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Essays in Corporate Diversification, Market Efficiency, and Allocation of Scarce Resources

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Essays in Corporate Diversification, Market Efficiency, and Allocation of Scarce Resources
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BORGHESI, RICHARD ( Author, Primary )
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2008

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Betting ( jstor )
Bonuses ( jstor )
Business structures ( jstor )
Cooperative games ( jstor )
Diversification ( jstor )
Gini coefficient ( jstor )
Modeling ( jstor )
P values ( jstor )
Salary ( jstor )
Statistical models ( jstor )

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University of Florida
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University of Florida
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Copyright Richard Borghesi. 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.
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8/31/2006
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ESSAYS IN CORPORATE DIVERSIFICATION, MARKET EFFICIENCY, AND ALLOCATION OF SCARCE RESOURCES By RICHARD BORGHESI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004

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Copyright 2004 by Richard Borghesi

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This research is dedicated to my parents.

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ACKNOWLEDGMENTS I thank Andy Naranjo, Stas Nikolova and Glenn Williams their insightful comments and friendship. I am also indebted to Karl Hackenbrack, Joel Houston, Gary McGill, M. Nimalendran, and Jay Ritter for their time and effort in helping me complete this work. iv

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TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES...........................................................................................................ix ABSTRACT.........................................................................................................................x CHAPTER 1 INTRODUCTION........................................................................................................1 2 VALUE, SURVIVAL, AND THE EVOLUTION OF FIRM ORGANIZATIONAL STRUCTURE...............................................................................................................4 2.1 Data......................................................................................................................10 2.2 Firm Age and the Value of Diversification.........................................................11 2.3 The Endogeneity of Organizational Structure.....................................................16 2.4 Organizational Structure and Survival.................................................................18 2.5 Firm Age and the Evolution of Organizational Structure....................................23 2.6 Conclusions..........................................................................................................27 3 WEATHER BIASES IN THE NFL BETTING MARKET: EXPLAINING THE HOME UNDERDOG EFFECT..................................................................................44 3.1 Sports Betting......................................................................................................46 3.2 Data and Methodology........................................................................................48 3.2.1 Data............................................................................................................48 3.2.2 Methodology..............................................................................................49 3.3 Results..................................................................................................................51 3.3.1 Summary Statistics....................................................................................51 3.3.2 Temperature Conditions............................................................................55 3.3.3 Alternative Theories..................................................................................58 3.3.4 Regression Analysis..................................................................................60 3.3.4.1 Model specification.........................................................................60 3.3.4.2 Regression results............................................................................63 3.3.4.3 In-sample predictability...................................................................66 3.3.4.5 Noise reduction...............................................................................67 v

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3.3.4.6 Out-of-sample predictability...........................................................70 3.4 Conclusions..........................................................................................................73 4 ALLOCATION OF SCARCE FINANCIAL RESOURCES: INSIGHT FROM THE NFL SALARY CAP..........................................................................................84 4.1 The Collective Bargaining Agreement................................................................85 4.2 Analysis...............................................................................................................89 4.2.1 Data............................................................................................................89 4.2.2 Methodology..............................................................................................92 4.2.2.1 The Lorenz curve and Gini coefficient...........................................92 4.2.2.2 Regression analysis.........................................................................93 4.3 Results..................................................................................................................95 4.3.1 Compensation Distribution........................................................................95 4.3.2 Player Performance and Compensation.....................................................97 4.3.3 Positional Compensation and Statistical Rank..........................................99 4.3.4 Positional Compensation and Team Wins...............................................102 4.3.5 Parity........................................................................................................104 4.3.6 Salary Components and Team Performance...........................................105 4.4 Conclusions........................................................................................................106 5 CONCLUSION.........................................................................................................122 APPENDIX A SFAS131 SEGMENT DATA ISSUES....................................................................125 B EXCESS VALUE CALCULATIONS.....................................................................127 C SALARY CAP EXAMPLE......................................................................................129 LIST OF REFERENCES.................................................................................................131 BIOGRAPHICAL SKETCH...........................................................................................135 vi

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LIST OF TABLES Table page 2-1 Firm Characteristics by Year......................................................................................29 2-2 Summary Statistics by Organizational Form..............................................................30 2-3 Determinants of Excess Value for All Firms..............................................................32 2-4 Determinants of Excess Value by Age Group............................................................33 2-5 Determinants of Organizational Form........................................................................34 2-6 Annual Percentage of Firms that Declare Bankruptcy...............................................35 2-7 Firm Survivorship Model...........................................................................................35 2-8 Summary Statistics by Firm Age................................................................................36 2-9 The Effect of Excess Value on Changes in Herf........................................................39 2-10 The Effect of Changes in Herf on Excess Value......................................................39 3-1 NFL Closing Line Summary Statistics.......................................................................74 3-2 NFL Game Outcomes.................................................................................................75 3-3 NFL Cover Frequency................................................................................................76 3-4 Open-Air Stadium Game Day Temperature...............................................................77 3-5 Open-Air Stadium Game Outcomes...........................................................................78 3-6 Base Model and Temperature-Augmented Models....................................................79 3-7 Adjusted Base Model and Adjusted Temperature-Augmented Models.....................80 3-8 Home Underdog Attenuation......................................................................................81 3-9 December and January Home Underdog Attenuation................................................81 3-10 NFL Monthly Outcome Predictability......................................................................82 vii

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3-11 Nevada Football Betting...........................................................................................83 4-1 NFL Player Summary Statistics...............................................................................108 4-2 Determinants of Compensation by Defensive Position............................................109 4-3 Determinants of Compensation by Defensive Position............................................110 4-4 Team Defensive Performance..................................................................................112 4-5 Team Offensive Performance...................................................................................113 4-6 Team Positional Spending and Wins........................................................................114 4-7 Salary Components and Wins...................................................................................115 C-1 Initial Player Contract..............................................................................................130 C-2 Modified Player Contract.........................................................................................130 viii

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LIST OF FIGURES Figure page 2-1 Organizational Form and Firm Survival.....................................................................39 2-2 Mortality Rate by Firm Age.......................................................................................41 2-3 Firm Age and Survival...............................................................................................42 2-4 Mortality Rate by Firm Type......................................................................................43 4-1 NFL Compensation Trends......................................................................................116 4-2 NFL Player Base Salary Lorenz Curve....................................................................117 4-3 NFL Player Bonus Salary Lorenz Curve..................................................................118 4-4 NFL Player Total Salary Lorenz Curve....................................................................119 4-5 Total Equality vs. Ideal Distribution........................................................................120 4-6 Parity in the NFL......................................................................................................121 ix

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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 ESSAYS IN CORPORATE DIVERSIFICATION, MARKET EFFICIENCY, AND ALLOCATION OF SCARCE RESOURCES By Richard Borghesi August 2004 Chair: Andy Naranjo Cochair: Joel Houston Major Department: Finance, Insurance and Real Estate This dissertation is composed of three essays that address corporate diversification, market efficiency, and allocation of scarce financial resources. The analysis in chapter 2 examines the relationship between changes in firm organizational structure and fluctuations in market value. Organizational structure in this context is defined as the level of corporate diversification, and is measured as the dispersion of total firm sales among existing business segments. The speed and accuracy of the equities market’s reaction to events such as corporate reorganization are tested in chapter 3. Finally, in chapter 4, we supplement our organizational structure analysis by examining managerial decision-making in an environment where resources are artificially bounded. Previous literature has documented that firms operating in more than one industry trade at a discount on average relative to focused firms in similar industries. Using a sample of more than 60,000 firm-year observations over the time period 1981-2000, we find that magnitude of the diversification discount falls from 8 percent to just above 2 x

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percent when we control for firm age and survivorship biases. We also find that diversified firms have higher survival rates, diversification is particularly costly for younger firms, and focusing activities are particularly valuable for poorly performing conglomerates. Results suggest that optimal organizational structure evolves over time and that firm history plays an important role in defining the set of value-creating opportunities. In chapter 3, we test financial market efficiency by studying outcome predictability in the National Football League [NFL hereafter] betting market. Our main contribution to the existing literature is the identification of a highly significant increase in the magnitude of the market forecast error during the final few weeks of each season. We demonstrate that this anomaly, which arises because the impact of game day temperature on team performance is underestimated, largely explains the home underdog effect. In chapter 4, using NFL compensation data from 1994 to 2002, we examine the relationship between compensation distribution, performance, and organizational success. We find that the equity of wealth allocation among each team’s population of players is significantly related to performance. Specifically, we find evidence suggesting that teams are likely to perform better than expected if they consist of few highly talented impact players supplemented by a group of below-average bargain players. xi

