 4(3/4, Dec), 265-292 Milgrom, P. and N. Stokey, 1982, "Information, trade and common knowledge," Journal of Economic Theory 26, 17-27 Mirrlees, J., 1974, "Notes on welfare economics, information and uncertainty," Essays in Economics Behavior Under Uncertainty, edited by M. Balch, D. MeFadden and S. Wu. Amsterdam: North-Holland, 243-258 Nance, D. R., C. W. Smith, Jr. and C. W. Smithson, 1993, "On the determinants of corporate hedging," Journal of Finance, Vol. 48(1), 267-284 Pincus, M. and S. Rajgopal, 2002, "The interaction between accrual management and hedging: evidence from oil and gas firms," The Accounting Review, Vol. 77, No. 1 January, 127-160 Rogers, D. A., 2002, "Does executive portfolio structure affect risk management? CEO risk-taking incentives and corporate derivatives usage," Journal of Banking and Finance, 26, 271-295 Rothschild, M. and J. E. Stiglitz, 1970, "Increasing risk: 1. A definition," Journal of Economic Theory 2, 225-243 Ryan, S. G., 2002, Financial Instruments & Institutions, Accounting and Disclosure Rules, Chapter 10, John Wiley & Sons, Inc., Hoboken, NJ Schipper, K., 1989, "Commentary: earnings management," Accounting Horizons, December, 91-102 Schrand, C. and H. Unal, 1998, "Hedging and coordinated risk management: evidence from thrift conversions," Journal of Finance, Vol. LIII, No. 3 June, 979-1013 Schuetze, W. P., 2002, testimony on the hearing on accounting and investor protection issues raised by Enron and other public companies: oversight of the accounting profession, audit quality and independence, and formulation of accounting principles, February 26 Smith, C. W. and R. M. Stulz, 1985, "The determinants of firms' hedging policies," Journal of Financial and Quantitative Analysis, Vol. 20, No. 4 December, 391-405 BIOGRAPHICAL SKETCH Lin Nan was born in Beijing, China, in spring 1973. In June 1995, she received a Bachelor of Engineering in industrial economics from Tianjin University in Tianjin, China. She then worked at the Industrial and Commercial Bank of China (ICBC) for two years as Presidential Assistant. In 1997, Lin came to the United States and started her graduate education at the West Virginia University in Morgantown, West Virginia. She received her Master of Arts in economics in August 1999 and then joined the accounting doctoral program at the University of Florida in Gainesville, Florida. She is expected to graduate with a Ph.D. degree in August 2004. I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Joel S. Demski, Chair Frederick E. Fisher Eminent Scholar of Accounting I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adeqaIte, in cope and quality, as a-- dissertation for the degree of Doctor of Philosop Dv dE. M. Sappington Lanzillotti-McKethan Eminent Scholar of Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequa ,,in scope ad quality as a dissertation for the degree of Doctor of Philosophy. / Karl tEHackenbrack Associate Professor of Accounting I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosoph professor of Accounting This dissertation was submitted to the Graduate Faculty of the Fisher School of Accounting in the Warrington College of Business Administration and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 2004 Dean, Graduate School LD 1780 202,.m UNIVERSITY OF FLORIDA III 1IIII III IIIIi II I 2 II 11111IIIIII IIIIl 3 1262 08554 2073 |

Full Text |

xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd INGEST IEID E3UTBQQ5D_DLCFYE INGEST_TIME 2011-09-29T19:31:17Z PACKAGE AA00004697_00001 AGREEMENT_INFO ACCOUNT UF PROJECT UFDC FILES PAGE 1 '(5,9$7,9(6 $1' ($51,1*6 0$1$*(0(17 %\ /,1 1$1 $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$ PAGE 2 $EVWUDFW RI 'LVVHUWDWLRQ 3UHVHQWHG WR WKH *UDGXDWH 6FKRRO RI WKH 8QLYHUVLW\ RI )ORULGD LQ 3DUWLDO )XOILOOPHQW RI WKH 5HTXLUHPHQWV IRU WKH 'HJUHH RI 'RFWRU RI 3KLORVRSK\ '(5,9$7,9(6 $1' ($51,1*6 0$1$*(0(17 %\ /LQ 1DQ $XJXVW &KDLU -RHO 6 'HPVNL 0DMRU 'HSDUWPHQW )LVKHU 6FKRRO RI $FFRXQWLQJ 'HULYDWLYH LQVWUXPHQWV DUH SRSXODU KHGJLQJ WRROV IRU ILUPV WR UHGXFH ULVNV +RZHYHU WKH FRPSOH[LW\ RI GHULYDWLYHV EULQJV HDUQLQJV PDQDJHPHQW FRQFHUQ DQG WKHUH DUH UHFHQW DFFRXQWLQJ UXOHV WU\LQJ WR UHJXODWH WKH XVH RI GHULYDWLYHV 7KLV GLVVHUWDWLRQ VWXGLHV WKH MRLQW HIIHFW RI GHULYDWLYHVf KHGJLQJ IXQFWLRQ DQG HDUQLQJV PDQDJHPHQW IXQFWLRQ DQG H[SORUHV KRZ WKH UHFHQW UXOHV LQIOXHQFH ILUPVf KHGJLQJ EHKDYLRU 7KH WZRHGJHG IHDWXUH RI GHULYDWLYHV LV PRGHOHG E\ EXQGOLQJ D KHGJLQJ RSWLRQ DQG D PLVUHSRUWLQJ RSWLRQ $ PHDQ SUHVHUYLQJ VSUHDG VWUXFWXUH LV HPSOR\HG WR FDSWXUH WKH ULVNUHGXFWLRQ WKHPH RI KHGJLQJ 7KLV GLVVHUWDWLRQ VKRZV D WUDGHRII EHWZHHQ WKH EHQHILW IURP KHGJLQJ DQG WKH GHDG ZHLJKW ORVV IURP PLVUHSRUWLQJ ,W LV VKRZQ WKDW ZKHQ WKH PDQDJHUfV PLVUHSRUWLQJ FRVW GHFOLQHV ZLWK WKH HIIHFWLYHQHVV RI KHGJLQJ WKH SULQFLSDOfV SUHIHUHQFH IRU WKH KHGJHPLVUHSRUW EXQGOH GRHV QRW FKDQJH PRQRWRQLFDOO\ ZLWK WKH HIIHFWLYHQHVV RI KHGJLQJ 6SHFLILFDOO\ ZKHQ KHGJLQJ LV KLJKO\ HIIHFWLYH WKH SULQFLSDOfV SUHIHUHQFH IRU WKH EXQGOH LQFUHDVHV LQ WKH HIIHFWLYHQHVV ZKLOH ZKHQ KHGJLQJfV HIIHFWLYHQHVV LV PRGHUDWH WKH SULQFLSDOfV SUHIHUHQFH GHFUHDVHV LQ WKH HIIHFWLYHQHVV :KHQ KHGJLQJ LV RQO\ VOLJKWO\ HIIHFWLYH ZKHWKHU WKH SULQFLSDO SUHIHUV WKH PAGE 3 EXQGOH LV QRW LQIOXHQFHG E\ WKH HIIHFWLYHQHVV ,Q DGGLWLRQ WKLV GLVVHUWDWLRQ VKRZV WKDW VRPHWLPHV LW LV QRW HIILFLHQW WR WDNH DQ\ PHDVXUH WR UHVWUDLQ HDUQLQJV PDQDJHPHQW 5HFHQW UHJXODWLRQV UHTXLUH ILUPV WR UHFRJQL]H WKH LQHIIHFWLYH SRUWLRQ RI KHGJHV LQWR HDUQLQJV 7KLV GLVVHUWDWLRQ LQGLFDWHV WKDW WKLV HDUO\ UHFRJQLWLRQ PD\ FKDQJH WKH ILUPVf KHGJLQJ EHKDYLRU 6LQFH WKH HDUO\ UHFRJQLWLRQ LQFUHDVHV WKH LQWHULP HDUQLQJVf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f KHGJLQJ IXQFWLRQ DQG HDUQLQJV PDQDJHPHQW IXQFWLRQ DQG H[SORUHV KRZ WKH UHFHQW UXOHV LQIOXHQFH ILUPVf KHGJLQJ EHKDYLRU 7KH WZRHGJHG IHDWXUH RI GHULYDWLYHV LV PRGHOHG E\ EXQGOLQJ D KHGJLQJ RSWLRQ DQG D PLVUHSRUWLQJ RSWLRQ $ PHDQ SUHVHUYLQJ VSUHDG VWUXFWXUH LV HPSOR\HG WR FDSWXUH WKH ULVNUHGXFWLRQ WKHPH RI KHGJLQJ 7KLV GLVVHUWDWLRQ VKRZV D WUDGHRII EHWZHHQ WKH EHQHILW IURP KHGJLQJ DQG WKH GHDG ZHLJKW ORVV IURP PLVUHSRUWLQJ ,W LV VKRZQ WKDW ZKHQ WKH PDQDJHUfV PLVUHSRUWLQJ FRVW GHFOLQHV ZLWK WKH HIIHFWLYHQHVV RI KHGJLQJ WKH SULQFLSDOfV SUHIHUHQFH IRU WKH KHGJHPLVUHSRUW EXQGOH GRHV QRW FKDQJH PRQRWRQLFDOO\ ZLWK WKH HIIHFWLYHQHVV RI KHGJLQJ 6SHFLILFDOO\ ZKHQ KHGJLQJ LV KLJKO\ HIIHFWLYH WKH SULQFLSDOfV SUHIHUHQFH IRU WKH EXQGOH LQFUHDVHV LQ WKH HIIHFWLYHQHVV ZKLOH ZKHQ KHGJLQJfV HIIHFWLYHQHVV LV PRGHUDWH WKH SULQFLSDOfV SUHIHUHQFH GHFUHDVHV LQ WKH HIIHFWLYHQHVV :KHQ KHGJLQJ LV RQO\ VOLJKWO\ HIIHFWLYH ZKHWKHU WKH SULQFLSDO SUHIHUV WKH 9OO PAGE 10 EXQGOH LV QRW LQIOXHQFHG E\ WKH HIIHFWLYHQHVV ,Q DGGLWLRQ WKLV GLVVHUWDWLRQ VKRZV WKDW VRPHWLPHV LW LV QRW HIILFLHQW WR WDNH DQ\ PHDVXUH WR UHVWUDLQ HDUQLQJV PDQDJHPHQW 5HFHQW UHJXODWLRQV UHTXLUH ILUPV WR UHFRJQL]H WKH LQHIIHFWLYH SRUWLRQ RI KHGJHV LQWR HDUQLQJV 7KLV GLVVHUWDWLRQ LQGLFDWHV WKDW WKLV HDUO\ UHFRJQLWLRQ PD\ FKDQJH WKH ILUPVf KHGJLQJ EHKDYLRU 6LQFH WKH HDUO\ UHFRJQLWLRQ LQFUHDVHV WKH LQWHULP HDUQLQJVf ULVNLQHVV KHGJLQJ PD\ EHFRPH LQHIILFLHQW HYHQ WKRXJK LW VWLOO UHGXFHV WKH WRWDO ULVN ,Q WKLV VHQVH WKH QHZ UHJXODWLRQV PD\ QRW EHQHILW LQYHVWRUV WKRXJK WKHLU LQWHQWLRQ LV WR SURYLGH PRUH LQIRUPDWLRQ DERXW WKH ULVN DQG YDOXH RI GHULYDWLYHV WR WKH LQYHVWRUV YLX PAGE 11 &+$37(5 %$&.*5281' $1' /,7(5$785( 5(9,(: %DFNJURXQG 'HULYDWLYHV LQFOXGH fD ZLGH YDULHW\ RI ILQDQFLDO DQG FRPPRGLW\ LQVWUXPHQWV ZKRVH YDOXH GHSHQGV RQ RU LV GHULYHG IURP WKH YDOXH RI DQ XQGHUO\LQJ DVVHWOLDELOLW\ UHIHUHQFH UDWH RU LQGH[nf /LQVPHLHU f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f GHULYDWLYHV FRQWUDFWV VWRRG DW 86 WULOOLRQ ZLWK D JURVV PDUNHW YDOXH RI WULOOLRQ 7KH GHULYDWLYHV KDYH SOD\HG DQ LPSRUWDQW UROH LQ WKH ILUPVf ULVN PDQDJHPHQW DFWLYLWLHV 2Q WKH RWKHU KDQG WKH FRPSOH[LW\ RI ILQDQFLDO GHULYDWLYHV UDLVHV LQYHVWRUVf FRQFHUQ DERXW KRZ WKH GHULYDWLYHV FKDQJH WKH ILUPVf SHUIRUPDQFH DQG VXVSLFLRQ DERXW ZKHWKHU WKH GHULYDWLYHV DUH DEXVHG LQ WKH LQWHUHVW RI WKH PDQDJHPHQW 'XULQJ WKH SDVW WHQ \HDUV WKHUH DUH QXPHURXV VFDQGDOV LQYROYLQJ WKH XVH RI GHULYDWLYHV )RU H[DPSOH LQ 0DUFK D -DSDQHVH FRXUW ILQHG &UHGLW 6XLVVH )LUVW %RVWRQ PLOOLRQ PAGE 12 WKH ZRUOG FROODSVHG ,QYHVWLJDWLRQV UHYHDOHG WKDW LW KDG PDGH H[WHQVLYH XVH RI HQHUJ\ DQG FUHGLW GHULYDWLYHV WR EROVWHU UHYHQXHV 5HVSRQGLQJ WR WKH LQYHVWRUVf FRQFHUQ WKH )LQDQFLDO $FFRXQWLQJ 6WDQGDUGV %RDUG )$6%f UHFHQWO\ LVVXHG VHYHUDO QHZ VWDWHPHQWV RQ WKH PHDVXUHPHQW DQG GLVFORVXUH RI GHULYDWLYHV LQFOXGLQJ 6)$6 DQG 7KHUH DUH DOVR WRQV RI GHWDLOHG LPSOHPHQWDWLRQ JXLGDQFH IURP WKH (PHUJLQJ ,VVXHV 7DVN )RUFH (,7)f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fV IDLU YDOXH FDQQRW RIIVHW WKH GHFUHDVHLQFUHDVH LQ LWV KHGJHG LWHPf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n ULVNV WKDW LV WRROV RI KHGJLQJf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f DQDO\]H WKH GHWHUPLQDQWV RI ILUPVf KHGJLQJ SROLFLHV IURP WKH SHUVSHFWLYH RI ILUP YDOXH 7KH\ H[DPLQH WD[HV EDQNUXSWF\ FRVW DQG PDQDJHUVf ZHDOWK 5HJDUGLQJ KHGJLQJ DFWLYLWLHV DV D NLQG RI LQVXUDQFH 0D\HUV DQG 6PLWK f XVH WKH WKHRU\ RI ILQDQFH WR DQDO\]H WKH FRUSRUDWH GHPDQG IRU LQVXUDQFH IURP WKH SHUVSHFWLYHV RI WD[HV FRQWUDFWLQJ FRVWV DQG WKH LPSDFW RI ILQDQFLQJ SROLF\ RQ ILUPVf LQYHVWPHQW GHFLVLRQV 6PLWK DQG 6WXO] f FRQFOXGH WKDW KHGJLQJ UHGXFHV D ILUPfV WD[ OLDELOLW\ LI WKH SRVWWD[ ILUP YDOXH LV D FRQFDYH IXQFWLRQ RI WKH SUHWD[ ILUP YDOXH 1DQFH 6PLWK DQG 6PLWKVRQ f SURYLGH WKH HPSLULFDO HYLGHQFH WKDW ILUPV ZLWK PRUH RI WKH UDQJH RI WKHLU SUHWD[ LQFRPH LQ WKH VWDWXWRU\ SURJUHVVLYH UHJLRQ RI WKH WD[ VFKHGXOH RU KDYH PRUH WD[ SUHIHUHQFH LWHPV DUH PRUH OLNHO\ WR KHGJH 7KLV VXSSRUWV 6PLWK DQG 6WXO]fV VWDWHPHQW RQ WKH FRUSRUDWH KHGJLQJ LQFHQWLYH IURP WD[ OLDELOLW\ +RZHYHU *UDKDP DQG 5RJHUV f TXDQWLI\ WKH FRQYH[LW\EDVHG EHQHILWV RI KHGJLQJ E\ FDOFXODWLQJ WKH WD[ VDYLQJV WKDW UHVXOW IURP KHGJLQJ DQG GR QRW ILQG HYLGHQFH WKDW ILUPV KHGJH LQ UHVSRQVH WR WD[ FRQYH[LW\ 6PLWK DQG 6WXO] f DOVR VWXG\ KHGJLQJ IURP WKH SHUVSHFWLYH RI WKH PDQDJHUfV ZHDOWK 7KH\ LQGLFDWH WKDW WKH PDQDJHU ZRXOG OLNH WR KHGJH LI KLV HQGRISHULRG ZHDOWK LV D FRQFDYH IXQFWLRQ RI WKH HQGRISHULRG ILUP YDOXH ZKLOH WKH PDQDJHU ZRXOG QRW KHGJH LI KLV HQGRISHULRG ZHDOWK LV D FRQYH[ IXQFWLRQ RI ILUP YDOXH 5RJHUV f FRQVLGHUV ERWK WKH PDQDJHUfV VWRFN KROGLQJV DQG RSWLRQ KROGLQJV DQG ILQGV WKH ULVNWDNLQJ LQFHQWLYHV IURP RSWLRQV DUH QHJDWLYHO\ DVVRFLDWHG ZLWK WKH XVH RI PAGE 14 GHULYDWLYHV 7KLV HYLGHQFH LV FRQVLVWHQW ZLWK 6PLWK DQG 6WXO]fV VXJJHVWLRQ WKDW WKH PDQDJHUfV ZHDOWK SOD\V D UROH LQ KHGJLQJ GHFLVLRQ DQG LV DOVR FRQVLVWHQW ZLWK WKH QRWLRQ WKDW GHULYDWLYHV DUH WR UHGXFH ILUPVf ULVNV 0D\HUV DQG 6PLWK f DUJXH WKDW WKH FRUSRUDWLRQ GRHV QRW QHHG LQVXUDQFH WR UHGXFH WKH VWRFNKROGHUVf ULVN VLQFH WKH VWRFNKROGHUV FDQ HOLPLQDWH LQVXUDEOH ULVN WKURXJK GLYHUVLILFDWLRQ ,QVWHDG LQVXUDQFH LV RSWLPDOO\ GHVLJQHG WR VKLIW WKH ULVN RI PDQDJHUV DQG HPSOR\HHV WR VWRFNKROGHUV VLQFH WKH PDQDJHUV DQG RWKHU HPSOR\HHV GR QRW KDYH HQRXJK DELOLW\ WR GLYHUVLI\ FODLPV RQ KXPDQ FDSLWDO ,W WKHQ IROORZV WKDW WKH KLJKHU WKH HPSOR\HHVf IUDFWLRQ RI WKH FODLPV WR WKH ILUPfV RXWSXW WKH KLJKHU WKH SUREDELOLW\ WKDW WKH ILUP ZLOO SXUFKDVH LQVXUDQFH 6PLWK DQG 6WXO] f SRLQW RXW WKDW KHGJLQJ ORZHUV WKH SUREDELOLW\ RI LQFXUULQJ EDQNUXSWF\ FRVWV *UDKDP DQG 5RJHUV f VKRZ HPSLULFDO HYLGHQFH WKDW ILUPV ZLWK PRUH H[SHFWHG ILQDQFLDO GLVWUHVV KHGJH PRUH ZKLFK LV FRQVLVWHQW ZLWK WKH LGHD WKDW ILUPV KHGJH WR UHGXFH ULVNV 1DQFH 6PLWK DQG 6PLWKVRQ f ILQG WKDW ILUPV ZKR KDYH OHVV FRYHUDJH RI IL[HG FODLPV D SUR[\ IRU ILQDQFLDO GLVWUHVVf KHGJH PRUH ZKLFK LV DQRWKHU SLHFH RI HPSLULFDO HYLGHQFH WR VXSSRUW WKH ULVN UHGXFWLRQ LQFHQWLYH &RQWUDU\ WR ZRUNV VXFK DV 6PLWK DQG 6WXO] f DQG 1DQFH 6PLWK DQG 6PLWKVRQ f 6FKUDQG DQG 8QDO f HPSKDVL]H WKDW KHGJLQJ LV D PHDQV RI DOORFDWLQJ D ILUPfV ULVN H[SRVXUH DPRQJ PXOWLSOH VRXUFHV RI ULVN UDWKHU WKDQ UHGXFLQJ WRWDO ULVN +RZHYHU LQ VRPH VHQVH WKHLU DOORFDWLRQ WKHRU\ LV VWLOO FRQVLVWHQW ZLWK WKH ULVNUHGXFWLRQ WKHRU\ ,Q 6FKUDQG DQG 8QDOfV SDSHU WKH WRWDO ULVN LV UHIOHFWHG LQ WKH YDULDELOLW\ RI D ORDQ SRUWIROLRn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f IRFXV RQ RSWLPDO LQVXUDQFH WKURXJK KHGJLQJ E\ WKH PDQDJHU 7KH\ VKRZ WKDW XQGHU FHUWDLQ LQFHQWLYH FRQWUDFWV VKDUHKROGHUV ZLOO EH KXUW E\ WKH PDQDJHUfV KHGJLQJ EHKDYLRU VLQFH WKH PDQDJHU ZLOO GHYLDWH IURP WKH RSWLPDO PDQDJHULDO HIIRUW OHYHO ZLWK WKH DFTXLVLWLRQ RI LQVXUDQFH +RZHYHU LI WKH FRQWUDFW DQWLFLSDWHV WKH KHGJLQJ WKHQ WKH VKDUHKROGHUV ZLOO EHQHILW IURP WKDW KHGJLQJ 7KH UHDVRQ LV WKDW WKH VKDUHKROGHUV FDQ UHGXFH IL[HG SD\PHQWV WR WKH PDQDJHU WR DFTXLUH WKH GLUHFW JDLQ IURP KHGJLQJ UHDSHG E\ WKH PDQDJHU DQG WKH\ FDQ LQGXFH WKH PDQDJHU WR H[HUW PRUH HIIRUW E\ UDLVLQJ WKH PDQDJHUfV VKDUH RI ULVN\ UHWXUQV 7KHLU UHVXOW LV FRQVLVWHQW ZLWK WKLV SDSHUfV FRQFOXVLRQ WKDW KHGJLQJ UHGXFHV FRPSHQVDWLQJ ZDJH GLIIHUHQWLDOV LQ D /(1 IUDPHZRUN +RZHYHU XQOLNH WKH PRGHO LQ WKLV SDSHU WKH\ DVVXPH WKH RXWSXWV DUH DOZD\V SXEOLF DQG WKHLU ZRUN GRHV QRW FRQVLGHU HDUQLQJV PDQDJHPHQW ,Q DGGLWLRQ WKHLU DQDO\VLV IRFXVHV RQ KRZ KHGJLQJ LQIOXHQFHV ILUP YDOXH ZKLOH LQ WKH FXUUHQW SDSHU P\ IRFXV LV KRZ KHGJLQJ LQIOXHQFHV WKH LQIRUPDWLRQ FRQWHQW RI SHUIRUPDQFH PHDVXUHV $QRWKHU UHODWHG SDSHU LV 'H0DU]R DQG 'XIILH f ZKR DOVR DQDO\]H KHGJLQJ EHKDYLRU IURP WKH SHUVSHFWLYH RI LQIRUPDWLRQ FRQWHQW 7KH\ VKRZ WKDW ILQDQFLDO KHGJLQJ LPSURYHV WKH LQIRUPDWLYHQHVV RI FRUSRUDWH HDUQLQJV DV D VLJQDO RI PDQDJHULDO DELOLW\ DQG SURMHFW TXDOLW\ +RZHYHU LQ WKHLU PRGHO WKH PDQDJHUfV DFWLRQ LV JLYHQ VR WKHUH LV QR QHHG WR PRWLYDWH WKH PDQDJHU WR ZRUN GLOLJHQWO\ 0RUHRYHU PAGE 16 XQOLNH WKH PRGHO LQ P\ ZRUN WKHLU PRGHO GRHV QRW FRQVLGHU PDQLSXODWLRQ RI HDUQLQJV E\ WKH PDQDJHUV 5HFHQW +HGJLQJ 5HJXODWLRQV 7KLUGO\ UHFHQW QHZ )$6% UHJXODWLRQV RQ KHGJLQJ KDYH WULJJHUHG VRPH UHVHDUFK RQ KRZ WKH QHZ UXOHV DIIHFW ILUPVf KHGJLQJ EHKDYLRU 7KH UHFHQW UDSLG GHYHORSPHQW RI YDULRXV ILQDQFLDO GHULYDWLYHV DQG WKH FRPSOH[LW\ RI GHULYDWLYHV UDLVH WKH FRQFHUQ WKDW WKH H[SORVLRQ LQ WKHLU XVH PD\ HQGDQJHU LQYHVWRUVf LQWHUHVW VLQFH LW LV GLIILFXOW IRU LQYHVWRUV WR XQGHUVWDQG IURP WKH ILQDQFLDO UHSRUWV WKH PDJQLWXGH YDOXH DQG SRWHQWLDO ULVN RI WKH GHULYDWLYHV 6LQFH WKH )$6% KDV LVVXHG VHYHUDO QHZ UHJXODWLRQV RQ WKH GLVFORVXUH RI GHULYDWLYHV $PRQJ WKHVH UHJXODWLRQV 6)$6 ZKLFK ZDV ODWHU VXSHUVHGHG E\ 6)$6 f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f UHVSRQG WR WKH )$6% 'LVFXVVLRQ 'RFXPHQW DERXW KHGJH DFFRXQWLQJ DQG WKH )$6% ([SRVXUH 'UDIW 7KH\ DUJXH WKDW D PDUNWRPDUNHW DFFRXQWLQJ LV WKH EHVW DSSURDFK WR DFFRXQWLQJ IRU KHGJLQJ DFWLYLWLHV DQG WKH\ VXSSRUW WKH GLVFORVXUH SROLF\ 7KH\ FODLP WKDW GLVFORVXUHV DERXW PDQDJHPHQW REMHFWLYHV LQ XVLQJ GHULYDWLYHV IRU ULVN PDQDJHPHQW DUH XVHIXO WR ILQDQFLDO VWDWHPHQW XVHUV DQG DUH YDOXH UHOHYDQW .DQRGLD 0XNKHUML 6DSUD DQG 9HQXJRSDODQ f H[DPLQH WKH VRFLDO EHQHILWV DQG FRVWV XQGHU GLIIHUHQW KHGJH DFFRXQWLQJ PHWKRGV IURP D PDFURHFRQRPLF YLHZ 7KH\ FODLP WKDW KHGJH DFFRXQWLQJ SURYLGHV LQIRUPDWLRQ DERXW ILUPVf ULVN H[SRVXUH WR WKH PDUNHW WKXV KHOSV PDNH WKH IXWXUHV SULFH PRUH HIILFLHQW PAGE 17 0HOXPDG :H\QV DQG =LY f DOVR FRPSDUH GLIIHUHQW KHGJH DFFRXQWLQJ UXOHV EXW WKH\ IRFXV RQ WKH PDQDJHUVf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f DUJXH WKDW LW LV RSWLPDO IRU WKH VKDUHKROGHUV WR UHTXHVW RQO\ WKH DJJUHJDWH RXWSXW LQVWHDG RI GLVFORVXUH RI KHGJLQJ SRVLWLRQV 7KH UHDVRQ LV WKDW ZLWK QRQGLVFORVXUH RI KHGJLQJ SRVLWLRQV PDQDJHUV FKRRVH ULVN PLQLPL]DWLRQ IXOO KHGJLQJf VLQFH UHGXFHG RXWSXW YDULDELOLW\ OHDGV WR D PRUH VWDEOH ZDJH +RZHYHU ZKHQ WKH KHGJLQJ SRVLWLRQV DUH UHTXLUHG WR EH GLVFORVHG WKH PDQDJHUV GHYLDWH IURP RSWLPDO IXOO KHGJLQJ VLQFH GLVFORVHG KHGJLQJ HOLPLQDWHV QRLVH IURP WKH RXWSXWV DQG PDNHV WKH RXWSXWV PRUH VHQVLWLYH VLJQDOV RI WKH PDQDJHUVf DELOLW\ +ROGLQJ WKH YDULDELOLW\ RI RXWSXW IL[HG WKLV GLVFORVXUH PDNHV WKH PDQDJHULDO ZDJH PRUH YDULDEOH $ UHODWHG FRQFHUQ LV WKDW WKH UHFRUGHG YDOXH IRU GHULYDWLYHV FDQ EH PDQLSXODWHG E\ PDQDJHUV $ GHULYDWLYHfV IDLU YDOXHf UHIHUV WR WKH FXUUHQW PDUNHW SULFH RI VLPLODU GHULYDWLYHV +RZHYHU LW LV RIWHQ GLIILFXOW WR ILQG fVLPLODUf GHULYDWLYHV 0DQDJHUV WKHQ PXVW HVWLPDWH WKH fIDLU YDOXHf RI WKH GHULYDWLYHV EDVHG RQ WKH FXUUHQW PDUNHW SULFH RI RWKHU GHULYDWLYHV RU LQYRNH fPDUNWRPRGHOf WHFKQLTXHV 7KLV OHDYHV WKH fIDLU YDOXHf PAGE 18 RI WKH GHULYDWLYHV XS WR WKH PDQDJHUVf GLVFUHWLRQ ,Q WKLV VHQVH WKH QHZ DFFRXQWLQJ UXOHV IRU GHULYDWLYHV SURYLGH D QHZ ILHOG IRU HDUQLQJV PDQDJHPHQW DQG WKH FRPSOH[LW\ RI PDQ\ GHULYDWLYHV LV LWVHOI D FKRLFH YDULDEOH 7KHUHIRUH GHULYDWLYHV FDQ IXQFWLRQ ERWK DV WRROV IRU KHGJLQJ DQG IRU HDUQLQJV PDQDJHPHQW (YHQ LQ %DUWK (OOLRWW HW DO f DQG %DUWK &ROOLQV HW DO f WKH\ DGPLW WKDW WKH PDUNWRPDUNHW DSSURDFK LV DUELWUDU\ DQG FUHDWHV RSSRUWXQLWLHV IRU HDUQLQJV PDQDJHPHQW WKRXJK WKH\ LQVLVW WKDW WKH IDLU YDOXH DSSURDFK WR UHSRUW KHGJLQJ DFWLYLWLHV LV VWLOO WKH EHVW RSWLRQ $PRQJ HPSLULFDO VWXGLHV %DUWRQ f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fV VWXG\ RQO\ FRQVLGHUV WKH KHGJLQJ IXQFWLRQ RI GHULYDWLYHV DQG GRHV QRW FRQVLGHU WKH HDUQLQJV PDQDJHPHQW IXQFWLRQ RI GHULYDWLYHV )RFXVLQJ RQ WKH RLO DQG JDV LQGXVWU\ 3LQFXV DQG 5DMJRSDO f DOVR H[SORUH WKH LQWHUDFWLRQ EHWZHHQ DFFUXDO PDQDJHPHQW DQG KHGJLQJ 7KHLU HPSLULFDO UHVXOW LV SDUWLDOO\ FRQVLVWHQW ZLWK %DUWRQfV UHVXOW +RZHYHU WKH\ HPSKDVL]H WKDW WKHLU UHVXOW VXJJHVWV D VHTXHQWLDO SURFHVV ZKHUHE\ WKH PDQDJHUV ILUVW GHFLGH KRZ PXFK WR KHGJH DQG PDQDJH WKH DFFUXDOV RQO\ GXULQJ WKH IRXUWK TXDUWHU ZKLFK ZHDNHQV %DUWRQfV VXEVWLWXWLRQ K\SRWKHVLV PAGE 19 5HYLHZ RI (DUQLQJV 0DQDJHPHQW DQG ,QIRUPDWLRQ &RQWHQW /LWHUDWXUH RQ HDUQLQJV PDQDJHPHQW LV DV YDVW DV WKH RFHDQ 7KHUH DUH QXPHURXV VWXGLHV DWWHPSWLQJ WR GRFXPHQW WKH H[LVWHQFH RI HDUQLQJV PDQDJHPHQW DQG D ORW RI UHVHDUFK RQ ZKHQ DQG ZK\ WKH PDQDJHUV PDQDJH WKH HDUQLQJV DP QRW VR DPELWLRXV DV WR UHYLHZ DOO UHODWHG OLWHUDWXUH QRW WR VD\ WKHUH DUH DOUHDG\ VRPH JRRG UHYLHZV RI WKH HDUQLQJV PDQDJHPHQW OLWHUDWXUH VXFK DV 6FKLSSHU f +HDO\ DQG :DKOHQ f %HQHLVK f DQG /HY f +HUH IRFXV RQ WKH OLWHUDWXUH RQ HIILFLHQW HDUQLQJV PDQDJHPHQW )RU HPSLULFDO VWXGLHV UHVHDUFKHUV XVXDOO\ XVH WKH PDUNHW UHDFWLRQ WR DQ HDUQLQJV DQQRXQFHPHQW WR PHDVXUH WKH LQIRUPDWLRQ FRQWHQW LQ WKH HDUQLQJV $EQRUPDO GLVFUHWLRQDU\ DFFUXDOV DUH XVXDOO\ UHJDUGHG DV SUR[LHV IRU PDQDJHUVf PDQLSXODWLRQ DQG PDQ\ VWXGLHV IRFXV RQ ZKHWKHU WKH PDUNHW FDQ VHH WKURXJK WKH PDQDJHG HDUQLQJV 7KH K\SRWKHVLV LV WKDW LI WKH PDUNHW LV HIILFLHQW WKHQ WKH LQYHVWRUV ZLOO QRW EH IRROHG E\ WKH PDQLSXODWLRQ 7KHUH DUH IXUWKHU VWXGLHV RQ ZKR LV PRUH HDVLO\ IRROHG XQVRSKLVWLFDWHG LQYHVWRUVf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f PDQLSXODWLRQ )LUVW WKH HOLPLQDWLRQ RI GLVFUHWLRQ ZLOO VKXW WKH GRRUV RI FRPPXQLFDWLQJ PDQDJHUVf SULYDWH LQIRUPDWLRQ WR LQYHVWRUV 7DNHQ WR WKH H[WUHPH LI ZH WRWDOO\ HOLPLQDWH DQ\ PDQLSXODWLRQ DQG UHWXUQ WR D PDUNWRPDUNHW DFFRXQWLQJ WKHQ WKH H[LVWHQFH RI DFFRXQWLQJ LV PHDQLQJOHVV )LQDQFLDO VWDWHPHQWV VKRXOG EH VRXUFHV RI LQIRUPDWLRQ DQG FRPPXQLFDWLRQ WXQQHOV EHWZHHQ PDQDJHPHQW DQG LQYHVWRUV ,I ILQDQFLDO VWDWHPHQWV ZHUH UHGXFHG WR EH MXVW UHFRUGV RI WKH LQYHVWRUVf HVWLPDWHV PAGE 20 DERXW WKH ILUPVf RSHUDWLQJ DFWLYLWLHV EDVHG RQ RWKHU LQIRUPDWLRQ WKHQ ZH GLG QRW QHHG ILQDQFLDO VWDWHPHQWV RU DFFRXQWLQJ $FFUXDO DFFRXQWLQJ SURYLGHV D WXQQHO IRU WKH PDQDJHUV WR XVH WKHLU MXGJHPHQW DQG GLVFUHWLRQ WR EHWWHU FRPPXQLFDWH ZLWK WKH ILQDQFLDO VWDWHPHQWV XVHUV %HQHLVK f VWDWHV WKDW WKHUH DUH WZR SHUVSHFWLYHV RQ HDUQLQJV PDQDJHPHQW 2QH LV WKH RSSRUWXQLVWLF SHUVSHFWLYH ZKLFK FODLPV WKDW PDQDJHUV VHHN WR PLVOHDG LQYHVWRUV 7KH RWKHU LV WKH LQIRUPDWLRQ SHUVSHFWLYH ZKLFK UHJDUGV WKH PDQDJHULDO GLVFUHWLRQ DV D PHDQV IRU PDQDJHUV WR UHYHDO WR LQYHVWRUV WKHLU SULYDWH H[SHFWDWLRQV DERXW WKH ILUPfV IXWXUH FDVK IORZV 6LPLODUO\ 'HFKRZ DQG 6NLQQHU f FDOO IRU DWWHQWLRQ RQ KRZ WR GLVWLQJXLVK PLVOHDGLQJ HDUQLQJV PDQDJHPHQW IURP DSSURSULDWH GLVFUHWLRQV 7KH\ IXUWKHU LQGLFDWH WKDW LW LV KDUG WR GLVWLQJXLVK FHUWDLQ IRUPV RI HDUQLQJV PDQDJHPHQW IURP DSSURSULDWH DFFUXDO DFFRXQWLQJ FKRLFHV 'HPVNL f GHPRQVWUDWHV WKDW LQ D VHWWLQJ ZLWK EORFNHG FRPPXQLFDWLRQ ZKHQ WKH PDQDJHUfV PDQLSXODWLRQ UHTXLUHV KLV KLJK HIIRUW OHYHO LW PD\ EH HIILFLHQW IRU WKH SULQFLSDO WR PRWLYDWH HDUQLQJV PDQDJHPHQW ,I ZH HOLPLQDWH GLVFUHWLRQ LQ RUGHU WR SXW D VWRS WR WKH GHWULPHQWDO HDUQLQJV PDQDJHPHQW ZH PD\ FORVH WKH FRPPXQLFDWLRQ FKDQQHO EHWZHHQ WKH PDQDJHUV DQG WKH LQYHVWRUV 6HFRQGO\ HOLPLQDWLQJ HDUQLQJV PDQDJHPHQW HYHQ LI HDUQLQJV PDQDJHPHQW PHUHO\ JDUEOHV LQIRUPDWLRQ PD\ EH WRR FRVWO\ /LDQJ f DQDO\]HV HTXLOLEULXP HDUQLQJV PDQDJHPHQW LQ D UHVWULFWHG FRQWUDFW VHWWLQJ DQG VKRZV WKDW WKH SULQFLSDO PD\ UHGXFH DJHQF\ FRVW E\ WROHUDWLQJ VRPH HDUQLQJV PDQDJHPHQW ZKHQ WKH FRQWUDFW KHOSV DOORFDWH WKH FRPSHQVDWLRQ ULVN HIILFLHQWO\ $U\D *ORYHU DQG 6XQGHU f WHOO D VWRU\ RI SRVWXULQJ WKDW ZKHQ WKH FRPPLWPHQW LV OLPLWHG DQG WKH LQIRUPDWLRQ V\VWHP LV QRW WUDQVSDUHQW DOORZLQJ PDQLSXODWLRQ LV PRUH HIILFLHQW WKDQ IRUELGGLQJ LW 'HPVNL )ULPRU DQG 6DSSLQJWRQ f VKRZ WKDW DVVLVWLQJ WKH PDQDJHU WR PDQLSXODWH LQ DQ HDUO\ SHULRG PD\ KHOS HDVH WKH LQFHQWLYH SUREOHP RI D ODWHU SHULRG ,Q WKHLU PRGHO WKH SULQFLSDOfV DVVLVWDQFH UHGXFHV WKH PDQDJHUfV LQFHQWLYH WR GHYRWH HIIRUW WR IXUWKHU PDQLSXODWLRQ DQG LQGXFHV WKH PDQDJHU WR GHYRWH PRUH HIIRUW WR SURGXFWLRQ PAGE 21 $V VWDWHG LQ $U\D *ORYHU DQG 6XQGHU f ZKHQ WKH 5HYHODWLRQ 3ULQFLSOH LV EURNHQ GRZQ WKDW LV ZKHQ FRPPXQLFDWLRQ LV OLPLWHG WKH FRQWUDFW LV UHVWULFWHG RU FRPPLWPHQW LV PLVVLQJf HDUQLQJV PDQDJHPHQW PD\ EH HIILFLHQW ,Q WKLV SDSHU LQ PRVW FDVHV WKH H[LVWHQFH RI HDUQLQJV PDQDJHPHQW LQ HTXLOLEULXP FRPHV IURP WKH YLRODWLRQ RI WKH XQUHVWULFWHG FRQWUDFW DVVXPSWLRQ VLQFH DVVXPH D OLQHDU FRQWUDFW DOVR VXSSRVH DQ XQHYHQ SURGXFWLYLW\ VHWWLQJ WR LQGXFH HDUQLQJV PDQDJHPHQW IROORZLQJ D GHVLJQ LQ /LDQJ f 7KLV SDSHU VKRZV WKDW HYHQ LI HDUQLQJV PDQDJHPHQW PHUHO\ GHVWUR\V LQIRUPDWLRQ VRPHWLPHV LW LV QRW RQO\ LQHIILFLHQW WR PRWLYDWH WUXWKWHOOLQJ EXW DOVR LQHIILFLHQW WR WDNH DQ\ PHDVXUH WR UHVWUDLQ HDUQLQJV PDQDJHPHQW VLQFH UHVWUDLQLQJ PDQLSXODWLRQ PD\ EH WRR FRVWO\ ,Q WKH ODVW FKDSWHU RI WKLV SDSHU DOVR LQFOXGH DQ DQDO\VLV RI LQIRUPDWLYH HDUQLQJV PDQDJHPHQW WKH IRUHFDVW PRGHOf LQ ZKLFK HDUQLQJV PDQDJHPHQW FRQYH\V WKH PDQDJHUfV SULYDWH LQIRUPDWLRQ 5HYLHZ RI /(1 )UDPHZRUNV 0RVW RI P\ DQDO\VLV LQ WKLV SDSHU LV LQ D /(1 IUDPHZRUN /(1 OLQHDU FRQWUDFW QHJDWLYH H[SRQHQWLDO XWLOLW\ IXQFWLRQ DQG QRUPDO GLVWULEXWLRQf LV D KHOSIXO WHFKQRORJ\ IRU UHVHDUFK LQ DJHQF\ DQG KDV EHHQ HPSOR\HG LQ PRUH DQG PRUH DQDO\WLFDO UHVHDUFK $PRQJ WKH WKUHH DVVXPSWLRQV RI WKH /(1 IUDPHZRUN H[SRQHQWLDO XWLOLW\ DQG QRUPDO GLVWULEXWLRQ KDYH EHHQ ZLGHO\ XVHG DQG DFFHSWHG ZKLOH WKH OLQHDU FRQWUDFW DVVXPSWLRQ LV PRUH FRQWURYHUVLDO /DPEHUW f JLYHV D JRRG UHYLHZ RQ /(1 +H VXPPDUL]HV WKUHH FRPPRQ MXVWLILFDWLRQV IRU WKH OLQHDU FRQWUDFWLQJ VHWWLQJ 7KH ILUVW LV WKDW DFFRUGLQJ WR +ROPVWURP DQG 0LOJURP f D OLQHDU FRQWUDFW LV RSWLPDO LQ D FRQWLQXRXV WLPH PRGHO ZKHUH WKH DJHQWf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f DUH DPRQJ WKH ILUVW WR HPSOR\ /(1 LQ DQDO\WLFDO DQDO\VLV 7KH\ IRFXV RQ WKH FRQJUXLW\ DQG SUHFLVLRQ RI SHUIRUPDQFH PHDVXUHV LQ D PXOWLGLPHQVLRQDO HIIRUW VHWWLQJ ZKHUH WKH DJHQW DOORFDWHV KLV HIIRUW RQ PRUH WKDQ RQH WDVN 7KH\ VKRZ WKDW ZLWK VLQJOH PHDVXUH QRQFRQJUXLW\ RI WKH PHDVXUH FDXVHV D GHYLDWLRQ IURP WKH RSWLPDO HIIRUW DOORFDWLRQ DPRQJ WDVNV DQG QRLVH LQ WKH PHDVXUH PDNHV WKH ILUVWEHVW DFWLRQ PRUH FRVWO\ ,Q WKHLU VHWWLQJ WKH XVH RI DGGLWLRQDO PHDVXUHV PD\ UHGXFH ULVN DQG QRQFRQJUXLW\ 7KHUH DUH VRPH ZRUNV RQ VHOHFWLQJ SHUIRUPDQFH PHDVXUHV IRU FRQWUDFWLQJ SXUSRVHV XVLQJ /(1 IUDPHZRUNV ,QGMHMLNLDQ DQG 1DQGD f XVH D /(1 IUDPHZRUN WR VWXG\ WKH UDWFKHW HIIHFW LQ D PXOWLSHULRG PXOWLWDVN FRQWUDFW 7KH\ VKRZ WKDW LQ D WZRSHULRG VHWWLQJ ZKHQ WKH SHUIRUPDQFH PHDVXUHV DUH SRVLWLYHO\ FRUUHODWHG WKURXJK WLPH DQG ZKHQ WKH SULQFLSDO FDQQRW FRPPLW QRW WR XVH WKH ILUVW SHULRG SHUIRUPDQFH LQ WKH VHFRQG SHULRG FRQWUDFWLQJ WKH DJHQW LV LQFOLQHG WR VXSSO\ OHVV HIIRUW LQ WKH ILUVW SHULRG VLQFH D EHWWHU ILUVW SHULRG SHUIRUPDQFH LQFUHDVHV WKH VWDQGDUG IRU WKH VHFRQG SHULRG SHUIRUPDQFH 7R PRWLYDWH WKH DJHQW WR ZRUN KDUG LQ WKH ILUVW SHULRG WKH SULQFLSDO KDV WR SD\ PRUH IRU WKH ILUVW SHULRG ,QGMHMLNLDQ DQG 1DQGD DOVR VXJJHVW WKDW DQ DJJUHJDWH SHUIRUPDQFH PHDVXUH PD\ EH EHWWHU WKDQ D VHW RI GLVDJJUHJDWH PHDVXUHV DQG FRQVROLGDWLQJ PXOWLWDVN UHVSRQVLELOLW\ WR RQH DJHQW PD\ EH EHWWHU WKDQ VSHFLDOL]LQJ WKH UHVSRQVLELOLWLHV WR DYRLG WKH UDWFKHW HIIHFW $XWUH\ 'LNROOL DQG PAGE 23 1HZPDQ f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f DGRSW D PXOWLSHULRG /(1 IUDPHZRUN LQ SDUW RI WKHLU DQDO\VLV RQ DVVHW YDOXDWLRQ UXOHV ,Q D VHWWLQJ ZKHUH WKH DJHQWfV HIIRUW DIIHFWV WKH FDVK IORZV IURP RSHUDWLQJ DFWLYLWLHV WKH\ VKRZ WKDW LQFHQWLYH VFKHPHV EDVHG RQO\ RQ UHDOL]HG FDVK IORZV DUH XVXDOO\ QRW RSWLPDO VLQFH LW LV GLIILFXOW IRU WKH SULQFLSDO WR HOLPLQDWH WKH YDULDELOLW\ LQ FDVK IORZ IURP ILQDQFLQJ DFWLYLWLHV 'LVFUHWLRQDU\ UHSRUWLQJ DQG HDUQLQJV PDQDJHPHQW DUH DOVR DPRQJ WKH WRSLFV H[SORUHG XVLQJ /(1 IUDPHZRUNV &KULVWHQVHQ DQG 'HPVNL f XVH D FRYDULDQFH VWUXFWXUH WR PRGHO UHSRUWLQJ VFKHPHV HLWKHU FRQVHUYDWLYH RU DJJUHVVLYHf XQGHU D OLQHDU FRQWUDFW LQ D WZRSHULRG VHWWLQJ 7KH\ GLVFXVV ZKHQ UHSRUWLQJ GLVFUHWLRQ LV SUHIHUUHG WR LQIOH[LEOH UHSRUWLQJ DQG ZKHQ LW LV QRW DQG IXUWKHU H[SORUH WKH UROH RI DQ DXGLWRU LQ WKLV VHWWLQJ 7KH\ XVH DQ DV\PPHWULF SLHFHUDWH WR PRGHO WKH LQFHQWLYH IRU WKH H[HUFLVH RI UHSRUWLQJ GLVFUHWLRQ 6LPLODUO\ /LDQJ f XVHV D WLPHYDU\LQJ SURGXFWLRQ WHFKQRORJ\ DQG WKHUHIRUH XQHYHQ ERQXV VFKHPHV WKURXJK WLPH WR H[SORUH HDUQLQJV PDQDJHPHQW +H VWXGLHV WKH HTXLOLEULXP HDUQLQJV PDQDJHPHQW LQ D WZRSHULRG PXOWLSOD\HU PDQDJHUV VKDUHKROGHUV DQG UHJXODWRUVf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f 7KH SULQFLSDO WULHV WR PLQLPL]H KHU H[SHFWHG SD\PHQW WR WKH PDQDJHU ZKLOH PRWLYDWLQJ WKH PDQDJHU WR FKRRVH KLJK DV RSSRVHG WR ORZ DFWLRQV LQ ERWK SHULRGV 7KH PDQDJHUfV SUHIHUHQFH IRU WRWDO QHWf FRPSHQVDWLRQ LV FKDUDFWHUL]HG E\ FRQVWDQW DEVROXWH ULVN DYHUVLRQ LPSO\LQJ D XWLOLW\ IXQFWLRQ RI X6 fÂ§ Ff fÂ§HBUBA ZKHUH 6 LV WKH SD\PHQW WR WKH DJHQW F LV WKH PDQDJHUfV FRVW IRU KLV DFWLRQV DQG U LV WKH $UURZ3UDWW PHDVXUH RI ULVN DYHUVLRQ :LWKRXW ORVV RI JHQHUDOLW\ WKH PDQDJHUfV UHVHUYDWLRQ SD\PHQW LV VHW DW ,Q RWKHU ZRUGV KLV UHVHUYDWLRQ XWLOLW\ LV fÂ§ HBUA 3HUIRUPDQFH VLJQDOV RXWSXWVf DUH VWRFKDVWLF DQG WKHLU SUREDELOLW\ LV DIIHFWHG E\ WZR IDFWRUV WKH PDQDJHUfV DFWLRQ DQG VRPH H[RJHQRXV IDFWRU 7KH PDQDJHUfV DFWLRQ LV ELQDU\ ,Q HDFK SHULRG WKH PDQDJHU HLWKHU VXSSOLHV ORZ DFWLRQ / RU KLJK DFWLRQ + + / :LWKRXW ORVV RI JHQHUDOLW\ / LV QRUPDOL]HG WR ]HUR 7KH PDQDJHUfV SHUVRQDO FRVW IRU ORZ DFWLRQ LV ]HUR +LV SHUVRQDO FRVW IRU KLJK DFWLRQ LV & LQ HDFK SHULRG 7KH SULQFLSDO FDQQRW REVHUYH WKH PDQDJHUfV DFWLRQV $Q H[RJHQRXV IDFWRU DOVR DIIHFWV UHDOL]HG RXWSXW 7KH HIIHFW RI WKLV H[RJHQRXV IDFWRU RQ WKH RXWSXW FDQ EH PAGE 26 KHGJHG DW OHDVW SDUWLDOO\ E\ XVLQJ GHULYDWLYHV 1HLWKHU WKH SULQFLSDO QRU WKH PDQDJHU FDQ IRUHVHH WKH UHDOL]DWLRQ RI WKH H[RJHQRXV IDFWRU +HUH RXWSXW UHSUHVHQWV D QRLV\ SHUIRUPDQFH PHDVXUHPHQW RI WKH PDQDJHUfV DFWLRQ OHYHOV HJ HDUQLQJVf RXWSXW GRHV QRW QDUURZO\ UHIHU WR SURGXFWLRQ DQG FDQ EH QHJDWLYH XVH ;? WR UHSUHVHQW WKH RXWSXW IRU WKH ILUVW SHULRG DQG [ WR UHSUHVHQW WKH RXWSXW IRU WKH VHFRQG SHULRG %DVLF 6HWXS $VVXPH ;? N?D? f? DQG [ ND H ZLWK m ( ^+ ` L ( ^` DÂ UHSUHVHQWV WKH DFWLRQ OHYHO IRU SHULRG L N?N DUH SRVLWLYH FRQVWDQWV DQG UHSUHVHQW WKH SURGXFWLYLW\ LQ WKH ILUVW DQG WKH VHFRQG SHULRGV UHVSHFWLYHO\ 6XSSRVH N? N 7KH XQHYHQ SURGXFWLYLW\ IROORZV D GHVLJQ LQ /LDQJ f 7KH GLIIHUHQW SURGXFWLYLW\ LQGXFHV GLIIHUHQW ERQXV UDWHV WKURXJK WLPH DQG LV LPSRUWDQW IRU WKH HQVXLQJ RI HDUQLQJV PDQDJHPHQW 7KH DVVXPSWLRQ N? N LV UHOD[HG LQ &KDSWHU f 7KH YHFWRU >HLH@ IROORZV D MRLQW QRUPDO GLVWULEXWLRQ ZLWK D PHDQ RI > @ 7KHUH LV QR FDUU\RYHU HIIHFW RI DFWLRQ DQG WKH RXWSXWV RI HDFK SHULRG DUH LQGHSHQGHQW RI HDFK RWKHU ,I WKH RXWSXWV DUH QRW KHGJHG WKH FRYDULDQFH PDWUL[ RI >HLH@ LV e D D ,I WKH VHFRQG SHULRG RXWSXW LV KHGJHG DV GLVFXVV LQ D ODWHU VHFWLRQ DQ\ VXFK KHGJH LV FRQILQHG WR WKH VHFRQG SHULRGf WKH PDWUL[ LV eÂ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f DQG DOVR RIIHUV WUDFWDELOLW\ 7KH FRQFOXVLRQV LQ WKLV SDSHU SHUVLVW ZKHQ WKH RXWSXWV KDYH D QRQ]HUR FRYDULDQFH PAGE 27 7KH PDQDJHUfV FRQWUDFW RU FRPSHQVDWLRQ IXQFWLRQ LV DVVXPHG WR EH OLQHDU LQ WKH QRWHG RXWSXW VWDWLVWLFV 6SHFLILFDOO\ 6 6[ f : D[? c[ ZKHUH : LV D IL[HG ZDJH DQG D DQG c DUH WKH ERQXV UDWHV UHVSHFWLYHO\ DVVLJQHG WR WKH ILUVW SHULRG RXWSXW ;? DQG WKH VHFRQG SHULRG RXWSXW %HQFKPDUN 7KH EHQFKPDUN LV D SXEOLFRXWSXW QRKHGJHRSWLRQ PRGHO 7KHUH LV QR RSWLRQ WR KHGJH LQ WKLV EHQFKPDUN DQG HDUQLQJV PDQDJHPHQW PLVUHSRUWLQJ DFWXDO RXWSXWVf LV LPSRVVLEOH VLQFH WKH RXWSXW IRU HDFK SHULRG LV REVHUYHG SXEOLFO\ 7R VROYH WKH SULQFLSDOfV GHVLJQ SURJUDP LQ WKLV EHQFKPDUN VWDUW IURP WKH VHFRQG SHULRG 7R PRWLYDWH WKH PDQDJHUfV KLJK DFWLRQ LQ WKH VHFRQG SHULRG WKH SULQFLSDO VHWV WKH FRQWUDFW VR WKDW WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW ZKHQ KH FKRRVHV KLJK DFWLRQ LV DW OHDVW DV KLJK DV WKDW ZKHQ KH FKRRVHV ORZ DFWLRQ IRU HDFK UHDOL]DWLRQ RI [? 'HQRWH WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW ZKHQ KH FKRRVHV D JLYHQ ;? DW WKH EHJLQQLQJ RI WKH VHFRQG SHULRG DV &(^D? Af WKH LQFHQWLYH FRPSDWLELOLW\ FRQVWUDLQW IRU WKH VHFRQG SHULRG LV &(+[ &([Lf9[L ,&f :LWK ;L NQRZQ DQG ] D QRUPDO UDQGRP YDULDEOH ZLWK PHDQ ND DQG YDULDQFH FU LW LV ZHOO NQRZQ WKDW &(D?;?f : D]L cND fÂ§ FDLDf fÂ§ ÂW FmL Df UHSUHVHQWV WKH PDQDJHUfV FRVW IRU KLV DFWLRQVf 7KXV ,&f FDQ EH H[SUHVVHG DV : D]L cN+ & bSFU : D[ iW ZKLFK UHGXFHV WR > UHJDUGOHVV RI [? 'HQRWH WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG ZKHQ KH FKRRVHV m IROORZHG E\ D UHJDUGOHVV RI [? DV &(?^D? Df 7R PRWLYDWH D? + JLYHQ KLJK DFWLRQ LQ WKH VHFRQG SHULRG WKH LQFHQWLYH FRPSDWLELOLW\ FRQVWUDLQW IRU WKH ILUVW SHULRG LV PAGE 28 &([^++f!&([^4?+f ,&f ,I D + UHJDUGOHVV RI [? ,&f LV VDWLVILHG WKHQ LV D QRUPDO UDQGRP YDULDEOH ZLWK PHDQ : DN?L? N+ DQG YDULDQFH DD D 7KXV ,&Of LPSOLHV : DN? + N + & i D D 9f :N+&b ^D D Rf ZKLFK UHGXFHV WR D A 7KH LQGLYLGXDO UDWLRQDOLW\ FRQVWUDLQW UHTXLUHV WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW ZKHQ KH FKRRVHV KLJK DFWLRQV LQ ERWK SHULRGV LV QRW ORZHU WKDQ KLV UHVHUYDWLRQ ZDJH QRUPDOL]HG WR 7KH LQGLYLGXDO UDWLRQDOLW\ FRQVWUDLQW WKHUHIRUH LV &(?+@+f ,5f ([SDQGLQJ ,5f ZH JHW : DN?+ N+ fÂ§ & fÂ§ADD FUf 7KH SULQFLSDO PLQLPL]HV KHU H[SHFWHG SD\PHQW WR WKH PDQDJHU (?: DNL+ FLf cN+ Hf@ : DN?+ N+ +HU GHVLJQ SURJUDP LQ WKLV EHQFKPDUN PRGHO LV 3URJUDP >$@ ,5f ,&Of PLQ : DNL+ N+ : TL V W : DNL+ N+ & ?>DD Rf D A "!UU NLOO ,&f 7KH LQGLYLGXDO UDWLRQDOLW\ FRQVWUDLQW PXVW EH ELQGLQJ DV RWKHUZLVH WKH SULQFLSDO FDQ DOZD\V ORZHU : 7KXV WKH RSWLPDO IL[HG ZDJH PXVW EH fÂ§DN?+ fÂ§ N+ & MDFUFUf DQG WKH SULQFLSDOfV H[SHFWHG FRVW LV & AT7f 7KHUHIRUH WKH SULQFLSDOfV GHVLJQ SURJUDP UHGXFHV WR WKH PLQLPL]DWLRQ RI _DFU cRf VXEMHFW WR WKH WZR LQFHQWLYH FRQVWUDLQWV 7KH RSWLPDO IL[HG ZDJH LV FKRVHQ WR HQVXUH WKDW WKH LQGLYLGXDO UDWLRQDOLW\ FRQVWUDLQW ELQGV WKHUHIRUH IRFXV RQ WKH ERQXV UDWHV LQ WKH RSWLPDO FRQWUDFWV LQ RXU DQDO\VLV 'HQRWH Dr DV WKH RSWLPDO ILUVW SHULRG ERQXV UDWH DQG r$ WKH RSWLPDO VHFRQG SHULRG ERQXV UDWH ZH QRZ KDYH 7KLV UHVXOW KDV EHHQ VKRZQ LQ IRU H[DPSOH )HOWKDP DQG ;LH f PAGE 29 /HPPD 7KH RSWLPDO FRQWUDFW LQ WKH EHQFKPDUN PRGHO H[KLELWV Dr$ DQG Ur fÂ§ 3D fÂ§ Z 3URRI 6HH WKH $SSHQGL[ ,Q D IXOOLQIRUPDWLRQ VHWWLQJ WKH SULQFLSDO RQO\ QHHGV WR SD\ IRU WKH UHVHUYDWLRQ ZDJH DQG WKH SHUVRQDO FRVW RI KLJK DFWLRQV & ,Q WKH SUHVHQW EHQFKPDUN VHWWLQJ WKH SULQFLSDO QHHGV WR SD\ & A^Dr$D Ir$Df 7KH SULQFLSDO SD\V PRUH VLQFH WKH PDQDJHU EHDUV FRPSHQVDWLRQ ULVN ZLWK D ULVN SUHPLXP RU FRPSHQVDWLQJ ZDJH GLIIHUHQWLDO RI _DrFU r$Rf 1H[W LQWURGXFH WKH KHGJLQJ DQG HDUQLQJV PDQDJHPHQW RSWLRQV +HGJLQJ DQG (DUQLQJV 0DQDJHPHQW 2SWLRQV +HGJLQJ 2SWLRQ ,QLWLDOO\ VXSSRVH WKH VHFRQG SHULRG RXWSXW FDQ EH KHGJHG EXW QR SRVVLELOLW\ RI PDQDJLQJ HDUQLQJV LV SUHVHQW ,Q SUDFWLFH D KHGJLQJ GHFLVLRQ LV XVXDOO\ PDGH WR UHGXFH WKH ULVN LQ WKH IXWXUH RXWSXW 7R FDSWXUH WKLV IHDWXUH DVVXPH WKDW WKH KHGJLQJ GHFLVLRQ LV PDGH DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG EXW WKH KHGJH LV IRU WKH VHFRQG SHULRG RXWSXW RQO\ DQG GRHVQfW LQIOXHQFH WKH ILUVW SHULRG RXWSXW 5HFHQW )$6% UHJXODWLRQV RQ GHULYDWLYHV HJ 6)$6 1R UHTXLUH WKDW ILUPV UHFRJQL]H WKH LQHIIHFWLYH SRUWLRQ RI KHGJHV LQWR HDUQLQJV HYHQ EHIRUH WKH VHWWOHPHQW RI WKH GHULYDWLYHV ,Q WKLV FKDSWHU GR QRW FRQVLGHU WKH UHFRJQLWLRQ LQ HDUQLQJV IURP XQVHWWOHG GHULYDWLYHV 7KDW LV DVVXPH KHGJLQJ RQO\ LQIOXHQFHV WKH RXWSXW RI WKH VHFRQG SHULRG ZKHQ WKH KHGJH LV VHWWOHGf 7KH HVWLPDWLRQ RI WKH KHGJHfV LQHIIHFWLYHQHVV LQYROYHV HDUQLQJV PDQDJHPHQW DQG ZLOO DGGUHVV WKH PDQLSXODWLRQ DVVRFLDWHG ZLWK WKH XVH RI GHULYDWLYHV ODWHU &RQVLGHU D IDLU YDOXH KHGJH DV DQ H[DPSOH $W WKH GDWH RI ILQDQFLDO UHSRUWLQJ LI WKH LQFUHDVHGHFUHDVH LQ WKH IDLU YDOXH RI WKH GHULYDWLYH GRHVQfW FRPSOHWHO\ RIIVHW WKH GHFUHDVHLQFUHDVH LQ WKH IDLU YDOXH RI WKH KHGJHG LWHP WKH XQFRYHUHG SRUWLRQ LV UHJDUGHG DV WKH LQHIIHFWLYH SRUWLRQ RI WKH KHGJH DQG LV UHFRJQL]HG LQWR HDUQLQJV LPPHGLDWHO\ +RZHYHU WKLV JDLQ RU ORVV IURP XQVHWWOHG GHULYDWLYHV LV QRW DFWXDOO\ UHDOL]HG DQG WKH HVWLPDWLRQ RI WKH KHGJHfV LQHIIHFWLYHQHVV LV XVXDOO\ VXEMHFWLYH IRU WKH HYDOXDWLRQ RI GHULYDWLYHVf IDLU YDOXH LV XVXDOO\ VXEMHFWLYHf PAGE 30 &HQWUDOL]HGKHGJH FDVH )LUVW FRQVLGHU D FHQWUDOL]HGKHGJH FDVH ZKHUH WKH SULQFLSDO KDV XQLODWHUDO KHGJLQJ DXWKRULW\ /DWHU LQ WKLV FKDSWHU ZLOO GHOHJDWH WKH KHGJLQJ RSWLRQ WR WKH PDQDJHUf 1RWLFH WKDW WKH EHQFKPDUN LV LGHQWLFDO WR WKH FDVH KHUH LI WKH SULQFLSDO GHFLGHV QRW WR KHGJH ,I WKH SULQFLSDO KHGJHV WKH SULQFLSDOfV GHVLJQ SURJUDP FKDQJHV VOLJKWO\ IURP WKH RQH LQ WKH EHQFKPDUN 7KH H[SHFWHG SD\PHQW LV VWLOO ;9 DN?+ cN+ 7KH LQFHQWLYH FRQVWUDLQWV IRU WKH PDQDJHU UHPDLQ WKH VDPH VLQFH WKH KHGJLQJ GHFLVLRQ LV QRW PDGH E\ WKH PDQDJHU DQG WKH DFWLRQ FKRLFH LQFHQWLYHV DUH XQDIIHFWHG E\ KHGJLQJ DFWLYLWLHV +RZHYHU WKH LQGLYLGXDO UDWLRQDOLW\ FRQVWUDLQW FKDQJHV WR EH : DNL+ SN+ & bDD Df 7KH SULQFLSDOfV GHVLJQ SURJUDP LQ WKH FHQWUDOL]HGKHGJH PRGHO ZKHQ VKH KHGJHV LV PLQ : DNL+ N+ 3URJUDP >%@ :D V W : DNL+ N+ & ?DD Rf ,5f m .K ,&f 3 L6K ,&f XVH FWr%r% WR GHQRWH UHVSHFWLYHO\ WKH RSWLPDO ERQXV UDWHV LQ WKH ILUVW DQG WKH VHFRQG SHULRGV LQ 3URJUDP >%? 3DUDOOHOLQJ /HPPD LPPHGLDWHO\ FRQFOXGH /HPPD 7KH RSWLPDO FRQWUDFW LQ WKH FHQWUDOL]HGKHGJH PRGHO H[KLELWV Dr% cAMM DQG 3E Wef 3URRI 6HH WKH $SSHQGL[ 7KH RSWLPDO FRQWUDFW VKDUHV WKH VDPH ERQXV UDWHV ZLWK WKDW LQ WKH EHQFKPDUN EHFDXVH WKH PDQDJHUfV DFWLRQ DIIHFWV WKH RXWSXW PHDQ ZKLOH KHGJLQJ RQO\ DIIHFWV WKH RXWSXW ULVN $V LPSOLHG E\ WKH ,5f FRQVWUDLQW ZKHQ WKHUH LV QR KHGJLQJ RSWLRQ RU ZKHQ WKH SULQFLSDO GRHV QRW KHGJH WKH SULQFLSDOfV H[SHFWHG SD\PHQW LV &ADrÂD 3ÂDf ZKLOH LWV FRXQWHUSDUW ZLWK KHGJLQJ LV & ADrAD ILrÂ-Gf :LWK KHGJLQJ PAGE 31 KHU H[SHFWHG FRVW LV UHGXFHG E\ _ADfÂ§DGf 2EYLRXVO\ WKH SULQFLSDO SUHIHUV KHGJLQJ WR QR KHGJLQJ 8VLQJ G fÂ§ WR UHSUHVHQW WKH VWUDWHJ\ RI QR KHGJLQJ DQG G WR UHSUHVHQW WKH VWUDWHJ\ RI KHGJLQJ ZH KDYH /HPPD 7KH SULQFLSDO SUHIHUV G LQ WKH FHQWUDOL]HGKHGJH PRGHO 3URRI 6HH WKH DERYH DQDO\VLV 7KH SULQFLSDOfV H[SHFWHG FRVW LV ORZHU ZKHQ VKH KHGJHV EHFDXVH KHGJLQJ UHGXFHV WKH QRLVH LQ XVLQJ RXWSXW WR LQIHU WKH PDQDJHUf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f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fV FRPSHQVDWLRQ ULVN GHULYHG IURP QRLV\ RXWSXW VLJQDOV 7R LOOXVWUDWH WKLV FRQFOXVLRQ XVH &(LDLGDf WR GHQRWH WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG ZKHQ KH FKRRVHV D[ DQG G LQ PAGE 32 WKH ILUVW SHULRG DQG FKRRVHV D LQ WKH VHFRQG SHULRG %\ KHGJLQJ &(LFL? Jf : DNLL cND fÂ§ FDL Df fÂ§ _FW IDGf ,I WKH PDQDJHU GRHVQnW KHGJH &(LDL Df : DNLD[ ND FDO Df ÂD9 3Df 6LQFH D S &)LDL ODf &ALDLDf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n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mL ^ ` DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG $W WKH HQG RI WKH ILUVW SHULRG WKH PDQDJHU REVHUYHV SULYDWHO\ WKH ILUVWSHULRG RXWSXW ;? +H UHSRUWV [? ^[O;L fÂ§ $` WR WKH SULQFLSDO DQG FKRRVHV KLV DFWLRQ OHYHO PAGE 33 IRU WKH VHFRQG SHULRG D ^+ ` $W WKH HQG RI WKH VHFRQG SHULRG DJDLQ WKH PDQDJHU REVHUYHV SULYDWHO\ WKH VHFRQGSHULRG RXWSXW ] DQG UHSRUWV [ ;? fÂ§ ;L [ 7KH SULQFLSDO REVHUYHV WKH DJJUHJDWH RXWSXW RI WKH WZR SHULRGV DW WKH HQG RI WKH VHFRQG SHULRG DQG SD\V WKH PDQDJHU DFFRUGLQJ WR WKH FRQWUDFW 7KH OLQHDU FRQWUDFW KHUH EHFRPHV 6 : D[ [ 7KH PDQDJHU PD\ KDYH DQ RSWLRQ WR PLVUHSRUW WKH RXWSXW E\ PRYLQJ $ IURP WKH ILUVW WR WKH VHFRQG SHULRG $ FDQ EH QHJDWLYH 1HJDWLYH $ LPSOLHV WKDW WKH PDQDJHU PRYHV VRPH RXWSXW IURP WKH VHFRQG WR WKH ILUVW SHULRGf $VVXPH WKH PDQDJHU PDQLSXODWHV DW D SHUVRQDO FRVW RI _$ ZKLFK LV TXDGUDWLF LQ WKH DPRXQW RI PDQLSXODWLRQ 7KH PDQDJHU IDFHV WKH PLVUHSRUWLQJ RSWLRQ ZLWK SUREDELOLW\ T DQG KH GRHVQfW NQRZ ZKHWKHU KH FDQ PLVUHSRUW XQWLO WKH HQG RI WKH ILUVW SHULRG XVH P WR UHSUHVHQW WKH HYHQW WKDW WKH PLVUHSRUWLQJ RSWLRQ LV DYDLODEOH DQG P WR UHSUHVHQW LWV FRXQWHUSDUW ZKHQ WKH PLVUHSRUWLQJ RSWLRQ LV XQDYDLODEOH 7KH WLPH OLQH LV VKRZQ LQ )LJXUH 1RWLFH LQ WKH EHQFKPDUN FDVH RI /HPPD ZKHUH WKHUH LV QR RSWLRQ WR PLVUHSRUW WKH ERQXV UDWHV IRU WKH WZR SHULRGV DUH QRW HTXDO DQG Dr$ ,I WKH RXWSXWV ZHUH REVHUYHG SULYDWHO\ E\ WKH PDQDJHU WKH PDQDJHU ZRXOG KDYH D QDWXUDO LQFHQWLYH WR PRYH VRPH RXWSXW IURP WKH ILUVW WR WKH VHFRQG SHULRG VLQFH KH UHFHLYHV JUHDWHU FRPSHQVDWLRQ IRU HDFK XQLW RI RXWSXW SURGXFHG LQ WKH VHFRQG SHULRG ,I P WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW DW WKH EHJLQQLQJ RI WKH VHFRQG SHULRG EHFRPHV : D[L ND Df $ _$ FD[ Df bLY 1RWLFH WKDW ZLWK D OLQHDU FRQWUDFW WKH PDQDJHUfV PDQLSXODWLRQ FKRLFH LV VHSDUDEOH IURP KLV DFWLRQ FKRLFHV DQG WKH RXWSXW ULVN 7KLV VHSDUDELOLW\ LPSOLHV WKDW WKH RSWLPDO nf7KH TXDGUDWLF SHUVRQDO FRVW IROORZV D VLPLODU GHVLJQ LQ /LDQJ f ,W UHIOHFWV WKH IDFW WKDW HDUQLQJV PDQDJHPHQW EHFRPHV LQFUHDVLQJO\ KDUGHU ZKHQ WKH PDQDJHU ZDQWV WR PDQLSXODWH PRUH 7KH PDQDJHU HYHQ WKRXJK GHWHUPLQHG WR PDQLSXODWH PD\ QRW NQRZ ZKHWKHU KH FDQ PDQLSXODWH DW WKH EHJLQLQJ EXW KDV WR ZDLW IRU WKH FKDQFH WR PDQLSXODWH PAGE 34 VKLIWLQJ RFFXUV ZKHUH A> Df $ fÂ§ _$@ RU $r D 7KH RQO\ ZD\ WR GHWHU PDQLSXODWLRQ LQ WKLV VHWWLQJ LV WR VHW D DJDLQ VROYH WKH SULQFLSDOfV GHVLJQ SURJUDP VWDUWLQJ IURP WKH VHFRQG SHULRG 6LQFH WKH PDQDJHU DOZD\V FKRRVHV $r fÂ§ D DV ORQJ DV KH JHWV WKH PLVUHSRUWLQJ RSWLRQ ZH XVH &(D $r [[ P f WR GHQRWH WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW DW WKH EHJLQQLQJ RI WKH VHFRQG SHULRG ZKHQ KH JHWV WKH PLVUHSRUWLQJ RSWLRQ DQG FKRRVHV DIWHU SULYDWHO\ REVHUYLQJ WKH ILUVW SHULRG RXWSXW [[ :H XVH &ec [[P f WR GHQRWH WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW ZKHQ KH GRHVQfW JHW WKH PLVUHSRUWLQJ RSWLRQ 7KH LQFHQWLYH FRQVWUDLQWV IRU WKH VHFRQG SHULRG DUH &(+ $nMDT f &( $r[L f DQG &(+ DT f &( DT f 9DT :LWK WKH QRWHG VHSDUDELOLW\ LW LV UHDGLO\ DSSDUHQW WKDW ERWK FRQVWUDLQWV FROODSVH WR MXVW DV LQ WKH EHQFKPDUN XVH &([^D[?Df WR GLVWLQJXLVK IURP &([D[Df LQ WKH EHQFKPDUNf WR GHQRWH WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG ZKHQ KH FKRRVHV RL IROORZHG E\ D LQ WKH VHFRQG SHULRG $W WKH EHJLQQLQJ RI WKH ILUVW SHULRG VLQFH P LV UDQGRP WKH PDQDJHUfV H[SHFWHG XWLOLW\ DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG LV fÂ§ Tf(X>??n R$TRL HLf NQ^f fÂ§ f@ a?aT(X>?9 R$TIOL WRLfÂ§ $rf 3ND H $rf fÂ§ FDOW *f fÂ§ _$r@ 7KHUHIRUH &(?DL Df LV WKH VROXWLRQ WR X&([D[ Dff fÂ§ fÂ§ Tf(X> ,N FWTDLHLf NFL ffÂ§ FDL f@ T(X>: RLN[D[ &L fÂ§ $rf ?ND H $rf fÂ§FRLDf fÂ§ _$r@ B TnMHU>:rfNLDLNDFDLDfbDF77f@ BBTHU>?n9DNLDLNDFDLDfADDFUfA$fnaDf$ff` fÂ§ BHU>:DIFLDLAIFDFDLDfD77f@A B A BMB THaU>Df$nA$r@M BHU&(LD??Dff 7KXV fÂ§ U&([D[? Dff fÂ§ U?: DN[D[ MND fÂ§ f fÂ§ _DU 9f@ OQ>O Tf TH:n:@ DQG &([^D[?Rf : DN[D[ SND FD[Df ÂD9 "9f N OQ>O Tf THa3aDfO@ PAGE 35 &RPSDULQJ &(?^D?Df ZLWK &(?^D??Df LQ WKH EHQFKPDUN ZH KDYH &(?DL Df &(LD Df OQ>O Tf THaAaDf? ,PSRUWDQWO\ QRZ WKH DJHQWfV ULVN SUHPLXP UHIOHFWV WKH VXPPDWLRQ RI WKH HDUOLHU ULVN SUHPLXP GXH WR WKH YDULDQFH WHUPV DQG DQ DGGLWLRQDO FRPSRQHQW GXH WR WKH VKLIWLQJ PHDQ HIIHFWV LQWURGXFHG E\ HDUQLQJV PDQDJHPHQW 7KH DGGLWLRQDO FRPSRQHQW FRPHV IURP WKH H[WUD ERQXV IURP PDQLSXODWLRQ DQG WKH KLJKHU XQFHUWDLQW\ RI WKH FRPSHQVDWLRQ *LYHQ D + WKH LQFHQWLYH FRPSDWLELOLW\ FRQVWUDLQW IRU WKH ILUVW SHULRG LV &(L++f &(L4+f $JDLQ WKDQNV WR WKH VHSDUDELOLW\ EHWZHHQ WKH DFWLRQ FKRLFH DQG WKH PDQLSXODWLRQ DPRXQW FKRLFH WKLV FRQVWUDLQW UHGXFHV WR D MXVW DV LQ WKH EHQFKPDUN FDVH 7KH LQGLYLGXDO UDWLRQDOLW\ FRQVWUDLQW LQ WKLV PRGHO LV &(?+ +f RU 37 DN[+ SN+ & iD9 9f 0Q>O Tf THaIAffO@ 7KH SULQFLSDOfV H[SHFWHG SD\PHQW WR WKH PDQDJHU XSRQ VXEVWLWXWLQJ WKH PDQDJHUfV $ FKRLFH LV fÂ§ Tf(>: DWN?+ &Mf 3N+ ef@ ?T(>: F[N?+ f? fÂ§ fÂ§ Dff 3N+ H Dff` aTf>: DN?+ N+@ T>: D$?+ Dff c^N+ Dff@ : DN+ SN+ T^3 Df 1RZ WKH SULQFLSDOfV GHVLJQ SURJUDP LQ WKLV PLVUHSRUWLQJ PRGHO LV PLQ : RFN?+ 3N+ T3 fÂ§ Df 3URJUDP >&@ :DI` 6 W : DNO+ SN+ & iT9 SRf OQ>O Tf THaADA@ D F NL+ ,5f ,&f ,&f PAGE 36 6LPLODU WR WKH SUHYLRXV PRGHOV KHUH WKH LQGLYLGXDO UDWLRQDOLW\ FRQVWUDLQW PXVW ELQG DQG WKH SULQFLSDOfV H[SHFWHG FRVW FDQ EH H[SUHVVHG DV & _DFU FUf ` OQ>O Tf THaAaDf@ T^ Df )RU ODWHU UHIHUHQFH WKH UHGXFHG SURJUDP LV ZULWWHQ EHORZ PLQ _TFW Yf ? OQ>O Tf THaAaDn!@ T Df 3URJUDP ?&n` DIf 6 W D ,&f ,&f 'HILQH De rF DV WKH RSWLPDO ERQXV UDWHV LQ 3URJUDP >& @ ZH KDYH WKH IROORZLQJ UHVXOWV 3URSRVLWLRQ 7KH RSWLPDO FRQWUDFW LQ WKH PLVUHSRUWLQJ PRGHO H[KLELWV N[+ D& f Kc+ fÂ§ 3F &RUROODU\ :KHQ T LV VXIILFLHQWO\ ORZ WKH RSWLPDO FRQWUDFW LQ WKH PLVUHSRUWLQJ PRGHO H[KLELWV FWrF DQG rF &RUROODU\ :KHQ T LV VXIILFLHQWO\ KLJK DQG NL LV VXIILFLHQWO\ ODUJH WKH RSWLPDO FRQWUDFW LQ WKH PLVUHSRUWLQJ PRGHO H[KLELWV DrF DQG rF A" 3URRI 6HH WKH $SSHQGL[ &RPSDUH 3URJUDP >& @ ZLWK WKH EHQFKPDUN ZKHQ T ZH UHYHUW WR RXU EHQFKPDUN FDVH KRZHYHU ZKHQ T WKH PLVUHSRUWLQJ RSWLRQ LQWURGXFHV D VWULFW ORVV LQ HIILFLHQF\ 7KH SULQFLSDO PXVW FRPSHQVDWH IRU WKH PDQDJHUfV ULVN IURP WKH LPFHUWDLQ PLVUHSRUWLQJ RSWLRQ 7KHUH LV DOVR D ERQXV SD\PHQW HIIHFW IRU WKH PDQLSXODWHG DPRXQW RI RXWSXW ,Q DGGLWLRQ WKH SULQFLSDO PD\ FKRRVH WR UDLVH WKH ILUVW SHULRG ERQXV UDWH ZKLFK LQFUHDVHV WKH ULVNLQHVV RI WKH XQPDQDJHG FRPSHQVDWLRQ VFKHPH 1RWH LQ WKLV PRGHO ZH DOZD\V KDYH DrF IILFÂ‘ $OWKRXJK WKH PLVUHSRUWLQJ RSWLRQ PHUHO\ JDUEOHV WKH LQIRUPDWLRQ DQG GRHV QRW EHQHILW WKH SULQFLSDO LW LV QHYHU HIILFLHQW IRU WKH SULQFLSDO WR PRWLYDWH WUXWKWHOOLQJ DQG FRPSOHWHO\ HOLPLQDWH WKH PDQDJHUfV LQFHQWLYH WR PLVUHSRUW E\ VHWWLQJ D c ,QVWHDG LW LV HIILFLHQW WR WROHUDWH VRPH PLVUHSRUWLQJ 7KLV VXUSULVLQJ IDFW LV DOVR VKRZQ LQ /LDQJ f /LDQJ GRFXPHQWV PAGE 37 WKDW WKH RSWLPDO FRQWUDFW H[KLELWV De rF ZKLOH WKH DQDO\VLV LQ WKH SUHVHQW SDSHU SURYLGHV PRUH GHWDLOV RQ WKH RSWLPDO FRQWDFW 0RUH VXUSULVLQJO\ WKH SULQFLSDO QRW RQO\ WROHUDWHV VRPH PLVUHSRUWLQJ E\ VHWWLQJ rT T EXW VRPHWLPHV VKH HYHQ PDLQWDLQV WKH ERQXV UDWHV DW WKH OHYHOV LQ WKH EHQFKPDUN FDVH ZKHUH WKHUH LV QR PLVUHSRUWLQJ RSWLRQ $OWKRXJK DQ XQHYHQ ERQXV VFKHPH OHDGV WR PDQLSXODWLRQ LW PD\ QRW EH HIILFLHQW IRU WKH SULQFLSDO WR DGMXVW WKH ERQXV VFKHPH WR UHVWUDLQ PDQLSXODWLRQ 7KH UHDVRQ IRU WKLV FRQFOXVLRQ LV WKH IROORZLQJ 6LQFH WKH LQGXFHG PLVUHSRUWLQJ LV JLYHQ E\ $r c fÂ§ D WKH GHDG ZHLJKW ORVV RI PLVUHSRUWLQJ FDQ EH UHGXFHG E\ ORZHULQJ c fÂ§ D 7R ORZHU c fÂ§ D WKH SULQFLSDO HLWKHU ORZHUV RU UDLVHV D +RZHYHU KDV D ELQGLQJ ORZHU ERXQG DW DQG WKH SULQFLSDO FDQQRW UHGXFH EHORZ WKDW ERXQG 7KXV WKH RSWLPDO c UHPDLQV DW LWV ERXQG %\ UDLVLQJ D WKH SULQFLSDO UHGXFHV WKH GHDG ZHLJKW ORVV RI PLVUHSRUWLQJ EXW VLPXOWDQHRXVO\ LQFUHDVHV WKH ULVNLQHVV RI WKH XQPDQDJHG FRPSHQVDWLRQ VFKHPH ADDDf JRHV XSf +HQFH WKHUH LV D WUDGHRII :KHQ WKH FKDQFH RI PLVUHSRUWLQJ LV VPDOO T LV VXIILFLHQWO\ ORZf WKH SULQFLSDO ILQGV LW LQHIILFLHQW WR UDLVH WKH ERQXV UDWH VLQFH WKH FRUUHVSRQGLQJ UHGXFWLRQ LQ WKH PLVUHSRUWLQJ GHDG ZHLJKW ORVV GRHV QRW RXWZHLJK WKH LQFUHDVH LQ WKH ULVNLQHVV RI WKH XQPDQDJHG FRPSHQVDWLRQ VFKHPH 2Q WKH RWKHU KDQG ZKHQ WKH SUREDELOLW\ RI PLVUHSRUWLQJ LV VXIILFLHQWO\ KLJK WKH ORVVHV IURP PLVUHSRUWLQJ FRQVWLWXWH D ILUVW RUGHU HIIHFW ,Q WKLV FDVH WKH SULQFLSDO PD\ ILQG LW RSWLPDO WR UDLVH WKH ILUVW SHULRG ERQXV UDWH ,Q DGGLWLRQ ZKHQ WKH ILUVW SHULRG SURGXFWLYLW\ LV KLJK WKH ORZHU ERXQG IRU WKH ILUVW SHULRG ERQXV LV ORZ DQG WKH SULQFLSDO LV PRUH ZLOOLQJ WR UDLVH WKH ILUVW SHULRG ERQXV DERYH WKH ORZHU ERXQG WR UHGXFH WKH PLVUHSRUWLQJ GHDG ZHLJKW ORVV 7DEOH VKRZV D QXPHULFDO H[DPSOH WR LOOXVWUDWH 3URSRVLWLRQ DQG &RUROODULHV DQG ,Q WKLV QXPHULFDO H[DPSOH IL[ WKH YDOXHV RI WKH FRVW RI KLJK DFWLRQ & KLJK DFWLRQ OHYHO + RXWSXW YDULDQFH D ULVN DYHUVLRQ PAGE 38 U DQG WKH VHFRQG SHULRG SURGXFWLYLW\ N IRFXV RQ KRZ WKH RSWLPDO FRQWUDFW FKDQJHV ZLWK WKH PLVUHSRUWLQJ SUREDELOLW\ T DQG WKH ILUVW SHULRG SURGXFWLYLW\ N? :KHQ T LV YHU\ VPDOO T f WKH RSWLPDO FRQWUDFW KDV ERWK DrF DQG rF DW WKHLU ORZHU ERXQGV +RZHYHU ZKHQ T LV KLJK T f DQG NL LV ODUJH NL f WKH ILUVW SHULRG ERQXV UDWH DrF LQ WKH RSWLPDO FRQWUDFW GHYLDWHV IURP LWV ORZHU ERXQG F N?+n )RU VLPSOLFLW\ XVH WKH FDVH T fÂ§ WR H[SORUH PRUH GHWDLOV RQ WKH PLVUHSRUWLQJ RSWLRQ 8ELTXLWRXV PLVUHSRUWLQJ RSSRUWXQLWLHV T f :KHQ T 3URJUDP >&@ EHFRPHV PLQ : DN?+ N+ IW fÂ§ Df 3URJUDP >&T f :D V W : T$[+ N+ & ?^ Df iDD Df ,5f f c6U LFLf ,&f 7KH VLWXDWLRQ ZKHQ T LV VSHFLDO EHFDXVH WKHUH LV QR XQFHUWDLQW\ DERXW WKH PLVUHSRUWLQJ RSWLRQ 7KH SULQFLSDO NQRZV WKH PDQDJHU ZLOO DOZD\V VKLIW c fÂ§ D WR WKH VHFRQG SHULRG WR JHW DGGLWLRQDO ERQXV LQFRPH RI fÂ§Tf$r fÂ§Df 5HVSRQGLQJ WR WKLV VKH FDQ FXW WKH IL[HG ZDJH E\ fÂ§ Df WR UHPRYH WKH ERQXV SD\PHQW HIIHFW +RZHYHU DOWKRXJK WKH SULQFLSDO UHPRYHV IXOO\ WKH FHUWDLQ ERQXV SD\PHQW IURP KHU H[SHFWHG SD\PHQW WR WKH PDQDJHU VKH PXVW FRPSHQVDWH IRU WKH PDQDJHUfV GHDG ZHLJKW SHUVRQDO FRVW RI PLVUHSRUWLQJ 'HILQH Rr&Or&O DV WKH RSWLPDO ERQXV UDWHV IRU WKH PLVUHSRUWLQJ PRGHO ZKHQ :H KDYH WKH IROORZLQJ UHVXOW 3URSRVLWLRQ :KHQ T WKH RSWLPDO FRQWUDFW LQ WKH PLVUHSRUWLQJ PRGHO H[KLELWV 4FL A DQG 3r& LI NL N UFUf DFL -AK DQA #FL NILM RWKHUZLVH PAGE 39 3URRI 6HH WKH $SSHQGL[ ,I WKH SURGXFWLYLW\ RI WKH WZR SHULRGV LV YHU\ GLIIHUHQW WKDW LV N? LV PXFK KLJKHU WKDQ Nf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rF[3r&,f FWr$r$f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f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` DQG Ge ^` [[ REVHUYHG SXEOLFO\ 0DQDJHU FKRRVHV ( ^+ ` ; REVHUYHG SXEOLFO\ 0DQDJHU JHWV SDLG )LJXUH 7LPH OLQH IRU GHOHJDWHGKHGJH PRGHO VW 3HULRG QG 3HULRG 0DQDJHU REVHUYHV SULYDWHO\ [ [ UHSRUWHG 3ULQFLSDO VHHV DJJUHJDWH RXWSXWf 0DQDJHU FKRRVHV 0DQDJHU REVHUYHV DL ( ^+ ` SULYDWHO\ ;? DQG P ;? UHSRUWHG 0DQDJHU FKRRVHV D ^+ ` )LJXUH 7LPH OLQH IRU PLVUHSRUWLQJ PRGHO 7DEOH 1XPHULFDO ([DPSOH IRU 3URSRVLWLRQ &RUROODULHV DQG NL 4 F N?+ F N+ DrF 3F U\r fÂ§ 5r fÂ§ D& fÂ§ NL+f3F N"+ Qr 5r fÂ§ 6fÂ§ D& N[+n3F a N+ PAGE 42 &+$37(5 +('*(0,65(3257 %81'/( 02'(/ 7KH ODVW FKDSWHU DQDO\]HV WKH KHGJLQJ DQG PLVUHSRUWLQJ RSWLRQV UHVSHFWLYHO\ 1RZ EXQGOH WKH GHOHJDWHG KHGJLQJ RSWLRQ DQG WKH PLVUHSRUWLQJ RSWLRQ 7KLV EXQGOLQJ DOORZV XV WR VWXG\ WKH MRLQW HIIHFW RI WKH KHGJLQJ IXQFWLRQ DQG PDQLSXODWLRQ IXQFWLRQ RI GHULYDWLYHV %XQGOHG +HGJLQJ DQG 0LVUHSRUWLQJ 2SWLRQV 6XSSRVH DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG WKH PDQDJHU FKRRVHV KLV DFWLRQ OHYHO FWL ^+ `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f 6LPLODU WR WKH PLVUHSRUWLQJ PRGHO LI WKH PDQDJHU JHWV WKH PLVUHSRUWLQJ RSWLRQ KH VKLIWV fÂ§ D IURP WKH ILUVW WR WKH VHFRQG SHULRG 7KH WLPH OLQH RI WKH KHGJHPLVUHSRUW EXQGOH PRGHO LV VKRZQ LQ )LJXUH 6LPLODU WR /HPPD LQ WKH ODVW FKDSWHU KHUH WKH PDQDJHU DOZD\V SUHIHUV WR KHGJH 7R LOOXVWUDWH WKLV XVH &(LD[ G Df WR UHSUHVHQW WKH PDQDJHUfV EHJLQQLQJ FHUWDLQW\ HTXLYDOHQW ZKHQ KH FKRRVHV DL DQG G IROORZHG E\ D :KHQ WKH PDQDJHU FKRRVHV WR KHGJH &([DX Df : DN?D[ SND FDLDf iDD "HUÂf OQ>O fÂ§ Tf THaAaf@ :KHQ WKH PDQDJHU GRHV QRW KHGJH &(?^D? Df : PAGE 43 DNL&/? ND fÂ§ FDL f fÂ§ iD IDf ,W LV HDV\ WR YHULI\ WKDW &(?D? f &(LDL f 7KDW LV WKH PDQDJHU DOZD\V KHGJHV LQ WKLV EXQGOHG PRGHO 7KHUHIRUH WKH EXQGOHG PRGHO LV LGHQWLFDO WR WKH PLVUHSRUWLQJ PRGHO ZLWK WKH VHFRQG SHULRG RXWSXW KHGJHG LQ RWKHU ZRUGV ZLWK WKH VHFRQG SHULRG RXWSXW YDULDQFH UHGXFHG WR DGf 7KH SULQFLSDOfV GHVLJQ SURJUDP LQ WKLV EXQGOHG PRGHO LV PLQ : DNL+ ILNR+ T fÂ§ Df 3URJUDP >'? :D 6 W : DNL+ N+ & ?^RFD Df OQ>O Tf JHiAffO@ ,5f m!.K ,&f 3!W6K ,&f $JDLQ 3URJUDP >'@ FDQ EH UHGXFHG WR WKH PLQLPL]DWLRQ RI bDD SDÂf 0Q>O Tf THaAaDA? T fÂ§ Df VXEMHFW WR WKH LQFHQWLYH FRQVWUDLQWV )RU WKH FRQYHQLHQFH RI ODWHU DQDO\VLV VKRZ WKH UHGXFHG SURJUDP EHORZ PLQ ID [Âf OQ>O fÂ§ Tf TH A 4A@ TIL fÂ§ Df 3URJUDP >'n` V WÂ‘ D!ID ,&f L6K ,&f ,W LV UHDGLO\ YHULILHG WKDW WKH RSWLPDO ERQXV UDWHV LQ WKH EXQGOHG PRGHO DUH LGHQWLFDO WR WKRVH LQ WKH PLVUHSRUWLQJ PRGHO VLQFH WKH PDQDJHUfV DFWLRQ FKRLFHV GR QRW GHSHQG RQ KLV KHGJLQJ FKRLFH +RZHYHU FRPSDUHG ZLWK WKH PLVUHSRUWLQJ PRGHO WKH SULQFLSDOfV H[SHFWHG FRVW LV UHGXFHG E\ _"W fÂ§ FUGf WKDQNV WR WKH KHGJLQJ RSWLRQ 7KH SULQFLSDO GRHV QRW QHHG WR PRWLYDWH WKH PDQDJHU WR KHGJH VLQFH WKH PDQDJHU DOZD\V H[HUFLVHV WKH KHGJLQJ RSWLRQ $OWKRXJK WKH KHGJLQJ RSWLRQ DQG WKH PLVUHSRUWLQJ RSWLRQ ERWK DIIHFW RXWSXW VLJQDOV WKH\ DIIHFW WKH VLJQDOV LQ GLIIHUHQW ZD\V 7KH KHGJLQJ RSWLRQ LQIOXHQFHV RXWSXW VLJQDOV WKURXJK YDULDQFHV 7KH JUHDWHU LV WKH UHGXFWLRQ LQ WKH QRLV\ RXWSXWfV YDULDQFH D fÂ§ RGf WKH PRUH EHQHILFLDO LV WKH KHGJLQJ RSWLRQ 2Q WKH RWKHU KDQG WKH PAGE 44 PLVUHSRUWLQJ RSWLRQ LQIOXHQFHV RXWSXW VLJQDOV WKURXJK PHDQV :LWK WKH PLVUHSRUWLQJ RSWLRQ WKH PDQDJHU VKLIWV r' fÂ§ Dr' IURP WKH PHDQ RI WKH ILUVW SHULRG RXWSXW WR WKH PHDQ RI WKH VHFRQG SHULRG RXWSXW 7KH DPRXQW RI PDQLSXODWLRQ ILr' fÂ§ Dr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f GHILQH WKH UHOLDELOLW\ RI DFFRXQWLQJ PHDVXUHPHQWV DV WKH GHJUHH RI REMHFWLYLW\ ZKLFK XVHV WKH YDULDQFH RI WKH JLYHQ PHDVXUHPHQW DV DQ LQGLFDWRUf SOXV D ELDV IDFWRU WKH GHJUHH RI FORVHQHVV WR EHLQJ ULJKWf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fÂ§ DG LV VXIILFLHQWO\ ODUJH 3URRI 6HH WKH $SSHQGL[ 7DEOH LOOXVWUDWHV QXPHULFDO H[DPSOHV IRU WKH DERYH OHPPDV VXSSRVH WKH FRVW RI KLJK DFWLRQ & fÂ§ KLJK DFWLRQ + ULVN DYHUVLRQ GHJUHH U DQG WKH VHFRQG SHULRG SURGXFWLYLW\ A )URP WKH QXPHULFDO H[DPSOHV ZH VHH ZKHQ T LV VXIILFLHQWO\ ORZ T f WKH SULQFLSDO SUHIHUV WKH EXQGOH :KLOH ZKHQ T LV VXIILFLHQWO\ KLJK T f DQG N? LV VXIILFLHQWO\ ODUJH N? f WKH SULQFLSDO GRHV QRW SUHIHU WKH EXQGOH LI D DnG LV VPDOO D fÂ§ DG f 6KH SUHIHUV WKH EXQGOH ZKHQ D fÂ§ DG LV VXIILFLHQWO\ ODUJH D fÂ§ DG f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fÂ§ RG LV VXIILFLHQWO\ ODUJHf GRHV WKH SULQFLSDO WDNH WKH EXQGOH KHUH 1RZ IRFXV RQ WKH T FDVH )URP 3URJUDP >'n? ZKHQ T WKH SURJUDP EHFRPHV PLQ _TFW 3DGf ?^>L Df 3URJUDP >e!nT f@ D" 6 W D ,&f 6 6 ,&f 'HILQH Dr' DV WKH RSWLPDO ERQXV UDWHV LQ WKH EXQGOHG PRGHO ZKHQ T ZH KDYH PAGE 46 /HPPD :KHQ T WKH RSWLPDO FRQWUDFW LQ WKH KHGJHPLVUHSRUL EXQGOH PRGHO H[KLELWV DEL DQG 3rGL aK OI A 0O QUf TGL DQG 3rGL LA+ RWKHUZLVH 3URRI 6HH WKH $SSHQGL[ $V PHQWLRQHG HDUOLHU GXH WR WKH VHSDUDELOLW\ EHWZHHQ WKH PDQDJHUfV KHGJLQJ FKRLFH DQG KLV DFWLRQ FKRLFHV WKH RSWLPDO ERQXV VFKHPH LQ WKH EXQGOHG PRGHO LV LGHQWLFDO WR WKDW LQ WKH PLVUHSRUWLQJ PRGHO 3URSRVLWLRQ :KHQ T f LI N? N UFUf WKH KHGJHPLVUHSRUL EXQGOH LV SUHIHUUHG WR WKH EHQFKPDUN ZKHQ 0 JOUfLf IFM 7OUf f DQG f LI N? $O UDf WKH EXQGOH LV SUHIHUUHG WR WKH EHQFKPDUN ZKHQ IFOrDfD UDUf f 3!f 3URRI 6HH WKH $SSHQGL[ 3URSRVLWLRQ SURYLGHV D GHWDLOHG DQDO\VLV RQ WKH WUDGHRII EHWZHHQ WKH EHQHILW IURP WKH KHGJLQJ RSWLRQ DQG WKH FRVW IURP WKH PLVUHSRUWLQJ RSWLRQ ZKHQ Df T )LUVW IRU ERWK WKH FDVHV RI NL NR^ UDf DQG NL NO UDf WKH KHGJHPLVUHSRUW EXQGOH LV PRUH OLNHO\ WR EH SUHIHUUHG LQ RWKHU ZRUGV FRQGLWLRQ Df RU Ef LV PRUH OLNHO\ WR EH VDWLVILHGf ZKHQ FU LV KLJK ,QWXLWLYHO\ ZKHQ WKH XQKHGJHG RXWSXW VLJQDOV DUH YHU\ QRLV\ WKH SULQFLSDO KDV D VWURQJ SUHIHUHQFH IRU KHGJLQJ WR UHGXFH WKH QRLVH DQG LV PRUH OLNHO\ WR WDNH WKH EXQGOH UHJDUGOHVV RI WKH DFFRPSDQLHG FRVW RI PLVUHSRUWLQJ f'HILQH 4 bZf Un_f LQ FRQGLWLRQ Df ZH KDYH ie a r ,W LV HDV\ WR YHULI\ WKDW LQ FRQGLWLRQ Ef DOVR GHFUHDVHV LQ D PAGE 47 6HFRQG IRU ERWK FDVHV LW LV UHDGLO\ YHULILHG WKDW FRQGLWLRQV Df DQG Ef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f 7KH PRUH VLPLODU D[H N? DQG N WKH PRUH OLNHO\ LV FRQGLWLRQ Df RU Ef WR EH VDWLVILHG KHQFH WKH PRUH OLNHO\ LV WKH KHGJHPLVUHSRUW EXQGOH WR EH SUHIHUUHG )RXUWK IRU ERWK FDVHV WKH EHQHILW IURP KHGJLQJ LV KLJKHU ZKHQ KHGJLQJ JUHDWO\ UHGXFHV WKH QRLVH LQ RXWSXW VLJQDOV WKDW LV ZKHQ D fÂ§ DG LV ODUJHf 7KH PRUH WKH KHGJH FDQ ORZHU WKH VHFRQG SHULRG RXWSXW YDULDQFH WKH PRUH OLNHO\ LV FRQGLWLRQ Df RU Ef WR EH VDWLVILHG KHQFH WKH PRUH OLNHO\ LV WKH SULQFLSDO WR SUHIHU WKH EXQGOH 7KH QXPHULFDO H[DPSOHV LQ 7DEOH LOOXVWUDWH WKHVH FRPSDUDWLYH VWDWLF REVHUYDWLRQV :H VHH IURP WKH H[DPSOHV WKDW WKH SULQFLSDO LV PRUH OLNHO\ WR WDNH WKH EXQGOH ZKHQ FU fÂ§ DG LV ODUJH D LV KLJK U LV KLJK RU N? LV FORVH WR N 6XPPDU\ $ KHGJHPLVUHSRUW EXQGOH LV XVHG WR PRGHO WKH WZRHGJHG IHDWXUH RI GHULYDWLYH LQVWUXPHQWV LQ WKLV FKDSWHU DQDO\]H WKH WUDGHRII EHWZHHQ WKH LPSURYHPHQW RI SHUIRUPDQFH VLJQDOVf REMHFWLYLW\ EURXJKW E\ KHGJLQJ DQG WKH LQFUHDVH LQ WKH SHUIRUPDQFH VLJQDOVf ELDV GXH WR HDUQLQJV PDQDJHPHQW :LWK D /(1 IUDPHZRUN KHGJLQJ PDNHV LW HDVLHU IRU WKH SULQFLSDO WR LQIHU WKH PDQDJHUf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` ;? DQG P LI FKRVH G f [ UHSRUWHG G ( ^` [? UHSRUWHG 0DQDJHU 3ULQFLSDO VHHV FKRRVHV D ( ^+ ` DJJUHJDWH RXWSXWf )LJXUH 7LPH OLQH IRU KHGJHPLVUHSRUW EXQGOH PRGH 7DEOH 1XPHULFDO ([DPSOHV IRU /HPPD SDUDPHWHUV SULQFLSDOfV H[SHFWHG FRVW EHQFKPDUN EXQGOH O N? D DÂ ; T A D DG D PAGE 50 7DEOH 1XPHULFDO ([DPSOHV IRU 3URSRVLWLRQ SDUDPHWHUV NH\ SDUDPHWHUV SULQFLSDOfV H[SHFWHG FRVW EHQFKPDUN EXQGOH U NL D D KLJK D fÂ§ DG KLJKf N D? FU FU ORZ D fÂ§ RG ORZf NL N U U KLJKf FU RUI U U ORZf NL N U NLN FORVHf ,, FV E 7 Nf fÂ§ N? N QRW FORVHf PAGE 51 &+$37(5 0$1,38/$7,21 5(675$,1(' %< +('*( 326,7,21 ,Q WKH KHGJHPLVUHSRUW EXQGOH PRGHO LQ &KDSWHU D KHGJLQJ RSWLRQ LV EXQGOHG ZLWK D PLVUHSRUWLQJ RSWLRQ EXW WKH LQIOXHQFH RQ WKH RXWSXWV IURP PLVUHSRUWLQJ LV VHSDUDEOH IURP WKH HIIHFW RI KHGJLQJ ,Q WKLV FKDSWHU D VWURQJHU ERQG LV WLHG EHWZHHQ KHGJLQJ DQG PLVUHSRUWLQJ 7KLV VWURQJHU ERQG UHIOHFWV WKH IDFW WKDW JUHDWHU XVH RI GHULYDWLYHV FDQ SURYLGH H[SDQGHG RSSRUWXQLWLHV IRU HDUQLQJV PDQDJHPHQW &RVW RI (DUQLQJV 0DQDJHPHQW )LUPVf ULVNV LQYROYH PDQ\ XQFRQWUROODEOH IDFWRUV VXFK DV LQWHUHVW UDWH FKDQJHV IRUHLJQ H[FKDQJH UDWH FKDQJHV FUHGLW GHIDXOWV DQG SULFH FKDQJHV 5HGXFLQJ ILUPVf ULVNV PRUH HIIHFWLYHO\ UHTXLUHV PRUH KHGJLQJ ZKLOH WKH LQFUHDVH LQ WKH XVH RI GHULYDWLYHV LQ WXUQ PDNHV LW HDVLHU WR PDQLSXODWH HDUQLQJV :KHQ WKH PDQDJHU UHGXFHV ULVNV PRUH HIIHFWLYHO\ ZLWK PRUH GHULYDWLYHV KH DOVR REWDLQV DGGLWLRQDO ZD\V WR PDQLSXODWH ,Q RWKHU ZRUGV WKH FRVW RI HDUQLQJV PDQDJHPHQW LV ORZHUHG 7R UHIOHFW WKH DVVRFLDWLRQ EHWZHHQ WKH FRVW RI HDUQLQJV PDQDJHPHQW DQG WKH H[WHQW RI KHGJLQJ VXSSRVH WKH PDQDJHUfV SHUVRQDO FRVW RI HDUQLQJV PDQDJHPHQW LV A IJJMSUf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fV RSWLPDO PDQLSXODWLRQ DPRXQW ZLOO DJDLQ RFFXU ZKHQ WKH PDUJLQDO FRVW RI PDQLSXODWLRQ HTXDOV WKH PDUJLQDO PAGE 52 EHQHILW WKDW LV ZKHQ Ga 7KLV LPSOLHV $r 'IL fÂ§ Df $V LQ WKH SUHYLRXV KHGJHPLVUHSRUW EXQGOH PRGHO VXSSRVH WKH PDQDJHU JHWV WKH PLVUHSRUWLQJ RSWLRQ ZLWK SUREDELOLW\ T JLYHQ WKDW KH KHGJHV DQG KH GRHV QRW NQRZ ZKHWKHU KH FDQ PLVUHSRUW XQWLO WKH HQG RI WKH ILUVW SHULRG ,I KH REWDLQV WKH PLVUHSRUWLQJ RSWLRQ KH ZLOO VKLIW 'S fÂ§ Df IURP WKH ILUVW WR WKH VHFRQG SHULRG WR FDSWXUH DGGLWLRQDO ERQXV /HW &(>^D??D? G f GHQRWH WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG JLYHQ WKDW KH KHGJHV :H UHDGLO\ ILQG &(>DL DG f : GD$TDL IND FDLDf DD DÂf OQ>O Tf THL:rfr` 1RZ WKH PDQDJHUfV EHQHILW IURP PLVUHSRUWLQJ fÂ§ OQ>O fÂ§ Tf THaA'AaDA@ LV DVVRFLDWHG ZLWK WKH KHGJLQJ SRVLWLRQ ,Q DGGLWLRQ WKH ODUJHU WKH WKH PRUH WKH EHQHILW IURP PLVUHSRUWLQJ IRU WKH PDQDJHU UHJDUGOHVV RI WKH DGGLWLRQDO LQFUHDVHG ULVNLQHVV IURP WKH PLVUHSRUWLQJ RSWLRQ &RPSDUHG WR WKH SUHYLRXV PRGHO LQ &KDSWHU WKH PDQDJHU EHQHILWV QRW RQO\ IURP KHGJLQJ WKURXJK UHGXFHG ULVNLQHVV RI RXWSXWV EXW DOVR IURP DQ LQFUHDVHG PDUJLQDO JDLQ IURP PDQLSXODWLRQ 7KHUHIRUH LW LV HDV\ WR YHULI\ WKDW WKH PDQDJHU VWLOO DOZD\V SUHIHUV KHGJLQJ G f UHJDUGOHVV RI KLV DFWLRQ FKRLFHV 6LPLODU WR WKH DQDO\VLV LQ &KDSWHU WKH SULQFLSDOfV GHVLJQ SURJUDP WR HQFRXUDJH WKH PDQDJHUnV KLJK DFWLRQV LV 3URJUDP >(@ V W &(> ^++ G f ,5f ,&f PLQ : DN?+ ILK+ T'IL fÂ§ Df :D fÂ§ 9 N+ ,&f n1RWLFH WKDW fÂ§WOQ>O fÂ§ Tf THaA'AaDAÂ@ LV SRVLWLYH ,W LV WKH UHVXOW RI MRLQW HIIHFWV IURP LQFUHDVHG ULVNLQHVV RI FRPSHQVDWLRQ DQG DGGLWLRQDO ERQXV IURP PDQLSXODWHG RXWSXW QHW RI SHUVRQDO PDQLSXODWLRQ FRVW n'HILQH 4 ?OQ>O Tf THaiAmf@ :H KDYH IJ K?Ha cn=7Z6@ rf PAGE 53 $V XVXDO WKH ,5f FRQVWUDLQW PXVW ELQG VR :r fÂ§DNLDL fÂ§ N & _TFW FUÂf AOQ>O fÂ§ Tf THa'AB4f@f DQG WKH SULQFLSDOfV REMHFWLYH IXQFWLRQ FDQ EH UHZULWWHQ DV ?^ROR FWÂf e OQ>O fÂ§ Tf THaA'AaDA@ T' fÂ§ Df 1RZ WKH SULQFLSDOfV GHVLJQ SURJUDP UHGXFHV WR PLQ _Te "Âf ? OQ>O Tf TH '4f@ J' FWf D 6 W $ "! 3URJUDP >en@ ,&f ,&f 'HILQH FWr(IOr( DV WKH RSWLPDO ERQXV UDWHV LQ 3URJUDP >e@ :H KDYH 3URSRVLWLRQ 7KH RSWLPDO FRQWUDFW LQ WKH VWURQJ EXQGOH PRGHO KDV N?+ D( N+ a W!