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CHAPTER 1 INTRODUCTION This paper provides insight into the underlying motives and financial effects of managerial decision making. We begin by examining market reaction to changes in the scope of businesses in which individual firms operate. We then analyze the effectiveness of managers at allocating scarce financial resources. While fluctuations in market valuation are a useful benchmark for determining the soundness of such decisions, perfect market efficiency is not assumed. We instead supplement our analysis by examining the capacity of equities markets to determine the true value of securities. In recent literature, there has been ongoing debate over the value of corporate diversification strategies. Researchers document that diversified firms trade at a discount on average relative to single-segment firms in similar industries. Broadly speaking, the explanations for observed discount fall into two main categories. One view is that diversification destroys firm value (Berger and Ofek 1995). Some value-destruction theories suggest that the discount arises because of agency problems between managers and stockholders (May 1995) and persists because of an imperfect market for corporate control (Scharfstein and Stein 2000). Another view is that the observed diversification discount is due primarily to a variety of measurement issues, and that diversification does not necessarily destroy value (Campa and Kedia 2002; Graham, Lemmon, and Wolf 2002; and Villalonga 1999). In addition, a number of recent papers argue that, despite the associated discount, diversification may be an optimal value maximizing strategy for certain firms under 1

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2 specific circumstances (Matsusaka 2001). We attempt to explain the relationship between diversification and value by using a time-series approach to measure value fluctuations before and after organizational changes occur. It can be difficult to determine the true underlying value of diversified firms in part because internal accounting procedures are often complex when firms consist of more than one division. Also, managers have a motive to use creative accounting when assigning assets and sales figures to particular divisions. Even if there is no intent to deceive, investors may not immediately incorporate all relevant valuation information, so it is possible that the market price of a firm, especially those undergoing large organizational changes, may temporarily deviate from its true underlying value. In chapter 4, we use the NFL betting market to measure the degree of efficiency in the equities marketplace. This environment is a good proxy because in contrast to equities markets, where the fundamental values of securities are not typically revealed, sports betting markets provide observable outcomes in the form of the difference in points scored by opposing teams. Both types of markets are characterized by a large number of participants, competitive bidding, public and private information, transaction costs, and market professionals. Bettors (investors), moreover, make decisions based on the perceived quality (value) of the team (asset). Similar to securities prices at the end of trading, closing lines in sports betting markets should incorporate all available information plus any biases of the market participants. In chapter 5, we examine allocation of scarce financial resources, which is another important component to corporate diversification decisions. Firms experiencing diminishing returns to scale in their core businesses may divert resources into new

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3 business lines (Gomes and Livdan 2004). These resources typically consist of organizational talent and/or capital. To accurately measure the effect of resource allocation decisions, we again use the NFL player market as a model. The NFL enacted a team salary cap beginning in the 1994 season, so franchises operate with artificially bounded resource levels. The existence of this cap in addition to the discrete observable outcomes makes the NFL player market an ideal market in which to examine resource allocation decisions.

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CHAPTER 2 VALUE, SURVIVAL, AND THE EVOLUTION OF FIRM ORGANIZATIONAL STRUCTURE A large and growing literature has documented that diversified firms on average trade at a discount relative to single-segment firms in the same industries. Estimates of the magnitude of this discount are often quite large. In many respects, large and persistent discounts are puzzling, and therefore it is not surprising that a number of papers have sought to explain these observed discounts (Amihud and Lev 1981; Jensen 1986; Schleifer and Vishny 1989; Scharstein and Stein 2000; Whited 1999; and Gomes and Livdan 2004). Broadly speaking, the explanations for these observed discounts fall into two main categories. One view is that diversification reduces firm value, and that these discounts persist because of agency problems between firm managers and stockholders. More specifically, the agency explanation states that firm managers may benefit from diversification even though it reduces shareholder value. One possibility is that managers are motivated by the additional compensation and/or prestige that are associated with operating a diversified (and often larger) firm. Moreover, it may be easier for executives to skim profits as firms become more complex and accounting procedures become more opaque. Finally, because a large portion of managers’ wealth is tied to the corporation, some researchers suggest that managers pursue diversifying activity to reduce 4

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5 idiosyncratic risk. If the market for corporate control is imperfect, then diversification discounts caused by agency problems may persist over time. 1 Another view is that observed diversification discounts are due primarily to a variety of measurement issues, and that diversification does not necessarily reduce firm value. For example, Graham, Lemmon, and Wolf (2002) demonstrate that acquiring firms often acquire poorly performing firms that are already trading at a discount prior to the merger. So, it may be the case that poorly performing segments, which are acquired at a fairly priced discount, are responsible for the diversification discount. If so, the act of diversification itself does not destroy value. More generally, the observed discounts may be attributed to poorly performing firms choosing to diversify rather than diversification itself reducing value. In this spirit, much literature has suggested that the diversification discount is significantly reduced, or disappears altogether, after controlling for these other factors (Campa and Kedia 2002; Graham, Lemmon, and Wolf 2002; and Villalonga 1999). Building upon these ideas, a number of recent papers also argue that, despite the associated discount, diversification may be an optimal value maximizing strategy for certain firms, in specific circumstances. Matsusaka (2001) shows that firms which are particularly efficient in healthy industries destroy value by diversifying. On the other hand, diversification may be optimal for firms that are being outperformed by current competitors or for firms that can identify a better match with existing organizational 1 In support of the agency hypothesis, May (1995) finds that firms with greater blockholder ownership percentages tend to be less focused. He argues that managers are concerned with idiosyncratic risk and are therefore more interested in diversifying their risk exposure than in maximizing shareholder wealth. However, Denis, Denis, and Sarin (1997) find that firms with greater blockholder ownership tend to be more focused. They show that managers having a relatively high level of ownership are more likely to focus on creating shareholder value and are less concerned with exploiting the private benefits of diversification.

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6 skills. In this scenario, the opportunity to diversify essentially becomes a call option with a price equal to the cost of entering a new line of business through acquisition or research and development. If firms act rationally, then this explanation is consistent with the empirical observations that the stock market reacts positively both to refocusing activities (spin-offs and divestitures) and to diversifying acquisitions. Gomes and Livdan (2004) develop a model showing that the observed diversification discount is consistent with the maximization of shareholder value. In particular, conglomerates are able to create synergies by eliminating redundancies across different activities and avoiding decreasing returns to scale. Because firms differ in size and productivity, each firm has a different cost/benefit relationship with diversification. Gomes and Livdan (2004) propose that firms diversify when they become relatively unproductive in their current activities, and that diversification allows firms to explore profitable new opportunities. They conclude that the endogenous selection of firm focus is responsible for the diversification discount, as firms diversify only when they become relatively unproductive in their current activities. In another recent theoretical paper, Khoroshilov (2003) develops a dynamic model of firm organizational structure. He distinguishes between the “observed diversification discount” and the “real diversification discount” and suggests that self-selection biases may produce observed diversification discounts. Khoroshilov (2003) argues that it is therefore important to control for these selection biases when interpreting observed diversification discounts. Similarly, Burch, Nanda, and Narayanan (2003) argue that industry conditions have a significant effect on the excess value of diversified firms. Applying the existing value theories of conglomeration (market power, resources

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7 hypothesis, and internal capital markets), they conclude that conglomeration is favored when growth opportunities are low and when there are many firms competing in the industry. In many respects, the agency cost theory and the more recent optimality theories discussed above are not mutually exclusive. Moreover, the decision to diversify and the value of diversification both depend on the firm’s particular characteristics and experiences. These characteristics may include ownership structure (as in May 1995 and Denis et al. 1997), efficiency (as in Matsusaka 2001), or environment (as in Burch et al. 2003). Furthermore, each firm’s experiences influence how well prepared it is for changes. To examine these issues in greater detail, we examine the value of diversification and the decision to diversify for a large sample of publicly traded firms over a twenty year time period, 1981-2000. Building upon the ideas of previous literature, our analysis takes into account two other factors that are likely to affect both the decision to diversify and the value of diversification. The first factor is the age of the firm. 2 We begin with the observation that most firms begin as focused entities. As firms evolve over time, they become much more likely to expand the scope of their business and to alter their capital structure. In addition to its impact on the likelihood of diversification, firm age is also likely to affect the measured value of diversification. In the standard Berger and Ofek (1995) approach, a weighted average of pure-play market multiples are used to calculate the 2 There are a number of ways to define firm age (e.g., years since incorporation, years since IPO, and years since first listing on CRSP). We define firm age as the number of years since the firm’s IPO. We also compare the IPO dates to the initial CRSP listing dates and find that they match. We thank Jay Ritter for providing the IPO dates.