( &RUROODU\ :KHQ T LV VXIILFLHQWO\ ORZ WKH RSWLPDO FRQWUDFW LQ WKH VWURQJ EXQGOH PRGHO KDV Dr( ÂIIM DQG IIL( &RUROODU\ :KHQ T LV VXIILFLHQWO\ KLJK LV VXIILFLHQWO\ ODUJH DQG WKH GLIIHUHQFH EHWZHHQ NL DQG N LV VXIILFLHQWO\ ODUJH WKH RSWLPDO FRQWUDFW LQ WKH VWURQJ EXQGOH PRGHO KDV DQG IIL( Â 3URRI 6HH WKH $SSHQGL[ ,Q FRQWUDVW WR WKH PRGHO LQ &KDSWHU WKH KHGJH SRVLWLRQ QRZ SOD\V D UROH LQ GHFLGLQJ ZKHWKHU WR OLPLW HDUQLQJV PDQDJHPHQW :KHQ LV VXIILFLHQWO\ ODUJH WKH FRVW RI PLVUHSRUWLQJ $$f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nV PDQLSXODWLRQ DPRXQW WKURXJK LWV HIIHFW RQ WKH SHUVRQDO FRVW RI HDUQLQJV PDQDJHPHQW 7KH WUDGHRII EHWZHHQ KHGJLQJ DQG HDUQLQJV PDQDJHPHQW EHFRPHV PRUH FRPSOH[ /HPPD :KHQ T LV VXIILFLHQWO\ ORZ WKH VWURQJ EXQGOH LV SUHIHUUHG WR WKH EHQFKPDUN 3URRI 6HH WKH $SSHQGL[ 2EYLRXVO\ LI WKH SUREDELOLW\ RI PLVUHSRUWLQJ RSWLRQ LV YHU\ ORZ PLVUHSRUWLQJ LV DOO VHFRQG RUGHU HIIHFW HYHQ WKRXJK KHGJLQJ UHGXFHV WKH PLVUHSRUWLQJ FRVW +RZHYHU ZKHQ T LV KLJK DQG N? LV VLJQLILFDQWO\ ODUJHU WKDQ NA SOD\V D GRXEOH UROH LQ WKH SULQFLSDOfV YLHZ RI WKH VWURQJ EXQGOH $ KLJKO\ HIIHFWLYH KHGJH JUHDWO\ UHGXFHV WKH QRLVH LQ WKH RXWSXW VLJQDOV EXW DOVR JUHDWO\ UHGXFHV WKH PDQDJHUfV SHUVRQDO FRVW RI PDQLSXODWLRQ 7KLV LV PRVW HYLGHQW ZKHQ 8ELTXLWRXV 0LVUHSRUWLQJ 2SSRUWXQLWLHV :KHQ T WKDW LV ZKHQ WKH PDQDJHU FDQ DOZD\V PLVUHSRUW WKH SULQFLSDOfV GHVLJQ SURJUDP EHFRPHV PLQ ÂD9 IODGf A'> Df D V W 3URJUDP >eA@ f ,&Of ,t ,&f 'HILQH Dr(Or( DV WKH RSWLPDO ERQXV UDWHV IRU WKH VWURQJ EXQGOH PRGHO ZKHQ T :H KDYH WKH IROORZLQJ UHVXOW 3URSRVLWLRQ :KHQ T WKH RSWLPDO FRQWUDFW LQ WKH VWURQJ EXQGOH PRGHO KDV DK GAL6K 3rHL fÂ§ GIF RU r FUO MMIFff Dr(L DQG #r( rWKHUZLVH 3URRI 6HH WKH $SSHQGL[ :H XVH )LJXUH WR VKRZ KRZ WKH ILUVW SHULRG RSWLPDO ERQXV UDWH Dr(O FKDQJHV ZLWK WKH KHGJLQJ SRVLWLRQ ' PAGE 55 1RWLFH WKDW Dr( MMUD SIIIL f ZKHQ N AB f ,Q RWKHU ZRUGV WKH SULQFLSDO UDLVHV D IURP LWV ORZHU ERXQG ZKHQ =f NMNBO Â‘ ,QWXLWLYHO\ LI LV ODUJH HDUQLQJV PDQDJHPHQW LV JRLQJ WR EH D ILUVW RUGHU HIIHFW DQG WKH RSWLPDO FRQWUDFW KDV WR UHGXFH WKH PDQLSXODWLRQ LQFHQWLYH E\ LQFUHDVLQJ D 0RUH SUHFLVHO\ ZKHQ WKH RSWLPDO ILUVW SHULRG ERQXV UDWH LV IL[HG DW A ZKLOH ZKHQ N-OBO WKH RSWLPDO ILUVW SHULRG ERQXV UDWH LQFUHDVHV JUDGXDOO\ DW D GHFUHDVLQJ UDWH 5LJKW DIWHU H[FHHGV fÂ§ DV WKH KHGJH EHFRPHV PRUH HIIHFWLYH JHWV ODUJHUf WKH SULQFLSDO KDV WR LQFUHDVH WKH ILUVW SHULRG ERQXV UDWH VKDUSO\ WR FRSH ZLWK WKH LQFUHDVHG PDQLSXODWLRQ +RZHYHU ZKHQ WKH KHGJH JHWV HYHQ PRUH HIIHFWLYH DSSURDFKHV Df WKH SULQFLSDO GRHV QRW QHHG WR LPSURYH WKH ILUVW SHULRG ERQXV VR PXFK WR GHDO ZLWK PDQLSXODWLRQ 7XUQLQJ WR WKH TXHVWLRQ DW KDQG ZH KDYH WKH IROORZLQJ FKDUDFWHUL]DWLRQ 3URSRVLWLRQ :KHQ T fÂ§ &DVH f ,I DM DO WKH VWURQJ EXQGOH LV SUHIHUUHG WR WKH EHQFKPDUN ZKHQ c A YAfAr1f NI fÂ§FUAIU7f &DVH f ,I D DO rAf WKH VWURQJ EXQGOH LV SUHIHUUHG WR WKH EHQFKPDUN ZKHQ W 9A ;f %nf 2WKHUZLVH LW LV QRW HIILFLHQW IRU WKH SULQFLSDO WR WDNH WKH VWURQJ EXQGOH 3URRI 6HH WKH $SSHQGL[ &RUROODU\ ,Q &DVH f RU f RI 3URSRVLWLRQ I FRQGLWLRQ ;f RU %nf LV OHVV VWULQJHQW ZLWK KLJKHU ULVN DYHUVLRQ GHJUHH U?DQG FRQGLWLRQ ;f RU %nf LV OHVV VWULQJHQW ZKHQ NL DQG t DUH VLPLODU LQ PDJQLWXGH 3URRI 6HH WKH $SSHQGL[ &RQGLWLRQ $nf RU %nf LV OHVV VWULQJHQW PHDQV WKH FRQGLWLRQ LV PRUH OLNHO\ WR EH VDWLVILHG :LWK D OHVV VWULQJHQW FRQGLWLRQ $f RU %f WKH SULQFLSDO LV PRUH OLNHO\ +HUH DfÂ§ 8 >fUI7a NS + UJa G' UUUÂ U 'fn N+ DQG r r Kf G' UR 'S N+ PAGE 56 WR SUHIHU WKH VWURQJ EXQGOH ,QWXLWLYHO\ D KLJKHU U LQGLFDWHV WKDW WKH PDQDJHU LV PRUH ULVN DYHUVH :KHQ WKH PDQDJHU LV YHU\ ULVN DYHUVH WKH SULQFLSDO PXVW SD\ D KLJK ULVN SUHPLXP WR WKH PDQDJHU IRU WKH QRLV\ RXWSXW VLJQDOV 7KXV WKH SULQFLSDO ZRXOG OLNH WR UHGXFH WKH QRLVH DQG KDV D VWURQJ SUHIHUHQFH IRU KHGJLQJ +HQFH VKH LV PRUH OLNHO\ WR WDNH WKH VWURQJ EXQGOH ,Q DGGLWLRQ ZKHQ SURGXFWLYLW\ GRHV QRW FKDQJH PXFK WKURXJK WLPH N? DQG N DUH VLPLODU LQ PDJQLWXGHf WKH ERQXV UDWHV ZLOO QRW FKDQJH PXFK WKURXJK WLPH HLWKHU :LWK OLWWOH DGGLWLRQDO ERQXV JDLQ IURP PLVUHSRUWLQJ HYHQ ZKHQ WKH FRVW RI PLVUHSRUWLQJ LV ORZ WKH PDQDJHUfV PDQLSXODWLRQ ZLOO QRW EULQJ JUHDW GDPDJH 7KXV WKH SULQFLSDO LV PRUH OLNHO\ WR WDNH WKH VWURQJ EXQGOH ,Q RWKHU ZRUGV WKH FRQGLWLRQV IRU WKH VWURQJ EXQGOH WR EH SUHIHUUHG DUH OHVV VWULQJHQW &RUROODU\ :KHQ DG D>O fÂ§ IFOABf Df LI DG FUsAf WKHQ WKH VPDOOHU WKH R? WKH OHVV VWULQJHQW LV FRQGLWLRQ $f Ef LI *aAUf FUG D fÂ§ f WKHQ WKH ODUJHU WKH DG WKH OHVV VWULQJHQW LV FRQGLWLRQ $f &RUROODU\ :KHQ DG DO fÂ§ f FUG GRHV QRW LQIOXHQFH WKH SULQFLSDOfV GHFLVLRQ RQ ZKHWKHU WR WDNH WKH VWURQJ EXQGOH 3URRI 6HH WKH $SSHQGL[ ,Q WKH VWURQJ EXQGOH WKH JRRG IURP KHGJLQJ DQG WKH EDG IURP PDQLSXODWLRQ DUH FROLQHDU VR D ORZ DG LQ DQG RI LWVHOI LV QRW D FDXVH IRU MR\ 7KH SULQFLSDOfV SUHIHUHQFH IRU WKH EXQGOH LV QRW PRQRWRQLF LQ DG 7R H[SORUH WKH LQWXLWLRQ EHKLQG WKHVH UHVXOWV UHFDOO )LJXUH ,Q )LJXUH ZKHQ LV VPDOO DG LV ODUJHf WKH SULQFLSDO GRHV QRW UDLVH WKH ILUVW SHULRG ERQXV UDWH D IURP LWV ORZHU ERXQG VLQFH LW LV QRW ZRUWK UDLVLQJ WKH ERQXV UDWH WR UHVWUDLQ HDUQLQJV PDQDJHPHQW &RUUHVSRQGLQJO\ KHUH LQ &RUROODU\ ZKHQ DnG LV VXIILFLHQWO\ ODUJH WKH HIIHFWLYHQHVV RI KHGJLQJ GRHV QRW DIIHFW WKH SULQFLSDOfV GHFLVLRQ RQ ZKHWKHU WR WDNH WKH VWURQJ EXQGOH 6LQFH WKH KHGJH LV SRRUO\ HIIHFWLYH PAGE 57 DQG WKH PDQLSXODWLRQ FRVW LV KLJK QHLWKHU KHGJLQJ QRU PDQLSXODWLRQ KDV VLJQLILFDQW LQIOXHQFH ,Q )LJXUH ZKHQ JHWV ODUJHU DQG H[FHHGV DG JHWV VPDOOHU WKDQ FUO IFL>Bff WKH SULQFLSDO KDV WR UDLVH D JUHDWO\ WR GHDO ZLWK WKH LQFUHDVHG PDQLSXODWLRQ ZKLOH ZKHQ DSSURDFKHV D DG DSSURDFKHV ]HURf WKH SULQFLSDO UDLVHV WKH ILUVW SHULRG ERQXV UDWH RQO\ DW D GHFUHDVLQJ UDWH ,Q &RUROODU\ ZH VHH ZKHQ D? LV LQWHUPHGLDWH WKH PDUJLQDO EHQHILW IURP KHGJLQJfV HIIHFWLYHQHVV FDQQRW EHDW WKH PDUJLQDO ORVV IURP PDQLSXODWLRQ DQG WKH SULQFLSDO LV PRUH OLNHO\ WR WDNH WKH EXQGOH ZLWK D OHVV HIIHFWLYH KHGJH :KHQ DG DSSURDFKHV ]HUR KRZHYHU WKH PDUJLQDO EHQHILW IURP KHGJLQJfV HIIHFWLYHQHVV EHDWV WKH PDUJLQDO ORVV IURP PDQLSXODWLRQ DQG WKH SULQFLSDO LV PRUH OLNHO\ WR WDNH WKH EXQGOH ZLWK D PRUH HIIHFWLYH KHGJH )LJXUHV $ DQG % VKRZ KRZ WKH SULQFLSDOfV SUHIHUHQFH IRU WKH VWURQJ EXQGOH FKDQJHV ZLWK WKH HIIHFWLYHQHVV RI WKH KHGJH UHSUHVHQWHG E\ MGf 7R IXUWKHU LOOXVWUDWH WKH WHQVLRQ EHWZHHQ WKH EHQHILW IURP WKH KHGJHfV HIIHFWLYHQHVV DQG WKH ORVV IURP WKH PRUH PDQLSXODWLRQ DURXQG HUAf LQ )LJXUH $ ZH XVH D QXPHULFDO H[DPSOH WR VKRZ KRZ WKH SULQFLSDOfV SUHIHUHQFH IRU WKH HIIHFWLYHQHVV RI WKH KHGJH FKDQJHV ,Q WKLV H[DPSOH ZH VXSSRVH U N? $L FU VR WKDW 7:f W fÂ§ NLNLf rV VDWLVILHG 7KH YDOXH RI AUf KHUH LV 7KH QXPHULFDO H[DPSOH LV SUHVHQWHG LQ 7DEOH 6XPPDU\ )URP WKH DQDO\VLV LQ WKLV FKDSWHU ZH VHH ZKHQ WKH PDQDJHUfV SHUVRQDO FRVW RI PDQLSXODWLRQ GHFUHDVHV ZLWK WKH HIIHFWLYHQHVV RI WKH KHGJH WKHUH LV PRUH WHQVLRQ ZKHQ WKH SULQFLSDO GHFLGHV ZKHWKHU WR WDNH WKH KHGJHPLVUHSRUW EXQGOH :KHQ WKH KHGJH LV KLJKO\ HIIHFWLYH WKH PRUH HIIHFWLYH WKH KHGJH WKH PRUH OLNHO\ WKH SULQFLSDO SUHIHUV WKH EXQGOH VLQFH WKH PDUJLQDO EHQHILW IURP KHGJLQJfV HIIHFWLYHQHVV EHDWV WKH PDUJLQDO ORVV IURP ORZHU PDQLSXODWLRQ FRVW :KHQ WKH KHGJH LV PRGHUDWHO\ HIIHFWLYH KRZHYHU WKH SULQFLSDO LV PRUH OLNHO\ WR WDNH WKH EXQGOH ZLWK D OHVV HIIHFWLYH KHGJH VLQFH WKH PDUJLQDO ORVV IURP PLVUHSRUWLQJ LV PRUH FRQVLGHUDEOH FRPSDUHG ZLWK WKH PDUJLQDO PAGE 58 EHQHILW IURP WKH KHGJHfV HIIHFWLYHQHVV %XW ZKHQ WKH KHGJH LV SRRUO\ HIIHFWLYH WKH HIIHFWLYHQHVV SOD\V QR UROH LQ WKH SULQFLSDOfV GHFLVLRQ RQ ZKHWKHU WR WDNH WKH EXQGOH VLQFH ERWK WKH KHGJLQJ EHQHILW DQG WKH ORVV IURP PDQLSXODWLRQ DUH LQVLJQLILFDQW PAGE 59 ' )LJXUH DQG Dr WKH VPDOOHU WKH DG WKH ODUJHU WKH DG WKH PRUH OLNHO\ WKH PRUH OLNHO\ DG KDV QR LQIOXHQFH WKH EXQGOH LV SUHIHUUHG WKH EXQGOH LV SUHIHUUHG rG D ZIDf WKH VPDOOHU WKH FUG WKH PRUH OLNHO\ WKH EXQGOH LV SUHIHUUHG DG KDV QR LQIOXHQFH rG % f IHf )LJXUH FUÂ DQG SUHIHUHQFH $f:KHQ FUAAf FU^ONAfÂ§f %f:KHQ A IH77AUUf PAGE 60 7DEOH 1XPHULFDO ([DPSOH IRU SULQFLSDOfV SUHIHUHQFH DQG DG SULQFLSDOfV H[SHFWHG FRVW r rWef EHQFKPDUN VWURQJ EXQGOH DG DG D DG U?M PAGE 61 &+$37(5 ($5/< 5(&2*1,7,21 02'(/ 7KH )$6% KDV UHFHQWO\ LVVXHG VHYHUDO QHZ UHJXODWLRQV RQ WKH PHDVXUHPHQW DQG GLVFORVXUH RI GHULYDWLYHV 7KHUH LV DOVR VXEVWDQWLDO GHWDLOHG LPSOHPHQWDWLRQ JXLGDQFH IURP WKH (PHUJLQJ ,VVXHV 7DVN )RUFH (,7)f 7KH QHZ UHJXODWLRQV DUH LQWHQGHG WR UHFRJQL]H WKH HIIHFW RI D KHGJH RQ HDUQLQJV DQG XVH PDUNWRPDUNHW WHFKQLTXHV WR HYDOXDWH WKH XQVHWWOHG GHULYDWLYHV SUHVXPDEO\ VR LQYHVWRUV XQGHUVWDQG WKH SRWHQWLDO ULVN DQG YDOXH RI WKH GHULYDWLYH FRQWUDFWV KHOG E\ ILUPV +RZHYHU WKH PDUNWRPDUNHW WHFKQLTXH PD\ EH SUREOHPDWLF 7KH SULRU FKDSWHUV KDYH GLVFXVVHG WKH FDVH LQ ZKLFK WKLV WHFKQLTXH LV DEXVHG WR PDQLSXODWH HDUQLQJV ,Q WKLV FKDSWHU IXUWKHU H[SORUH LWV LPSDFW RQ WKH ILUPVf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f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n a $U DGf ZLWK DG D ,Q WKLV ZD\ DJDLQ ZH FDSWXUH WKH ULVN UHGXFWLRQ WKHPH RI KHGJLQJ E\ D PHDQ SUHVHUYLQJ VSUHDG VWUXFWXUH 6LQFH LQ WKLV FKDSWHU DP QRW LQWHUHVWHG LQ HDUQLQJV PDQDJHPHQW UHOD[ WKH HDUOLHU DVVXPSWLRQ N? N DQG DOORZ NL DQG N WR EH DQ\ SRVLWLYH YDOXH :LWK KHGJLQJ EXW ZLWKRXW HDUO\ UHFRJQLWLRQf WKH VHFRQG SHULRG RXWSXW YDULDQFH LV UHGXFHG IURP D WR R? ,I ILUPV KDYH WR UHFRJQL]H WKH LQHIIHFWLYH SRUWLRQ RI KHGJH EHIRUH WKH VHWWOHPHQW RI GHULYDWLYH FRQWUDFWV VXSSRVH ;L tLmL HL SHn DQG [ ND fÂ§ SfHA S f 'XH WR WKH HDUO\ UHFRJQLWLRQ SDUW RI WKH UHGXFHG YDULDQFH LV UHFRJQL]HG LQ WKH ILUVW SHULRG DQG WKH UHPDLQLQJ YDULDQFH LV UHFRJQL]HG LQ WKH VHFRQG SHULRG ZKHQ WKH GHULYDWLYH FRQWUDFW LV VHWWOHG &HQWUDOL]HG &DVH )LUVW FRQVLGHU WKH FDVH LQ ZKLFK WKH SULQFLSDO LV HQGRZHG ZLWK WKH KHGJLQJ DXWKRULW\ DQG GHFLGHV WR KHGJH 6XSSRVH WKH RXWSXWV DUH SXEOLFO\ REVHUYHG 3DUDOOHOLQJ HDUOLHU ZRUN LW LV URXWLQH WR YHULI\ WKDW WKH LQFHQWLYH FRQVWUDLQWV FROODSVH WR WKH IROORZLQJ WZR FRQVWUDLQWV D fÂ§ NL+ & N+ 3! fÂ§ ,&f ,&f PAGE 63 0RUHRYHU WKH LQGLYLGXDO UDWLRQDOLW\ FRQVWUDLQW LV : DN?+ ILN+ fÂ§ & IDU SR?f ?IL SfDG 7KHUHIRUH WKH SULQFLSDOfV GHVLJQ SURJUDP LV PLQ : DN?+ N+ :D 6 W 3URJUDP >)@ : DN?+ ILN+ & ?ROR SRf IO SfD ,5f m r" LFLf 3!K ,&f 6LQFH DV XVXDO ,5f PXVW ELQG WKH UHGXFHG YHUVLRQ RI 3URJUDP >)@ LV PLQ iDFU SDGf iO SfFU 3URJUDP>)n@ 43 6 W 4 ,&,f I!!bbc ,&f 1RWLFH WKH RQO\ GLIIHUHQFH IURP WKH SULRU FHQWUDOL]HG FDVH LQ &KDSWHU LV WKDW SDUW RI WKH VHFRQG SHULRG RXWSXW YDULDQFH LV PRYHG WR WKH ILUVW SHULRG 'HQRWH WKH RSWLPDO ERQXV UDWHV IRU 3URJUDP >)@ DV D) DQG 4r) ,W LV UHDGLO\ YHULILHG WKDW WKH RSWLPDO VROXWLRQ LV Dr) DQG r) 7KH RSWLPDO ERQXV UDWHV KHUH DUH LGHQWLFDO WR WKRVH LQ WKH EHQFKPDUN FDVH ZKHUH HLWKHU WKH SULQFLSDO GRHV QRW KHGJH RU WKHUH LV QR KHGJLQJ RSWLRQ DW DOO 7KLV IROORZV EHFDXVH KHGJLQJ RQO\ LQIOXHQFHV WKH RXWSXW YDULDQFH DQG GRHV QRW DIIHFW WKH LQFHQWLYH FRQVWUDLQWV ,Q WKLV FDVH WKH SULQFLSDOfV H[SHFWHG FRVW LV % & ÂDD SFUÂf A fÂ§ SfFUG &RPSDUHG WR KHU H[SHFWHG FRVW LI VKH GRHV QRW KHGJH $ & ?RJ i6HU KHGJLQJ LV HIILFLHQW ZKHQ $ % RU ZKHQ D r$ 6LQFH Dr) DQG ILr) WKLV LPSOLHV KHGJLQJ LV HIILFLHQW ZKHQ SDr S IFI fÂ§ fÂ§SfFUJ ABOSf DG 3URSRVLWLRQ ,Q WKH FHQWUDOL]HG FDVH KHGJLQJ LV HIILFLHQW ZKHQ FRQGLWLRQ >4@ LV VDWLVILHG 3URRI 6HH WKH DERYH DQDO\VLV PAGE 64 )URP FRQGLWLRQ >"@ ZH VHH ZKHQ KHGJLQJ JUHDWO\ UHGXFHV WKH RXWSXW QRLVH ZKHQ DG LV VPDOOf WKH SULQFLSDO SUHIHUV WR KHGJH ,Q DGGLWLRQ ZKHQ N[ } N WKH SULQFLSDO SUHIHUV WR KHGJH :LWK N[ } N Dr m r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f WR GHQRWH WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG WKHVH WZR FRQVWUDLQWV DUH &(; G +f &(; G +f &(O^+G ?+f!&(O^G +f ([SDQGLQJ WKH FRQVWUDLQWV ZH JHW : DN?+ N+ & ?RO?R SDf i"O SfD : DN[+ tN+ & ?FFR ?tR : DN?+ SN+ & ?D^D SDf i"O SfD : N+ & ?RFD ?SR 7KH\ UHGXFH WR "9 3fD@!DSD &^"9OSfT@D9D` D fÂ§ IFLWI LFLf ,&f PAGE 65 7KH VHFRQG FRQVWUDLQW LV UHGXQGDQW IRU 3>D fÂ§ fÂ§ SfDG@ DSRG DQG rrrf 1RZ WKH QHZ GHVLJQ SURJUDP LV PLQ ?RW^R SDGf iO SfFUG 3URJUDP>*n@ D V W D ,&f 3!L6K ,&f 39 SfD@ FFSRG ,&f 3OXJ WKH RSWLPDO ERQXV UDWHV D) DQG r) LQWR WKH ,& FRQVWUDLQWV )RU ,&ODf ZH KDYH cr) >D fÂ§ SfDG@ fÂ§ Dr)SDG ^bf>r rr &RQGLWLRQ >4@ LPSOLHV fÂ§! WKXV ,&ODf LV VDWLVILHG 7KHUHIRUH WKH RSWLPDO ERQXV UDWHV LQ 3URJUDP >)@ DUH DOVR WKH RSWLPDO ERQXV UDWHV LQ 3URJUDP >*n? ,Q DGGLWLRQ ,&ODf VDWLVILHG LPSOLHV WKH PDQDJHU ZLOO DOZD\V KHGJH DV ORQJ DV >4@ KROGV WKXV LW LV IUHH IRU WKH SULQFLSDO WR PRWLYDWH KHGJLQJ 1R PDWWHU ZKHWKHU LW LV WKH SULQFLSDO RU WKH PDQDJHU ZKR KDV WKH DXWKRULW\ WR KHGJH KHGJLQJ LV HIILFLHQW ZKHQ FRQGLWLRQ >4@ LV VDWLVILHG /HPPD :KHQ >4@ KROGV DQG KHGJLQJ LV PRWLYDWHG WKH RSWLPDO FRQWUDFW KDV Dr .+ DQG 3r rif 3URRI 6HH WKH DERYH DQDO\VLV 7KH LQWXLWLRQ EHKLQG WKLV SURSRVLWLRQ LV WKH IROORZLQJ :KHQ >4@ LV VDWLVILHG XQGHU WKH EHQFKPDUN ERQXV VFKHPH Dr A DQG 3r DOWKRXJK WKH ILUVW SHULRG RXWSXW LV PRUH ULVN\ ZLWK WKH KHGJH WKH WRWDO ULVN SUHPLXP IRU WKH WZR SHULRGV RXWSXWV ADrD SDGf ]nO fÂ§ SfFUG LV VWLOO ORZHU WKDQ WKH ULVN SUHPLXP ZLWKRXW WKH KHGJH _DrFU ArD +RZHYHU ZKHQ >4@ LV QRW VDWLVILHG Dr cAMc DQG 3r DUH QRW WKH RSWLPDO UDWHV IRU 3URJUDP >*@ 'HILQH K S L 3" G DV FRQGLWLRQ >4@ :H KDYH WKH IROORZLQJ OHPPD PAGE 66 /HPPD :KHQ >4@ KROGV DQG KHGJLQJ LV PRWLYDWHG WKH RSWLPDO FRQWUDFW KDV Dr .+ DQG 3r SfA NL+n 3URRI 6HH WKH $SSHQGL[ )URP WKH DERYH OHPPD ZKHQ >4@ KROGV WKH SULQFLSDO KDV WR VHW D KLJKHU VHFRQG SHULRG ERQXV UDWH WR PRWLYDWH KHGJLQJ >4@ LPSOLHV WKDW N? LV ORZ :KHQ N? LV ORZ WKH ORZHU ERXQG RI D LV KLJK :LWK D KLJK ERQXV UDWH LQ WKH ILUVW SHULRG WKH LQGXFHG LQFUHDVHG ULVN LQ WKH ILUVW SHULRG ZLOO EH KLJK 7KXV WKH PDQDJHU LV UHOXFWDQW WR KHGJH 7R PRWLYDWH KHGJLQJ WKH SULQFLSDO KDV WR UHGXFH WKH ZHLJKW RI WKH ILUVW SHULRG ERQXV LQ WKH PDQDJHUf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f WR GHQRWH WKH PDQDJHUfV FHUWDLQW\ HTXLYDOHQW DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG WKH LQFHQWLYH FRQVWUDLQWV IRU WKH ILUVW SHULRG JLYHQ DA + EHFRPH &(>^+G +f!&(>^+G O+f ,&Onf &(>+ G +f &(> G O+f &(? ^+ G +f! &(? G +f 5HZULWH WKH ,&O f FRQVWUDLQWV ZH KDYH e9 F+IO9fÂ§DfÂ§SfAr:` D NL+ +HUH ,&OMf LV UHGXQGDQW VLQFH >D fÂ§ fÂ§ SfRÂ@ UDWLRQDOLW\ FRQVWUDLQW LQ WKLV FDVH LV &(>+G +f LF2 LF2 LF2 DSRG 7KH LQGLYLGXDO DQG LW PXVW ELQG PAGE 67 7KHUHIRUH WKH SURJUDP FDQ EH UHZULWWHQ DV PLQ I DFU b]FU / mA D VW D A A 7 3 fÂ§ N+ 3URJUDP >L@ LFLOf ,&f m: 9 3fA@ ,&2 /HPPD :KHQ >4@ KROGV WKH RSWLPDO FRQWUDFW WKDW SUHFOXGHV KHGJLQJ KDV Df IH6" DQG I L6K 3URRI 6HH WKH $SSHQGL[ 1RZ ZKHQ >4@ KROGV DQG KHGJLQJ LV GLVFRXUDJHG WKH SULQFLSDOfV H[SHFWHG FRVW LV "irf9Itf9 $nf ZKLOH ZKHQ KHGJLQJ LV HQFRXUDJHG KHU H[SHFWHG FRVW LV & Lrf9 3Af Sf0 %nf &RPSDULQJ $n ZLWK %n ZH KDYH %n$n =efU7 QQ? s? I B LQ B UB&B?A B UBFB? $ nAn : 3 DGf >NO+! LUBLBffFU X Sf tG NNL+! r AN+!D UB&Bf UBA1U3AO3fAO B UB&BQ ANL+! rG A NN+ 8OSfU 9IFn D U & ?fÂ§ U c & ?B nNL+ n 3 GU fÂ§ fÂ§AfW n N+ n r fÂ§ Uef7> S9 B aan +n 8 QAFUOSfD IFIBU&?B U 3A A Q f D AfOSfA f IF_! 7KHUHIRUH ZLWK FRQGLWLRQ >4@ VDWLVILHG %n$n! 7KXV KHGJLQJ LV QRW HIILFLHQW A A ,Q RWKHU ZRUGV WKH SULQFLSDO SUHIHUV QRW WR KHGJH ZKHQ DBAAA fÂ§AfÂ§fÂ§ G QR PDWWHU ZKHWKHU WKH SULQFLSDO RU WKH PDQDJHU KDV WKH KHGJLQJ DXWKRULW\ 3URSRVLWLRQ ,I >4@ KROGV HQFRXUDJLQJ KHGJLQJ LV HIILFLHQW DQG WKH RSWLPDO FRQWUDFW KDV Dr DQG r cA? ,I >4@ KROGV GLVFRXUDJLQJ KHGJLQJ LV HIILFLHQW DQG WKH RSWLPDO FRQWDFW KDV Dr DQG r fÂ§ 3URRI 6HH WKH DERYH DQDO\VLV PAGE 68 7DEOH KDV D QXPHULFDO H[DPSOH WR LOOXVWUDWHV WKH FRQFOXVLRQ LQ 3URSRVLWLRQ DVVXPH U & DQG + XVH G WR GHQRWH WKH FDVH WKDW WKH SULQFLSDO HQFRXUDJHV KHGJH DQG XVH G WR GHQRWH WKH FDVH WKDW KHGJH LV GLVFRXUDJHG )URP WKH DERYH SURSRVLWLRQ DQG WKH QXPHULFDO H[DPSOH LQ 7DEOH LW LV VKRZQ WKDW WKH GHOHJDWHG FDVH LV VLPLODU WR WKH FHQWUDOL]HG FDVH LQ WKDW KHGJLQJ LV ,Q WKH GHOHJDWHG FDVH WKHUH LV QR PRUDO KD]DUG N" HIILFLHQW RQO\ ZKHQ TGSf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fV LQHIIHFWLYH SRUWLRQ LQ VRPH FDVHV KHGJLQJ LV QRW HIILFLHQW DQ\ PRUH VLQFH LW DGGV PRUH ULVN WR WKH ILUVW SHULRG RXWSXW WKRXJK WKH ULVN LQ WKH VHFRQG SHULRG RXWSXW LV UHGXFHG :KHQ WKH ILUVW SHULRG RXWSXW KDV D VXIILFLHQWO\ JUHDW ZHLJKW LQ GHFLGLQJ WKH PDQDJHUfV FRPSHQVDWLRQ LQFUHDVHG ULVNLQHVV LQ WKH ILUVW SHULRG RXWSXW JUHDWO\ LQFUHDVHV WKH PDQDJHUfV FRPSHQVDWLRQ ULVN 7KH SULQFLSDO KDV WR SD\ D UHODWLYHO\ ODUJH FRPSHQVDWLQJ ZDJH GLIIHUHQWLDO WKXV KHGJLQJ EHFRPHV XQDWWUDFWLYH ,Q DGGLWLRQ WKH OHVV HIIHFWLYH LV WKH KHGJH WKDW LV A LV FORVHU WR f WKH OHVV OLNHO\ LV KHGJLQJ WR EH HIILFLHQW 0RUHRYHU WKH ODUJHU WKH SRUWLRQ RI WKH LQHIIHFWLYHQHVV LV UHFRJQL]HG HDUOLHU WKDW LV WKH KLJKHU WKH Sf WKH OHVV OLNHO\ KHGJLQJ LV HIILFLHQW 6XPPDU\ ,Q &KDSWHUV DQG KHGJLQJ LV HIILFLHQW VLQFH LW UHGXFHV WKH VHFRQG SHULRG RXWSXW YDULDQFH DQG WKHUHIRUH UHGXFHV ERWK WKH PDQDJHUfV FRPSHQVDWLRQ ULVN DQG PAGE 69 WKH SULQFLSDOfV FRPSHQVDWLQJ ZDJH GLIIHUHQWLDO +RZHYHU ZKHQ LQWURGXFH WKH HDUO\ UHFRJQLWLRQ RI D SRUWLRQ RI WKH KHGJHfV LQHIIHFWLYHQHVV LW LV VKRZQ WKDW VRPHWLPHV KHGJLQJ EHFRPHV XQGHVLUDEOH 7KH UHDVRQ LV WKDW WKH HDUO\ UHFRJQLWLRQ LQFUHDVHV WKH ULVNLQHVV RI WKH ILUVW SHULRG RXWSXW :KHQ WKH ILUVW SHULRG RXWSXW FDUULHV D JUHDW ZHLJKW LQ WKH PDQDJHUfV FRPSHQVDWLRQ RU ZKHQ D ODUJH SHUFHQWDJH RI WKH LQHIIHFWLYHQHVV KDV WR EH UHFRJQL]HG HDUO\ WKH HDUO\ UHFRJQLWLRQ SROLF\ PDNHV KHGJLQJ XQDWWUDFWLYH ,Q DGGLWLRQ ZLWKRXW WKH HDUO\ UHFRJQLWLRQ DV ORQJ DV D KHGJLQJ LV HIILFLHQW ZKLOH ZLWK WKH HDUO\ UHFRJQLWLRQ RQO\ ZKHQ WKH HIIHFWLYHQHVV LV VXIILFLHQWO\ KLJK ZLOO KHGJLQJ EH HIILFLHQW 7KH DQDO\VLV RI WKLV FKDSWHU VKHGV OLJKW RQ KRZ VRPH UHFHQW DFFRXQWLQJ UHJXODWLRQV PD\ LQIOXHQFH WKH ILUPVf ULVN PDQDJHPHQW EHKDYLRU 5HFHQW DFFRXQWLQJ UHJXODWLRQV UHTXLUH WKDW ILUPV UHFRJQL]H WKH LQHIIHFWLYHQHVV RI KHGJH LQWR HDUQLQJV HYHQ EHIRUH WKH VHWWOHPHQW RI GHULYDWLYHV FRQWUDFWV $OWKRXJK WKH LQWHQWLRQ RI WKH QHZ UXOHV LV WR SURYLGH LQYHVWRUV ZLWK PRUH LQIRUPDWLRQ RQ WKH ILUPVf XVH RI GHULYDWLYHV WKH\ PD\ KDYH D VLGH HIIHFW RI GLVFRXUDJLQJ WKH ILUPVf ULVN PDQDJHPHQW DFWLYLWLHV PAGE 70 7DEOH 1XPHULFDO ([DPSOH IRU 3URSRVLWLRQ Dr 3r F N\+ F N+ SULQFLSDOfV H[SHFWHG FRVW 4 G G G 4 G n)RU WKH FDVH ZLWK FRQGLWLRQ >4@ DVVXPH N\ IF 7KHUHIRUH fÂ§fÂ§ ZKLFK VDWLVILHV >4O .L )RU WKH FDVH ZLWK FRQGLWLRQ >4@ DVVXPH N\ F D b fÂ§fÂ§AfÂ§fÂ§ ZKLFK VDWLVILHV >4@ N fÂ§[fÂ§W fÂ§Sf D DQG S DQG S 7KHUHIRUH PAGE 71 &+$37(5 27+(5 5(/$7(' 723,&6 ,Q WKLV FKDSWHU EULHIO\ H[SORUH WKH UHODWLRQVKLS EHWZHHQ ULVNLQHVV DQG DJHQF\ SUREOHPV ,Q DGGLWLRQ DOVR DQDO\]H D PRGHO ZLWK LQIRUPDWLYH HDUQLQJV PDQDJHPHQW ZKHUH PDQLSXODWLRQ LV GHVLUDEOH 5LVNLQHVV DQG $JHQF\ )RU WKH PDLQ PRGHO LQ WKLV SDSHU DVVXPH RXWSXW IROORZV D QRUPDO GLVWULEXWLRQ DQG VKRZ WKDW KHGJLQJ UHGXFHV WKH ILUPVf ULVNV DQG KHOSV UHGXFH WKH FRPSHQVDWLQJ ZDJH GLIIHUHQWLDO +RZHYHU ZH QHHG WR EH FDXWLRXV QRW WR WDNH WKLV UHVXOW FDVXDOO\ DQG FRQFOXGH WKDW DV ORQJ DV KHGJLQJ UHGXFHV WKH ULVN LQ RXWSXW LW LPSURYHV WKH DJHQF\ SUREOHP 7KH QRUPDO GLVWULEXWLRQ DVVXPSWLRQ PD\ SOD\ DQ LPSRUWDQW UROH KHUH ,Q D FRQWLQXRXV VHWWLQJ .LP DQG 6XK f LOOXVWUDWH WKDW LI WKHUH DUH WZR LQIRUPDWLRQ V\VWHPV ZKRVH GLVWULEXWLRQV EHORQJ WR WKH QRUPDO IDPLO\ WKH V\VWHP ZLWK WKH KLJKHU OLNHOLKRRG UDWLR YDULDQFH LV PRUH HIILFLHQW FRVWV OHVV IRU WKH SULQFLSDO WR LQGXFH WKH PDQDJHUnV FHUWDLQ DFWLRQ OHYHOf ,Q D ELQDU\ DFWLRQ VHWWLQJ LW LV HDV\ WR YHULI\ WKDW WKH KHGJHG SODQ DOVR KDV D KLJKHU OLNHOLKRRG UDWLR YDULDQFH $ OLNHOLKRRG UDWLR GLVWULEXWLRQ ZLWK D KLJKHU YDULDQFH PDNHV LW HDVLHU IRU WKH SULQFLSDO WR LQIHU WKH PDQDJHUfV DFWLRQ IURP WKH RXWSXW DQG WKHUHIRUH KHOSV UHGXFH WKH FRPSHQVDWLQJ ZDJH GLIIHUHQWLDO :LWKRXW WKH QRUPDO GLVWULEXWLRQ DVVXPSWLRQ UHGXFWLRQ LQ ULVNLQHVV PD\ QRW LPSURYH DQ DJHQF\ SUREOHP &RQVLGHU D ILQLWH VXSSRUW QXPHULFDO H[DPSOH LQ ZKLFK KHGJLQJ GULYHV XS WKH FRPSHQVDWLQJ ZDJH GLIIHUHQWLDO )RU VLPSOLFLW\ DVVXPH D RQHSHULRG FHQWUDOL]HGKHGJH FDVH ZLWK WKUHH SRVVLEOH RXWSXWV ^` :KHQ WKH SULQFLSDO GRHV QRW KHGJH RU ZKHQ WKHUH LV QR KHGJLQJ RSWLRQf WKH SUREDELOLW\ GLVWULEXWLRQ RI ^` JLYHQ WKH PDQDJHUfV KLJK DFWLRQ LV 3X J _f DQG ZKHQ PAGE 72 WKH PDQDJHU FKRRVHV ORZ DFWLRQ WKH GLVWULEXWLRQ LV f %XW ZKHQ WKH SULQFLSDO KHGJHV WKH SUREDELOLW\ GLVWULEXWLRQ JLYHQ KLJK DFWLRQ LV 3OLG Af DQG WKH GLVWULEXWLRQ JLYHQ ORZ DFWLRQ LV 3LÂ f $OVR DVVXPH & DQG U *LYHQ WKH DFWLRQ LW LV UHDGLO\ YHULILHG WKDW 3 LV D PHDQ SUHVHUYLQJ VSUHDG RI 3DG DQG 3Â LV D PHDQ SUHVHUYLQJ VSUHDG RI 3AG ,Q RWKHU ZRUGV WKH XQKHGJHG SODQ LV PRUH ULVN\ DFFRUGLQJ WR 5RWKVFKLOG DQG 6WLJOLW] f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f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fV RXWSXW DW WKH EHJLQQLQJ RI WKH ILUVW SHULRG +HUH IXUWKHU DVVXPH WKH DJHQW FDQ KHGJH RQO\ ZKHQ KH FKRRVHV KLJK DFWLRQ LQ WKH ILUVW SHULRG 7KDW LV DVVXPH WKH KHGJLQJ DFWLYLWLHV QHHG HIIRUW DQG D VODFN PDQDJHU ZLOO QRW EH DEOH WR KHGJH ,Q DGGLWLRQ LI WKH DJHQW GHFLGHV WR KHGJH DQG PAGE 73 FKRRVHV KLJK DFWLRQ LQ WKH VHFRQG SHULRG KH FDQ DOVR SHUIHFWO\ IRUHFDVW WKH RXWSXW RI WKH VHFRQG SHULRG DW WKH EHJLQQLQJ RI WKH VHFRQG SHULRG 7KH SULQFLSDO FDQQRW REVHUYH WKH DJHQWfV FKRLFHV RU WKH RXWSXWV IRU HDFK SHULRG EXW FDQ REVHUYH WKH DFWXDO DJJUHJDWH RXWSXW DW WKH HQG RI WKH VHFRQG SHULRG )RU VLPSOLFLW\ DVVXPH WKH FRVW RI PLVUHSRUWLQJ LV ]HUR DQG WKH DJHQW FDQ PLVUHSRUW IUHHO\ DV ORQJ DV WKH DJJUHJDWH UHSRUWHG RXWSXW MT [ LV HTXDO WR WKH DFWXDO DJJUHJDWH RXWSXW ;? I [ 7KH WLPH OLQH IRU WKH IRUHFDVW PRGHO LV VKRZQ LQ )LJXUH ,Q WKLV PRGHO DOWKRXJK WKH SULQFLSDO FDQQRW REVHUYH WKH RXWSXW RI HDFK SHULRG DQG FDQQRW NQRZ WKH DJHQWfV IRUHFDVW VKH FDQ GHVLJQ D FRQWUDFW WKDW DFKLHYHV ILUVW EHVW WR HQFRXUDJH KLJK DFWLRQV DQG KHGJH 7KLQN DERXW WKH FRQWUDFW WKDW SD\V WKH DJHQW WKH ILUVWEHVW FRPSHQVDWLRQ LI WKH DJHQW UHSRUWV HTXDO RXWSXWV IRU SHULRG DQG SHULRG EXW SD\V WKH DJHQW D SHQDOW\ LI WKH UHSRUWHG RXWSXWV IRU WKH WZR SHULRGV DUH QRW HTXDO 8QGHU WKLV FRQWUDFW WKH DJHQW FDQ IRUHFDVW WKH VHFRQG SHULRGfV RXWSXW RQO\ ZKHQ KH ZRUNV KDUG DQG KHGJHV DQG RQO\ ZKHQ KH IRUHFDVWV WKH VHFRQG SHULRGfV RXWSXW LV KH DEOH WR PDQDJH WKH HDUQLQJV VR WKDW WKH WZR SHULRGVf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fI+G[fG[G[ 3URJUDP >,@ 6R6L VWI X6L &fI+[LfI+G[fG[LG[ 8 I I X6L fÂ§ &f I+^[LfI+G[fG[LG[ (Xf IRU DQ\ FKRLFH RWKHU WKDQ HLH + KHGJH DQG HTXDO ;?[ ZKHUH 6? LV WKH SD\PHQW WR HTXLYDOHQW UHSRUWHG RXWSXWV DQG 6T LV D SHQDOW\ PAGE 74 3URSRVLWLRQ ,Q WKH IRUHFDVW PRGHO ILUVW EHVW FDQ EH DFKLHYHG E\ 6L & fÂ§ 0Q8f IRU HTXLYDOHQW UHSRUWHG RXWSXWV IRU WKH WZR SHULRGV DQG SHQDOW\ 6R m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` ,I D? + UHSRUW ;? &KRRVH FDQ KHGJH IRU QG D ( ^+/`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f XVH RI GHULYDWLYHV WKH )$6% KDV LVVXHG YDULRXV UXOHV UHFHQWO\ RQ WKH UHFRJQLWLRQ DQG GLVFORVXUH RI GHULYDWLYHV VXFK DV 6)$6 DQG 7KHUH DUH DOVR QXPHURXV GHWDLOHG JXLGDQFHV IURP (PHUJLQJ ,VVXHV 7DVN )RUFH (,7)f RQ KRZ WR LPSOHPHQW WKHVH FRPSOLFDWHG QHZ UXOHV 7KH PDLQ VWUDWHJ\ RI WKH UHJXODWRUV WR ILJKW WKH DEXVH RI GHULYDWLYHV LV WR UHTXLUH ILUPV WR GLVFORVH WKH IDLU YDOXH RI ERWK WKH GHULYDWLYHV DQG WKH KHGJHG LWHPV 7KH UHJXODWRUV EHOLHYH LQYHVWRUV FDQ XQGHUVWDQG EHWWHU WKH YDOXH RI WKH GHULYDWLYH FRQWUDFWV WKURXJK WKH PDQDJHUVf HVWLPDWHV RI WKH GHULYDWLYHVf IDLU YDOXH +RZHYHU WR GR WKLV GLVFUHWLRQDU\ HYDOXDWLRQ RI WKH IDLU YDOXH LV QHFHVVDU\ VLQFH PDQ\ XQVHWWOHG GHULYDWLYHVf IDLU YDOXH LV QRW DYDLODEOH IURP WKH PDUNHW 7KH PRUH GLVFUHWLRQ IRU WKH PDQDJHUV PD\ RIIHU PRUH HDUQLQJV PDQDJHPHQW RSSRUWXQLWLHV FRQWUDU\ WR WKH LQLWLDO LQWHQWLRQ RI WKH QHZ DFFRXQWLQJ UXOHV 0RUHRYHU DQRWKHU LQWHQWLRQ RI WKH QHZ UHJXODWLRQV LV WR KHOS WKH LQYHVWRUV XQGHUVWDQG EHWWHU WKH SRWHQWLDO ULVN RI GHULYDWLYHV WKURXJK WKH PDQDJHUVf HDUO\ GLVFORVXUH PAGE 77 RI WKH LQHIIHFWLYHQHVV RI KHGJLQJ +RZHYHU WKH HDUO\ UHFRJQLWLRQ RI WKH KHGJLQJf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f DQG ,&f UHVSHFWLYHO\ :LWK WKH UHGXFHG SURJUDP WKH ILUVW RUGHU FRQGLWLRQV DUH fÂ§ UDD+L DQG fÂ§UDIW IL 6LQFH D ! DQG IW ! ZH JHW +L UDD DQG Â UDIW 7KLV LPSOLHV ERWK ,&Of DQG ,&f ELQG RU Dr IWr$ Â‘ 3URRI IRU /HPPD 3URRI 7KH SULQFLSDOfV GHVLJQ SURJUDP FDQ EH H[SUHVVHG DV WKH PLQLPL]DWLRQ RI ?^DR IWRGf VXEMHFW WR WKH LQFHQWLYH FRQVWUDLQWV $JDLQ OHW [L GHQRWH WKH /DJUDQJLDQ PXOWLSOLHUV RI ,&Of DQG ,&f UHVSHFWLYHO\ ZLWK WKH UHGXFHG SURJUDP ZH KDYH WKH ILUVW RUGHU FRQGLWLRQV fÂ§ UDD DQG fÂ§UDÂc L +HQFH UDD DQG UDG 7KLV LPSOLHV ERWK ,&Of DQG ,&f DUH ELQGLQJ DQG WKXV D? A DQG 3r$ ÂÂ Â‘ 3URRI IRU 3URSRVLWLRQ 3URRI 'HILQH ;M DV WKH /DJUDQJLDQ PXOWLSOLHU IRU ,&Of DQG IRU ,&f :LWK WKH UHGXFHG 3URJUDP >&n@ WKH ILUVW RUGHU FRQGLWLRQV DUH 7RD 03 a Df 0L )2&,f DQG UFU T Df Q )2&f ,Q WKH RSWLPDO VROXWLRQ LI QHLWKHU FRQVWUDLQW LV ELQGLQJ cL[ IL 6XEVWLWXWH +L Q LQWR WKH ILUVW RUGHU FRQGLWLRQV DQG DGG WKH WZR FRQGLWLRQV WRJHWKHU ZH JHW fÂ§UD3 fÂ§ UDD ZKLFK LPSOLHV D IW 7KLV FRQWUDGLFWV D ! DQG IW cAL 7KHUHIRUH +? [ LV QRW WUXH LQ WKH RSWLPDO VROXWLRQ DQG DW OHDVW RQH RI WKH FRQVWUDLQWV LV ELQGLQJ PAGE 79 ,I +L Â 2 WKHQ D DQG S Â )&f LPSOLHV S ZKHUH 0 f 5HZULWLQJ 0 ZH KDYH 0 ^ f Hi"mff > fÂ§ A fÂ§ HBAB4ff@` :LWK 0 ZH JHW 3 fÂ§D D +RZHYHU $T $ LPSOLHV 3 GRHV QRW VDWLVI\ WKH FRQVWUDLQW 7KHUHIRUH D NA5n t fÂ§ FDQQrI EH WUXH +HQFH UHJDUGOHVV RI +L ,&f DOZD\V ELQGV LPSO\LQJ b ri"f 7KXV DQG +L 0RUHRYHU LI ,&Of ELQGV WKHQ D LI ,&Of LV VODFN WKHQ IURP )2&,f D UDL$, 3 IW +HQFH ZH DOZD\V KDYH DrF crF P 3URRI IRU &RUROODU\ 3URRI 8VLQJ WKH ILUVW RUGHU FRQGLWLRQV GLVSOD\HG LQ WKH SURRI RI 3URSRVLWLRQ ZH VHH ZKHQ T LV VXIILFLHQWO\ QHDU ]HUR )2&,f UHGXFHV WR fÂ§UDD (? +L DQG )2&f UHGXFHV WR fÂ§UD3 H ] ZKHUH (? DQG H DUH VPDOO 7KLV LPSOLHV +L DQG L 7KDW LV ZKHQ T LV VXIILFLHQWO\ VPDOO ERWK LQFHQWLYH FRQVWUDLQWV ELQG DQG De MJ\ 3F LIH Â‘ 3URRI IRU &RUROODU\ 3URRI 8VLQJ WKH ILUVW RUGHU FRQGLWLRQ )2&,f LQ WKH SURRI RI 3URSRVLWLRQ DJDLQ LI +? DQG D WKHQ 0L r1` 4H:Fa7LIIU! B B&B[ m rmf OTJH f Lf FDQ EH UHH[SUHVVHG DV fI If IFf 9 Uefee!r$IH NO f fÂ§ TTH 1RZ VXSSRVH T LV VXIILFLHQWO\ KLJK DQG $T LV VXIILFLHQWO\ ODUJH 7KLV LPSOLHV WKH LQHTXDOLW\ LQ LLf LV UHYHUVHG DQG DrF P 3URRI IRU 3URSRVLWLRQ 3URRI 'HILQH [O[ DV WKH /DJUDQJLDQ PXOWLSOLHUV RI WKH WZR FRQVWUDLQWV UHVSHFWLYHO\ :H JHW WKH IROORZLQJ ILUVW RUGHU FRQVWUDLQWV UDD 3 Df +L )2&Onf fÂ§UD3 a3aDf + )2&nf PAGE 80 )URP 3URSRVLWLRQ ZH NQRZ ÂÂ DQG ÂM ,I LM Â WKHQ DQG IURP )2&Off ZH JHW fÂ§UDD fÂ§ Df fÂ§ ZKLFK LPSOLHV D SAU AÂ ,I Â WKHQ ERWK LQFHQWLYH FRQVWUDLQWV DUH VDWLVILHG DQG DrFL fÂ§ DQG ILrFL cAM DUH WKH RSWLPDO ERQXV UDWHV 7KH FRQGLWLRQ fU7 A A UHGXFHV WR NL N^ UUf ,I ri" WKHQ D GRHV QRW VDWLVI\ WKH FRQVWUDLQW D Â DQG WKH RSWLPDO FRQWUDFW PXVW KDYH DrFL DQG DV ERWK LQFHQWLYH FRQVWUDLQWV ELQG Â‘ &KDSWHU 3URRI IRU /HPPD 3URRI )URP &KDSWHU ZKHQ T LV VXIILFLHQWO\ ORZ WKH RSWLPDO FRQWUDFW LQ WKH PLVUHSRUWLQJ PRGHO LV De 7KH PLVUHSRUWLQJ PRGHO 3URJUDP >&@ LV LGHQWLFDO WR WKH EXQGOHG PRGHO 3URJUDP >'n@ H[FHSW WKDW WKH VHFRQG SHULRG RXWSXW YDULDQFH GHFUHDVHV WR DG LQ WKH EXQGOHG PRGHO ,W LV HDV\ WR YHULI\ WKDW 4F Â 3F f UHPDLQV RSWLPDO LQ WKH EXQGOHG PRGHO ZKHQ T LV VXIILFLHQWO\ QHDU ]HUR 7KH SULQFLSDOfV H[SHFWHG FRVW LQ WKH EXQGOHG PRGHO WKHUHIRUH JHWV FORVH WR & ADe"FU 3FDGf ZKHQ T LV QHDU ]HUR ,Q WKH EHQFKPDUN PRGHO ZKHUH WKHUH LV QHLWKHU KHGJLQJ QRU PLVUHSRUWLQJ RSWLRQ KHU H[SHFWHG FRVW LV & _De"FU rF"Df ZKLFK LV KLJKHU WKDQ & _DAD 7KH KHGJHPLVUHSRUW EXQGOH LV SUHIHUUHG Â‘ 3URRI IRU /HPPD 3URRI )URP &RUROODU\ ZKHQ T LV VXIILFLHQWO\ KLJK DQG N? LV VXIILFLHQWO\ ODUJH WKH RSWLPDO FRQWUDFW H[KLELWV DrF rF :H UHZULWH DrF DV e V ,Q DGGLWLRQ IURP 3URSRVLWLRQ ZH NQRZ DrF H rF ,Q WKH EHQFKPDUN PRGHO ZKHUH WKHUH LV QHLWKHU D KHGJLQJ QRU D PLVUHSRUWLQJ RSWLRQ WKH SULQFLSDOfV H[SHFWHG FRVW LV & ATrM AWf ZKLOH LQ WKH EXQGOHG PRGHO LW LV & ARWr-D 3rFrGf eOQ>O Tf THaAFDfFf? DrFf ,I PAGE 81 I TAR 3$Df ^I Rtr 3FDGf 0L f f TH tK DKf` T3rF a rFf` Lrf9Af^A>r Afrf@ OQ> f THaAaAaH@f A Hf` LLLf WKHQ KHGJHPLVUHSRUW EXQGOH LV SUHIHUUHG WR QR KHGJLQJ QR PLVUHSRUWLQJ %XW LLLf LV SRVLWLYH RQO\ ZKHQ FU fÂ§ R? LV VXIILFLHQWO\ ODUJH Â‘ 3URRI IRU /HPPD 3URRI 5HIHU WR WKH SURRI IRU 3URSRVLWLRQ 3URJUDP >&nT f@ LV LGHQWLFDO WR 3URJUDP >'nT f@ H[FHSW WKDW LQ WKH EXQGOHG PRGHO SURJUDPfV REMHFWLYH IXQFWLRQ WKH VHFRQG SHULRG YDULDQFH LV DG LQVWHDG RI D ,W LV HDV\ WR YHULI\ WKHVH WZR SURJUDPV VKDUH WKH VDPH RSWLPDO ERQXV FRHIILFLHQWV ^Dr'O 3r'Of cr&Of P 3URRI IRU 3URSRVLWLRQ 3URRI ,Q WKH EHQFKPDUN PRGHO ZKHUH WKHUH LV QHLWKHU D KHGJLQJ QRU D PLVUHSRUWLQJ RSWLRQ WKH SULQFLSDOfV H[SHFWHG FRVW LV & AD$D 3$Df ZKLOH LQ WKH EXQGOHG PRGHO LW LV & iDL 3PDGf ?3P a DELf $V ORQJ DV 3Drf a >_D'LD 3r'?DGf a DRLf@ 2} WKH KHGJHPLVUHSRUW EXQGOH LV SUHIHUUHG f :KHQ N? A UDf WKH RSWLPDO FRQWUDFW H[KLELWV Dr' rGL bKf 6XEVWLWXWH Dr$S$ DQG Dr'YSr' LQWR iDIU 3$Df >IFNAFU 'LrGf :EL a DRLf@ :H KDYH LmDA >imR9 'rf ?3r', rELf` UFUfÂ§D L/ UDf &B??UD WRr L n+n ,OI 7M_ A MWI OUfIFI & ?URO7DfNbUDNIUDDAfOUDfNAfÂ§UDfN? n+n OUfIFIF r .ifUDrfA?N?^UDO AfA A>A UULMf U@` 7KXV ZH QHHG UD WUDfA $>P UFU UFUf UDf@ 7KLV LPSOLHV JDUJfJJf LPSOLHV DOUUf f :KHQ NL NOUDf WKH RSWLPDO FRQWUDFW H[KLELWV DA 3r' RWr'93r'Lf LV LGHQWLFDO WR Dr$3$f 6XEVWLWXWH Dr$3$ DQG Rr'SrP LQWR _Dr$D 3r$Df a >mG9 mQ2 .ASL a 4SLf@ ZH KDYH PAGE 82 ,.9A9f>LDÂ9D,9fA LmPf@ ,if>AÂÂf@ 7KXV ZH QHHG Â Âf 2 ZKLFK LPSOLHV Â‘ &KDSWHU 3URRI IRU 3URSRVLWLRQ 3URRI 'HILQH IL? DV WKH /DJUDQJLDQ PXOWLSOLHU IRU ,&Of DQG Â IrU ,&f 7KH ILUVW RUGHU FRQGLWLRQV DUH URnHF mf r )2&,f aUDG3 Df ,M )2&f 6XSSRVH QHLWKHU FRQVWUDLQW LV ELQGLQJ LPSO\LQJ ILY Â fÂ§ 6XEVWLWXWH ÂO cM LQWR WKH ILUVW RUGHU FRQGLWLRQV DQG DGG WKH WZR FRQGLWLRQV WRJHWKHU ZH JHW fÂ§UDG fÂ§ UDD ZKLFK LPSOLHV D fÂ§ 7KLV FRQWUDGLFWV D MSMM DQG ! 7KHUHIRUH cL[LL LV QRW WUXH DQG DW OHDVW RQH RI WKH FRQVWUDLQWV LV ELQGLQJ ,I +? L WKHQ D DQG )2&f LPSOLHV fÂ§ UD,7TFW ZKHUH 7 b'Ff UUUUIfÂ§Wf' 5HZULWLQJ 7 ZH KDYH 7 TTHO:rnr f f OBBH'DfrfT iGTfA B_BMM B B HI'4ff@` R :LWK 7 ZH JHW U-I7TD D +RZHYHU $\ $\ LPSOLHV GRHVQfW VDWLVI\ WKH FRQVWUDLQW A 7KHUHIRUH N+ Â‘ D 0f t A 6f FDQQRW EH WUXH N+ +HQFH UHJDUGOHVV RI SO ,&f DOZD\V ELQGV LPSO\LQJ r( 7KXV Â DQG +? 