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8 implied value of diversified firms. Clearly, these multiples may be affected by factors other than the firm’s organizational structure. The existing literature has attempted to control for these other factors, but the previous studies have generally not controlled for firm age. A notable exception is the recent work of Bevelander (2002) who finds that firm age is significantly related to Tobin’s q, and that the magnitude of the diversification discount is reduced after controlling for firm age. Age may be a useful proxy for growth opportunities and other factors that are likely to have profound effect on the market multiples of individual firms. Furthermore, on an economy-wide level, the estimated value of diversification is likely to vary over time with changes in the average age of publicly traded firms. Indeed, Fama and French (2003) demonstrate that the percentage of new firms and the characteristics of new lists have changed substantially since 1973. In our analysis, we account both for this possibility and for potential performance differences caused by the changing macro-level economic conditions over the 20-year sample period. Another measurement issue that may be important and has yet to be addressed in the extant literature is survivorship bias. As our results show, diversified firms fail less often than focused firms. The calculated diversification discounts, then, are biased since the value of diversified firms is compared only to the best pure plays – those that survive. In our analysis, we account for the impact that bankrupt firms have on excess value calculations. Consistent with previous studies, we find that the observed diversification discount is relatively large (around 8%) and persists over our sample period. Lending support to the agency view, we find that the magnitude of the diversification discount is related to

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9 the level of insider and institutional ownership. However, we find that after taking into account the measurement issues related to firm age and survival, the magnitude of the observed discount falls to just above 2%. Thus, while diversification may, on average, lead to small reductions in value, the large majority of the diversification discount can be attributed to measurement issues related to the different characteristics of focused and diversified firms. Our results support some of the more recent theoretical papers that suggest diversification may be value enhancing for some firms. We find that the value (and cost) of diversification depends critically on firm age and past performance. Furthermore, our results indicate that diversification is an important mechanism for firm survival and that it often enables firms to explore better opportunities. More specifically, we find that diversification tends to be less costly for older firms. This result suggests that firm history plays an important role in defining the set of value-creating opportunities. It also supports the dynamic diversification model proposed by Khoroshilov (2003) in which the amount following a diversifying activity is an important component of observed diversification discounts. Furthermore, it is consistent with the model proposed by Gomes and Livdan (2004), which suggests that older firms can redirect resources away from business units experiencing diminishing returns while also benefiting from synergies. On the other hand, as in Matsusaka’s (2003) model, firms that are particularly productive have little to gain from pursuing new businesses. Our results indicate that very young firms are less likely to add value by diversifying. These firms trade at the

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10 largest discount relative to their age-matched focused peers. It is likely that these firms are sacrificing good projects for diversification efforts. To further explore these issues, we also examine in detail the evolution of organizational structure over the past two decades. As expected, we find that these firms tend to become more diversified as they get older and larger over time. Interestingly, we find that past performance relative to peers has little effect on the firm’s decision to diversify, though there are contemporaneous effects. Past performance, however, does have a significant impact on the value of diversification. Among the surviving firms, we find that there is a fair amount of mean reversion in excess value. We also find that regardless of firm age, when focused firms become diversified, their observed excess value falls. On the flip side, we find that diversified firms that become focused experience an increase in excess value, and that this effect is particularly pronounced for poorly performing conglomerates that subsequently decide to become focused. 2.1 Data We obtain firmand segment-level data from Standard and Poor’s Compustat Industrial and Compustat Industry Segment (CIS) databases from 1981-2000. The industrial files contain firm-level accounting data on 10,000 active and 9,700 inactive companies. These data are gathered from income statements, balance sheets, flows of funds, and other resources. The segment-level database breaks down the accounting figures into firm-reported business segments. Prior to 1997, the definition of ‘business segment’ follows Financial Accounting Standards Board’s (FASB) Statement No. 14, Financial Reporting for Segments of a Business. This document is referred to as SFAS (Statement of Financial Accounting Standards) 14. Under SFAS 14, financial statements were disaggregated and

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11 standardized in definition. Beginning in 1997, under the newer SFAS 131, a ‘management approach’ is taken in which information on business segments is reported based on how management internally evaluates the operating performance of its business units (Berger and Hahn 2003). More business segments have been reported annually following the conversion in accounting procedures. In Appendix A, we provide additional details on potential data problems arising from SFAS 131 and how we adjust for them. As a robustness check, we also separately examine the 1981-1996 sample period. We collect equity data and information for Compustat firms from the Center for Research in Securities Prices (CRSP) database. CRSP contains stock price data for firms trading on the NYSE, AMEX, and NASDAQ markets as well as delisting information. To analyze agency issues, we also gather stock ownership data for insiders and institutional owners from Lancer Analytics and Thompson Financial. The insider equity ownership database contains data from insider SEC filings. The institutional database contains institutional 13(f) common stock holdings and transactions. Institutional ownership data are complete from 1981-2000, and insider ownership data are available from 1986-2000. 2.2 Firm Age and the Value of Diversification Table 2-1 illustrates the trends in average firm age, organizational structure, and the cost of diversification from 1981 to 2000. The average age of firms in the sample is 14.3 years. We also find that the average firm age has decreased over time, which is consistent with Fama and French (2003), who also find that publicly traded firms have become younger, on average, in recent years.

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12 Approximately 1/3 rd of all firms are diversified. For each diversified firm, we calculate a Herfindahl (Herf) measure of industry concentration based on each firm’s segment. A purely focused firm would have a Herf equal to one. The average Herf for the firms in our sample is about 0.85. Consistent with Comment and Jarrell (1995), we also find that the level of corporate diversification has decreased over time. However, as discussed earlier, the inception of SFAS 131 in 1997 resulted in a greater number of reported segments and thus an increase in the number of diversified firms. The final column of Table 2-1 highlights the changes in the discount of diversified firms. As in Berger and Ofek (1995), we calculate a measure of excess value for diversified firms based on value-to-sales ratios of equivalent pure-plays. 3 We screen our sample by eliminating those firms having less than $20 million in annual sales, industry segments operating in financial services (SIC codes 6000-6999), firms with missing or inaccurate segment sales, and those with no matching equity data. We keep only firms with common ordinary shares (CRSP share codes 10 and 11), thus excluding ADRs and closed end mutual funds from our sample. Looking at the last column of Table 2-1, we see that the mean diversification discount over the full sample period is 7.87% and, excluding the SFAS 131 years, ranges from 2.11% (in 1987) to 13.06% (in 1983). 3 There are many possible approaches to calculating pure-play values used to determine the diversification discount. One issue is whether to align equity returns with Compustat fiscal year or with calendar year. One advantage of matching calendar year returns with fiscal year accounting data is that market anomalies are captured in such a way that value-to-sales ratios for all firms in a particular year will include such events. Since there is likely to be more systematic volatility in equity prices than in accounting figures, this approach makes value ratios more comparable. We test the effect of aligning equity prices with fiscal years and find that our results are robust to either approach. Please also see Appendix B for additional details on the excess value formulation. Whether concurrent or lagged equity data should be used is also a point of contention. If concurrent prices are used, then perfect market efficiency must be assumed. On the other hand, lagging equity prices behind the release of performance data allows for a weaker assumption about market efficiency. Fama and French (1992) match the accounting returns with equity data that is lagged by between six and 18 months. This ensures that accounting variables are known before they are assumed to be incorporated into prices. We lag our prices as in Fama and French and find that our results do not change.

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13 Consistent with Lang and Stulz (1994) and Berger and Ofek (1995), our results suggest that diversified firms consistently trade at a discount compared to equivalent pure-plays. 4 Focused and diversified firms differ not only in excess value, but also in other fundamental characteristics. Table 2-2 shows that level of diversification level is highly correlated with age, excess value, ownership, and capital structure. Single-segment firms are younger (mean age 10.8 years vs. 21.3 years) and smaller (mean sales $674.90MM vs. $1,580.85MM) than their diversified counterparts. In addition, the most diversified firms have the largest diversification discounts. To analyze the determinants of excess value, we use fixed-effects regression procedures with the following general model specification: itititbY )(X , (1) where Y it is excess value for firm i in period t, and X it is a corresponding vector of explanatory variables including firm age (measured as the natural logarithm of the number of years since IPO), size (measured as the natural logarithm of sales), Herf (based on sales), insider and institutional ownership, excess age and excess ownership (relative to focused peers in the same industries), a focus dummy, an interaction term between Herf and age, leverage (the ratio of long-term debt to the sum of long term debt and market value of equity), profitability (EBITDA/assets), volatility (annual standard deviation of returns based on monthly share prices), and level of growth opportunities (defined as the ratio of capital expenditures to sales). 4 Lang and Stulz (1994) find that the q ratios of diversified firms are between 10% and 50% lower than those of focused firms. Berger and Ofek (1995) find a mean diversification discount of 9.70% from 1986 to 1991 using sales multiples.

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14 There are a number of testable hypotheses. First, if diversification is valuedestroying, then we would expect Herf and excess value to have a negative relation. This relation would also be affected by ownership characteristics if agency theories hold. If we find that diversifying firms with greater insider ownership are particularly valuedestroying, then our analysis would support May’s (1995) idiosyncratic risk reduction hypothesis. On the other hand, if firms with more insider holdings are better diversifiers, then our results would be more consistent with the results of Denis, Denis, and Sarin (1997), which show that managers are more inclined to pursue a wealth-maximizing strategy. Furthermore, if agency issues partly explain the level of diversification, and diversification is value destroying, firms with more institutional ownership should either be less diversified or destroy less value when they do diversify. While institutions generally hold stock in larger, more established firms, we should be able to interpret the coefficient estimate properly because we control for size and age in our regression analysis. One potential advantage that diversified firms have over their focused counterparts is that they are able to take advantage of the tax shields of debt. Because their divisional earnings are not perfectly correlated, aggregate firm earnings are smoothed, and lending becomes less risky ceteris paribus. Therefore, if we observe that diversified firms are characterized by less volatile earnings and a higher debt ratio than focused firms, then organizations are likely using diversification as a means to increase debt. The regression results are summarized in Table 2-3. Looking first at Model 1, we find that excess value is negatively related to firm size and firm age. These results may

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15 suggest that older and larger firms are less efficient. More likely, however, these results reflect the fact that older and larger firms tend to have lower expected growth rates, which translates into lower multiples and lower estimates of excess value. Model 1 also shows that firms with higher proportions of insider and institutional ownership tend to have higher levels of excess value, which lends support to the agency hypothesis. Finally, we see that there is a positive and significant link between Herf and excess value. This confirms that diversification destroys value even after controlling for firm size and firm age. We find similar results in Model 2, where we use a bivariate measure of corporate focus in place of our Herf measure. We next consider two alternative specifications. The first (Model 3) replaces the absolute measures of firm age and the ownership with measures that are calculated relative to their industry averages. For example, excess age is calculated as the natural log of firm age minus the natural log of the median firm age of the matched pure-play firms that are used to calculate excess value. The estimates for excess age and excess ownership show that these explanatory variables are important not only in absolute terms, but also in relative terms. Firms that are younger than their pure-play counterparts and those with more blockholder ownership have higher levels of excess value. The second alternative (Model 4) includes our additional explanatory variables. Here we see that volatility is positively correlated with Herf, and that diversified firms use more debt. Interestingly, the negative coefficient on the interaction term indicates that while diversification reduces value for all firms, organizational focus is even more important for younger firms.

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16 As discussed earlier, because focused and diversified firms differ significantly in a range of firm characteristics (e.g., age, performance, debt, etc.), it is important to also consider other pure-play matches rather than just comparing firms within the same SIC codes. To demonstrate this point, we recalculate the diversification discount by imposing an additional age-matching requirement. We place firms into age buckets and compare pure play firms to diversified firms only if they fall into both the same age category and same SIC category. We use two versions of the age restrictions. In the first, we split firms into two age groups – young (less than 10 years old) and old (at least 10 years old). In the second, we break them into three age groups – young (less than 5 years old), mature (between 6 and 20 years old), and old (at least 21 years old). Table 2-4 shows that diversification destroys value, but the negative effect is significantly reduced when age matching is utilized. In Table 2-1, the data showed that there exists an average diversification discount of 7.87% for conglomerates. However, after incorporating the age match restriction into these calculations, the diversification discount falls to 5.50% when we use two age categories, and to 3.51% when we use three age categories. 5 2.3 The Endogeneity of Organizational Structure While our earlier results suggest that there is a relation between age and organizational structure, the relation is indirect. Ultimately, the choices that management 5 While a combined ageand SIC-matching approach is ceteris paribus better than simply SIC-matching, a problem arises because the number of 4-digit SIC pure-play matches is reduced when the age constraint is introduced. In Berger and Ofek (1995), 44.6% of all segments of diversified companies are based on four-digit SIC codes, 25.4% on three-digit codes, and 30.0% on two-digit codes. When firms are broken into two age categories, over the same time period we find that 27.2% of the observations are four-digit, are 22.9% three-digit, and 49.9% are two-digit. Imposing the stricter three age group matching, 17.6% of observations are four-digit, 15.4% are three-digit, and 67.0% are two-digit. There is a trade-off, then, between capturing the age effect and ensuring the accuracy of industry matches. However, we obtain the same qualitative results regardless of whether we rely only on SIC matching or require both SIC and age matching.

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17 makes directly determine organizational structure. For instance, the decision to sell off existing business lines or to expand into new industries determines whether firms will become more or less focused. Agency issues also influence strategic decisions about diversification, and the opportunity set depends in part on capital structure, size, and management’s experience. We now look at the evolution of organizational structure over time to determine whether firms diversify in a predictable manner. To test the determinants of organizational form in a static setting, we again use fixed-effects regression procedures with a model specification similar to that in equation (1). The explanatory variables we include are age, size, leverage, and ownership. The results of our regression analysis are presented in Table 2-5. The data confirm that diversified firms are bigger, older, and have more debt than focused firms and that this relationship is also persistent over time. The results also support the agency view of diversification. After controlling for firm characteristics, we find that firms with more institutional ownership are less likely to be diversified. In Table 2-3 we showed that the discount caused by diversification strategies seems to be lower in magnitude among those firms with higher managerial stakes. However, in Table 2-5 we see that insider ownership is not important in determining whether or not firms diversify once other firm characteristics have been taken into account. While this model provides us with a good understanding of firm organizational form in a static framework, we must also consider that firms change in response to external events. Recent successes or failures may affect managers’ judgment and attitude towards risk-taking. For instance, executives of top performing firms may be

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18 overconfident and adopt diversification strategies founded on hubris. If this were true, we would expect diversification strategies of successful firms to reduce value. To analyze the time-series relationship between performance and organizational form, we construct two models. In the first, the endogenous variable is change in Herf. Our explanatory variables include three measures of past performance that vary in length (change in excess value over the past one, two, and three years), a dummy for age, and dummies for firms in the top or bottom quartile of excess value. In the second, the excess value and Herf variables are transposed, and we instead model excess value as a function of changes in Herf. Though not shown, the results indicate that lagged changes in performance are positively correlated with changes in organizational form. Results also show that lagged changes in Herf are positively associated with changes in excess value. The implication is that excess value and organizational form are determined simultaneously, and that firms are behaving optimally. Somewhat contrary to the hubris hypothesis, we find that past success inspires managers to concentrate more on existing businesses. To correct for potential simultaneity issues, we also specify a SUR model in which Herf is determined by ownership, age, and excess value measures. The resulting Herf is used as an explanatory variable to determine excess value. Though not reported, the results are again similar. 2.4 Organizational Structure and Survival While the value of diversification depends on the particular characteristics and history of each firm, we also find that there is another important, yet unexplored, relationship between organizational structure and firm history. We observe that survival depends on focus. Table 2-6 displays summary statistics on firms that declare

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19 bankruptcy. It illustrates that focused firms and younger firms have higher mortality rates than diversified firms. Old focused firms are the most likely to declare bankruptcy. The relationship between survival and organizational form is also graphically depicted in Figure 2-1. This diagram shows that firms which eventually declare bankruptcy are more focused than those that survive. This phenomenon is not driven by systematic changes in firms as they approach bankruptcy. On the contrary, in each of the five years prior to firms declaring bankruptcy, we find that mean change in Herf is no different than zero. Figures 2-2 and 2-3 compare the mortality rate of focused and diversified firms at different ages. Again we see that young firms and focused firms are more likely to fail. Our results are consistent with those of Fama and French (2003), who also observe that younger firms are more likely to be delisted for poor performance than are seasoned firms. We also find that the lowest incidence of mortality occurs in older diversified firms. There is, then, a strong relationship between age, focus, and mortality. Figure 2-4 shows the relationship between excess value and mortality over time and compares firms by performance. Here, ‘bad’ firms are those having negative excess values, and ‘good’ firms are those with positive excess values. We see that bad focused firms fail more often than bad diversified firms. More importantly, however, we see that good focused firms fail more often than good diversified firms. Intuitively, it would seem that if firm finds a particularly good match for its organizational talents, it should devote itself exclusively to that industry. However, the data reveals that operating a good focused firm is not necessarily optimal. Instead, it appears that even after firms find a good match, they can still benefit from diversification. This finding is consistent with