0RUHRYHU LI ,&Of ELQGV WKHQ D LI ,&Of LV VODFN WKHQ IURP )2&,f R UD77T f +HQFH ZH DOZD\V KDYH Dr( r( Â‘ 3URRI IRU &RUROODU\ 3URRI 8VLQJ WKH ILUVW RUGHU FRQGLWLRQV GLVSOD\HG LQ WKH SURRI RI 3URSRVLWLRQ ZH VHH ZKHQ T LV VXIILFLHQWO\ QHDU ]HUR )2&,f UHGXFHV WR fÂ§UDD H[ +L DQG )2&f UHGXFHV WR fÂ§UDG H ] ZKHUH J\ DQG V DUH VPDOO 7KLV LPSOLHV +L DQG Â Â‘ 3URRI IRU &RUROODU\ 3URRI 8VLQJ WKH ILUVW RUGHU FRQGLWLRQ )2&,f LQ WKH SURRI RI 3URSRVLWLRQ DJDLQ PAGE 83 LI DQG D cAJ WKHQ aL'%S$Uf r rH GA$ff':H rf OfÂ§TTH r r Lf FDQ EH UHH[SUHVVHG DV Âf Lf LLf OBH'tf ee! 1RZ VXSSRVH T LV VXIILFLHQWO\ KLJK N? DQG N DUH VXIILFLHQWO\ GLIIHUHQW DQG LV ODUJH 7KLV LPSOLHV WKH LQHTXDOLW\ LQ LLf LV UHYHUVHG DQG Dr( BU'nefB8f ,Q DGGLWLRQ GHILQH fÂ§IfÂ§ f'U c0 :H KDYH TTHL':AaA A B 0 B OX B H6rJrf V H3IOmf}MJefB/BB/fJf 8 OTTHW0f3` BHA-Dff DQG B Q8 B WZf ; HLArfUJef;-UfB"fL Â£;7;f A BH'4ff )URP WKH SURRI IRU 3URSRVLWLRQ ZH NQRZ 7 fÂ§ fÂ§H A'rMBDfL f' Vi4JTf H BB A JTH 7KHUHIRUH r n BU'8LBAf DQG ERWK MIÂƒ DQG W 27KLV LPSOLHV OTTH A rX IFAF WKDW WKH ODUJHU D FUÂ WKH PRUH OLNHO\ LLf LV UHYHUVHG DQG Dr( $OVR WKH ODUJHU Â fÂ§ IFIf LQ RWKHU ZRUGV WKH JUHDWHU WKH GLIIHUHQFH EHWZHHQ N? DQG Nf WKH PRUH OLNHO\ LLf LV UHYHUVHG DQG Dr Â‘ 3URRI IRU /HPPD 3URRI )URP &RUROODU\ ZKHQ T LV VXIILFLHQWO\ ORZ WKH RSWLPDO FRQWUDFW LQ WKH VWURQJ EXQGOH PRGHO LV Dr( DQG cr( fÂ§ DV LQ WKH EHQFKPDUN ZKHUH WKHUH LV QHLWKHU D KHGJLQJ QRU D PLVUHSRUWLQJ RSWLRQ 7KH SULQFLSDOfV H[SHFWHG FRVW LQ WKH EXQGOHG PRGHO WKHUHIRUH JHWV FORVH WR & D77"fA MWAfFUG@ ZKHQ T LV QHDU ]HUR ,Q WKH EHQFKPDUN PRGHO ZKHUH WKHUH LV QHLWKHU D KHGJLQJ QRU D PLVUHSRUWLQJ RSWLRQ KHU H[SHFWHG FRVW LV & A>MaMMfM AfFW@ ZKLFK LV KLJKHU WKDQ & A>ÂcMMft MAM`f7G@ 7KH VWURQJ EXQGOH LV SUHIHUUHG Â‘ 3URRI IRU 3URSRVLWLRQ 3URRI 'HILQH T T DV WKH /DJUDQJLDQ PXOWLSOLHUV RI WKH WZR FRQVWUDLQWV UHVSHFWLYHO\ PAGE 84 :H JHW WKH IROORZLQJ ILUVW RUGHU FRQVWUDLQWV fÂ§UDD fÂ§ Df ÂT UDO3 '^ Df IL )URP 3URSRVLWLRQ ZH NQRZ Q DQG T ,I T Q WKHQ c $$ DQG IURP )2&, f ZH JHW fÂ§UDD fÂ§ Df )2&,nf )2&nf ZKLFK LPSOLHV D 4UÂc U ,I & 'UFN+n 'UR N+ fÂ§ NU+ & fÂ§L Rr B & A WKHQ ERWK LQFHQWLYH FRQVWUDLQWV DUH VDWLVILHG DQG Dr(; 'UD DQG IrP DUH WKH RSWLPDO ERQXV UDWHV 7KH FRQGLWLRQ GWM e cA FDQ EH UHZULWWHQ LQWR RU DG 8' WKHQ 4 'UD N+ GRHV QrW VDWLVI\ ,&O DQG WKH RSWLPDO FRQWUDFW PXVW KDYH D(O DQG ILr(O fÂ§ DV ERWK LQFHQWLYH FRQVWUDLQWV ELQG Â‘ 3URRI IRU 3URSRVLWLRQ 3URRI ,Q WKH EHQFKPDUN PRGHO ZKHUH WKHUH LV QHLWKHU D KHGJLQJ QRU D PLVUHSRUWLQJ RSWLRQ WKH SULQFLSDOfV H[SHFWHG FRVW LV $ & A>MA(fFU aeKfM`L ZKLOH LQ WKH VWURQJ EXQGOH PRGHO LW LV % & bDr(D ILreL-Gf ?'^cr(O Dr(Lf $V ORQJ DV $ fÂ§ % WKH VWURQJ EXQGOH LV SUHIHUUHG f :KHQ DG DO fÂ§ WKH RSWLPDO FRQWUDFW KDV D( SO] -iK DQA ID cIH 7KHf % .GAfrfA irtfA AAfWtf :H KDYH Â XbP\E\ AQ\ E\ PQE\ A>RAfA 'NAf U'f@` $ % UHTXLUHV UD ÂU.AfA '^ SAf U'@ ZKLFK LPSOLHV b RAf N B '?F'UMffÂ§'?UFf IFI R+'f 0 A JJUIfJaUJf NI R^SRMOURf UD 'UDf D ?@ f :KHQ DG D fÂ§ IFLAf WKH RSWLPDO FRQWUDFW H[KLELWV D( cAK DQG ID cIH7KHQ A SÂ ÂPf P'Lc Â EQ $ fÂ§ % UHTXLUHV fÂ§ $ fÂ§ $f ZKLFK LPSOLHV fÂ§ \MU P PAGE 85 7fÂ§AUf B 3RURf B J'UUf f 9$ t 3URRI IRU &RUROODU\ 3URRI ,Q FRQGLWLRQ $f FDVH f GHILQH = N UHZULWWHQ DV = G= BB >'U7fRf'URfRRURf` GU D 'UFUf B S UfÂ§e!WUffÂ§WU]fÂ§UUfL &7 'UFUf '>fÂ§'UFUffÂ§fÂ§UFUf@ fÂ§ 'ULUf B DUf>UUUL7` a 'UFUf B JAf>aOUfJJ@ f 'UFUf 6LQFH _A WKH KLJKHU WKH ULVN DYHUVLRQ GHJUHH U WKH VPDOOHU WKH = DQG WKH PRUH OLNHO\ WKH FRQGLWLRQ $nf LV VDWLVILHG ,Q RWKHU ZRUGV $f LV OHVV VWULQJHQW ZLWK KLJKHU U ,Q FRQGLWLRQ %f FDVH f LW LV HDV\ WR YHULI\ WKDW WKH KLJKHU WKH U WKH VPDOOHU LV fÂ§ \U DQG PRUH OLNHO\ LV FRQGLWLRQ %f VDWLVILHG ,Q RWKHU ZRUGV %f LV OHVV VWULQJHQW ZLWK KLJKHU U ,W LV DOVR HDV\ WR YHULI\ WKDW LQ HLWKHU FDVH f RU f WKH FORVHU DUH N? DQG N WKH OHVV VWULQJHQW FRQGLWLRQ $f RU %f LV Â‘ 3URRI IRU &RUROODU\ DQG 3URRI ,Q FDVH f DG DO fÂ§ IFLABf DQG WKH VWURQJ EXQGOH LV SUHIHUUHG ZKHQ 0 rrfJUJf IL A B FRfRaURf IFI &7FU7AU7f f = fÂ§ fÂ§&7AU&7f ZH QDnf 4= RRR+URf^RURRDf`RRR"OURfRRfRURf GR > 2MKUDAf B JJfÂ§JUJf^JfÂ§JaFUffÂ§JURUfFUfÂ§WffÂ§UJf` RRRURf RfÂ§R RUR fÂ§R RRfÂ§UR RU R R R fÂ§UR fÂ§RURR 9 FUU fÂ§FUUFUf RfÂ§RRfÂ§URRUR RRURf U?fB OUfROUfR R2MURf :KHQ O UfD fÂ§ O UfDG WKDW LV ZKHQ DG FUAf MS" WKH VPDOOHU N WKH FUÂ WKH OHVV FRQVWUDLQLQJ LV cA = :KHQ UfD fÂ§ UfFUG WKDW LV ZKHQ DG DMS] WKH ODUJHU PAGE 86 2 f IF WKH DG WKH OHVV FRQVWUDLQLQJ LV = ,Q FDVH f IURP %nf ZH VHH DG GRHV QRW SOD\ D UROH LQ WKH SULQFLSDOfV GHFLVLRQ RQ ZKHWKHU WR WDNH WKH EXQGOH Â‘ &KDSWHU 3URRI IRU /HPPD 3URRI 'HQRWH WKH /DJUDQJLDQ FRHIILFLHQWV IRU ,&Of ,&f DQG ,&ODf LQ 3URJUDP >* @ DV ÂM S DQG S 7KH ILUVW RUGHU FRQGLWLRQV DUH UDD SDGf S DSDGS )2&,f UO SfDG S >D ^O SfDG@S )2&f )URP )2&,f LI S[ WKHQ fÂ§ UDD SFUGf fÂ§ DSDnGS fÂ§ ZKLFK LPSOLHV S 7KHUHIRUH ZH PXVW KDYH S[ WKDW LV Dr )URP )2&f LI S WKHQ fÂ§U fÂ§ SfDG ZKLFK LV QRW WUXH 7KHUHIRUH ZH FDQQRW KDYH ERWK S DQG S ,I S S WKHQ >FU fÂ§ SfRÂ@ DSDG ZKLFK LPSOLHV IWr ,I WKLV 3r Â WKHQ Dr IF6" DQG 3 ?@ar7H RSWLPDO 3 NI^ BB DBBSf Ar 6K LP3OLHV ; I f ZKLFK LV FRQGLWLRQ Sf >"@f ,Q RWKHU ZRUGV LI FRQGLWLRQ >4@ LV VDWLVILHG WKH RSWLPDO FRQWUDFW KDV Dr fÂ§ DQG S % 3URRI IRU /HPPD 3URRI 'HILQH WKH /DJUDQJLDQ FRHIILFLHQWV IRU ,&bf ,&nf DQG ,&OAf LQ 3URJUDP ?+nf DV S? Sn DQG S 7KH ILUVW RUGHU FRQGLWLRQV DUH UDD S? DSDGS )2&Onf fÂ§UtR SO fÂ§ S>DG fÂ§ fÂ§ SfFG? )2&f )URP )2& f LW LV HDV\ WR YHULI\ ZH FDQQRW KDYH Sn VLQFH LQ WKDW ZD\ S 7KHUHIRUH S DQG S ,I S> S WKHQ Dr DQG DrSD? 3>F fÂ§ fÂ§ SfFUÂ@ ZKLFK PAGE 87 MA A LPSOLHV FRQGLWLRQ >4@ME DBABS\DL f ,Q RWKHU ZRUGV ZLWK FRQGLWLRQ >4@ VDWLVILHG WKH RSWLPDO FRQWUDFW VKRZV Dr cI/ DQG cr Â‘ &KDSWHU 3URRI IRU 3URSRVLWLRQ 3URRI 7KH SURJUDP IRU WKH SULQFLSDO LV PLQ I I 6L I+[fI+G[fG[G[ 6R6L VWI I X6L &fI+[OfI+G^[fG[G[ 8 ,5f IX6La&fI+^[fI+G[fG[LG[ I X6&fI+[LfI/[fG[LG[ I I X6[ ;A;? B7R fÂ§ 7 M &f I+^[?f I/^[fG[?G[ ,&f X6L&fI+[LfI+G[fG[LG[ I X6&fI/[LfI+[fG[[G[ X6[ f fÂ§[ M &fI/[LfI+^[fG[G[ ,&f I I X6L &fI+[fI+G[fG[G[ I I X6fI/[LfI/[fG[G[ I X6fI/[LfI/[fG[G[ ,&f I X6L &fII[fI1G[fG[G[ I I X6 &fI+[[fI+G[fG[G[ ;A,O I I X6 &fIK[?fI+G[fG[LG[ ,&f ; ;? :LWK D VXIILFLHQWO\ ORZ 6R LW LV REYLRXV WKDW WKH ,& FRQVWUDLQWV DUH QRW ELQGLQJ 7KLQN DERXW 6T fÂ§RR $OO WKH ULJKW KDQG VLGHV RI WKH ,& FRQVWUDLQWV DUH HTXLYDOHQW WR fÂ§RR WKHQ 7KHUHIRUH QRQH RI WKH ,& FRQVWUDLQWV LV ELQGLQJf :LWK QRQH RI WKH ,& FRQVWUDLQWV ELQGLQJ ZH UHGXFH WKH SURJUDP LQWR D ILUVWEHVW RQH 7KHUHIRUH ZH KDYH I I X6[&fI+[[fI+G^[fG[[G[ 8 RU X6[a&f 8 7KDW LV WKH RSWLPDO 6[ & fÂ§ e OQfÂ§8f Â‘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f$FFRXQWLQJ IRU KHGJLQJ DQG RWKHU ULVNDGMXVWLQJ DFWLYLWLHV TXHVWLRQV IRU FRPPHQW DQG GLVFXVVLRQf $FFRXQWLQJ +RUL]RQV 9RO 1RO 0DUFK %DUWK 0 ( : &ROOLQV 0 &URRFK $ (OOLRW 7 )UHFND ( $ ,PKRII -U : 5 /DQGVPDQ DQG 5 6WHSKHQV 5HVSRQVH WR WKH )$6% H[SRVXUH GUDIW f'LVFORVXUH DERXW GHULYDWLYH ILQDQFLDO LQVWUXPHQWV DQG IDLU YDOXH RI ILQDQFLDO LQVWUXPHQWVf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f )LQDQFLDO $FFRXQWLQJ 6WDQGDUGV %RDUG )$6%f 'LVFORVXUH DERXW GHULYDWLYH ILQDQFLDO LQVWUXPHQWV DQG IDLU YDOXH RI ILQDQFLDO LQVWUXPHQWV 6WDWHPHQW RI )LQDQFLDO $FFRXQWLQJ 6WDQGDUGV 1R $FFRXQWLQJ IRU GHULYDWLYH LQVWUXPHQWV DQG KHGJLQJ DFWLYLWLHV 6WDWHPHQW RI )LQDQFLDO $FFRXQWLQJ 6WDQGDUGV 1R $FFRXQWLQJ IRU GHULYDWLYH LQVWUXPHQWV DQG KHGJLQJ DFWLYLWLHVfÂ§GHIHUUDO RI WKH HIIHFWLYH GDWH RI )$6% VWDWHPHQW 1R fÂ§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f *UHHQVSDQ $ )LQDQFLDO GHULYDWLYHV VSHHFK EHIRUH WKH )XWXUHV ,QGXVWU\ $VVRFLDWLRQ %RFD 5DWRQ )ORULGD 0DUFK +HDO\ 3 0 DQG 0 :DKOHQ $ UHYLHZ RI WKH HDUQLQJV PDQDJHPHQW OLWHUDWXUH DQG LWV LPSOLFDWLRQV IRU VWDQGDUG VHWWLQJ $FFRXQWLQJ +RUL]RQV 9RO 1R 'HFHPEHU +ROPVWURP % DQG 3 0LOJURP $JJUHJDWLRQ $QG /LQHDULW\ ,Q 7KH 3URYLVLRQ 2I ,QWHUWHPSRUDO ,QFHQWLYHV (FRQRPHWULFD 9RO f ,MLUL < DQG 5 -DHGLFNH 5HOLDELOLW\ DQG REMHFWLYLW\ RI DFFRXQWLQJ PHDVXUHPHQWV 7KH $FFRXQWLQJ 5HYLHZ -XO\ ,QGMHMLNLDQ 5 DQG 1DQGD '\QDPLF LQFHQWLYHV DQG UHVSRQVLELOLW\ DFFRXQWLQJ -RXUQDO RI $FFRXQWLQJ DQG (FRQRPLFV .DQRGLD & $ 0XNKHUML + 6DSUD DQG 5 9HQXJRSDODQ +HGJH GLVFORVXUHV IXWXUH SULFHV DQG SURGXFWLRQ GLVWRUWLRQV -RXUQDO RI $FFRXQWLQJ 5HVHDUFK 9RO 6XSSOHPHQW .LP 6 (IILFLHQF\ RI DQ LQIRUPDWLRQ V\VWHP LQ DQ DJHQF\ PRGHO (FRQRPHWULFD 9RO 1R .LP 6 DQG < 6 6XK 5DQNLQJ RI DFFRXQWLQJ LQIRUPDWLRQ V\VWHPV IRU PDQDJHPHQW FRQWURO -RXUQDO RI $FFRXQWLQJ 5HVHDUFK 9RO 1R $XWXPQ /DPEHUW 5 $ &RQWUDFWLQJ WKHRU\ DQG DFFRXQWLQJ -RXUQDO RI $FFRXQWLQJ DQG (FRQRPLFV /HY % &RUSRUDWH HDUQLQJV 7DFWV DQG ILFWLRQ -RXUQDO RI (FRQRPLF 3HUVSHFWLYHV 9RO 1R 6SULQJ /HYLWW $ 7KH QXPEHUV JDPH UHPDUNV RI &KDLUPDQ DW WKH 1<8 &HQWHU IRU /DZ DQG %XVLQHVV 1HZ PAGE 91 0D\HUV DQG & : 6PLWK 2Q WKH FRUSRUDWH GHPDQG IRU LQVXUDQFH -RXUQDO RI %XVLQHVV 9RO 1R 0HOXPDG 1 :H\QV DQG $ =LY &RPSDULQJ DOWHUQDWLYH KHGJH DFFRXQWLQJ VWDQGDUGV VKDUHKROGHUVf SHUVSHFWLYH 5HYLHZ RI $FFRXQWLQJ 6WXGLHV 9RO 'HFf 0LOJURP 3 DQG 1 6WRNH\ ,QIRUPDWLRQ WUDGH DQG FRPPRQ NQRZOHGJH -RXUQDO RI (FRQRPLF 7KHRU\ 0LUUOHHV 1RWHV RQ ZHOIDUH HFRQRPLFV LQIRUPDWLRQ DQG XQFHUWDLQW\ (VVD\V LQ (FRQRPLFV %HKDYLRU 8QGHU 8QFHUWDLQW\ HGLWHG E\ 0 %DOFK 0H)DGGHQ DQG 6 :X $PVWHUGDP 1RUWK+ROODQG 1DQFH 5 & : 6PLWK -U DQG & : 6PLWKVRQ 2Q WKH GHWHUPLQDQWV RI FRUSRUDWH KHGJLQJ -RXUQDO RI )LQDQFH 9RO f 3LQFXV 0 DQG 6 5DMJRSDO 7KH LQWHUDFWLRQ EHWZHHQ DFFUXDO PDQDJHPHQW DQG KHGJLQJ HYLGHQFH IURP RLO DQG JDV ILUPV 7KH $FFRXQWLQJ 5HYLHZ 9RO 1R -DQXDU\ 5RJHUV $ 'RHV H[HFXWLYH SRUWIROLR VWUXFWXUH DIIHFW ULVN PDQDJHPHQW" &(2 ULVNWDNLQJ LQFHQWLYHV DQG FRUSRUDWH GHULYDWLYHV XVDJH -RXUQDO RI %DQNLQJ DQG )LQDQFH 5RWKVFKLOG 0 DQG ( 6WLJOLW] ,QFUHDVLQJ ULVN $ GHILQLWLRQ -RXUQDO RI (FRQRPLF 7KHRU\ 5\DQ 6 )LQDQFLDO ,QVWUXPHQWV t ,QVWLWXWLRQV $FFRXQWLQJ DQG 'LVFORVXUH 5XOHV &KDSWHU -RKQ :LOH\ t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f KHGJLQJ SROLFLHV -RXUQDO RI )LQDQFLDO DQG 4XDQWLWDWLYH $QDO\VLV 9RO 1R 'HFHPEHU PAGE 92 %,2*5$3+,&$/ 6.(7&+ /LQ 1DQ ZDV ERUQ LQ %HLMLQJ &KLQD LQ VSULQJ ,Q -XQH VKH UHFHLYHG D %DFKHORU RI (QJLQHHULQJ LQ LQGXVWULDO HFRQRPLFV IURP 7LDQMLQ 8QLYHUVLW\ LQ 7LDQMLQ &KLQD 6KH WKHQ ZRUNHG DW WKH ,QGXVWULDO DQG &RPPHUFLDO %DQN RI &KLQD ,&%&f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Â‘ +EUB4 -RHO 6 'HPVNL &KDLU )UHGHULFN ( )LVKHU (PLQHQW 6FKRODU RI $FFRXQWLQJ FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHGDWH LQ Â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fURIHVVRU RI $FFRXQWLQJ 7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH *UDGXDWH )DFXOW\ RI WKH )LVKHU 6FKRRO RI $FFRXQWLQJ LQ WKH :DUULQJWRQ &ROOHJH RI %XVLQHVV $GPLQLVWUDWLRQ DQG WR WKH *UDGXDWH 6FKRRO DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXLUHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ $XJXVW 'HDQ *UDGXDWH 6FKRRO PAGE 94 /' t/ $ 81,9(56,7< 2) )/25,'$ DERIVATIVES AND EARNINGS MANAGEMENT By LIN NAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DERIVATIVES AND EARNINGS MANAGEMENT By Lin Nan August 2004 Chair: Joel S. Demski Major Department: Fisher School of Accounting Derivative instruments are popular hedging tools for firms to reduce risks. However, the complexity of derivatives brings earnings management concern and there are recent accounting rules trying to regulate the use of derivatives. This dissertation studies the joint effect of derivativesâ€™ hedging function and earnings management function, and explores how the recent rules influence firmsâ€™ hedging behavior. The two-edged feature of derivatives is modeled by bundling a hedging option and a misreporting option. A mean preserving spread structure is employed to capture the risk-reduction theme of hedging. This dissertation shows a trade-off between the benefit from hedging and the dead weight loss from misreporting. It is shown that when the managerâ€™s misreporting cost, declines with the effectiveness of hedging, the principalâ€™s preference for the hedge-misreport bundle does not change monotonically with the effectiveness of hedging. Specifically, when hedging is highly effective, the principalâ€™s preference for the bundle increases in the effectiveness, while when hedgingâ€™s effectiveness is moderate, the principalâ€™s preference decreases in the effectiveness. When hedging is only slightly effective, whether the principal prefers the bundle is not influenced by the effectiveness. In addition, this dissertation shows that sometimes it is not efficient to take any measure to restrain earnings management. Recent regulations require firms to recognize the ineffective portion of hedges into earnings. This dissertation indicates that this early recognition may change the firmsâ€™ hedging behavior. Since the early recognition increases the interim earningsâ€™ riskiness, hedging may become inefficient even though it still reduces the total risk. In this sense, the new regulations may not benefit investors, though their intention is to provide more information about the risk and value of derivatives to the investors. Copyright 2004 by Lin Nan To my parents Manping Wang and Weihan Nan, and to Laurence ACKNOWLEDGEMENTS I am very grateful to Joel S. Demski, my Chair, for his guidance and encouragement. I also thank David Sappington, Karl Hackenbrack, Froystein Gjesdal, and Doug Snowball for their helpful comments. IV TABLE OF CONTENT ACKNOWLEDGMENTS iv ABSTRACT vii CHAPTER 1 BACKGROUND AND LITERATURE REVIEW 1 Background 1 Literature Review on Hedging 3 Review of Earnings Management and Information Content 9 Review of LEN Framework 11 Summary 14 2 BASIC MODEL 15 The Model 15 Basic Setup 16 Benchmark 17 Hedging and Earnings Management Options 19 Summary. 30 3 HEDGE-MISREPORT MODEL 32 Bundled Hedging and Misreporting Options 32 Whether to Take the Bundle 34 Summary 37 4 MANIPULATION RESTRAINED BY HEDGE POSITION 41 Cost of Earnings Management 41 "Strong Bundle" Model 41 Whether to Take the Strong Bundle 43 Summary. 47 5 EARLY RECOGNITION MODEL 51 Early Recognition of Hedging 51 Centralized Case 53 Delegated Case 54 v Summary. 59 6 OTHER RELATED TOPICS 61 Riskiness and Agency. 61 Informative Earnings Management: Forecast Model 62 Summary 64 7 CONCLUDING REMARKS 66 APPENDIX 68 REFERENCE LIST 78 BIOGRAPHICAL SKETCH 82 vi Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DERIVATIVES AND EARNINGS MANAGEMENT By Lin Nan August 2004 Chair: Joel S. Demski Major Department: Fisher School of Accounting Derivative instruments are popular hedging tools for firms to reduce risks. However, the complexity of derivatives brings earnings management concern and there are recent accounting rules trying to regulate the use of derivatives. This dissertation studies the joint effect of derivativesâ€™ hedging function and earnings management function, and explores how the recent rules influence firmsâ€™ hedging behavior. The two-edged feature of derivatives is modeled by bundling a hedging option and a misreporting option. A mean preserving spread structure is employed to capture the risk-reduction theme of hedging. This dissertation shows a trade-off between the benefit from hedging and the dead weight loss from misreporting. It is shown that, when the managerâ€™s misreporting cost declines with the effectiveness of hedging, the principalâ€™s preference for the hedge-misreport. bundle does not change monotonically with the effectiveness of hedging. Specifically, when hedging is highly effective, the principalâ€™s preference for the bundle increases in the effectiveness, while when hedgingâ€™s effectiveness is moderate, the principalâ€™s preference decreases in the effectiveness. When hedging is only slightly effective, whether the principal prefers the Vll bundle is not influenced by the effectiveness. In addition, this dissertation shows that sometimes it is not efficient to take any measure to restrain earnings management. Recent regulations require firms to recognize the ineffective portion of hedges into earnings. This dissertation indicates that this early recognition may change the firmsâ€™ hedging behavior. Since the early recognition increases the interim earningsâ€™ riskiness, hedging may become inefficient even though it still reduces the total risk. In this sense, the new regulations may not benefit investors, though their intention is to provide more information about the risk and value of derivatives to the investors. viu CHAPTER 1 BACKGROUND AND LITERATURE REVIEW Background Derivatives include â€œa wide variety of financial and commodity instruments whose value depends on or is derived from the value of an underlying asset/liability, reference rate, or index'â€™ (Linsmeier 2003). Financial derivatives have been developed rapidly and employed widely since the early 1990s. Alan Greenspan, the Chairman of the Federal Reserve Board, said in a speech before the Futures Industry Association in 1999 that, "by far the most significant event in finance during the past decade has been the extraordinary development and expansion of financial derivatives." Financial derivatives are very popular tools for risk-reduction in many firms and the global derivatives market has grown rapidly. At the end of June 2003, the Bank for International Settlements estimated that the total estimated notional amount of over-the-counter (OTC) derivatives contracts stood at US$169.7 trillion with a gross market value of $7.9 trillion.1 The derivatives have played an important role in the firmsâ€™ risk management activities. On the other hand, the complexity of financial derivatives raises investorsâ€™ concern about how the derivatives change the firmsâ€™ performance, and suspicion about whether the derivatives are abused in the interest of the management. During the past ten years, there are numerous scandals involving the use of derivatives. For example, in March 2001, a Japanese court fined Credit Suisse First Boston 40 million Yen for using complex derivatives transactions to conceal losses. Also in 2001, Enron, the seventh largest company in the United States and the largest energy trader in â€™Notional amount is the market value of the hedged items whose risk is hedged by the use of derivatives. It is different from the market value of the derivatives. 1 2 the world, collapsed. Investigations revealed that it had made extensive use of energy and credit derivatives to bolster revenues. Responding to the investorsâ€™ concern, the Financial Accounting Standards Board (FASB) recently issued several new statements on the measurement and disclosure of derivatives, including SFAS 133, 137, 138 and 149. There are also tons of detailed implementation guidance from the Emerging Issues Task Force (EITF). As of the November 12-13, 2003. EITF meeting, there are at least 38 issues directly addressing the accounting for derivative instruments. Although the FASB makes all these new regulations, it is unlikely that the new regulations will eliminate earnings management through derivatives. In addition, some new rules may even provide new avenues for earnings management. For example, SFAS 133 requires firms recognize both derivatives and hedged items at their fair value, even before the settlement of the derivative contracts. When the increase/decrease in a derivativeâ€™s fair value cannot offset the decrease/increase in its hedged itemâ€™s fair value, the uncovered part is regarded as the ineffective portion of the hedge and is recorded immediately into earnings. However, evaluating the "fair value" of unsettled derivatives is often subjective. Managers can either estimate the fair value based on the current market price of other derivatives, or invoke "mark-to-model" techniques. With a subjective estimation of the fair value, the estimation of the ineffective portion is also discretionary. Derivative instruments, therefore, have a two-edged feature. They can be used as tools to reduce firms' risks (that is, tools of hedging), but they can also be used as tools of earnings management. This two-edged feature provides us an ideal setting to study the joint effect of hedging and earnings management, which is one of the focuses of this dissertation. 3 Literature Review on Hedging Among the research on hedging activities, the incentives for hedging, how hedging activities influence contracting between the principal and the manager, and how the FASB regulations affect hedging behavior are most explored. Hedging Incentives First, for the research on hedging incentives, there are some finance studies on why firms hedge. Smith and Stulz (1985) analyze the determinants of firmsâ€™ hedging policies from the perspective of firm value. They examine taxes, bankruptcy cost, and managersâ€™ wealth. Regarding hedging activities as a kind of insurance, Mayers and Smith (1982) use the theory of finance to analyze the corporate demand for insurance from the perspectives of taxes, contracting costs and the impact of financing policy on firmsâ€™ investment decisions. Smith and Stulz (1985) conclude that, hedging reduces a firmâ€™s tax liability if the post-tax firm value is a concave function of the pre-tax firm value. Nance, Smith, and Smithson (1993) provide the empirical evidence that firms with more of the range of their pretax income in the statutory progressive region of the tax; schedule, or have more tax preference items, are more likely to hedge. This supports Smith and Stulzâ€™s statement on the corporate hedging incentive from tax liability. However, Graham and Rogers (2002) quantify the convexity-based benefits of hedging by calculating the tax savings that result from hedging and do not find evidence that firms hedge in response to tax convexity. Smith and Stulz (1985) also study hedging from the perspective of the managerâ€™s wealth. They indicate that the manager would like to hedge if his end-of-period wealth is a concave function of the end-of-period firm value, while the manager would not hedge if his end-of-period wealth is a convex function of firm value. Rogers (2002) considers both the managerâ€™s stock holdings and option holdings, and finds the risk-taking incentives from options are negatively associated with the use of 4 derivatives. This evidence is consistent with Smith and Stulzâ€™s suggestion that the managerâ€™s wealth plays a role in hedging decision, and is also consistent with the notion that derivatives are to reduce firmsâ€™ risks. Mayers and Smith (1982) argue that the corporation does not "need" insurance to reduce the stockholdersâ€™ risk since the stockholders can eliminate insurable risk through diversification. Instead, insurance is optimally designed to shift the risk of managers and employees to stockholders, since the managers and other employees do not have enough ability to diversify claims on human capital. It then follows that the higher the employeesâ€™ fraction of the claims to the firmâ€™s output, the higher the probability that the firm will purchase insurance. Smith and Stulz (1985) point out that hedging lowers the probability of incurring bankruptcy costs. Graham and Rogers (2002) show empirical evidence that firms with more expected financial distress hedge more, which is consistent with the idea that firms hedge to reduce risks. Nance, Smith and Smithson (1993) find that firms who have less coverage of fixed claims (a proxy for financial distress) hedge more, which is another piece of empirical evidence to support the risk reduction incentive. Contrary to works such as Smith and Stulz (1985) and Nance, Smith and Smithson (1993), Schrand and Unal (1998) emphasize that hedging is a means of allocating a firmâ€™s risk exposure among multiple sources of risk rather than reducing total risk. However, in some sense, their allocation theory is still consistent with the risk-reduction theory. In Schrand and Unalâ€™s paper, the total risk is reflected in the variability of a loan portfolio's cash flow. They further classify the risk into two types: core-business risk, from which the firm can earn economic rent for bearing since it has an information advantage in the activities related to this risk; and homogenous risk, where the firm does not have any information advantage and cannot earn rent. Schrand and Unal claim that the firms use hedging to increase core-business risk and reduce homogenous risk. In other words, the firms confidently play with core-business risk in which they have expertise and more "control," but reduce the uncontrollable 5 homogenous risk by hedging. The uncontrollable homogenous risk is the real risk for the firms. Though there are a number of incentives for hedging activities, here in this paper I focus on the risk-reduction incentive. Risk reduction is the initial intention of the invention of various financial derivatives, and it is the main purpose of hedging activities. Hedging and Contracting Secondly, for the research on contracting, there are some, but not many, studies on how the hedging activities affect contracting. Campbell and Kracaw (1987) focus on optimal insurance through hedging by the manager. They show that under certain incentive contracts, shareholders will be hurt by the managerâ€™s hedging behavior since the manager will deviate from the optimal managerial effort level with the acquisition of insurance. However, if the contract anticipates the hedging, then the shareholders will benefit from that hedging. The reason is that the shareholders can reduce fixed payments to the manager to acquire the direct gain from hedging reaped by the manager and they can induce the manager to exert more effort by raising the managerâ€™s share of risky returns. Their result is consistent with this paperâ€™s conclusion that hedging reduces compensating wage differentials in a LEN framework. However, unlike the model in this paper, they assume the outputs are always public and their work does not consider earnings management. In addition, their analysis focuses on how hedging influences firm value, while in the current paper my focus is how hedging influences the information content of performance measures. Another related paper is DeMarzo and Duffie (1995), who also analyze hedging behavior from the perspective of information content. They show that financial hedging improves the informativeness of corporate earnings as a signal of managerial ability and project quality. However, in their model, the managerâ€™s action is given, so there is no need to motivate the manager to work diligently. Moreover, 6 unlike the model in my work, their model does not consider manipulation of earnings by the managers. Recent Hedging Regulations Thirdly, recent new FASB regulations on hedging have triggered some research on how the new rules affect firmsâ€™ hedging behavior. The recent rapid development of various financial derivatives and the complexity of derivatives raise the concern that the explosion in their use may endanger investorsâ€™ interest, since it is difficult for investors to understand from the financial reports the magnitude, value and potential risk of the derivatives. Since 1994, the FASB has issued several new regulations on the disclosure of derivatives. Among these regulations, SFAS 119 (which was later superseded by SFAS 133) requires more disclosure on the use of derivatives, and SFAS 133 requires that an entity recognize all derivatives as either assets or liabilities in the statement of financial position and measure those instruments at fair value. These regulations are complex, to say the least, and have led to considerable debate. Responding to the controversy, the FASB issued SFAS 137 to defer the effective date for SFAS 133 from June 1999 to June 2000, and later also issued SFAS 138 and 149 as amendments of SFAS 133. Recent research provides both pros and cons of the hedging disclosure policy. Barth et al. (1995) respond to the FASB Discussion Document about hedge accounting and the FASB Exposure Draft. They argue that a mark-to-market accounting is the best approach to accounting for hedging activities and they support the disclosure policy. They claim that disclosures about management objectives in using derivatives for risk management are useful to financial statement users and are value relevant. Kanodia, Mukherji, Sapra, and Venugopalan (2000) examine the social benefits and costs under different hedge accounting methods from a macroeconomic view. They claim that hedge accounting provides information about firmsâ€™ risk exposure to the market, thus helps make the futures price more efficient. 