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20 Gomes and Livdan (2004), who present evidence that firms benefit by perpetually exploring productive new opportunities. In Table 2-7, we further explore the conditional relations between survival, age, organizational form, ownership, and financial measures using Cox’s (1972) proportional hazard model. This approach is useful for two reasons. First, the exponential nature of the model is well suited to our analysis because survival times are nonnegative and because of the right-tailed nature of survival times (Simonoff and Ma 2003). Second, it enables us to estimate a hazard ratio for each explanatory variable. The lower the hazard ratio, the less likely the firm will become bankrupt. The Cox model assumes that the survival time of each member of a population follows it own hazard function, h i (t), expressed as )(0)();()(zziethththii , (2) where h 0 (t) is an arbitrary and unspecified baseline hazard function, is a vector of unknown regression parameters associated with the explanatory variables, and z i is a vector of explanatory variables including age, size, capital structure, and ownership concentration. Firms that merge within the sample period or survive past the sample period are censored; noncensored survival times are measured for those firms that delist for cause (CRSP delist codes 400 through 599). Results of the proportional hazard model are presented in Table 2-7. Model 1 shows a significant reduction in the likelihood of bankruptcy as size, institutional ownership, profitability, and level of growth opportunities increase. On the other hand, decreases in leverage and volatility are associated with an increase in survival time. We also see that Herf has a positive parameter estimate, meaning that the higher the Herf (the

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21 more focused), the greater the chance of bankruptcy. Age and insider ownership, however, are unimportant once we account for the other explanatory variables. Model 2 incorporates relative (excess) age and ownership variables, and shows similar trends. Excess insider ownership is insignificant in determining survival time. Once again, though, institutional ownership plays an important role, and firms with a greater proportion of ownership in the hands of institutional investors are more likely to survive. There exists an interesting relationship between excess age and survival. Firms that have been in their industries longer than their competitors are more likely to survive. One possible explanation is that the model picks up a survivorship bias. Alternatively, firms may become more efficient through their growing expertise in a particular process or technology. This may provide them with an advantage over competitors. Results are unchanged when a discrete diversification dummy is substituted for Herf in each model (not shown). This dummy is set to one for focused firms (Herf greater than 0.9) and is set to zero for diversified firms (Herf no greater than 0.9). In each of these discrete models, there is a positive coefficient estimate for Herf. The interpretation again is that focused firms have higher hazard ratios than diversified firms, and are therefore more likely to become bankrupt. As a further robustness test for the hazard model, we specify a logit regression of the form iiiXbbY )(0 , (3) where Y i = 0 for firms declaring bankruptcy and Y i = 1 those who survive. Firms that merge are removed from the sample. X is a vector of explanatory variables. P i , the probability that the firm survives, is determined by the expression

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22 )e(eP)(Y)(Yi*i*i1 . (4) With this specification, the likelihood of survival increases as coefficient estimates become more positive. We obtain negative and highly significant parameter estimate for Herf in each model, meaning that P, the probability of survival, is less for firms that are more focused (high Herfs) than for those firms that are diversified (low Herfs). We also classify each firm into age categories and find that the results are unchanged. We conclude our survival analysis by examining the survivorship bias created by the relationship between focus and mortality. In Compustat, data for firm-years in which the organization declares bankruptcy are often missing. Because poor performance generally precedes bankruptcy, it is in these missing years that firms are more likely to have lower value to sales ratios than in other years. Since excess value calculations depend on focused firms’ value ratios, and because focused firms are more likely to have missing data in particularly bad years, a bias is created that makes diversified firms look comparatively worse. Furthermore, as firms approach bankruptcy, they are more likely to slip below $20MM in sales, causing them to be eliminated from the sample even if data are present for the final year of operation. We test the impact that these missing data points have on the observed diversification discount by inserting a value-to-sales ratio of zero for bankrupt firms that have missing data or sales below $20MM in their last year of operation before declaring bankruptcy. Because median SIC value-to-sales ratios are used in excess value calculations, this modification shifts the value ratio down one notch to the next lower ratio.

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23 Once bankrupt firms are properly accounted for, the aggregate diversification discount drops from 7.87% to 2.71%. So, about 2/3rds of the diversification discount disappears when the survivorship bias is removed. In addition, when we apply both the age matching fix and the survivorship fix, we find that the diversification discount is further reduced to 2.33%. 2.5 Firm Age and the Evolution of Organizational Structure So far, we have established a link between firm age and the value of diversification and shown that organizational form is an endogenous decision that affects survival. To complete the picture, we now discuss the role of these observations within a context that suggests diversification is an optimal evolutionary response to external pressures. We offer the view that each firm makes its selection from a menu of possible organizational structure choices available to it given its particular history. Summary statistics on the life cycle of firms are presented in Table 2-8. The data reveals that most firms (around 88%) begin their life cycle by specializing in a single industry. The average level of focus then decreases, and by their mid-twenties, about half of all firms are diversified. From the patterns in excess value, it appears that investors are overly exuberant about newly traded firms. This enthusiasm quickly reverses, and firms then typically trade at a discount until much later in their corporate life span. This observation confirms the importance of considering age when calculating the diversification discount. Since focused firms are generally younger, and since younger firms trade at a relative premium compared to older firms, comparing the value ratios of the two creates misleading results. This point is made clear by noting that the youngest diversified firms are characterized by the smallest diversification discount, yet trade at the largest discount relative to the age-matched set of focused firms.

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24 Ownership structure plays a significant role in determining the organizational form of public corporations. If diversification is a value-reducing strategy, then the firms with relatively more concentrated ownership should be more focused. Regardless of organizational structure, insider ownership falls and institutional ownership rises as firms grow older. By the 5 th year, insiders own 31% less stock than they did immediately following the IPO. On the other hand, institutional holdings increase as firms age. These observations are likely caused by a combination of insiders selling to avoid idiosyncratic risk and an increase in the size of the firm following its IPO. The relationship between ownership structure and organizational form is significant, with focused firms characterized by a greater proportion of insider ownership and lower institutional holdings. Also, diversified firms typically take advantage of lower volatility by taking on additional debt. Finally, we see that diversified firms on average pay more dividends than focused firms. The only explanatory variables in which we find insignificant differences are EBITDA/assets and excess returns. So, unconditionally comparing diversified firms to focused firms in the same industries is problematic. Results confirm that the traditional method of calculating the difference in value between diversified and focused firms, which assumes differences only in organizational structure, may be inappropriate. As expected, volatility decreases with age. Also, consistent with Roper (2003), we see that new firms begin with relatively little debt and that debt increases with age. This trend may be caused by the positive relation between diversification and age. That is, focused firms maintain low debt while diversified firms use relatively more debt. Table

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25 2-8 also shows that older firms pay more dividends and, while profitability does not differ between focused and diversified firms, profitability improves with age. We would expect that the most efficient firms benefit the least from diversification. If this were true, then we would expect that when the most efficient firms diversify, excess value should subsequently decrease. In addition, there should be a stronger negative reaction when young efficient firms diversify. In order to illustrate the evolution of organizational form within firms, we construct a group time-series tests that enable us to examine the cause-effect relationship between changes in organizational form and excess value. We separate the data into five year time blocks and compute changes in mean firm characteristics from one time block to the next. For this analysis, we also classify firms into categories based on focus and performance. Firms are defined as focused (diversified) if their mean 5-year Herf is greater than 0.9 (no greater than 0.9), and are defined as top (bottom) if they are in the top (bottom) quartile of excess value. Firms missing more than two years of data within a time block are removed from the sample. We first test the determinants of organizational form through time. Results are given in Table 2-7. Table 2-9 shows the impact of past profitability on future Herf changes. Past excess value does not drive changes in Herf for either diversified or focused firms. 6 For focused firms, the results illustrate that diversification increases with age. For diversified firms, Herf decreases with increases in size. We next test the effect of changes in focus on excess value. Though not reported, the results indicate that diversified firms that become focused show significant increases 6 Note that we are looking at past values and changes in this analysis, not contemporaneous effects as with our earlier simultaneity analysis.

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26 in excess value. The opposite relationship holds for focused firms, which experience a significant drop in excess value upon diversifying. These results suggest that even after controlling for the age, size, and ownership, that diversification reduces value. Next we account for past performance by inserting prior excess value as an explanatory variable. Table 2-10 shows that when average diversified firms become focused, they experience a positive and significant increase in excess value. In Model 1, we see that the poor-performing diversified firms show a highly significant increase in excess value when they focus. In addition, the top-performing group of diversified firms experiences a highly significant drop in excess value when they focus. The significance of the interaction terms suggests that focusing activities are much more beneficial for poor-performing firms than for successful firms. Among the focused firms, those that become diversified experience a significant drop in excess value, although the effects are somewhat lessened for bad focused firms that diversify. While there is no change in excess value for average diversified firms that remain diversified, we see that when good diversified firms remain diversified, value is destroyed. On the other hand, the bad diversified firms that focus experience an increase in excess value. Although each of these results is consistent with predictions, some of the effect may result from mean reversion. To test for the mean reversion explanation, we add dummies that account for past performance (results not shown). With this specification, we obtain negative (positive) and highly significant estimates for top (bottom) performing firms, which indicates that mean reversion plays an important role. After accounting for this effect, however, we find that diversification still reduces value while focusing increases value.