7 Melumad, Weyns, and Ziv (1999) also compare different hedge accounting rules, but they focus on the managersâ€™ decision making process. They show that under comprehensive fair-value hedge accounting, investors can infer the necessary information from the reported earnings for the valuation of the firm, though the market does not directly observe intermediate output and hedge position. In this case the managers choose the same hedge position as in the public information case. In contrast, under the no-hedge accounting rules, the managers choose a lower hedge position than in the public information case. This is because the investors cannot infer new information from the earnings report to revise their evaluation and the market price at the interim date has less variance. Melumad, Weyns and Ziv support hedge accounting against no-hedge accounting, but they believe only comprehensive fair-value hedge accounting is efficient while recent accounting regulations, e.g., SFAS No. 133, only require limited fair-value hedge accounting or cash-flow hedge accounting. On the other side, DeMarzo and Duffie (1995) argue that it is optimal for the shareholders to request only the aggregate output instead of disclosure of hedging positions. The reason is that with nondisclosure of hedging positions, managers choose risk minimization (full hedging) since reduced output variability leads to a more stable wage. However, when the hedging positions are required to be disclosed, the managers deviate from optimal full hedging since disclosed hedging eliminates noise from the outputs and makes the outputs more sensitive signals of the managersâ€™ ability. Holding the variability of output fixed, this disclosure makes the managerial wage more variable. A related concern is that the recorded value for derivatives can be manipulated by managers. A derivativeâ€™s "fair valueâ€ refers to the current market price of similar derivatives. However, it is often difficult to find â€œsimilarâ€ derivatives. Managers then must estimate the â€œfair valueâ€ of the derivatives based on the current market price of other derivatives or invoke â€œmark-to-modelâ€ techniques. This leaves the â€œfair valueâ€ 8 of the derivatives up to the managersâ€™ discretion. In this sense, the new accounting rules for derivatives provide a new field for earnings management, and the complexity of many derivatives is itself a choice variable. Therefore, derivatives can function both as tools for hedging and for earnings management. Even in Barth, Elliott et al. (1995) and Barth, Collins et al. (1995), they admit that the mark-to-market approach is arbitrary and creates opportunities for earnings management, though they insist that the "fair value" approach to report hedging activities is still the best option. Among empirical studies, Barton (2001) is probably the first to study the interaction between hedging and earnings management. He measures derivatives using notional amounts and discretionary accruals using the modified Jones model. Barton finds that firms with larger derivatives portfolios have lower levels of discretionary accruals. He suggests managers use discretionary accruals and derivatives as partial substitutes to smooth earnings so as to reduce agency costs, income taxes, and information asymmetry, and to increase personal wealth and utility. Since he believes that the earnings management through accruals and derivatives use are some kind of substitutes, his paper suggests that SFAS No. 133 may cause fewer hedging activities but more accrual management. Unlike the analysis of the current paper, Bartonâ€™s study only considers the hedging function of derivatives and does not consider the earnings management function of derivatives. Focusing on the oil and gas industry, Pincus and Rajgopal (2002) also explore the interaction between accrual management and hedging. Their empirical result is partially consistent with Bartonâ€™s result. However, they emphasize that their result suggests a sequential process whereby the managers first decide how much to hedge and manage the accruals only during the fourth quarter, which weakens Bartonâ€™s substitution hypothesis. 9 Review of Earnings Management and Information Content Literature on earnings management is as vast as the ocean. There are numerous studies attempting to document the existence of earnings management, and a lot of research on when and why the managers manage the earnings. I am not so ambitious as to review all related literature, not to say there are already some good reviews of the earnings management literature, such as Schipper (1989), Healy and Wahlen (1999), Beneish (2001), and Lev (2003). Here I focus on the literature on "efficient" earnings management. For empirical studies, researchers usually use the market reaction to an earnings announcement to measure the information content in the earnings. Abnormal discretionary accruals are usually regarded as proxies for managersâ€™ manipulation and many studies focus on whether the market can "see through" the managed earnings. The hypothesis is that if the market is efficient, then the investors will not be fooled by the manipulation. There are further studies on who is more easily fooled (unsophisticated investors). The unspoken words here are that the manipulation of earnings is "bad," and it is just a garbling of the information. This opinion about earnings manipulation is even stronger among investors and regulators after the scandals of Enron and WorldCom. The SEC has been taking measures to fight earnings management. Walter P. Schuetze, a former chief accountant in the SEC, even proposes mark-to-market accounting to eliminate the manipulation of earnings. However, recently researchers began to question whether it is worth eliminating managersâ€™ manipulation. First, the elimination of discretion will shut the doors of communicating managersâ€™ private information to investors. Taken to the extreme, if we totally eliminate any manipulation and return to a mark-to-market accounting, then the existence of accounting is meaningless. Financial statements should be sources of information and communication tunnels between management and investors. If financial statements were reduced to be just records of the investorsâ€™ estimates 10 about the firmsâ€™ operating activities based on other information, then we did not "need" financial statements or accounting. Accrual accounting provides a tunnel for the managers to use their judgement and discretion to better communicate with the financial statements users. Beneish (2001) states that there are two perspectives on earnings management. One is the opportunistic perspective, which claims that managers seek to mislead investors. The other is the information perspective, which regards the managerial discretion as a means for managers to reveal to investors their private expectations about the firmâ€™s future cash flows. Similarly, Dechow and Skinner (2000) call for attention on how to distinguish misleading earnings management from appropriate discretions. They further indicate that it is hard to distinguish certain forms of earnings management from appropriate accrual accounting choices. Demski (1998) demonstrates that in a setting with blocked communication, when the managerâ€™s manipulation requires his high effort level, it may be efficient for the principal to motivate earnings management. If we eliminate discretion in order to put a stop to the "detrimental" earnings management, we may close the communication channel between the managers and the investors. Secondly, eliminating earnings management, even if earnings management merely garbles information, may be too costly. Liang (2003) analyzes equilibrium earnings management in a restricted contract setting and shows that the principal may reduce agency cost by tolerating some earnings management when the contract helps allocate the compensation risk efficiently. Arya, Glover and Sunder (2003) tell a story of "posturing," that when the commitment is limited and the information system is not transparent, allowing manipulation is more efficient than forbidding it. Demski, Frimor and Sappington (2004) show that assisting the manager to manipulate in an early period may help ease the incentive problem of a later period. In their model the principalâ€™s assistance reduces the managerâ€™s incentive to devote effort to further manipulation and induces the manager to devote more effort to production. 11 As stated in Arya, Glover and Sunder (1998), when the Revelation Principle is broken down (that is, when communication is limited, the contract is restricted, or commitment is missing), earnings management may be efficient. In this paper, in most cases the existence of earnings management in equilibrium comes from the violation of the unrestricted contract assumption, since I assume a linear contract. I also suppose an uneven productivity setting to induce earnings management, following a design in Liang (2003). This paper shows that, even if earnings management merely destroys information, sometimes it is not only inefficient to motivate truth-telling but also inefficient to take any measure to restrain earnings management, since restraining manipulation may be too costly. In the last chapter of this paper, I also include an analysis of informative earnings management (the forecast model), in which earnings management conveys the managerâ€™s private information. Review of LEN Frameworks Most of my analysis in this paper is in a LEN framework. LEN (linear contract, negative exponential utility function, and normal distribution) is a helpful technology for research in agency and has been employed in more and more analytical research. Among the three assumptions of the LEN framework, exponential utility and normal distribution have been widely used and accepted, while the linear contract assumption is more controversial. Lambert (2001) gives a good review on LEN. He summarizes three common justifications for the linear contracting setting. The first is that according to Holmstrom and Milgrom (1987), a linear contract is optimal in a continuous time model where the agentâ€™s action affects a Brownian motion process. However, it is not easy to fit their model into multi-action settings. The second justification is that the contracts in practice are usually simple, instead of in the complicated form of the optimal contracts from agency models. The argument against this justification, however, is that even in practice, contracts are not strictly linear. The third justification is 12 tractability. Linear contracts are usually not the optimal contracts, but they provide great tractability and help researchers explore some agency questions that were hard to analyze in the conventional agency models. For example, LEN is especially helpful in multi-action or multi-period agency problems. This is the most important reason that LEN has become more popular. However, as mentioned by Lambert, we achieve this tractability with a cost of restricting the generality. Nevertheless, except for some questions that cannot be addressed by linear assumptions such as the study on contract shapes, the LEN setting still provides plentiful insight. Feltham and Xie (1994) are among the first to employ LEN in analytical analysis. They focus on the congruity and precision of performance measures in a multidimensional effort setting, where the agent allocates his effort on more than one task. They show that with single measure, noncongruity of the measure causes a deviation from the optimal effort allocation among tasks, and noise in the measure makes the first-best action more costly. In their setting, the use of additional measures may reduce risk and noncongruity. There are some works on selecting performance measures for contracting purposes using LEN frameworks. Indjejikian and Nanda (1999) use a LEN framework to study the ratchet effect in a multi-period, multi-task contract. They show that in a two-period setting, when the performance measures are positively correlated through time, and when the principal cannot commit not to use the first period performance in the second period contracting, the agent is inclined to supply less effort in the first period, since a better first period performance increases the "standard" for the second period performance. To motivate the agent to work hard in the first period, the principal has to pay more for the first period. Indjejikian and Nanda also suggest that an aggregate performance measure may be better than a set of disaggregate measures, and consolidating multi-task responsibility to one agent may be better than specializing the responsibilities to avoid the ratchet effect. Autrey, Dikolli and 13 Newman (2003) model career concerns in a multi-period LEN framework. In their model, there are both public performance measures and private measures that are only available to the principal. Their work shows that the public measures create career concerns and help the principal reduce the compensation to the agent, while the private measures enable the principal to reward the agent more efficiently. They suggest that it is better to use a combination of both public and private measures in contracting. LEN technology is also employed in the research on valuation and accrual accounting. Dutta and Reichelstein (1999) adopt a multi-period LEN framework in part of their analysis on asset valuation rules. In a setting where the agentâ€™s effort affects the cash flows from operating activities, they show that incentive schemes based only on realized cash flows are usually not optimal since it is difficult for the principal to eliminate the variability in cash flow from financing activities. Discretionary reporting and earnings management are also among the topics explored using LEN frameworks. Christensen and Demski (2003) use a covariance structure to model reporting schemes (either conservative or aggressive) under a linear contract in a two-period setting. They discuss when reporting discretion is preferred to inflexible reporting and when it is not, and further explore the role of an auditor in this setting. They use an asymmetric piece-rate to model the incentive for the exercise of reporting discretion. Similarly, Liang (2003) uses a time-varying production technology and therefore uneven bonus schemes through time to explore earnings management. He studies the equilibrium earnings management in a two-period, multi-player (managers, shareholders, and regulators) setting. His work shows that a zero-tolerance policy to forbid earnings management may not be economically desirable. In this paper, LEN provides great tractability, and also induces earnings management. 14 Summary Prior research on derivatives explores the incentives for hedging, how hedging influences contracting, and the pros and cons of the recent derivatives disclosure regulations. Derivatives are popular instruments for hedging. However, the complexity of derivatives also makes them handy tools for managers to manipulate earnings. Up to now there is little theoretical research on the joint effect of the hedging function and the earnings management function of derivatives, though there is a lot of research on either hedging or earnings management. In addition, this chapter also provides a review of the LEN framework, which is a component of my following models to study the joint effect of hedging and manipulation. CHAPTER 2 BASIC MODEL To study the joint effect of hedging and earnings management through the use of derivatives, I use a two-period LEN model. A no-hedging, no-misreporting case is employed as the benchmark. The hedging option and the misreporting option then will be introduced into the benchmark to study the influence of hedging and manipulation. The Model The main model in this paper is a two-period model in a LEN framework. There is a risk neutral principal and a risk averse agent (manager). The principal tries to minimize her expected payment to the manager while motivating the manager to choose high as opposed to low actions in both periods. The managerâ€™s preference for total (net) compensation is characterized by constant absolute risk aversion, implying a utility function of u(S â€” c) = â€”e_r(5_^, where S is the payment to the agent, c is the managerâ€™s cost for his actions, and r is the Arrow-Pratt measure of risk aversion. Without loss of generality, the managerâ€™s reservation payment is set at 0. In other words, his reservation utility is â€” e_r^. Performance signals (outputs) are stochastic, and their probability is affected by two factors: the managerâ€™s action and some exogenous factor. The managerâ€™s action is binary. In each period, the manager either supplies low action, L, or high action, H, H > L. Without loss of generality, L is normalized to zero. The managerâ€™s personal cost for low action is zero. His personal cost for high action is C > 0 in each period. The principal cannot observe the managerâ€™s actions. An exogenous factor also affects realized output. The effect of this exogenous factor on the output can be 15 16 hedged at least partially by using derivatives. Neither the principal nor the manager can foresee the realization of the exogenous factor. Here, "output" represents a noisy performance measurement of the managerâ€™s action levels (e.g., earnings); "output" does not narrowly refer to production and can be negative. I use X\ to represent the output for the first period, and x2 to represent the output for the second period. Basic Setup Assume X\ â€” k\a\ + â‚¬\ and x2 = k2a2 + e2, with Â«, E {H, 0}, i E {1,2}. aÂ¿ represents the action level for period i. k\, k2 are positive constants and represent the productivity in the first and the second periods, respectively. Suppose k\ > k2. The uneven productivity follows a design in Liang (2003). The different productivity induces different bonus rates through time and is important for the ensuing of earnings management. (The assumption ki > k2 is relaxed in Chapter 5.) The vector [ei,e2] follows a joint normal distribution with a mean of [0, 0]. There is no carryover effect of action, and the outputs of each period are independent of each other.1 If the outputs are not hedged, the covariance matrix of [ei,e2] is Â£ = a2 0 0 a2 . If the second period output is hedged (as I discuss in a later section, any such hedge is confined to the second period), the matrix is Â£<Â¿ = a2 0 0 a2 a2d < a2. The hedging process is stylized with a mean preserving spread structure: assuming the same action level, the hedged production plan has a lower variance, <72, than that of the unhedged one, a2, though they share the same mean. Thus the unhedged production plan is a mean preserving spread of its hedged counterpart. In this way, hedging lowers the variance of output due to the uncontrollable exogenous factor and reduces the noisy output risk. This structure captures the risk reduction theme of Rothschild and Stiglitz (1970), and also offers tractability. 1 The conclusions in this paper persist when the outputs have a non-zero covariance. 17 The managerâ€™s contract or compensation function is assumed to be "linear" in the noted output statistics. Specifically, S = S(x 1,2:2) = W + olx 1 + /3x2, where W is a fixed wage, and a and ,6 are the bonus rates respectively assigned to the first period output, x\, and the second period output, 22- Benchmark The benchmark is a public-output, no-hedge-option model. There is no option to hedge in this benchmark, and earnings management (misreporting actual outputs) is impossible since the output for each period is observed publicly. To solve the principalâ€™s design program in this benchmark, I start from the second period. To motivate the managerâ€™s high action in the second period, the principal sets the contract so that the managerâ€™s certainty equivalent, when he chooses high action, is at least as high as that when he chooses low action, for each realization of X\. Denote the managerâ€™s certainty equivalent when he chooses a-Â¿ given x\ at the beginning of the second period as CE2{a2\^1), the incentive compatibility constraint for the second period is CE2{H-,x 1) > CE2(0â€˜,xl)y xx (IC2) With Xi known and x2 a normal random variable with mean k2a2 and variance cr2, it is well known that CE2(a2]Xi) = W + ax\ + ft k2a2 â€” c(ai,a2) â€” Â¿/32 as W + olx\ + (3k2H - C - %p2cr2 > W + ax 1 - Â§/32 Denote the managerâ€™s certainty equivalent at the beginning of the first period when he chooses Â«1 followed by a2 regardless of x\ as CE\{a\, a2). To motivate a\ = H given high action in the second period, the incentive compatibility constraint for the first period is 18 CE1(H;H)>CEl(0;H) (ICl) If a2 = H. regardless of x\, (IC2) is satisfied, then S(:ri,Â£2) is a normal random variable with mean W + akxax + Pk2H and variance a2a2 + p2a2. Thus (ICl) implies W + aki H + pk2 H - 2C - Â§ {a2 a2 + /? V) > W + f3k2H-C-% (a2 a2 + /32a2), which reduces to a > 7^7. The individual rationality constraint requires the managerâ€™s certainty equivalent when he chooses high actions in both periods is not lower than his reservation wage, normalized to 0. The individual rationality constraint therefore is CEX{H;H) > 0 (IR) Expanding (IR), we get W + akxH + f3k2H â€” 2C â€”^(a2a2 + /32a2) > 0. The principal minimizes her expected payment to the manager, E[W + a(kxH + ci) + Â¡3(k2H + e2)] = W + akxH + 0k2H. Her design program in this benchmark model is Program [zl] (IR) (ICl) min W + akxH + f3k2H W, qi(9 s. t. W + akxH + f3k2H - 2C -\[a2a2 + /?V) > 0 a ^ 1777 /5>rr77 k2H (IC2) The individual rationality constraint must be binding, as otherwise the principal can always lower W. Thus, the optimal fixed wage must be â€”ak\H â€” f5k2H + 2C + (j(a2cr2+/32 Â¡32o2) subject to the two incentive constraints.2 The optimal fixed wage is chosen to ensure that the individual rationality constraint binds. I therefore focus on the bonus rates in the optimal contracts in our analysis. Denote a*4 as the optimal first period bonus rate and /3*A the optimal second period bonus rate, we now have 2This result has been shown in, for example, Feltham and Xie (1994). 19 Lemma 2.1: The optimal contract in the benchmark model exhibits a*A = -Â¡~ and r* â€” Pa â€” k2H- Proof: See the Appendix. In a full-information setting the principal only needs to pay for the reservation wage and the personal cost of high actions, 0 + 2C. In the present benchmark setting, the principal needs to pay 0 + 2C + ^{a*Aa2 + /T42 differential of \[a*Ao2 + /3*Aa2). Next I introduce the hedging and earnings management options. Hedging and Earnings Management Options Hedging Option Initially suppose the second period output can be hedged, but no possibility of managing earnings is present. In practice, a hedging decision is usually made to reduce the risk in the future output. To capture this feature, assume that the hedging decision is made at the beginning of the first period, but the hedge is for the second period output only and doesnâ€™t influence the first period output. Recent FASB regulations on derivatives, e.g. SFAS No. 133, require that firms recognize the ineffective portion of hedges into earnings even before the settlement of the derivatives.3 In this chapter I do not consider the recognition in earnings from unsettled derivatives. (That is, I assume hedging only influences the output of the second period, when the hedge is settled.) The estimation of the hedgeâ€™s ineffectiveness involves earnings management, and I will address the manipulation associated with the use of derivatives later. 3 Consider a fair value hedge as an example. At the date of financial reporting, if the increase/decrease in the fair value of the derivative doesnâ€™t completely offset the decrease/increase in the fair value of the hedged item, the uncovered portion is regarded as the ineffective portion of the hedge, and is recognized into earnings immediately. However, this gain or loss from unsettled derivatives is not actually realized, and the estimation of the hedgeâ€™s ineffectiveness is usually subjective (for the evaluation of derivativesâ€™ fair value is usually subjective). 20 Centralized-hedge case First, consider a centralized-hedge case, where the principal has unilateral hedging authority. (Later in this chapter I will delegate the hedging option to the manager.) Notice that the benchmark is identical to the case here if the principal decides not to hedge. If the principal hedges, the principalâ€™s design program changes slightly from the one in the benchmark. The expected payment is still XV + ak\H + fik2H. The incentive constraints for the manager remain the same, since the hedging decision is not made by the manager and the action choice incentives are unaffected by hedging activities. However, the individual rationality constraint changes to be W + ak\H + pk2H - 2C ~^(a2cr2 + p2a2d) > 0. The principalâ€™s design program in the centralized-hedge model when she hedges is min W + akiH + Â¡5k2H Program [B] W,ot,/3 s. t. W + ak1H + pkiH-2C -Â§(aV +p2a2d) > 0 (IR) Â« > Kh (IC1) P > iSh (IC2) I use ct*B,/3*B to denote respectively the optimal bonus rates in the first and the second periods in Program [B\. Paralleling Lemma 2.1, I immediately conclude Lemma 2.2: The optimal contract in the centralized-hedge model exhibits a*B = -Â¡^jÂ¡ and Pb = tSh- Proof: See the Appendix. The optimal contract shares the same bonus rates with that in the benchmark, because the managerâ€™s action affects the output mean, while hedging only affects the output risk. As implied by the (IR) constraint, when there is no hedging option or when the principal does not hedge, the principalâ€™s expected payment is 2C+^(a^a2+ PaCt2), while its counterpart with hedging is 2C + ^(a*?a2 + P*2Â°d)- With hedging, 21 her expected cost is reduced by |/3^2( represent the strategy of hedging, we have Lemma 2.3: The principal prefers d â€” 1 in the centralized-hedge model. Proof: See the above analysis. The principalâ€™s expected cost is lower when she hedges, because hedging reduces the noise in using output to infer the managerâ€™s input, and thus provides a more efficient information source for contracting. Therefore, the compensating wage differential is reduced. Delegated-hedge case Next, I change the setting into a delegated one. In practice, managers, not shareholders, typically decide on the use of derivative instruments, since the managers usually have expertise in financial engineering. To capture this fact, I change the model so the manager, rather than the principal, makes the hedging decision. This decision is made by the manager at the beginning of the first period, but hedges the second periodâ€™s output. The time line of this delegated-hedge model is shown in Figure 2-1. It has been shown that when the principal makes the hedging decision, she prefers hedging since hedging reduces the compensating wage differential. The question now, is whether hedging is still preferred when the hedging decision is delegated to the manager. With the hedging decision delegated to the manager, although the manager has the option not to hedge, the manager will always choose to hedge. This is because hedging reduces the output variance and therefore reduces the managerâ€™s compensation risk derived from noisy output signals. To illustrate this conclusion, I use CE\(a\, d;a2) to denote the managerâ€™s certainty equivalent at the beginning of the first period when he chooses ax and d in 22 the first period and chooses a2 in the second period. By hedging, CEi(ci\, 1;g2) =W + akiÃ¼i + fk2a2 â€” c(ai, a2) â€” ^(oc2a2 + /32af). If the manager doesn't hedge. CEi(ax, 0;a2) = W + akiax + f5k2a2 - c(al5 a2) - Â¿(aV2 + /32 Lemma 2.4: For any action choice, the manager always prefers d = 1. Proof: See the above analysis. As with the centralized model, allowing the manager to hedge the output is efficient. The manager gladly exercises this option and in equilibrium the compensating wage differential is reduced. Proposition 2.1: Hedging is efficient regardless of whether the manager or the principal is endowed with unilateral hedging authority. Proof: See the analysis in this section. In the LEN framework, hedging lowers the output variance but has no effect on the output mean, while the manager's action affects the output mean but not the variance. Therefore, there is separability between the action choices and the hedging choice. The optimal bonus rates are not affected by the hedging choice. Misreporting Option To this point, I have focused on settings where the realized output is observed publicly. Here I introduce the option to manipulate performance signals. I presume hedging is not possible in this subsection, but will combine both hedging and earnings management options later in the next chapter. Suppose the output for each period is only observable to the manager. The manager chooses the first period action level, Â«i G { //, 0}, at the beginning of the first period. At the end of the first period the manager observes privately the first-period output X\. He reports x\ G {xj,Xi â€” A} to the principal and chooses his action level 23 for the second period, a2 6 {H, 0}. At the end of the second period, again the manager observes privately the second-period output, x2, and reports x2 = X\â€”X\ + x2. The principal observes the aggregate output of the two periods at the end of the second period and pays the manager according to the contract. The linear contract here becomes S = W + axi + (3x2. The manager may have an option to misreport the output by moving A from the first to the second period. (A can be negative. Negative A implies that the manager moves some output from the second to the first period.) Assume the manager manipulates at a personal cost of |A2, which is quadratic in the amount of manipulation.4 The manager faces the misreporting option with probability q, and he doesnâ€™t know whether he can misreport until the end of the first period.5 I use m = 1 to represent the event that the misreporting option is available, and m = 0 to represent its counterpart when the misreporting option is unavailable. The time line is shown in Figure 2-2. Notice in the benchmark case of Lemma 2.1 where there is no option to misreport, the bonus rates for the two periods are not equal, and a*A = -Â¡^jj < /3*A = If the outputs were observed privately by the manager, the manager would have a natural incentive to move some output from the first to the second period, since he receives greater compensation for each unit of output produced in the second period. If m = 1, the managerâ€™s certainty equivalent at the beginning of the second period becomes W + axi + /3k2a2 + (/3 â€” a) A - |A2 - c(ai, a2) - %/32cr2. Notice that with a linear contract, the managerâ€™s manipulation choice is separable from his action choices and the output risk. This separability implies that the optimal 'â€™The quadratic personal cost follows a similar design in Liang (2003). It reflects the fact that earnings management becomes increasingly harder when the manager wants to manipulate more. 3 The manager, even though determined to manipulate, may not know whether he can manipulate at the begining, but has to wait for the chance to manipulate. 