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27 Next we replace the binary Herf measure with a continuous term in order to measure the degree of change in organizational form (results not shown). This explanatory variable is interacted with a Herf dummy to account for initial organizational form (the firm’s mean Herf in the prior time block). Results indicate that when focused firms become diversified, a significant drop in excess value results. The larger the decrease in Herf, the more value is destroyed. Likewise, diversified firms that become even more diversified suffer from value loss. These results confirm that diversifying is bad, and the level of diversification is correlated with the amount of value destruction even after controlling for firm characteristics. Finally, we specify a model that includes an interaction term between direction of diversification and a dummy for age. In Table 2-10, Model 2 confirms that diversification destroys value. We again see that when focused firms diversify, they lose value, and when diversified firms focus, they gain value. 2.6 Conclusions The results of our analysis indicate that organizational structure is largely endogenous, and show that diversification may be desirable for certain firms under specific sets of conditions. Diversification increases the likelihood of survival and allows firms to explore new opportunities and potentially capitalize on finding better matches. The results also indicate that old firms have the most to gain from diversification. These firms are the most likely to capitalize on the benefits of diversification (e.g., reduction in overhead) and are also more likely than relatively younger firms to be experiencing decreasing returns to scale on existing business lines. However, not all firms should explore new opportunities in lieu of specialization. As in Matsusaka’s (2003) model, firms that are particularly productive have little to gain

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28 from pursuing new businesses. Our results indicate that very young firms are less likely to add value by diversifying. These firms trade at the largest discount relative to their age-matched focused peers. It is likely that these firms are sacrificing good existing projects for diversification efforts. Additionally, while firm survival offers benefits to managers, it may not be optimal for shareholders. If the firm has few or no positive NPV opportunities, then the risk/return tradeoff of using remaining funds to explore new business ventures is likely too high, and it would be optimal for the firm to return cash to the shareholders.

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29 Table 2-1. Firm Characteristics by Year (1981 – 2000). Age is the average number of years that firms have operated following their IPOs. Herf is a Herfindahl index calculated based on net sales for all firms in the sample. % Diversified is the proportion of firms with a Herf below 0.90. Excess Value is the average sales imputed diversification discount for diversified firms. FASB accounting standard SFAS 131 began in 1998 and resulted in firms reporting more segments than in prior periods. Year Firms Age Herf % Diversified Excess Value 1981 2,385 16.0 0.7610 48.81% -0.1005 1982 2,362 16.4 0.7697 47.16% -0.1159 1983 2,510 15.9 0.7898 42.83% -0.1306 1984 2,567 15.6 0.8039 40.28% -0.1040 1985 2,587 15.8 0.8206 37.69% -0.1018 1986 2,681 15.2 0.8395 34.13% -0.0609 1987 2,772 14.7 0.8542 31.46% -0.0211 1988 2,729 14.6 0.8650 29.61% -0.0638 1989 2,626 14.9 0.8730 28.29% -0.0437 1990 2,637 15.2 0.8745 27.83% -0.0404 1991 2,706 15.2 0.8804 26.87% -0.0910 1992 2,932 14.7 0.8846 25.78% -0.0595 1993 3,271 13.7 0.8970 23.11% -0.0838 1994 3,525 13.3 0.8993 22.44% -0.0696 1995 3,686 13.1 0.9057 20.78% -0.0490 1996 3,933 12.6 0.9158 18.71% -0.0658 1997 4,063 12.5 0.9152 18.73% -0.0599 1998 3,699 12.8 0.8215 38.36% -0.0175 1999 3,342 13.6 0.7926 45.27% -0.1192 2000 3,252 13.5 0.7987 43.67% -0.1089 All 60,265 14.3 0.8530 31.66% -0.0787

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Table 2-2. Summary Statistics by Organizational Form (1981 – 2000). Herf is a Herfindahl index calculated based on net sales. Age is the number of years that firms have operated since their IPOs. Sales are the average total firm sales in millions of dollars. Excess Value is the average sales imputed diversification value corresponding to each Herf portfolio. % Insider and % Institutional are the proportion of the shares of common stock outstanding owned by insiders and institutions respectively. Volatility is the annual standard deviation of monthly stock returns. Leverage is the ratio of long-term debt to the sum of long-term debt and market value of equity. Dividend yield is common dividends divided by common share price. Profitability is defined as EBITDA/Assets. Excess return is the total portfolio return corresponding to each Herf portfolio in excess of CRSP’s value-weighted total market return portfolio. Herf Firm-Years Age Sales ($MM) Excess Value % Insider % Institutional All 60,265 14.3 $961.71 -0.0308 11.04% 26.01% 0.10 – 0.19 131 37.6 $7,024.01 -0.1488 3.03% 34.47% 0.20 – 0.29 1,374 30.8 $3,080.68 -0.0806 6.18% 33.69% 0.30 – 0.39 3,148 25.4 $1, 976.85 -0.0791 7.21% 30.47% 0.40 – 0.49 2,584 22.1 $1,834.53 -0.0611 8.05% 29.54% 0.50 – 0.59 5,211 19.6 $1,135.10 -0.0971 9.13% 25.03% 0.60 – 0.69 2,944 19.8 $1,257.52 -0.0879 8.45% 25.82% 0.70 – 0.79 2,175 18.8 $1,207.93 -0.0667 10.14% 27.13% 0.80 – 0.89 1,512 16.9 $1,190.52 -0.0362 9.70% 25.86% 0.90 – 1.00 41,186 10.9 $674.90 -0.0086 12.05% 25.25% Multi Segment 20,001 21.3 $1,569.81 -0.0794 8.66% 27.50% Single Segment 40,264 10.8 $659.63 -0.0066 12.07% 25.28% Difference 10.5 $910.18 * -0.0728 * -3.41% * 2.22% * 30 * Significant at the 1% level

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Table 2-2. Continued. 31 Herf Firm-Years Volatility Leverage Dividend Yield Profitability Excess Returns All 60,265 0.4722 0.1290 0.0155 0.1250 -0.0135 0.10 – 0.19 131 0.3298 0.1472 0.0352 0.1475 -0.0092 0.20 – 0.29 1,374 0.3562 0.1504 0.0272 0.1380 -0.0092 0.30 – 0.39 3,148 0.3912 0.1456 0.0256 0.1311 -0.0180 0.40 – 0.49 2,584 0.4150 0.1503 0.0223 0.1254 -0.0359 0.50 – 0.59 5,211 0.4407 0.1464 0.0224 0.1206 -0.0095 0.60 – 0.69 2,944 0.4368 0.1510 0.0196 0.1226 -0.0088 0.70 – 0.79 2,175 0.4419 0.1453 0.0213 0.1278 0.0085 0.80 – 0.89 1,512 0.4688 0.1405 0.0149 0.1273 -0.0027 0.90 – 1.00 41,186 0.4948 0.1206 0.0124 0.1245 -0.0144 Multi Segment 20,001 0.4290 0.1466 0.0217 0.1251 -0.0106 Single Segment 40,264 0.4939 0.1203 0.0124 0.1249 -0.0150 Difference -0.0649 * 0.0263 * 0.0093 * 0.0002 0.0044 * Significant at the 1% level

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32 Table 2-3. Determinants of Excess Value for All Firms (1981 – 2000). The general model specification is Y it = b(X it ), where Y it is the sales imputed excess value for firm i in year t and X it is a corresponding vector of explanatory variables listed below. Each model is estimated using fixed-effects regression procedures. Model 1 Model 2 Model 3 Model 4 (N = 47,855) (N = 31,259) (N = 47,855) (N = 46,586) Variable Estimate t-Statistic Estimate t-Statistic Estimate t-Statistic Estimate t-Statistic Log (Age) -0.1023 -21.03 -0.1025 -21.07 0.0217 1.63 Log (Sales) -0.0864 -18.52 -0.0876 -18.83 -0.0463 -8.28 -0.0841 -17.51 Sales Herf 0.1530 10.29 0.1622 9.04 0.3975 10.88 Focused Dummy 0.0660 9.47 % Insider 0.0006 6.74 0.0006 6.70 0.0005 5.97 % Institutional 0.0037 28.00 0.0037 28.17 0.0031 23.48 ExcessAge -0.0719 -17.51 Excess % Insider 0.0081 6.95 Excess % Institutional 0.0454 17.21 Herf * Log (Age) -0.1016 -7.82 Leverage -0.4913 -18.05 Profitability 0.3580 18.60 Volatility 0.0440 6.89 CES 0.3304 22.03