24 "shifting" occurs where jÂ¿\{f3 - a) A â€” |A2] = 0, or A* = Â¡3 - a. The only way to deter manipulation in this setting is to set a = Â¡3. I again solve the principalâ€™s design program starting from the second period. Since the manager always chooses A* = (3 â€” a as long as he gets the misreporting option, we use CE2(a2, A*; xi, m = 1) to denote the managerâ€™s certainty equivalent at the beginning of the second period when he gets the misreporting option and chooses 02 after privately observing the first period output X\. We use CE2(a2- X\,m = 0) to denote the managerâ€™s certainty equivalent when he doesnâ€™t get the misreporting option. The incentive constraints for the second period are CE2(H, A*;xi, 1) > CE2(0. A*;xi, 1), and CE2(H; aq, 0) > CE2(0; aq, 0), Vaq. With the noted separability, it is readily apparent that both constraints collapse to /3 > just as in the benchmark. I use CÂ£â€™i(a1;a2) (to distinguish from C'Â£â€™i(ai;a2) in the benchmark) to denote the managerâ€™s certainty equivalent at the beginning of the first period when he chooses a\ followed by a2 in the second period. At the beginning of the first period, since m is random, the managerâ€™s expected utility at the beginning of the first period is: (1 â€” q)Eu[\\' +ej)-(-/3(A;2(i2 + c2) â€” c(fli,a2)] -\-qEu[W -t-ck(oti -f-Cjâ€” A*) +(3(k2a2 + e2 + A*) â€” c(alta2) â€” ^A*2]. Therefore, CE\(ai\a2) is the solution to u(CE\(a\, a2)) = (1 â€” q)Eu[ Ik + a(AqGq+ei) + (3(k2(i2 + e2) â€” c(ai, a2)] +qEu[W + a(fcidi + Ci â€” A*) +(3(k2a2 + e2 + A*) â€”c(aj, a2) â€” |A*2] = _ q'je-r[W+<*kiai+0k2a2-c(al,a2)-ii(a2cT2+/32(T2)] __qe-rlVV+akiai+0k2a2-c(ai,a2)-^(a2a2+02cr2)-^Aâ€™'2+(0~a)Aâ€™â€˜} â€” _e-dW+afciai+/?fc2a2-c(ai,a2)-5(a2<72+/32 Thus, â€”r(CÂ£'i(a1; a2)) = â€” r[W + ak\a\ + /3k2a2 â€” c(ai,a2) â€” |(a2 Â¿(aV2 + P2a2) - i ln[(l - q) + qe~^~a)2\ 25 Comparing CE\{a\, a2) with CE\{a\,a2) in the benchmark, we have CEx(ax; a2) = CEi(ai; a2) - J ln[(l - q) + Importantly, now, the agentâ€™s risk premium reflects the summation of the earlier risk premium, due to the variance terms, and an additional component due to the shifting mean effects introduced by earnings management. The additional component comes from the extra bonus from manipulation and the higher uncertainty of the compensation. Given a2 = H, the incentive compatibility constraint for the first period is CEi(H,H) > CEx(0;H). Again, thanks to the separability between the action choice and the manipulation amount choice, this constraint reduces to a > just as in the benchmark case. The individual rationality constraint in this model is CEX(H; H) > 0, or PT + akxH + (3k2H - 2C -Â§(aV + /3V) -Â¿ln[(l - q) + ^e-fC^-^)2l] > 0. The principalâ€™s expected payment to the manager, upon substituting the managerâ€™s A choice, is (I â€” q)E[W + at(k\H + Cj) + (3{k2H + 62)] -\-qE[W + cx(k\H -t- ei â€” (/5 â€” oc)) + 0(k2H + e2 + (/3 â€” a))] = (1 - q)[W + akxH + /3k2H] +q[W + a(kxH - (Â¡3 - a)) + p{k2H + (0 - a))] = W + akxH + (3k2H + q(0 - a)2. Now the principalâ€™s design program in this misreporting model is: min W + ock\H -f (3k2H + q(fi â€” a)2 Program [C] W,a,0 S. t. W + akxH + Pk2H - 2C -\[pc2o2 + /?V) -J ln[(l - q) + qe~^-a^] > 0 a > c k-iH (IR) (IC1) (IC2) 26 Similar to the previous models, here the individual rationality constraint must bind, and the principalâ€™s expected cost can be expressed as 2C +iÂ¿{ct2cr2+(32a2) +; ln[(l - q) + qe~^3~a)2} + q(0 - a)2. For later reference, the reduced program is written below. min |(a2cr2 + /32cr2) + Â£ ln[(l - q) + qe 2^ Q)2] + q(/3 - a)2 Program [C'\ Q,|S S. t. Q > ^ (IC1) (IC2) Define a*c. 3*c as the optimal bonus rates in Program [C ], we have the following results. Proposition 2.2: The optimal contract in the misreporting model exhibits Corollary 2.1: When q is sufficiently low, the optimal contract in the misreporting model exhibits a*c = and fi*c <* _ _c_ c k2H- Corollary 2.2: When q is sufficiently high and k\ is sufficiently large, the optimal contract in the misreporting model exhibits a*c > and (3*c = Proof: See the Appendix. Compare Program [C ] with the benchmark: when q = 0. we revert to our benchmark case; however, when q > 0, the misreporting option introduces a strict loss in efficiency. The principal must compensate for the managerâ€™s risk from the imcertain misreporting option. There is also a bonus payment effect for the manipulated amount of output. In addition, the principal may choose to raise the first period bonus rate, which increases the riskiness of the unmanaged compensation scheme. Note in this model we always have a*c < ffic. Although the misreporting option merely garbles the information and does not benefit the principal, it is never efficient for the principal to motivate truth-telling and completely eliminate the managerâ€™s incentive to misreport by setting a = Â¡3. Instead, it is efficient to tolerate some misreporting. This surprising fact is also shown in Liang (2003). Liang documents 27 that the optimal contract exhibits a*c (3*c, while the analysis in the present paper provides more details on the optimal contact. More surprisingly, the principal not only tolerates some misreporting by setting (Xq < (3q, but sometimes she even maintains the bonus rates at the levels in the benchmark case where there is no misreporting option. Although an uneven bonus scheme leads to manipulation, it may not be efficient for the principal to adjust the bonus scheme to restrain manipulation. The reason for this conclusion is the following. Since the induced misreporting is given by A* = Â¡3 â€” a, the dead weight loss of misreporting can be reduced by lowering /? â€” a. To lower Â¡3 â€” a, the principal either lowers 3 or raises a. However, /3 has a binding lower bound at and the principal cannot reduce (3 below that bound. Thus the optimal Â¡3 remains at its bound. By raising a, the principal reduces the dead weight loss of misreporting, but simultaneously increases the riskiness of the unmanaged compensation scheme (|(a2a2+/3V2) goes up). Hence there is a trade-off. When the chance of misreporting is small (q is sufficiently low), the principal finds it inefficient to raise the bonus rate, since the corresponding reduction in the misreporting dead weight loss does not outweigh the increase in the riskiness of the unmanaged compensation scheme. On the other hand, when the probability of misreporting is sufficiently high, the losses from misreporting constitute a first order effect. In this case, the principal may find it optimal to raise the first period bonus rate. In addition, when the first period productivity ki is high, the lower bound for the first period bonus is low, and the principal is more willing to raise the first period bonus above the lower bound to reduce the misreporting dead weight loss. Table 2-1 shows a numerical example to illustrate Proposition 2.2, and Corollaries 2.1 and 2.2. In this numerical example, I fix the values of the cost of high action C = 25, high action level H = 10, output variance a2 = 0.5, risk aversion 28 r = 0.5. and the second period productivity k2 = 15. I focus on how the optimal contract changes with the misreporting probability q and the first period productivity k\. When q is very small (q = 0.01), the optimal contract has both a*c and Â¡3*c at their lower bounds. However, when q is high (q = 0.9) and k\ is large (k\ = 200), the first period bonus rate a*c in the optimal contract deviates from its lower bound c kiHâ€™ For simplicity, I use the case q = 1 to explore more details on the misreporting option. Ubiquitous misreporting opportunities (q = 1) When q = 1, Program [C] becomes min W + ak\H +/3k2H + (ft â€” a)2 Program [C(q = 1)1 W,a,f) s. t. W + akiH +/3k2H -2C + \{/3 - a)2 -Â§(a2a2 + 02a2) > 0 (IR) â€œ > iSf (ici) 0 > Ã© (IC2) The situation when q = 1 is special, because there is no uncertainty about the misreporting option. The principal knows the manager will always shift Â¡3 â€” a to the second period to get additional bonus income of (/3â€”q)A* = (/?â€”a)2. Responding to this, she can cut the fixed wage by ((3 â€” a)2 to remove the bonus payment effect. However, although the principal removes fully the certain bonus payment from her expected payment to the manager, she must compensate for the managerâ€™s dead weight personal cost of misreporting. Define o*Cl,(3*Cl as the optimal bonus rates for the misreporting model when <7 =1. We have the following result. Proposition 2.3: When q = 1, the optimal contract in the misreporting model exhibits Qci= and Pci= bÂ¡H */ ^ Mi + â„¢2); aci = J^h an<^ Pci = otherwise. 29 Proof: See the Appendix. If the productivity of the two periods is very different (that is, k\ is much higher than k2), the naive bonus rates for the two periods are very different too, and the manager prefers to move a great amount of output between periods to take advantage of the uneven bonus scheme. In this case, the principal raises the first period bonus rate to make the bonus scheme more even to reduce the dead weight loss of misreporting. However, keep in mind that this brings a cost of higher risk premium for unmanaged noisy output. Unexpectedly, even when q = 1, in some cases the principal still maintains the bonus rates at the levels as in the setting where there is no misreporting option. The optimal contract may still exhibit {ol*C\iPci) â€” {qAâ€™0a)- other words, even when the misreporting opportunities are ubiquitous, it may still be optimal not to restrain misreporting. With an attempt to restrain misreporting by raising a from its lower bound, the increase in the riskiness of the unmanaged compensation scheme may outweigh the reduction in the dead weight loss of misreporting. It is a general belief of investors and regulators that we must take measures to address detrimental earnings management. In September 1998, Arthur Levitt, Chairman of SEC, warned that earnings management is tarnishing investorsâ€™ faith in the reliability of the financial system, and kicked off a major initiative against earnings management. From then on, the SEC has taken a variety of new and renewed measures to fight earnings management. However, according to our results in Propositions 2.2 and 2.3, in some cases it is optimal not to take any measure to restrain earnings management. Even when misreporting opportunities axe ubiquitous, it may be better just to live with misreporting instead of taking any action to fight it. This conclusion may sound counter-intuitive and cowardly, but is in the best interest of investors. 30 Summary This chapter shows that in a LEN framework, hedging option reduces the compensating wage differential for the principal and reduces the compensation risk for the manager. On the other hand, the introduction of a misreporting option complicates the agency problem. Surprisingly, although manipulation is detrimental to the principal, sometimes it is not efficient to take any action to restrain earnings management. 31 1st Period 2nd Period Manager chooses ai E {i/,0}, and dÂ£ {0,1}. xx observed publicly. Manager chooses 02 E {H, 0}. X2 observed publicly. Manager gets paid. Figure 2-1: Time line for delegated-hedge model 1st Period 2nd Period Manager observes privately x2. x2 reported. (Principal sees aggregate output.) Manager chooses Manager observes ai E {H, 0}. privately X\ and m. X\ reported. Manager chooses a2 G {H, 0}. Figure 2-2: Time line for misreporting model Table 2-1: Numerical Example for Proposition 2.2, Corollaries 2.1 and 2.2 ki Q c k\H c k2H a*c Pc 20 0.01 0.125 0.1667 0.1250 0.1667 n* â€” R* â€” aC â€” kiHâ€™PC k2H 200 0.9 0.125 0.1667 0.1304 0.1667 n,* Sâ€” R* â€” aC > kxH'Pc ~ k2H CHAPTER 3 HEDGE-MISREPORT BUNDLE MODEL The last chapter analyzes the hedging and misreporting options respectively. Now I bundle the delegated hedging option and the misreporting option. This bundling allows us to study the joint effect of the hedging function and manipulation function of derivatives. Bundled Hedging and Misreporting Options Suppose at the beginning of the first period, the manager chooses his action level cti G {H. 0}. and has the option to hedge. Hedging again only affects the output in the second period but the hedging decision is made at the beginning of the first period. Further, suppose the hedging option is bundled with the misreporting option. If and only if the manager chooses hedging, with probability q can he later misreport the output by moving some amount of output between periods. This "hedge-misreport bundle" setting reflects the current concern that, managers use derivatives to reduce risks but can also use the derivatives as tools of earnings management. At the end of the first period the manager observes privately the first-period output xx, and at this point he observes whether he can misreport (if he chose hedging). Similar to the misreporting model, if the manager gets the misreporting option, he shifts 3 â€” a from the first to the second period. The time line of the hedge-misreport bundle model is shown in Figure 3-1. Similar to Lemma 2.4 in the last chapter, here, the manager always prefers to hedge. To illustrate this, I use CEi(ax, d; a2) to represent the managerâ€™s beginning certainty equivalent when he chooses ai and d followed by Â«2- When the manager chooses to hedge, CEx(au 1; a2) = W -\-akxax +/3k2a2 -c(ai,a2) - Â§(qV2 + /?2erÂ¿) - 7 hi[(l â€” q) + qe~2^-al2l]. When the manager does not hedge, CE\{ax, 0; a2) = W + 32 33 akiCL\ + (3k2a2 â€” c^, 02) â€” Â§(a2<72 + Â¡32a2). It is easy to verify that CE\{a\, l;a2) > CE\(a,\, 0; 02). That is, the manager always hedges in this bundled model. Therefore the bundled model is identical to the misreporting model with the second period output hedged (in other words, with the second period output variance reduced to ad). The principalâ€™s design program in this bundled model is min W + akiH +/3k2H + q(/3 â€” a)2 Program [D\ W,a,0 S. t. W + akiH + (3k2H - 2C -\{oc2a2 + (32a2) -J ln[(l - q) + qe~W-a? 1] > 0 (IR) Â«>Kh (IC1) Â£ > ife (IC2) Again, Program [D] can be reduced to the minimization of %(a2a2 + ft2 a d) + Mn[(l - q) + qe~^~a^\+ q(/3 â€” a)2 subject to the incentive constraints. For the convenience of later analysis. I show the reduced program below, min ^(a2a2 + /32aÂ¿) + - ln[(l â€” q) + qe~^~a^2]+ q(/3 â€” a)2 Program [D'\ OL$ s.t.a>T^ (IC1) 0 > jSh (IC2) It is readily verified that the optimal bonus rates in the bundled model are identical to those in the misreporting model, since the managerâ€™s action choices do not depend on his hedging choice. However, compared with the misreporting model, the principalâ€™s expected cost is reduced by ^/32(a2 â€” cr2d), thanks to the hedging option. The principal does not need to motivate the manager to hedge, since the manager always exercises the hedging option. Although the hedging option and the misreporting option both affect output signals, they affect the signals in different ways. The hedging option influences output signals through variances. The greater is the reduction in the noisy outputâ€™s variance (a2 â€” o2d), the more beneficial is the hedging option. On the other hand, the 34 misreporting option influences output signals through means. With the misreporting option, the manager shifts 3*D â€” a*D from the mean of the first period output to the mean of the second period output. The amount of manipulation f3*D â€” a*D and the increased compensating wage differential due to misreporting depend on a host of factors, including the misreporting probability q, the action productivity, and rcr2. In addition, note that although we target earnings management associated with the use of derivatives, the analysis of the influence on performance signals from earnings management holds for general earnings management activities. Whether to Take the Bundle The hedge-misreport bundle is a mixture of "good" and "bad." As analyzed in the prior chapter, the hedging option alone, no matter whether centralized or delegated, is always preferred, since it lowers the output variance and reduces the compensating wage differential. However, the misreporting option complicates the agency problem. It is just a garbling of information and reduces the reliability of performance signals. In their classic article, Ijiri and Jaedicke (1966) define the reliability of accounting measurements as the degree of objectivity (which uses the variance of the given measurement as an indicator) plus a bias factor (the degree of "closeness to being right"). In their terms, we say that the hedging option improves the objectivity of performance signals, and therefore improves the reliability of the signals. On the other hand, the misreporting option increases the bias by shifting output between periods, and reduces the reliability of performance signals. If the principal faces a take-it-or-leave-it choice on the hedge-misreport bundle, she needs to see whether the increase in the reliability of performance signals from the hedging option exceeds the decrease in the reliability from the misreporting option. Lemma 3.1: When q is sufficiently low, the hedge-misreport bundle is preferred to the benchmark. 35 Lemma 3.2: When q is sufficiently high and k\ is sufficiently large, the hedge-misreport bundle is preferred to the benchmark only if a2 â€” ad is sufficiently large. Proof: See the Appendix. Table 3-1 illustrates numerical examples for the above lemmas. I suppose the cost of high action C â€” 25, high action H = 10, risk aversion degree r = 0.5, and the second period productivity ^ = 1.5. From the numerical examples, we see when q is sufficiently low (q = . 1), the principal prefers the bundle. While when q is sufficiently high (q = .8) and k\ is sufficiently large (k\ = 5), the principal does not prefer the bundle if a2 - a'd is small (a2 â€” ad = .25). She prefers the bundle when a2 â€” ad is sufficiently large (a2 â€” ad = .6). When the probability that the manager can misreport, q, is sufficiently low, misreporting is of limited concern. The increase in agency cost due to the misreporting option is outweighed by the reduction in agency cost due to hedging, and it is optimal for the principal to take the hedge-misreport bundle. With high probability of misreporting option and high first period productivity hi, however, the misreporting option in the bundle can impose severe damage and greatly increases the compensating wage differential. In this case, the principal admits the hedge-misreport bundle only when the benefit from hedging is sufficiently large. That is, only when the hedging option greatly reduces the noise in the output signals (a2 â€” od is sufficiently large) does the principal take the bundle here. Now focus on the q â€” 1 case. From Program [D'\, when q = 1, the program becomes min Ua2a2 + P2cr2d) +\(0 - a)2 Program [D' (q =1)] a,(3 S. t. a > (IC1) 0 S SÃ (IC2) Define a*D1, as the optimal bonus rates in the bundled model when q = 1, we have 36 Lemma 3.3: When q = 1, the optimal contract in the hedge-misreport bundle model exhibits abi = T^iSh and P*di = -Â£h */ ^ Ml + nr2); a*D1 = and P*di = ÃÂ£h otherwise. Proof: See the Appendix. As mentioned earlier, due to the separability between the managerâ€™s hedging choice and his action choices, the optimal bonus scheme in the bundled model is identical to that in the misreporting model. Proposition 3.1: When q = 1, (1) if k\ > k2( 1 + ra2), the hedge-misrepori bundle is preferred to the benchmark when a2-(l+rg2)(<72â€”a2) fcj (2) if k\ < k2(l + ra2), the bundle is preferred to the benchmark when (fcl-*a)a > r(a2- Proof: See the Appendix. Proposition 3.1 provides a detailed analysis on the trade-off between the benefit from the hedging option and the cost from the misreporting option when a) q= l. First, for both the cases of ki > k2( 1 + ra2) and ki < k2(l + ra2), the hedge-misreport bundle is more likely to be preferred (in other words, condition (a) or (b) is more likely to be satisfied) when cr2 is high.1 Intuitively, when the unhedged output signals are very noisy, the principal has a strong preference for hedging to reduce the noise and is more likely to take the bundle, regardless of the accompanied cost of misreporting. â€˜Define Q = %7w) 37 Second, for both cases, it is readily verified that conditions (a) and (b) are more likely to be satisfied when the Arrow-Pratt degree of risk aversion, r, is high. When the manager is very risk averse, the principal must pay a high compensating wage differential to the manager for the noisy output signals. Thus, the principal would like to reduce the noise in output signals and so has a strong preference for hedging. Hence she is more likely to take the hedge-misreport bundle regardless of the accompanying cost of misreporting. Third, for both cases, the harm from misreporting behavior is smaller when k\ and k2 are similar in magnitude, (hi and k2 are similar in magnitude implies the bonus rates can be set closer, and the potential damage from misreporting is small.) The more similar are k\ and k2, the more likely is condition (a) or (b) to be satisfied, hence the more likely is the hedge-misreport bundle to be preferred. Fourth, for both cases, the benefit from hedging is higher when hedging greatly reduces the noise in output signals (that is, when a2 â€” a2d is large). The more the hedge can lower the second period output variance, the more likely is condition (a) or (b) to be satisfied, hence the more likely is the principal to prefer the bundle. The numerical examples in Table 3-2 illustrate these comparative static observations. We see from the examples that the principal is more likely to take the bundle when cr2 â€” a2d is large, cr2 is high, r is high, or k\ is close to k2. Summary A hedge-misreport bundle is used to model the two-edged feature of derivative instruments in this chapter. I analyze the trade-off between the improvement of performance signalsâ€™ objectivity brought by hedging and the increase in the performance signalsâ€™ bias due to earnings management. With a LEN framework, hedging makes it easier for the principal to infer the managerâ€™s action from output signals, and thus helps lower the compensating wage differential. In addition, hedging is efficient regardless of whether the manager or the principal is endowed with unilateral hedging 38 authority. On the other hand, earnings management merely garbles information. It is also shown that hedging and earnings management influence performance signals from different angles, and their net influence depends on various factors. 39 1st Period 2nd Period Manager chooses Manager observes privately x2 observed privately. Oi E {i/,0}, X\ and m (if chose d = 1). x2 reported. d E {0,1} x\ reported. Manager (Principal sees chooses a2 E {H, 0}. aggregate output.) Figure 3-1: Time line for hedge-misreport bundle mode Table 3-1: Numerical Examples for Lemma 3.1, 3.2 parameters principalâ€™s expected cost benchmark ? bundle 9=1 kx =3 a2 - aÂ¿ = .25 50.4340 -< 50.2977 q = -8 /cj =5 a2 - a2d = .25 50.3785 >- 50.4454 ? = â€¢ 8 =5 a2 - = .6 50.6056 50.5239 40 Table 3-2: Numerical Examples for Proposition 3.1 parameters key parameters principalâ€™s expected cost benchmark ? bundle r = .5 ki= 2 a2 = .75 (cr2 high; a'2 â€” high) 50.8138 -< 50.5534 k2 = 1.5 a\ = .25 cr2 = .30 ( 50.3548 ki= 2 k2 = 1.5 r = .9 (r high) 50.9766 50.7509 a2 = .5 <73 = .25 r = .01 (r low) 50.0109 50.0104 ki = 1.6, k2 = 1.5 r = .5 (k\,k2 close) 50.6524 50.4842 a2 = .5 <72 = .25 k\ = 5, kâ€˜2 â€” 1.5 50.3785 50.4514 (k\, k2 not close) CHAPTER 4 MANIPULATION RESTRAINED BY HEDGE POSITION In the hedge-misreport bundle model in Chapter 3, a hedging option is bundled with a misreporting option, but the influence on the outputs from misreporting is separable from the effect of hedging. In this chapter, a stronger bond is tied between hedging and misreporting. This stronger bond reflects the fact that greater use of derivatives can provide expanded opportunities for earnings management. Cost of Earnings Management Firms' risks involve many uncontrollable factors, such as interest rate changes, foreign exchange rate changes, credit defaults, and price changes. Reducing firmsâ€™ risks more effectively requires more hedging, while the increase in the use of derivatives, in turn, makes it easier to manipulate earnings. When the manager reduces risks more effectively with more derivatives, he also obtains additional ways to manipulate. In other words, the cost of earnings management is lowered. To reflect the association between the cost of earnings management and the extent of hedging, I suppose the managerâ€™s personal cost of earnings management is ^ (ggjpr) A2. To simplify the notation, define D = a2 - a2d, and express the manipulation cost as The personal cost of manipulation is still quadratic in the amount of manipulation. In addition, now the marginal cost of manipulation is associated with the hedge position. I call this new setting the "strong bundle" model. As in the previous model, I suppose the manager can manipulate only if he hedges. Without hedging, there is no way to manipulate earnings, or it is extremely costly to manipulate. "Strong Bundle" Model With personal cost of manipulation Â¿A2, the managerâ€™s optimal manipulation amount will again occur when the marginal cost of manipulation equals the marginal 41 42 benefit, that is, when This implies A* = D(fi â€” a). As in the previous hedge-misreport bundle model, suppose the manager gets the misreporting option with probability q given that he hedges, and he does not know whether he can misreport until the end of the first period. If he obtains the misreporting option, he will shift D(p â€” a) from the first to the second period to capture additional bonus. Let CE[(ai] a2; d = 1) denote the managerâ€™s certainty equivalent at the beginning of the first period, given that he hedges. We readily find CE[(ai, a2,d = 1) = W + akidi + f3k2d2 - c(ai,a2) - |(a2a2 + /32a%) - ; ln[(l - q) + qe-rD^a?) Now the managerâ€™s benefit from misreporting, â€”4 ln[(l â€” q) + qe~^D^~a^2]1, is associated with the hedging position, D. In addition, the larger the D. the more the benefit from misreporting for the manager, regardless of the additional increased riskiness from the misreporting option2. Compared to the previous model in Chapter 3, the manager benefits not only from hedging through reduced riskiness of outputs, but also from an increased marginal gain from manipulation. Therefore, it is easy to verify that the manager still always prefers hedging (d = 1), regardless of his action choices. Similar to the analysis in Chapter 3, the principalâ€™s design program to encourage the manager's high actions is: 2 Program [E] s. t. CE[{H;H-,d = 1) > 0 (IR) (IC1) min W + ak\H + fik2H + qD(/3 â€” a) W,a,0 a â€” k^H B> â€” V - k2H (IC2) 'Notice that â€”-tln[(l â€” q) + qe~^D^~a^2] is positive. It is the result of joint effects from increased riskiness of compensation and additional bonus from manipulated output net of personal manipulation cost. 2Define Q =-\in[(l - q) + qe~Â§^-Â«)2]. We have fg = > 0. 43 As usual, the (IR) constraint must bind, so W* = â€”akiai â€” /3k2Ã¼2 4- 2C + |(q2ct2 + (32al) + ~ln[(l â€” q) + qe~2D^~al2]^ and the principalâ€™s objective function can be rewritten as \[o2a2 + /32ctÂ¿) + Â£ ln[(l â€” q) + qe~^D^~a^2] + qD(/3 â€” a)2. Now the principalâ€™s design program reduces to min \{oi2o2 + /?2oÂ¿) + \ ln[(l - q) + qe q)2] + qD(/3 - a)2 a,(3 S. t. A p> k2H Program [E'\ (IC1) (IC2) Define a*E,/3*E as the optimal bonus rates in Program [Ã‰). We have Proposition 4.1: The optimal contract in the strong bundle model has klH ^ aE < k2H PE- Corollary 4.1: When q is sufficiently low, the optimal contract in the strong bundle model has aE = and p*E = Corollary 4.2: When q is sufficiently high, D is sufficiently large, and the difference between ki and k.2 is sufficiently large, the optimal contract in the strong bundle model has â„¢d ffiE = Â¿7. Proof: See the Appendix. In contrast to the model in Chapter 3, the hedge position now plays a role in deciding whether to limit earnings management. When D is sufficiently large, the cost of misreporting (^A2) is low. If the probability of misreporting is not trivial, the potential misreporting damage is severe. With a severe misreporting threat, it is efficient for the principal to raise a to limit earnings management. Whether to Take the Strong Bundle In the hedge-misreport bundle model in Chapter 3, although hedging is a prerequisite for the manager to misreport, the benefit from hedging and the cost from misreporting are separable. Whether it is efficient to take the bundle depends on a clear-cut trade-off between the reduced output variance and the garbled output 44 means. In the current strong bundle model, hedging is not only a prerequisite for earnings management, but also affects the manager's manipulation amount through its effect on the personal cost of earnings management. The trade-off between hedging and earnings management becomes more complex. Lemma 4.1: When q is sufficiently low, the strong bundle is preferred to the benchmark. Proof: See the Appendix. Obviously, if the probability of misreporting option is very low, misreporting is all second order effect, even though hedging reduces the misreporting cost. However, when q is high and Aq is significantly larger than /c2, D plays a double role in the principalâ€™s view of the strong bundle. A highly effective hedge greatly reduces the noise in the output signals, but also greatly reduces the managerâ€™s personal cost of manipulation. This is most evident when q = 1. Ubiquitous Misreporting Opportunities When q = 1. that is, when the manager can always misreport, the principalâ€™s design program becomes min Â§(a2<72 + ffia2d) + \D(Â¡5 - a)2 a,/9 s. t. Program [i?