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Table 2-4. Determinants of Excess Value by Age Group (1981 – 2000). The general model specification is Y it = b(X it ), where Y it is the sales imputed excess value for firm i in year t and X it is a corresponding vector of explanatory variables listed below. Each model is estimated using fixed-effects regression procedures. 33 Two Age Groups Three Age Groups Model 1 Model 4 Model 1 Model 4 (N = 47,765) (N = 46,497) (N = 47,570) (N = 46,300) Variable Estimate t-Statistic Estimate t-Statistic Estimate t-Statistic Estimate t-Statistic Log (Age) -0.1018 -20.25 0.0577 4.18 -0.0516 -10.06 0.0983 6.95 Log (Sales) -0.0778 -16.15 -0.0756 -15.25 -0.0823 -16.72 -0.0795 -15.62 Sales Herf 0.1670 10.85 0.4965 13.10 0.1234 7.85 0.4311 11.10 % Insider 0.0006 6.60 0.0005 5.87 0.0006 6.49 0.0005 5.76 % Institutional 0.0035 25.84 0.0029 21.12 0.0036 25.67 0.0031 21.64 Herf * Log (Age) -0.1349 -10.03 -0.1257 -9.10 Leverage -0.5473 -19.52 -0.4786 -16.64 Profitability 0.3750 19.16 0.3168 15.82 Volatility 0.0453 6.88 0.0533 7.89 CES 0.3163 20.56 0.3056 19.11

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34 Table 2-5. Determinants of Organizational Form (1981 – 2000). The general model specification is Y it = b(X it ), where Y it is the sales Herf for firm i in year t and X i is a corresponding vector of explanatory variables listed below. Each model is estimated using fixed-effects regression procedures. Full Sample Estimates Sub-Sample Estimates 1981 – 2000 1981 2000 1986 1993 1994 2000 (N = 60,238) (N = 47,835) (N = 22,348) (N = 25,486) Variable Estimate t-Statistic Estimate t-Statistic Estimate t-Statistic Estimate t-Statistic Log (Age) -0.0125 -8.95 -0.0083 -5.08 -0.0111 -5.69 0.0032 0.92 Log (Sales) -0.0429 -33.39 -0.0476 -30.46 -0.0460 -22.20 -0.0576 -19.75 Leverage -0.0662 -8.29 -0.0570 -6.31 -0.0412 -4.25 -0.0849 -5.50 % Insider 0.0000 0.05 0.0000 0.78 0.0000 -0.67 % Institutional 0.0004 8.70 0.0003 5.68 0.0003 4.47

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Table 2-6. Annual Percentage of Firms that Declare Bankruptcy (1981 – 2000). This table shows the percentage of firms each year that declare bankruptcy. Firms are classified as diversified if their Herf is below 0.90 and focused if their Herf is greater than 0.90. The young age category represents firms that are less than 10 years old, while the old age category contains only firms that are at least 10 years old. 35 Type Young Old All Diversified 0.93% 0.32% 0.50% Focused 1.02% 0.79% 0.93% Table 2-7. Firm Survivorship Model (1981 – 2000). This table displays firm survival regression estimates using a Cox proportional hazard model. The survival time of each firm is assumed to follow its own hazard function, h i (t), expressed as )()();()(zzeththth. The model is constructed so that the lower the estimated coefficient, the smaller the hazard ratio, and the more likely the firm is to survive. 0iii Model 1 Model 2 Events (Bankruptcies) = 7,061 Censored (Survivors) = 39,525 Events (Bankruptcies) = 3,502 Censored (Survivors) = 27,757 Variable Estimate Chi-square p-Value Hazard Ratio Estimate Chi-square p-Value Hazard Ratio Log (Age) -762.78 0.08 0.7827 0.0000 Log (Sales) -0.2264 406.34 0.0000 0.7974 -0.4432 946.57 0.0000 0.6419 Sales Herf 0.4102 37.83 0.0000 1.5072 0.9255 96.66 0.0000 2.5232 % Insider -0.0002 0.13 0.7223 0.9998 % Institutional -0.0196 785.23 0.0000 0.9806 Leverage 2.0688 435.85 0.0000 7.9156 Profitability -0.8366 725.14 0.0000 0.4332 Volatility 0.1418 198.00 0.0000 1.1524 CES -0.9916 37.17 0.0000 0.3710 Excess Age -1.1220 2399.21 0.0000 0.3256 Excess % Insider 0.0027 0.12 0.7314 1.0027 Excess % Institutional -0.1766 280.60 0.0000 0.8381

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Table 2-8. Summary Statistics by Firm Age (1981 – 2000). FASB accounting standard SFAS 131 began in 1998 and resulted in firms reporting more segments than in prior periods. Age Firm-Years Herf % Diversified Sales ($MM) Excess Value Focused Diversified Focused Diversified Difference 0 3,840 0.9516 0.1177 $268.72 $663.65 0.1639 0.0180 0.1459 1 4,254 0.9377 0.1469 $297.51 $757.50 0.0939 -0.0358 0.1297 2 3,880 0.9268 0.1698 $313.84 $559.48 0.0458 -0.0465 0.0923 3 3,495 0.9232 0.1817 $345.28 $549.06 0.0048 -0.0581 0.0629 4 3,091 0.9173 0.1973 $355.70 $702.06 -0.0253 -0.0712 0.0459 5 2,621 0.9107 0.2079 $367.07 $719.95 -0.0356 -0.1249 0.0893 0 – 5 21,181 0.9295 0.1665 $319.06 $655.53 0.0521 -0.0548 0.1069 6 – 10 10,199 0.8913 0.2480 $406.63 $594.73 -0.0646 -0.1178 0.0532 11 – 15 8,451 0.8565 0.3194 $468.75 $557.68 -0.0690 -0.1176 0.0486 16 – 20 5,936 0.8189 0.3876 $597.21 $768.73 -0.0560 -0.0937 0.0377 21 – 25 4,801 0.8004 0.4228 $1,018.20 $1,051.92 -0.0644 -0.1127 0.0483 26 – 30 2,889 0.7499 0.5213 $1,546.10 $1,974.84 -0.0590 -0.0912 0.0322 31 – 40 2,596 0.7009 0.6133 $2,119.02 $2,224.62 -0.0008 -0.0657 0.0649 41 – 50 1,294 0.6626 0.6708 $2,707.78 $3,202.35 0.0658 -0.0217 0.0875 51 – 60 1,652 0.6126 0.7064 $5,382.61 $4,707.85 0.0457 -0.0560 0.1017 61 – 70 1,049 0.6531 0.6835 $7,741.85 $6,625.30 0.0709 0.0983 -0.0274 71+ 217 0.6561 0.6636 $10,352.32 $9,696.84 0.1337 0.0466 0.0871 All 60,265 0.8530 0.3166 $674.90 $1,580.85 -0.0086 -0.0787 0.0701 36

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Table 2-8. Continued. Age Firm-Years % Insider % Institutional Volatility Focused Diversified Focused Diversified Focused Diversified 0 3,840 18.80% 16.47% 0.5531 0.5738 19.95% 21.25% 1 4,254 18.24% 14.80% 0.5669 0.5652 23.27% 23.12% 2 3,880 15.03% 13.67% 0.5528 0.5748 24.33% 23.75% 3 3,495 12.81% 12.71% 0.5614 0.5750 24.89% 26.09% 4 3,091 12.45% 12.70% 0.5740 0.5630 26.38% 27.26% 5 2,621 10.86% 11.29% 0.5631 0.5673 26.39% 26.42% 0 – 5 21,181 15.12% 13.50% 0.5616 0.5697 23.89% 24.76% 6 – 10 10,199 10.75% 10.63% 0.5231 0.4995 24.46% 22.59% 11 – 15 8,451 9.29% 9.58% 0.4644 0.4541 23.01% 20.99% 16 – 20 5,936 8.94% 7.81% 0.4186 0.3984 26.44% 23.57% 21 – 25 4,801 8.99% 6.37% 0.3672 0.3595 30.54% 27.48% 26 – 30 2,889 9.28% 6.63% 0.3993 0.3738 36.60% 37.97% 31 – 40 2,596 9.54% 5.25% 0.3210 0.3240 33.54% 34.53% 41 – 50 1,294 5.75% 2.51% 0.2543 0.2763 20.77% 31.45% 51 – 60 1,652 5.79% 2.34% 0.3180 0.3148 23.54% 32.51% 61 – 70 1,049 5.97% 7.34% 0.3287 0.3019 29.41% 43.51% 71+ 217 6.73% 2.54% 0.3721 0.3674 44.55% 55.05% All 60,265 12.05% 8.54% 0.4948 0.4239 25.25% 27.65% 37