{] â€œ > Â¡Q7 (IC1) fi>t& (IC2) Define aEl, pE1 as the optimal bonus rates for the strong bundle model when q = 1. We have the following result. Proposition 4.2: When q = 1, the optimal contract in the strong bundle model has = d^iSh â„¢d if D > (or a2 < Proof: See the Appendix. We use Figure 4-1 to show how the first period optimal bonus rate, aEl, changes with the hedging position, D. 45 Notice that a*E1 = jj+ra2 pfffi > 7^7 when D > klT/^_x â– In other words, the 2 principal raises a from its lower bound when D > kjk2_l â– Intuitively, if D is large, earnings management is going to be a first order effect, and the optimal contract has to reduce the manipulation incentive by increasing a. More precisely, when D < kJkâ€˜_l, the optimal first period bonus rate is fixed at while when D > kJl2_l, the optimal first period bonus rate increases gradually at a decreasing rate.3 Right after D exceeds 2 , as the hedge becomes more effective (D gets larger), the principal has to increase the first period bonus rate sharply to cope with the increased manipulation. However, when the hedge gets even more effective (D approaches a2), the principal does not need to improve the first period bonus so much to deal with manipulation. Turning to the question at hand, we have the following characterization. Proposition 4.3: When q â€” 1 : Case (1): If a2 < Â¡4 ^ (g2-^)^-â„¢2) fcj <72(cr2â€” the strong bundle is preferred to the benchmark when t > 1 - V^- (X) (B') Otherwise, it is not efficient for the principal to take the strong bundle. Proof: See the Appendix. Corollary 4.3: In Case (1) or (2) of Proposition f.3, condition (X) or (B') is less stringent with higher risk aversion degree r\and condition (X) or (B') is less stringent when ki and &2 are similar in magnitude. Proof: See the Appendix. Condition (A') or (B') is less stringent means the condition is more likely to be satisfied. With a less stringent condition (A7) or (B7), the principal is more likely 3 Here 8â€”2 U DJrrrr- kp H r(7~ 3D (ro2 + D)2 k2H > 0, and 7? k2n) 8D2 - -2 (rtr-i + Dp k2H <0. 46 to prefer the strong bundle. Intuitively, a higher r indicates that the manager is more risk averse. When the manager is very risk averse, the principal must pay a high risk premium to the manager for the noisy output signals. Thus, the principal would like to reduce the noise and has a strong preference for hedging. Hence she is more likely to take the strong bundle. In addition, when productivity does not change much through time (k\ and k2 are similar in magnitude), the bonus rates will not change much through time either. With little additional bonus gain from misreporting, even when the cost of misreporting is low, the managerâ€™s manipulation will not bring great damage. Thus the principal is more likely to take the strong bundle. In other words, the conditions for the strong bundle to be preferred are less stringent. Corollary 4,4: When ad < a2 [l â€” (a) if ad < cr2(-Â±^), then the smaller the ad , the less stringent is condition (A1); (b) if Corollary 4.5: When ad > Proof: See the Appendix. In the strong bundle, the "good" from hedging and the "bad" from manipulation are colinear, so a low ad in and of itself is not a cause for joy. The principalâ€™s preference for the bundle is not monotonic in ad. To explore the intuition behind these results, recall Figure 4-1: In Figure 4-1, when D is small (ad is large), the principal does not raise the first period bonus rate o from its lower bound, since it is not worth raising the bonus rate to restrain earnings management. Correspondingly, here in Corollary 4.5, when a'd is sufficiently large, the effectiveness of hedging does not. affect the principalâ€™s decision on whether to take the strong bundle. Since the hedge is poorly effective 47 and the manipulation cost is high, neither hedging nor manipulation has significant influence. In Figure 4-1, when D gets larger and exceeds (ad gets smaller than cr2(l - fci/[2_1)), the principal has to raise a greatly to deal with the increased manipulation, while when D approaches a2 (ad approaches zero), the principal raises the first period bonus rate only at a decreasing rate. In Corollary 4.4, we see when a\ is intermediate, the marginal benefit from hedgingâ€™s effectiveness cannot beat the marginal loss from manipulation, and the principal is more likely to take the bundle with a less effective hedge. When ad approaches zero, however, the marginal benefit from hedgingâ€™s effectiveness beats the marginal loss from manipulation, and the principal is more likely to take the bundle with a more effective hedge. Figures 4-2A and 4-2B show how the principalâ€™s preference for the strong bundle changes with the effectiveness of the hedge (represented by a2d). To further illustrate the tension between the benefit from the hedgeâ€™s effectiveness and the loss from the more manipulation around er2(-^) in Figure 4-2A, we use a numerical example to show how the principalâ€™s preference for the effectiveness of the hedge changes. In this example we suppose r = .5,k\ = 5, = 1, cr2 = .5 so that cr2(-4^) < cr2(l â€” kl/rk2_l) is satisfied. The value of <72(^r) here is .4165. The numerical example is presented in Table 4-1. Summary From the analysis in this chapter, we see when the managerâ€™s personal cost of manipulation decreases with the effectiveness of the hedge, there is more tension when the principal decides whether to take the hedge-misreport bundle. When the hedge is highly effective, the more effective the hedge, the more likely the principal prefers the bundle since the marginal benefit from hedgingâ€™s effectiveness beats the marginal loss from lower manipulation cost. When the hedge is moderately effective, however, the principal is more likely to take the bundle with a less effective hedge, since the marginal loss from misreporting is more considerable compared with the marginal 48 benefit from the hedgeâ€™s effectiveness. But when the hedge is poorly effective, the effectiveness plays no role in the principalâ€™s decision on whether to take the bundle, since both the hedging benefit and the loss from manipulation are insignificant. 49 D Figure 4-1: D and a* the smaller the ad, the larger the ad, the more likely the more likely ad has no influence the bundle is preferred the bundle is preferred Â°d Â°2(&) a2<-1 - wfa) the smaller the crd, the more likely the bundle is preferred ad has no influence Â°d B *2(1 - ITTfe) Figure4-2: ad and preference. A)When cr2(^^) < a2(l-k-fÂ¿2~)- B)When< ^2(1 - feTT^rr)- 50 Table 4-1: Numerical Example for principalâ€™s preference and ad principalâ€™s expected cost *2 < *2(tÂ£) = .4165 benchmark strong bundle = -25 50.8125 -< 50.7813 q a. to II CO Ol 50.8125 >- 50.8398 > o2^) = .4165 a2 = .42 50.8125 >- 50.8456 a2d = .4999 50.8125 50.8125 CHAPTER 5 EARLY RECOGNITION MODEL The FASB has recently issued several new regulations on the measurement and disclosure of derivatives. There is also substantial detailed implementation guidance from the Emerging Issues Task Force (EITF). The new regulations are intended to recognize the effect of a hedge on earnings and use "mark-to-market" techniques to evaluate the unsettled derivatives, presumably so investors understand the potential risk and value of the derivative contracts held by firms. However, the "mark-to-market" technique may be problematic. The prior chapters have discussed the case in which this technique is abused to manipulate earnings. In this chapter, I further explore its impact on the firmsâ€™ risk management behavior. Early Recognition of Hedging In practice, over-the-counter derivative contracts are difficult to evaluate, for they are not traded on exchange markets. For OTC derivatives, their "fair value" is more easily manipulated. However, for derivative instruments that are frequently traded on exchange markets, such as futures and options, their market value is readily available. Manipulation may not be a major concern for these derivatives. However, the new regulation of evaluating unsettled derivatives may still influence the firmsâ€™ risk management behavior. According to FASB Statement 133, the ineffectiveness of a hedge would result from "a difference between the basis of the hedging instrument and the hedged item or hedged transaction, to the extent that those bases do not move in tandem," or "differences in critical terms of the hedging instrument and hedged item or hedging transaction, such as differences in notional amounts, maturities, quantity, location, or 51 52 delivery dates." In practice, the effectiveness of hedging refers to the degree to which the fair value changes in the derivatives offset the corresponding fair value changes in the hedged item. For this chapter. I assume the manager cannot manipulate the fair value of unsettled derivatives. There is no other option of earnings management either. Without hedging, X\ = k\a\ + and X2 = k2a2 + e2, where [^1,62] follow a joint a2 0 normal distribution with zero means, and the covariance matrix is . As 0 a2 in the previous models, suppose any hedge is for the second period only. If the firm does not recognize the hedging influence earlier, the second period output will be X2 = k2a2 + e'2, where e'2 ~ Ar(0, ad) with ad < a2. In this way, again we capture the risk reduction theme of hedging by a mean preserving spread structure. Since in this chapter I am not interested in earnings management, I relax the earlier assumption k\ > k2, and allow k\ and k2 to be any positive value. With hedging (but without early recognition), the second period output variance is reduced from a2 to o\. If firms have to recognize the ineffective portion of hedge before the settlement of derivative contracts, I suppose Xi = kia\ + ei + pe'2 and x2 = k2a2 + (1 â€” p)Â¿2,P Â£ (0Â» 1)- Due to the early recognition, part of the reduced variance is recognized in the first period and the remaining variance is recognized in the second period, when the derivative contract is settled. Centralized Case First consider the case in which the principal is endowed with the hedging authority and decides to hedge. Suppose the outputs are publicly observed. Paralleling earlier work, it is routine to verify that the incentive constraints collapse to the following two constraints: a > â€” kiH C k2H P> â€” (IC1) (IC2) 53 Moreover, the individual rationality constraint is W + ak\H + fik2H â€” 1C + p2Â°d) - hP2(\ - p)2(j2d > o. Therefore, the principalâ€™s design program is min W + ak\H + 0k2H W,a,(3 S. t. Program [F] W + ak\H + (3k2H - 1C ~^a2(a2 + p2a2d) - f/52(l - p)2a2 > 0 (IR) (ici) P>17h (IC2) Since, as usual, (IR) must bind, the reduced version of Program [F] is min Â§a2(cr2 + p2a2d) + Â§/32(l - p)2a2d Program[F'] Q,P S. t. Q > jÂ£y (ICI) 0 > m (IC2) Notice the only difference from the prior centralized case in Chapter 2 is that part of the second period output variance is moved to the first period. Denote the optimal bonus rates for Program [F] as aF and 3F. It is readily verified that the optimal solution is a*F = and (3*F = The optimal bonus rates here are identical to those in the benchmark case where either the principal does not hedge or there is no hedging option at all. This follows because hedging only influences the output variance and does not affect the incentive constraints. In this case, the principalâ€™s expected cost is B = 2C + \ct2(cr2 + p2crd) + %/32(l â€” p)2crd. Compared to her expected cost if she does not hedge, A = 1C + \oÃ2g2 + \fi2o2, hedging is efficient when A - B > 0, or when < a Â°-A. Since a*F = and Â¡3*F = this implies hedging is efficient when 4 > p2a* * = p2 fcf â€” <72-(l-p)2<72 4-(l -p)2 â€d Proposition 5.1: In the centralized case, hedging is efficient when condition [Q] is satisfied. Proof: See the above analysis. 54 From condition [(?]. we see when hedging greatly reduces the output noise (when a2d is small), the principal prefers to hedge. In addition, when k\ Â» k2, the principal prefers to hedge. With ki Â» k2, a* Â« Â¡5*. When the first period bonus rate is low, the compensating wage differential for the increased risk in the first period output is not significant, and the principal is willing to hedge to obtain the benefit from hedging regardless of the increased risk in the first period output. Moreover, when p is small, there is only a small increase in the riskiness of the first period output since only a small portion of the ineffectiveness is recognized earlier, and the insignificant early recognition will not overturn the preference for hedging. Delegated Case Now consider the case in which the manager makes the hedging decision. As in the centralized case, suppose the outputs are publicly observed. When [Q] is satisfied, will hedging still be efficient in the delegated case? Since the manager makes the hedging decision, to motivate him to hedge, there are two more incentive constraints besides the constraints in Program [F\. Using CEi(ai,d]a2) to denote the managerâ€™s certainty equivalent at the beginning of the first period, these two constraints are: CEX {H,d=V,H)>CEl{H,d = 0; H) CEX{H, d = 1; H) > CEi(0, d = 0; H) Expanding the constraints, we get W + ak\H + /3k2H -2C- \ol\o2 + p2a2) - Â§/?2(l - p)2a2 > W + akxH + &k2H - 2C - \cc2o2 - \&2o2 W + ak\H + (3k2H - 2C - Â£a2(a2 + p2a2) - Â§/?2( 1 - p)2a2 > W + Â¡3k2H - C - \oc2a2 - Â§/3V They reduce to /?V â€”(l-p)2a2]>a2p2<72 C-${/?V-(l-p)2^]-aWd a â€” kiH (ici.) (ICU) 55 The second constraint is redundant, for f32[a2 â€” (1 â€” p)2crd] > a2p2ad and <***â€¢ Now the new design program is: min Â§a2(a2 + p2ad) + Â§/32(l - p)2crd Program[G'] a,(3 s. t. a>^Â¡ (IC1) P>iSh (IC2) PV - (1 - p)2a2} > ccp2o2d (IC1.) Plug the optimal bonus rates qJt = and /3*F = into the IC constraints. For (ICla), we h&ve P*F[o2-(\-p)2aâ€˜d\-a*Fp2a2d = (%)2[Â° ~(1^p) ^ Condition [Q] implies > 0, thus (ICla) is satisfied. Therefore, the optimal bonus rates in Program [F\ are also the optimal bonus rates in Program [G'\. In addition, (ICla) satisfied implies the manager will always hedge as long as [Q] holds, thus it is free for the principal to motivate hedging. No matter whether it is the principal or the manager who has the authority to hedge, hedging is efficient when condition [Q] is satisfied. Lemma 5.1: When [Q] holds and hedging is motivated, the optimal contract has a* = KH aTld f = Sil- Proof: See the above analysis. The intuition behind this proposition is the following: When [Q] is satisfied, under the benchmark bonus scheme a* = ^77 and Â¡3* = Gjj, although the first period output is more risky with the hedge, the total risk premium for the two periods outputs, ^a*2(a2 + p2a2d) + ^Â¡3'2{\ â€” p)2a2d, is still lower than the risk premium without the hedge, \ot*2a2 + ^3*2a2. However, when [Q] is not satisfied, a* = -Â¡^jÂ¡ and (3* = -Â¡^jj are not the optimal rates for Program [G1]. Define ^ ; p2 5-(i -p)2 d as condition [Q]. We have the following lemma. 56 Lemma 5.2: When [Q] holds and hedging is motivated, the optimal contract has a* = KH and P* = -P)2Â°'d kiH" Proof: See the Appendix. From the above lemma, when [Q] holds, the principal has to set a higher second period bonus rate to motivate hedging. [Q] implies that Aq is low. When k\ is low, the lower bound of a, is high. With a high bonus rate in the first period, the induced increased risk in the first period will be high. Thus the manager is reluctant to hedge. To motivate hedging, the principal has to reduce the weight of the first period bonus in the managerâ€™s compensation, either by reducing a or by increasing ft. Since a has its lower bound at jâ€”jj, the principal cannot reduce the first period rate below that bound. The only way is to increase the second period bonus rate, ft. Here hedging is not so attractive as in the case when [Q]. The question now is what if the principal does not encourage hedging when [Q], If the principal does not encourage hedging, the incentive constraints for the second period are the same as when the principal encourages hedging, since the hedging choice is already made at the beginning of the first period. Using CE[(ax,d-,a2) to denote the managerâ€™s certainty equivalent at the beginning of the first period, the incentive constraints for the first period given a^ = H become CE[(H,d = 0; H) > CE[(H.d = l; H) (ICl') CE[(H,d = 0\H)> CE[(0, d = 1; H) CE[(H,d = 0; H) > CE[(0,d = 0;H) Rewrite the (ICl ) constraints, we have 0V-(l-p)2a*\ Here (IClj,) is redundant, since /?2[cr2 â€” (1 â€” p)2oÂ¿] rationality constraint in this case is CE[(H,d = 0: H) (icO (icO (icO < a2p2o2d. The individual > 0, and it must bind. 57 Therefore, the program can be rewritten as min f a2cr2 + %0zcr a,0 c S. t. Q > kiH 3 ^ T ^ â€” r-2// Program [i/7] (icO (IC2) Â«W > /*V - (1 - p)V2] (ICO Lemma 5.3: WTien [Q] holds, the optimal contract that precludes hedging has a* = Â£'h and P' = Proof: See the Appendix. Now, when [Q] holds and hedging is discouraged, the principalâ€™s expected cost is 2C+Â§(*)V+Â¡(Â¿7)V, (A') while when hedging is encouraged, her expected cost is 2C + Â§(*) V + AÂ¿) + - p)2*2 (B') Comparing A' with B', we have B'-A'=-(-Â£-)2((t2 + n2n2\ 4- ^ _n _ n\2<72 - ^(-^-)2a2 - Z(-Â£-)2rr2 D A 2\k1H> + P ad) + 2\kiHf =L(_C_)2 2 2 , r/_^N2fP2^(l-P)2^l _ r t _C_\2 -2 2^kiH> P Â°d ^ 2\kxH > U2-(l-p)2 2^kiH> P ad 2'H' U lltf cr2-(l-p)2CT2 XfJ r IC\2â€”2 1 r P2<^ *?1 ^ n -2(77) a fc7l72-(l-p)2 Therefore, with condition [Q] satisfied, B'-A'>0. Thus hedging is not efficient. 2^2 2 In other words, the principal prefers not to hedge when ^ < er2_^1_â€˜â€˜j2;^ = ga ^â€”â€”, Â° d no matter whether the principal or the manager has the hedging authority. Proposition 5.2: If [Q] holds, encouraging hedging is efficient, and the optimal contract has a* = and 3* = If [Q] holds, discouraging hedging is efficient, and the optimal contact has a* = and 3* â€” Proof: See the above analysis. 58 Table 5-1 has a numerical example to illustrates the conclusion in Proposition 5.2. I assume r = 0.5, C = 25, and H = 10. I use d = 1 to denote the case that the principal encourages hedge, and use d = 0 to denote the case that hedge is discouraged. From the above proposition and the numerical example in Table 5-2, it is shown that the delegated case is similar to the centralized case in that hedging is In the delegated case, there is no moral hazard 1^2 2 efficient only when -4 > 9 q-d-p)2 d problem on hedging. The principal still follows the rules in the centralized case to decide whether to encourage hedging. The principal need not motivate hedging when [Q], and need not forbid hedging when [Q]. This is because the principal and the manager share the same interest. The lower the induced output risk for the manager, the less the compensating wage differential the principal has to pay. More importantly, recall that in the previous chapters when there is no early recognition, hedging is always efficient since it reduces the compensating wage differential. However, with the early recognition of hedgingâ€™s ineffective portion, in some cases hedging is not efficient any more, since it adds more risk to the first period output, though the risk in the second period output is reduced. When the first period output has a sufficiently great weight in deciding the managerâ€™s compensation, increased riskiness in the first period output greatly increases the managerâ€™s compensation risk. The principal has to pay a relatively large compensating wage differential, thus hedging becomes unattractive. In addition, the less effective is the hedge (that is, ^ is closer to 1), the less likely is hedging to be efficient. Moreover, the larger the portion of the ineffectiveness is recognized earlier (that is, the higher the p), the less likely hedging is efficient. Summary In Chapters 2 and 3, hedging is efficient since it reduces the second period output variance, and therefore reduces both the managerâ€™s compensation risk and 59 the principalâ€™s compensating wage differential. However, when I introduce the early recognition of a portion of the hedgeâ€™s ineffectiveness, it is shown that sometimes hedging becomes undesirable. The reason is that the early recognition increases the riskiness of the first period output. When the first period output carries a great weight in the managerâ€™s compensation, or when a large percentage of the ineffectiveness has to be recognized early, the early recognition policy makes hedging unattractive. In addition, without the early recognition, as long as a2 > hedging is efficient; while with the early recognition, only when the effectiveness is sufficiently high will hedging be efficient. The analysis of this chapter sheds light on how some recent accounting regulations may influence the firmsâ€™ risk management behavior. Recent accounting regulations require that firms recognize the ineffectiveness of hedge into earnings even before the settlement of derivatives contracts. Although the intention of the new rules is to provide investors with more information on the firmsâ€™ use of derivatives, they may have a side effect of discouraging the firmsâ€™ risk management activities. 60 Table 5-1: Numerical Example for Proposition 5.2. a* P* c kyH c k2H principalâ€™s expected cost Q1 d= 1 1.250 1.667 1.25 1.667 50.2631 d = 0 4.410 1.667 52.7778 d= 1 2.500 .095 50.8929 Q2 d = 0 2.500 .833 2.50 .833 50.8681 'For the case with condition [Q], I assume k\ = 2,k2 = Therefore = 1.7 > â€”3â€” = .142. which satisfies [Ql. Ki 2 For the case with condition [Q], I assume ky = 1, k2 = 3, a2 =0.111 < â€”7â€”^â€”â€” = .142, which satisfies [Q]. *â– 2 -J-(I-P)2 1.5, CHAPTER 6 OTHER RELATED TOPICS In this chapter I briefly explore the relationship between riskiness and agency problems. In addition, I also analyze a model with "informative" earnings management, where manipulation is desirable. Riskiness and Agency For the main model in this paper I assume output follows a normal distribution, and show that hedging reduces the firmsâ€™ risks and helps reduce the compensating wage differential. However, we need to be cautious not to take this result casually and conclude that "as long as hedging reduces the risk in output, it improves the agency problem." The normal distribution assumption may play an important role here. In a continuous setting, Kim and Suh (1991) illustrate that if there are two information systems whose distributions belong to the normal family, the system with the higher likelihood ratio variance is more efficient (costs less for the principal to induce the manager's certain action level). In a binary action setting, it is easy to verify that the hedged plan also has a higher likelihood ratio variance. A likelihood ratio distribution with a higher variance makes it easier for the principal to infer the managerâ€™s action from the output, and therefore helps reduce the compensating wage differential. Without the normal distribution assumption, reduction in riskiness may not improve an agency problem. Consider a finite support numerical example in which hedging drives up the compensating wage differential. For simplicity, assume a one-period, centralized-hedge case with three possible outputs, {1,2,3}. When the principal does not hedge (or when there is no hedging option), the probability distribution of {1,2,3} given the managerâ€™s high action is PÂ¡Â¡ = (|, g, |), and when 61 62 the manager chooses low action the distribution is = (5,5,5). But when the principal hedges, the probability distribution given high action is Plid = (5, 5, ^), and the distribution given low action is Pid = (4,5,5)- Also assume C â€” 25 and r = 0.01. Given the action, it is readily verified that P# is a mean preserving spread of Pud and Pi is a mean preserving spread of PLÂ¿. In other words, the unhedged plan is more risky, according to Rothschild and Stiglitz (1970). However, in this example, the principal pays 54.1149 to encourage high action when she hedges, while she only pays 37.7216 when she does not hedge or when there is no hedging option. Risk reduction is usually believed to be beneficial to investors. However, as illustrated here there is no necessary connection between risk reduction and improvement in the agency problem. Counter-intuitively, risk-reducing activities may increase the compensating wage differential. In other words, even though hedging activities reduce firmsâ€™ risks, in some cases they are detrimental to investors. Informative Earnings Management: Forecast Model To this point, the misreporting behavior is just garbling, and it merely destroys information. That is, the misreporting behavior is bad for the principal, although sometimes the principal tolerates some misreporting behavior because the elimination is too costly. However, when misreporting carries some private information, in some cases it is good for the principal to encourage earnings management. Consider an extreme case in which earnings management is not only encouraged but enforced by the principal for her interest. I will show that with some engineering, encouraging manipulation may lead to first best solution. As in the previous models, the agent chooses a first period action level and decides whether to hedge the second periodâ€™s output at the beginning of the first period. Here I further assume the agent can hedge only when he chooses high action in the first period. That is, I assume the hedging activities need effort, and a slack manager will not be able to hedge. In addition, if the agent decides to hedge and 63 chooses high action in the second period, he can also perfectly forecast the output of the second period at the beginning of the second period. The principal cannot observe the agentâ€™s choices or the outputs for each period, but can observe the actual aggregate output at the end of the second period. For simplicity, assume the cost of misreporting is zero and the agent can misreport freely, as long as the aggregate reported output, jq + x2, is equal to the actual aggregate output, X\ -f- x2. The time line for the forecast model is shown in Figure 6-1. In this model, although the principal cannot observe the output of each period and cannot know the agentâ€™s forecast, she can design a contract that achieves first best to encourage high actions and hedge. Think about the contract that pays the agent the first-best compensation if the agent reports equal outputs for period 1 and period 2, but pays the agent a penalty if the reported outputs for the two periods are not equal. Under this contract, the agent can forecast the second periodâ€™s output only when he works hard and hedges, and only when he forecasts the second periodâ€™s output is he able to manage the earnings so that the two periodsâ€™ outputs are equivalent. With any other choice of actions, he cannot perfectly smooth the earnings to avoid the penalty, and the chance to get two equivalent outputs by accident is small. Therefore, the only choice for the agent to avoid the penalty is to supply high effort in both periods, hedge, and smooth the reported earnings. In this case, earnings management is not only encouraged but enforced. It helps the principal to reap the rent from the agent. Income smoothing here is desirable to the principal. The program for the principal in the forecast model is min f f Si ffÃ(x1)fHd(x2)dx1dx2 Program [I] So,Si s.t.J f u(Si - 2C)fH(xi)fHd(x2)dxidx2 > U f f u(S 1 â€” 2C) fh{x\) fHd{x2)dxidx2 > E(u) for any choice other than ei,e2 = H, hedge, and equal X\,x2, where S1 is the payment to equivalent reported outputs, and So is a penalty. 64 Proposition 6.1: In the forecast model, first best can be achieved by Si = 2C â€” Mn(â€”U) for equivalent reported outputs for the two periods and penalty So Â« 0 otherwise. Proof: See the Appendix. Summary In this chapter it is shown that there is no necessary connection between the reduction in riskiness and the improvement in agency problems. It is a general belief that risk reduction activities are beneficial to the investors, while this chapter illustrates that this may not be true in some cases. A model with informative earnings management is also included in this chapter. When earnings management conveys the managers private information, manipulation may be efficient and desirable. It is shown that in a well-constructed model, encouraging manipulation can achieve the first best. 65 1st Period 2nd Period Agent chooses Agent observes X\, a\ E {H, L}. If a\ = H, report X\. Choose can hedge for 2nd a2 E {H.L}.Can forecast period output. x2 if a2 = H and hedged Figure 6-1: Time line for forecast model Agent observes x2, reports x2. Principal observes X\ + x2. CHAPTER 7 CONCLUDING REMARKS Derivative instruments arouse mixed feelings. They are inexpensive hedging instruments that cost much less than real option hedging, while their complexity makes them harbors for earnings management. Investors and regulators are concerned and nervous about the potential damage from abusing derivatives, but cannot forgo the convenience and benefit from hedging through derivatives. Derivative instruments are like nuclear power stations, when they work well, they provide users with clean and cheap energy, while when anything goes wrong, their destructive power is dreadful. This has led to great effort aimed at restraining the abuse of derivatives. To help investors get more information about and more control of firmsâ€™ use of derivatives, the FASB has issued various rules recently on the recognition and disclosure of derivatives, such as SFAS 133, 137, 138 and 149. There are also numerous detailed guidances from Emerging Issues Task Force (EITF) on how to implement these complicated new rules. The main strategy of the regulators to fight the abuse of derivatives is to require firms to disclose the fair value of both the derivatives and the hedged items. The regulators believe investors can understand better the value of the derivative contracts through the managersâ€™ estimates of the derivativesâ€™ fair value. However, to do this, discretionary evaluation of the fair value is necessary, since many unsettled derivativesâ€™ fair value is not available from the market. The more discretion for the managers may offer more earnings management opportunities, contrary to the initial intention of the new accounting rules. Moreover, another intention of the new regulations is to help the investors understand better the potential risk of derivatives through the managersâ€™ early disclosure 66 67 of the ineffectiveness of hedging. However, the early recognition of the hedgingâ€™s ineffectiveness raises the riskiness of interim earnings. With a higher risk in the interim earnings, the firms may be discouraged from risk reduction activities, which may not be a desirable consequence for investors and regulators. In addition, the discouragement of hedging may force the managers to look for other ways to secure their wealth. Unfortunately, more earnings management is a promising candidate. As shown in this dissertation, the current accounting regulations on derivative instruments may be inefficient. But shall we give up the effort to restrain the abuse of derivatives? Or shall we just discard derivative instruments? I would say no. It is not the purpose of this paper to criticize the current rules and claim the effort is totally in vain. Instead, the intention is to explore the complicated feature of derivatives so we get better ideas on how to keep the benefit of cheaper hedging while minimizing the potential destruction from derivatives abuse. An ancient Chinese saying says, "a thorough understanding of both yourself and your enemy guarantees a victory." I hope this research may shed some light on the feature of our enemy, the dark-side of derivatives, and help us find more efficient ways to regulate the use of derivatives. APPENDIX Chapter 2: Proof for Lemma 2.1: Proof. We use //j,/x2 to denote the Lagrangian multipliers for (ICl) and (IC2) respectively. With the reduced program, the first order conditions are â€” ra2a+nl = 0 and â€”ra2ft + fi2 = 0. Since a > > 0 and ft > > 0, we get = ra2a > 0 and /Â¿2 = ra2ft > 0. This implies both (ICl) and (IC2) bind, or a*4 = ft*A = â– Proof for Lemma 2.2: Proof. The principalâ€™s design program can be expressed as the minimization of %(a2a2 + ft2ad) subject to the incentive constraints. Again let /x1,/i2 denote the Lagrangian multipliers of (ICl) and (IC2) respectively, with the reduced program, we have the first order conditions â€” ra2a + â€” 0 and â€”radft + /x2 = 0. Hence = ra2a > 0 and /12 = radft > 0. This implies both (ICl) and (IC2) are binding, and thus a\ = ^ and P*A = -Â¿n. â– Proof for Proposition 2.2: Proof. Define /Xj as the Lagrangian multiplier for (ICl) and //2 for (IC2). With the reduced Program [C'], the first order conditions are -To2a - + 2 In the optimal solution, if neither constraint is binding, /.il = f.i2 = 0. Substitute Hx = H2 = 0 into the first order conditions and add the two conditions together, we get â€”ra2ft â€” ra2a - 0, which implies a = ft = 0. This contradicts a > > 0 and ft > ^7 > 0. Therefore, /i1 = Â¡jl2 = 0 is not true in the optimal solution, and at least one of the constraints is binding. 68 69 If Hi > 0,^2 = 0, then a = and 0 > (FOC2) implies 0 = ra^Mqoc, where M = 2- â€¢ Rewriting M, we have M = {(1 - Ã) (1 - e-Â§(/3-Â«)2) +[1 -q(l â€” e_^_Q)2)]} > 0. With M > 0, we get 0 = â€”ot < a = However, k\ > k2 implies 0 does not satisfy the constraint 0 > â€”jj. Therefore, (a = k0R' & â€” 1Â£h) cannÂ°f be true. Hence, regardless of Hi, (IC2) always binds, implying /% = *Â§?â€¢ Thus, /Â¿2 > 0 and Hi > 0. Moreover, if (ICl) binds, then a = if (ICl) is slack, then from (FOCI) a = ra2+M 0 < 0â– Hence we always have a*c < 0*c. m Proof for Corollary 2.1: Proof. Using the first order conditions displayed in the proof of Proposition 2.2, we see when q is sufficiently near zero, (FOCI) reduces to â€”ra2a + E\ + Hi =0 and (FOC2) reduces to â€”ra20 + e2 + h2 = 0> where E\ and e2 are small. This implies Hi > 0 and /i2 > 0. That is, when q is sufficiently small, both incentive constraints bind and o& = jgy, 0*c = Â¿7. â– Proof for Corollary 2.2: Proof. Using the first order condition (FOCI) in the proof of Proposition 2.2 again, if H\ > 0 and a = then Mi = â„¢2}t7h ~ (2? - Qe-Wc-T&? _ _c_ wl-faiAPc klH) > a 1â€”q+qe 0) (i) can be re-expressed as Now suppose q is sufficiently high and k\ is sufficiently large. This implies the inequality in (ii) is reversed and a*c > â– Proof for Proposition 2.3: Proof. Define Hi, H2 as the Lagrangian multipliers of the two constraints respectively. We get the following first order constraints: -ra2a +(0 - a) + Hi = 0 (FOCl') â€”ra20 -(0-a) + h2 = 0 (FOC2') 70 From Proposition 2.2, we know Â¿Â¿2 > 0, and /Â¿j > 0. If /ij = 0,/Â¿2 > 0, then /3 = and from (FOClâ€™) we get â€”ra2a + (/3 â€” a) â€” 0, which implies a = p^-r/3 = If i+br*Â§7 > Â¿7â€™ then both incentive constraints are satisfied, and ajt.j = and fi*ci = are the optimal bonus rates. The condition 1+â€˜r(T2 7^77 > ^7 reduces to > k2{ 1 + r and the optimal contract must have a*ci = -Â¡^jj and Â¡3*CI = as both incentive constraints bind. â– Chapter 3: Proof for Lemma 3.1: Proof. From Chapter 2, when q is sufficiently low, the optimal contract in the misreporting model is (oÂ£ = 7^, Â¡3*c = j~Ã¼)- The misreporting model, Program [C], is identical to the bundled model, Program [D'], except that the second period output variance decreases to a2d in the bundled model. It is easy to verify that (Qc = 7777= 1777) remains optimal in the bundled model when q is sufficiently near zero. The principalâ€™s expected cost in the bundled model therefore gets close to 2C + ^(aÂ£?cr2 + f3*c is higher than 2C + |(a^2a2 + The hedge-misreport. bundle is preferred. â– Proof for Lemma 3.2: Proof. From Corollary 2.2, when q is sufficiently high and k\ is sufficiently large, the optimal contract exhibits a*c > -Â¡^j, /3*c = We rewrite a*c as + Â£, e > 0. In addition, from Proposition 2.2, we know a*c = + e < /3*c = ^77. In the benchmark model where there is neither a hedging nor a misreporting option, the principalâ€™s expected cost is 2C +^(a*2a2 + /3^2 71 f (q^o-2 + fÃo2) - {Â§(fÃa2 + fÃa2d) + Â± ln[(l - q) + qe S&c *Â¿)2]+ q(p*c _ a*c)2} +7 ln[(! - 9) + 9e-2(ij77-i777-Â£)2] + q{J2_ - Â¿ - e)2} > 0 (iii) then hedge-misreport bundle is preferred to no hedging, no misreporting. But (iii) is positive only when cr2 â€” a\ is sufficiently large. â– Proof for Lemma 3.3: Proof. Refer to the proof for Proposition 2.3. Program [C'(q = 1)] is identical to Program [D'(q = 1)] except that in the bundled model programâ€™s objective function, the second period variance is ad instead of a2. It is easy to verify these two programs share the same optimal bonus coefficients. {a*Dl, Â¡3*Cl). m Proof for Proposition 3.1: Proof. In the benchmark model where there is neither a hedging nor a misreporting option, the principalâ€™s expected cost is 2C +Â¿(aAa2 + fÃa2), while in the bundled model it is 2C +%{a%lo3 + fÃxa2d) + \(fÃ - a*D1)2. As long as Â§(a^V + fÃa2) - [Â£(am0â€™2 + Pmad) + \(P*d\ ~ aoi)2] > OÂ» the hedge-misreport bundle is preferred. (1). When k\ > ^(1 + ra2), the optimal contract exhibits (a*D1 = Pd\ = -Â¿f)- Substitute a*A,pA and a*Dvp*D1 into Â¿(fÃa2 + fÃa2) - [Â¿(fÃa2 + PmÂ°d) + \(P*d\ ~ Â«di)2]- We have TÂ¿(fÃa2 + fÃa2) - [Â§(a&a2 + fÃfÃd) + \(p*Dl - a*D1)2] r(a2 â€”a2 di (ra2)'2 \(C_\2\ra ra* . 2ITfcf (l+r 2 ' H' " (l+r<72)2fcpc2 *" = 2()2(i+rg2)2fc'jfc|{ra2(l + ra2)2k2 - k\[ra2 - r(a2 - 0(1 + â„¢2)2 + (ra2)2}} Thus, we need ra2( 1 + ra2)2k\ - k\[ra2 - r(a2 - ad)( 1 +ra2)2 + (ra2)2] > 0. This implies 4 > g2-(1+rg2)(g2-g2) implies > a2(l+ra2) (2). When kx < k2(l+ra2), the optimal contract exhibits (a^ = (3*D1 = -Â¡^jj)- (ot*DV0*D1) is identical to (a*A,PA). Substitute fÃ,P*A and ot*m,/3*D1 into |(fÃa2 + fÃÂ°2) ~ [Â¿(fÃfÃ + fÃfÃ) + Â¿(Pdi ~ fÃ)% we have 72 iÃ^V+^Vj-gÃag^+aa^+i^ i-a^)2] = Â±(Â§)2F^-(Â¿-Â¿)2]. Thus, we need - (Â¿ - Â¿)2 > 0, which implies â– Chapter 4: Proof for Proposition 4.1: Proof. Define fi\ as the Lagrangian multiplier for (ICl) and /Â¿2 fÂ°r (IC2). The first order conditions are -ra2a-2^^g!^+2qD(0-Q)+fr=O (FOCI) ~radP + -2qD(0 - a) + ^ = 0. (FOC2) Suppose neither constraint is binding, implying fiv /Â¿2 â€” 0. Substitute H\, fx2 = 0 into the first order conditions and add the two conditions together, we get â€”ra2d(3 â€” ra2a = 0, which implies a = /? = 0. This contradicts a > ^ > 0 and (3 > -Â¡^ > 0. Therefore, /Â¿i, /^2 = 0 is not true and at least one of the constraints is binding. If Hi > 0, /f2 = 0, then a = -Â¡^ and Â¡3 > (FOC2) implies (3 = raI+Tqct, where T=( 2 Â£â€” lâ€”q+qe ^D(^Lali)D- Rewriting T, we have T = â€”â€” D (1_e-$D<0-Â°>2)9 e-Â§D(/3-a)2^ _ e-fd(/3-q)2^j| > q \Yi^h T > 0, we get (3 = rJlTqot < a = However, Ay > Ay implies (3 doesnâ€™t satisfy the constraint 3 > -~jÂ¡. Therefore, k2>! ' (a = ^ iS?) cannot be true. k2H Hence, regardless of Hi, (IC2) always binds, implying Â¡3*E = Thus, /i2 > 0 and H\ > 0. Moreover, if (ICl) binds, then a = if (ICl) is slack, then from (FOCI) o = r-aT+Tq(3 < 3- Hence we always have a*E < Â¡3*E. â– Proof for Corollary 4.1: Proof. Using the first order conditions displayed in the proof of Proposition 4.1, we see when q is sufficiently near zero, (FOCI) reduces to â€”ra2a + Â£\ + Hi =0 and (FOC2) reduces to â€”rcrdÂ¡3 + sy + H2 = 0> where E\ and s2 are small. This implies Hi > 0 and /Â¿2 > 0. â– Proof for Corollary 4.2: Proof. Using the first order condition (FOCI) in the proof of Proposition 4.1 again, 73 if > 0 and a = -Â¡^g, then ~LD(Bf--At)2 * = ^ - *e Wa**^ - *) > 0. lâ€”q+qe * *1" (i) can be re-expressed as - *(* - - Â¿) > 0. (i) (ii) l_9+9e"5D(&) ^-4>2 Now suppose q is sufficiently high, k\ and k2 are sufficiently different, and D is large. This implies the inequality in (ii) is reversed and a*E > -Â¡f^. -cr>(*)2(TL._JL)2 In addition, define G = (2 2 â€”4â€” )D(t~ - t~)- We have 9G _ M _ J_u/9 _ e-SÂ°(g-Â°>2 s e-$P(fl-Â«.)Â»jg(Â£)2(_L__L)2(1.,) and 3(7 _ nr,9 _ e-*^-Â°>2 x , e-^(^)2rg(Â£)22(X_X)2(1_9)i *5=5> ^ 2 l-q+ge-ÃD(^Q)2 ^ + (l-rte-iW-â€)^ i' From the proof for Proposition 4.1, we know T = (2 â€” -â€”e ~^DÂ°j_a)i )D > s-$Q(3-q)2 -9+9e" ,2 __ ^2 1-g+qe' 0.Therefore (2 * ' _r ,2) > 0, and both ^ > 0 and , t. > O.This implies 1 -q+qe 2 ^ w c that the larger a2 - crÂ¿, the more likely (ii) is reversed and a*E > Also, the larger (^ â€” ^-) (in other words, the greater the difference between k\ and k2), the more likely (ii) is reversed and a* > â– Proof for Lemma 4.1: Proof. From Corollary 4.1, when q is sufficiently low, the optimal contract in the strong bundle model is a*E = -Â¡^ and fl*E â€” . as in the benchmark, where there is neither a hedging nor a misreporting option. The principalâ€™s expected cost in the bundled model therefore gets close to 2C + 2((T777)2(7-2 + (jt7^)2crd] when Q is near zero. In the benchmark model where there is neither a hedging nor a misreporting option, her expected cost is 2C + ^[(j~]j)2(j2 + (^7)2ct2], which is higher than 2C + Â¿[(Â¿â€œ^O2*?2 + (j~f?)2<7Â¿]. The strong bundle is preferred. â– Proof for Proposition 4.2: Proof. Define /q, /q as the Lagrangian multipliers of the two constraints respectively. 74 (FOCI') (FOC2') We get the following first order constraints: â€”ra2a + D(/3 â€” a) + ^ = 0 -raÂ¿P - D((3 - a) + /i2 = 0 From Proposition 4.1, we know n2 > 0, and Â¡jlx > 0. If /ij = 0, /i2 > 0, then f3 = and from (FOCI ) we get â€”ra2a + D((3 â€” a) = 0, which implies q = = d^7Â¿Ã- If dT^Sh ^ *57- then both incentive constraints are satisfied, and aE1 = D+ra2 and j3*El = -Â¡Â£jj are the optimal bonus rates. The condition D+Ta2 -Â¡^jj > can be rewritten into D > klâ„¢â€˜_x (or ad < ff2(! - fcirfe))- If D < kir[~2_x, then a = D+rtj2 ^77 does not satisfy ICl and the optimal contract must have aE1 = and (3E1 â€” as both incentive constraints bind. â– Proof for Proposition 4.3: Proof. In the benchmark model where there is neither a hedging nor a misreporting option, the principalâ€™s expected cost is A = 2C +^[{j^ji)2(j2 + (~Â£h)2(J\ while in the strong bundle model it is B = 2C +%{a*E1a2 + P*^2) + oD{P*El - aj^)2. As long as A â€” B > 0, the strong bundle is preferred. (1). When ad < a2(l â€” the optimal contract has aE1 = and Pn = Â¡fe- Theâ€œ B = Kd^)2(*)2^2 + + ^(Ã³^)2(Â¿7)2- We have Â¿ =^my+y - ^ny - y - = mny - k^Yâ„¢2 + D^)2 - rZ?)]} A - B > 0 requires ro2 - ^[(p^)2â„¢2 + D(~^Â¡)2 - rD] > 0, which implies S| > (dTâ„¢*)2 + D k2 _ D\c2(D+r(j2)â€”(D+ra2) fcf > oHD+nity M v. (g2-gS)(g3~rg2) fcf <72(<72-<7^+r<72)2 â€™ r<72 D (D+rij2)2 <72 2>2i (2). When > cr2(l â€” fc1/fc2_i), the optimal contract exhibits aE1 = and Ã±i = Â¡feâ€¢Then ^ - 5 = r2&D - P(Â¿ - Â¿)2(S)2 = - (Â¿ - A)2]- A â€” Â£? > 0 requires p- â€” (A _ A-)2 -> q, which implies jr- > 1 â€” s/r. â– 75 Proof for Corollary 4.3: Proof. In condition (A7), case (1), define Z = = Z{d+Z2)2 â€¢ (A') is k2 rewritten as Â£Â§â– > Z. K1 dZ __ D [(D+rg2)2(-g2)-2(D+rg2)g2(g2-rg2)] dr a2 (D+rg2)4 _ p râ€”(D-t-rg2)g2â€”2g2(g2â€”r D[â€”(D+rg2)â€”2(g2â€”rg2)] â€” (D+rcr2)3 _ (o2-02)[-02+riT2-02] (D+ra2)3 (DW]i < 0 Since |^ < 0 , the higher the risk aversion degree r, the smaller the Z, and the more likely the condition (A') is satisfied. In other words, (A7) is less stringent with higher r. In condition (B7), case (2), it is easy to verify that the higher the r, the smaller is 1 â€” y/r, and more likely is condition (B7) satisfied. In other words, (B7) is less stringent with higher r. It is also easy to verify that in either case (1) or (2), the closer are k\ and k2, the less stringent condition (A7) or (B7) is. â– Proof for Corollary 4.4 and 4.5: Proof. In case (1), ad < a2(l â€” ki/l2_l), and the strong bundle is preferred when M > (*2-*2)(g2-rg2) D fi ^ _ (cr2- da d [g2(g2â€”g2+rg2 2(rr2 xt2 _i_rrr2\f (xt2 xr2 irrr2\ _ g2(g2â€”g2+7~g2){(g2~g2+7~g2)(g2â€”2g2+rg2)+2(g2â€”g2)(g2â€”rg2)} g4(g2â€”gj+rg2)4 g4â€”2g2g2+2rg4â€”g2g2+2g4â€”rg2cr2+r2g4+2g2g2 â€” 2rg4â€”2g4+2rg2g2 a2 (a2 â€”aÂ¿+ra2)3 * t(jâ€”TO 1/ â€” g2(g2-g2+rg2)3 _ (l+r2)g2-(l+r)g2 (g2â€”g^+rg2)3 When (l + r2)cr2 â€”(l + r)(7Â¿ > 0, that is, when < cr2(^^), > 0, the smaller the a2d, the less constraining is > Z. When (1 + r2)a2 â€” (1 + r)ad < 0, that is, when ad > cr2(-Â¡^r), < 0, the larger d 76 O â€¢ fc2 the ad, the less constraining is > Z. In case (2), from (B') we see ad does not play a role in the principalâ€™s decision on whether to take the bundle. â– Chapter 5: Proof for Lemma 5.2: Proof. Denote the Lagrangian coefficients for (ICl), (IC2) and (ICla) in Program [G ] as px, p2 and p3. The first order conditions are: -ra(a2 + p2a2d) + px- 2ap2a2dp3 = 0 (FOCI) -r0(l - p)2a2d + p2 + 20[a2 - {l - p)2a2d]p3 = 0 (FOC2) From (FOCI), if px = 0, then â€” ra(a2 + p2ad) â€” 2ap2a'dp3 â€” 0, which implies p3 < 0. Therefore we must have px > 0, that is, a* = jrjj. From (FOC2), if p2 = 0,= 0, then â€”r0( 1 â€” p)2(rd = 0, which is not true. Therefore, we cannot have both p2 and P3 = 0. If p2 = 0)^3 > 0, then 02[a2 â€” (1 - p)2oÂ¿] = a2p2ad, which implies 0* = -Ã)***w- If this P* > then a* = /ft and F = yJ^r^aiKH *Te optimal. 0* = ^p)^H - k2â€ž â€”kâ€” > Sh imPlies ~n-pFÂ°! > Sâ€™ which is condition -p) [Â£?]â€¢ In other words, if condition [Q] is satisfied, the optimal contract has a* = and 0T = â– Proof for Lemma 5.3: Proof. Define the Lagrangian coefficients for (ICl^), (IC2â€™) and (IC1â€ž) in Program \H') as p[, p2 and p3. The first order conditions are: -raa2 + p\ + 2ap2adp3 = 0 (FOCl') â€”r0a2 + p'2 â€” 20p'3[a2d â€” (1 â€” p)2c7d\ = 0 (FOC2) From (FOC2 ), it is easy to verify we cannot have p!2 = 0, since in that way pl3 < 0. Therefore, p!2 > 0, and 0* = If p[ > 0, p3 = 0, then a* = and a*2p2ad > 0*2[c2 â€” (1 â€” p)2crÂ¿], which 77 j^2 2^.2 â€” implies condition [Q],jb < â€¢ In other words, with condition [Q] satisfied, the optimal contract shows a* = -jâ€”jj, and Â¡3* = â– Chapter 6: Proof for Proposition 6.1: Proof. The program for the principal is min f f Si fH(xi)fHd(x2)dx1dx2 Sq>S\ s.t.f f u(Si - 2C)fH(xi)fHd(x2)dx1dx2 > U (IR) /f u(Si~2C)fH{x1)fHd(x2)dxidx2 > f J u(S0-C)fH(xi)fL(x2)dx1dx2+ f f u(Sx 71 o jifzx' ^ X2=X\ C')///(^l)/L(^2)d^ldX2 (IC1) J J u(Si-2C)fH(xi)fHd(x2)dxidx2> J f u(S0-C)fL(xi)fH(x2)dxxdx2+ J J u(Sx X2y^X\ 2^2 â€”x j C)fL(xi)fH{x2)dx1dx2 (IC2) f f u(Si -2C)fH(x1)fHd(x2)dx1dx2 > f f u(S0)fL{xi)fL(x2)dxidx2 + / f u(Si)fL(x1)fL(x2)dx1dx2 (IC3) / f u(Si - 2C)ffÃ(x1)fHd(x2)dx1dx2 > f f u(S0 - 2C)ffÃ(xi)ffÃd(x2)dx1dx2 + 12^11 f f u(S 1 - 2C)fh{x\)fHd(x2)dxidx2 (IC4) X2=X\ With a sufficiently low 5o, it is obvious that the IC constraints are not binding. (Think about 5b = â€”00 . All the right hand sides of the IC constraints are equivalent to â€”00 then. Therefore none of the IC constraints is binding.) With none of the IC constraints binding, we reduce the program into a first-best one. Therefore we have, f f u(Sx - 2C)fH(x1)fHd(x2)dx1dx2 = U or u(Sx~2C) = U. That is, the optimal Sx = 2C â€” Â£ ln(â€”U). â– REFERENCE LIST Autrey, R., S. Dikolli. and P. Newman, 2003, "The effect of career concerns on the contracting use of public and private performance measures," University of Texas at Austin working paper Arya, A., J. Glover, and S. Sunder, 1998, "Earnings management and the revelation principle," Review of Accounting Studies, 3, 7-34 , 2003, "Are unmanaged earnings always better for shareholders?," Accounting Horizons, Vol. 17, Supplement, 117-128 Barth, M. E., J. A. Elliot, D. W. Collins, G. M. Crooch, T. J. Frecka, E. A. Imhoff, Jr., W. R. Landsman, and R. G. Stephens, 1995, "Response to the FASB discussion document â€˜Accounting for hedging and other risk-adjusting activities: questions for comment and discussionâ€™," Accounting Horizons, Vol. 9. No.l March, 87-91 Barth, M. E., D. W. Collins, G. M. Crooch, J. A. Elliot, T. J. Frecka, E. A. Imhoff, Jr., W. R. Landsman, and R. G. Stephens, 1995, "Response to the FASB exposure draft â€˜Disclosure about derivative financial instruments and fair value of financial instrumentsâ€™," Accounting Horizons, Vol. 9. No.l March, 92-95 Barton, J., 2001, "Does the use of financial derivatives affect earnings management decisions?", The Accounting Review, Volume 76, No.l, 1-26 Beneish, M. D., 2001, "Earnings management: A perspective," Managerial Finance, 27, 12, 3-17 Campbell T. S. and W. A. Kracaw, 1987, "Optimal managerial incentive contracts and the value of corporate insurance," Journal of Financial and Quantitative Analysis, Vol. 22, No. 3 September, 315-328 Christensen, P. O., J. S. Demski, and H. Frimor, 2002, "Accounting policies in agencies with moral hazard and renegotiation," Journal of Accounting Research, Vol. 40, No. 4 September, 1071-1090 Christensen, J. A. and J. S. Demski, 2003, "Endogenous reporting discretion and auditing," working paper Christensen, J. A. and J. S. Demski, 2003, Accounting theory: an information content perspective, Chapter 17, McGraw-Hill/Irwin, New York. NY 78 79 Dadalt, P., G. D. Gay, and J. Nam, 2002, "Asymmetric information and corporate derivatives use," Journal of Futures Markets, Vol. 22, No. 3, 241-267 Dechow, P. M. and D. J. Skinner, 2000. "Earnings management: Reconciling the views of accounting academics, practitioners, and regulators," Accounting Horizons, Vol. 14 No. 2, June, 235-250 DeMarzo, P. M. and D. Duffie, 1995, "Corporate incentives for hedging and hedge accounting," The Review of Financial Studies, Fall 1995 Vol. 8, No. 3, 743-771 Demski, J. S., 1998, "Performance measure manipulation," Contemporary Accounting Research, Vol. 15 No.3, 261-285 Demski, J. S., and H. Frimor, 1999, "Performance measure garbling under renegotiation in multi-period agencies," Journal of Accounting Research, Vol. 37, supplement 1999, 187-214 Demski, J. S., H. Frimor, and D. Sappington, 2004, "Effective manipulation in a repeated setting," Journal of Accounting Research, Vol. 42, No. 1, March, 31-49 Dutta, S. and F. Gigler, 2002, "The effect of earnings forecasts on earnings management," Journal of Accounting Research, Vol. 40, No. 3 June, 631-655 Dutta, S. and S. Reichelstein, 1999, "Asset valuation and performance measurement in a dynamic agency setting," Review of Accounting Studies, 4, 235-258 Dye, R. A., 1988, "Earnings management in an overlapping generation model," Journal of Accounting Research, Vol. 26(2), 195-235 Financial Accounting Standards Board (FASB), 1994, "Disclosure about derivative financial instruments and fair value of financial instruments," Statement of Financial Accounting Standards No. 119 , 1998, "Accounting for derivative instruments and hedging activities," Statement of Financial Accounting Standards No. 133 , 1999, "Accounting for derivative instruments and hedging activitiesâ€”deferral of the effective date of FASB statement No. 133â€”an amendment of FASB Statement No. 133," Statement of Financial Accounting Standards No. 137 , 2000, "Accounting for certain derivative instruments and certain hedging activities, an amendment of FASB Statement No. 133," Statement of Financial Accounting Standards No. 138 , 2003, "Amendment of Statement 133 on derivative instruments and hedging activities," Statement of Financial Accounting Standards No. 149 80 Feltham, G. A. and J. Xie, 1994, "Performance measure congruity and diversity in multi-task principal/agent relations," The Accounting Review, Vol. 69, No. 3, July, 429-453 Graham, J. R. and D. A. Rogers, 2002, "Do Firms Hedge In Response To Tax Incentives?," Journal of Finance, Vol. 57(2, Apr), 815-839 Greenspan, A., 1999, "Financial derivatives", speech before the Futures Industry Association, Boca Raton, Florida, March 19 Healy, P. M. and J. M. Wahlen, 1999, "A review of the earnings management literature and its implications for standard setting," Accounting Horizons. Vol. 13 No. 4 December, 365-383 Holmstrom, B. and P. Milgrom, 1987, "Aggregation And Linearity In The Provision Of Intertemporal Incentives," Econometrica, Vol. 55(2), 303-328 Ijiri, Y. and R. K. Jaedicke, 1966, "Reliability and objectivity of accounting measurements," The Accounting Review, July, 474-483 Indjejikian, R. and D. Nanda, 1999, "Dynamic incentives and responsibility accounting," Journal of Accounting and Economics, 27, 177-201 Kanodia, C., A. Mukherji, H. Sapra, and R. Venugopalan, 2000, "Hedge disclosures, future prices, and production distortions," Journal of Accounting Research, Vol. 38 Supplement, 53-82 Kim, S. K., 1995, "Efficiency of an information system in an agency model," Econometrica, Vol. 63, No. 1, 89-102 Kim, S. K., and Y. S. Suh, 1991, "Ranking of accounting information systems for management control," Journal of Accounting Research, Vol. 29. No. 2 Autumn, 386-396 Lambert, R. A., 2001, "Contracting theory and accounting," Journal of Accounting and Economics, 32, 3-87 Lev, B, 2003, "Corporate earnings Tacts and fiction," Journal of Economic Perspectives, Vol 17, No. 2, Spring, 27-50 Levitt, A., 1998, "The numbers game", remarks of Chairman at the N.Y.U. Center for Law and Business, New York, N.Y. Sept. 28 Liang, P. J., in press, "Equilibrium earnings management, incentive contracts, and accounting standards," Contemporary Accounting Research Linsmeier, T., 2003, "Accounting for Derivatives in Financial Statements," Financial Accounting AAA Annual Conference presentation, Orlando 81 Mayers, D. and C. W. Smith, 1982, "On the corporate demand for insurance," Journal of Business, Vol. 55, No. 2, 281-296 Melumad, N. D., G. Weyns and A. Ziv, 1999, "Comparing alternative hedge accounting standards: shareholdersâ€™ perspective," Review of Accounting Studies, Vol. 4(3/4, Dec), 265-292 Milgrom, P. and N. Stokey, 1982, "Information, trade and common knowledge," Journal of Economic Theory 26, 17-27 Mirrlees, J., 1974, "Notes on welfare economics, information and uncertainty," Essays in Economics Behavior Under Uncertainty, edited by M. Balch, D. MeFadden and S. Wu. Amsterdam: North-Holland, 243-258 Nance, D. R., C. W. Smith, Jr. and C. W. Smithson, 1993, "On the determinants of corporate hedging," Journal of Finance, Vol. 48(1), 267-284 Pincus, M. and S. Rajgopal, 2002, "The interaction between accrual management and hedging: evidence from oil and gas firms," The Accounting Review, Vol. 77, No. 1 January, 127-160 Rogers, D. A., 2002, "Does executive portfolio structure affect risk management? CEO risk-taking incentives and corporate derivatives usage," Journal of Banking and Finance, 26, 271-295 Rothschild, M. and J. E. Stiglitz, 1970, "Increasing risk: 1. A definition," Journal of Economic Theory 2, 225-243 Ryan, S. G., 2002, Financial Instruments & Institutions, Accounting and Disclosure Rules, Chapter 10, John Wiley & Sons, Inc., Hoboken, NJ Schipper, K., 1989, "Commentary: earnings management," Accounting Horizons, December, 91-102 Schrand, C. and H. Unal, 1998, "Hedging and coordinated risk management: evidence from thrift conversions," Journal of Finance, Vol. LIII, No. 3 June, 979-1013 Schuetze, W. P., 2002, testimony on the hearing on accounting and investor protection issues raised by Enron and other public companies: oversight of the accounting profession, audit quality and independence, and formulation of accounting principles, February 26 Smith, C. W. and R. M. Stulz, 1985, "The determinants of firmsâ€™ hedging policies," Journal of Financial and Quantitative Analysis, Vol. 20, No. 4 December, 391-405 BIOGRAPHICAL SKETCH Lin Nan was born in Beijing, China, in spring 1973. In June 1995, she received a Bachelor of Engineering in industrial economics from Tianjin University in Tianjin, China. She then worked at the Industrial and Commercial Bank of China (ICBC) for two years as Presidential Assistant. In 1997, Lin came to the United States and started her graduate education at the West Virginia University in Morgantown, West Virginia. She received her Master of Arts in economics in August 1999 and then joined the accounting doctoral program at the University of Florida in Gainesville, Florida. She is expected to graduate with a Ph.D. degree in August 2004. 82 I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. <â– Hbr_Q Joel S. Demski, Chair Frederick E. Fisher Eminent Scholar of Accounting I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adeÃºdate, in scope and quality, asji, dissertation for the degree of Doctor of PhilosopD S? DgvfcFE. M. Sappington Lanzillotti-McKethan Eminent Scholar of Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequatÃ©^in scope apd qualify, as a dissertation for the degree of Doctor of Philosophy. Karl 'K Hackenbrack Associate Professor of Accounting I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy^ mÃ³VvbaTP â€™rofessor of Accounting This dissertation was submitted to the Graduate Faculty of the Fisher School of Accounting in the Warrington College of Business Administration and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 2004 Dean, Graduate School LD 1780 202Â¿Â¿_ i â– '* .tins UNIVERSITY OF FLORIDA 3 1262 08554 2073 |