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Table 2-8. Continued. 38 Age Firm-Years Leverage Dividend Yield Profitability Excess Returns Focused Diversified Focused Diversified Focused Diversified Focused Diversified 0 3,840 0.0886 0.1299 0.0195 0.0198 0.1475 0.1244 -0.1304 -0.1507 1 4,254 0.1035 0.1443 0.0050 0.0058 0.1168 0.0959 -0.0683 -0.1534 2 3,880 0.1138 0.1492 0.0043 0.0049 0.1125 0.0994 -0.0556 -0.0869 3 3,495 0.1184 0.1492 0.0039 0.0058 0.1128 0.0975 -0.0517 -0.0435 4 3,091 0.1241 0.1529 0.0048 0.0068 0.1090 0.0965 -0.0299 -0.0382 5 2,621 0.1265 0.1530 0.0043 0.0070 0.1129 0.1028 -0.0323 -0.0176 0 –5 21,181 0.1106 0.1471 0.0074 0.0078 0.1197 0.1017 -0.0647 -0.0793 6 – 10 10,199 0.1243 0.1514 0.0087 0.0126 0.1242 0.1207 0.0402 0.0166 11 – 15 8,451 0.1221 0.1453 0.0128 0.0170 0.1288 0.1297 0.0354 0.0069 16 – 20 5,936 0.1285 0.1454 0.0187 0.0206 0.1287 0.1313 0.0228 0.0181 21 – 25 4,801 0.1214 0.1398 0.0178 0.0235 0.1364 0.1317 0.0051 0.0008 26 – 30 2,889 0.1309 0.1483 0.0190 0.0239 0.1356 0.1364 -0.0332 -0.0205 31 – 40 2,596 0.1541 0.1602 0.0347 0.0357 0.1289 0.1373 0.0096 -0.0091 41 – 50 1,294 0.1916 0.1591 0.0591 0.0397 0.1137 0.1351 -0.0198 0.0032 51 – 60 1,652 0.1592 0.1440 0.0472 0.0557 0.1178 0.1321 -0.0096 0.0059 61 – 70 1,049 0.1559 0.1323 0.0282 0.0382 0.1233 0.1461 -0.0477 -0.0124 71+ 217 0.1287 0.1242 0.0331 0.0249 0.1516 0.1508 -0.0491 -0.0379 All 60,265 0.1206 0.1472 0.0124 0.0222 0.1245 0.1261 -0.0144 -0.0118

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39 Table 2-9. The Effect of Excess Value on Changes in Herf (1981 – 2000). Focused Diversified Variable Estimate T-Value Estimate T-Value Intercept -0.0018 -0.17 0.1313 4.02 Log (Sales) 0.0013 0.86 -0.0120 -2.75 Log (Firm Age) -0.0070 -1.98 0.0002 0.02 Past Excess Value -0.0021 -0.39 0.0160 0.96 Table 2-10. The Effect of Changes in Herf on Excess Value (1981 – 2000). Div Div is defined as the firm was classified as diversified during the 1986-1990 sample period and remained diversified during the subsequent 5-year period (i.e., 1991-1995). Similarly, Div Foc means that the firm was diversified and then became focused in the subsequent 5-year period. For these changing organizational form categories, firms are defined as focused (diversified) if their mean 5-year Herf is greater than 0.9 (no greater than 0.9), and are defined as top (bottom) if they are in the top (bottom) quartile of excess value. The young age category represents firms that are less than 10 years old. Model 1 Model 2 Variable Estimate T-Value Estimate T-Value Intercept -0.2538 -8.55 -0.2640 -8.43 Mean Log (Age) 0.0324 3.59 0.0418 4.12 Mean Log (Sales) 0.0156 2.67 0.0138 2.35 Div Div 0.0246 1.09 -0.0094 -0.44 Div Foc 0.0780 1.85 0.0620 1.66 Foc Div -0.1071 -2.09 -0.1470 -2.97 Interact (Div Div) * Top -0.1292 -3.63 Interact (Div Div) * Bottom 0.0646 1.86 Interact (Div Foc) * Top -0.2475 -3.25 Interact (Div Foc) * Bottom 0.1461 1.92 Interact (Foc Div) * Top -0.0925 -1.02 Interact (Foc Div) * Top 0.2070 1.75 Interact (Div Div) * Young 0.0900 2.18 Interact (Foc Div) * Young 0.1245 1.44 Interact (Div Foc) * Young -0.0517 -0.68

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40 0.550.650.750.850.95010203040506070AgeHerf Survive Bankrupt Figure 2-1. Organizational Form and Firm Survival

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41 0.0000.0020.0040.0060.0080.0100.0120.01451015202530354045AgeMortality Rate02,0004,0006,0008,00010,00012,00014,00016,00018,00020,000Observations Herf > 0.9 0.9 > Herf > 0.6 Herf < 0.6 Number Focused Firms Number of Diversified Firms Figure 2-2. Mortality Rate by Firm Age

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42 0.000.050.100.150.200.250.300.350.20.30.40.50.60.70.80.91HerfMortality Rate010,00020,00030,00040,00050,00060,000 Young Firm Mortality Old Firm Mortality Number of Young Firms Number of Old Firms Figure 2-3. Firm Age and Survival

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43 0.0000.0050.0100.0150.0200.0250.0300.0350.0401981198619911996YearMortality Rate Good Focused Firms Bad Focused Firms Good Diversified Firms Bad Diversified Firms Figure 2-4. Mortality Rate by Firm Type

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CHAPTER 3 WEATHER BIASES IN THE NFL BETTING MARKET: EXPLAINING THE HOME UNDERDOG EFFECT A great deal of financial economics research has been motivated by the idea that an examination of wager patterns in sports betting markets can provide insight into investor behavior and securities pricing in financial markets. Both types of markets are characterized by a large number of participants, competitive bidding, public and private information, transaction costs, and market professionals. Bettors (investors), moreover, make decisions based on the perceived quality (value) of the team (asset). Similar to securities prices at the end of trading, closing lines in sports betting markets should incorporate all available information plus any biases of the market participants. In contrast to equities markets, where the fundamental values of securities are not typically revealed, sports betting markets provide observable outcomes in the form of the difference in points scored by opposing teams. Because bettors and investors may misvalue or ignore pertinent valuation information, price inefficiencies potentially exist. 1 For instance, it is possible that bettors underweight the long-term performance of teams, or that they are slow to adjust to new information gathered about a team via its short-run performance. These ideas are not new. Past literature by Brown and Sauer (1989), Camerer (1989), and Gray and Gray (1997) establishes a link to momentum and contrarian investment strategies. There are 1 Coaches in the NFL may also behave sub-optimally. Recent research by Romer (2002) using NFL data suggests that simple models of optimizing behavior do not seem to explain the observed decision-making. 44

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45 also questions about whether the closing line incorporates all publicly available information and whether proper value is placed on home field advantage. A variety of econometric techniques are used to address these issues, including surveys of sports analysts and bettors, simple betting rules, OLS and discrete regression models, and predictive algorithms. Most authors choose ‘season’ as the unit of time measurement when attempting to identify and quantify biases. Several, including Harville (1980), Amoako-Adu, Marmer, and Yagil (1985), Zuber, Gandar, and Bowers (1985), and Sauer, Brajer, Ferris, and Marr (1988), consider only short-term biases. Others, including Golec and Tomarkin (1991) and Gray and Gray (1997), examine strictly long-term biases. However, little attention has been devoted to examining the timing of biases within seasons. That is, persistent deviations from rationality may occur within smaller subsections of individual seasons, so the selection of time units may be important. An examination into the timing of biases within seasons may shed light into a particularly important yet unexplained phenomenon, the home underdog effect. That is, betting on home underdogs is consistently profitable. We apply existing financial theories including the limits of arbitrage to explain why such a phenomenon persists in the long term. The majority of our inferences rely on statistical analysis, and we confirm our results and further examine the data using models similar to those proposed in previous studies. However, we improve upon these models in several important ways. Most importantly, we account for the possibility that biases manifest themselves during particular weeks rather than over entire seasons. In addition, we analyze the relationship between game day temperatures and forecast errors. The

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46 forecast error is the difference between the actual outcome (the realized difference in points scored between two teams) and the predicted outcome (the closing line). Finally, we remove the impact of a highly influential noise component, overtime scoring, from our analysis. Overtime scoring biases forecast error measurements, and significantly alters results. Our findings can be summarized as follows. We begin by confirming that significant mispricing exists in the NFL sports betting market. We then establish that the pattern of inefficiency occurs with regularity at the same point within each season. The vast majority of aggregate mispricing is driven by these short-term but large deviations from rationality. We also show that the impact of weather on game outcome is significantly mispriced. This anomaly drives the home underdog phenomenon and persists because of the limits of arbitrage. We conclude with a regression analysis that confirms the results of our statistical tests. 3.1 Sports Betting In football betting, prices are set through point spreads. The term ‘point spread’ in this paper is synonymous with the closing line, and is defined as the projected point differential between the winning team and the losing team just prior to kickoff. Point spreads often change from the time the first bet is placed to the time the last bet is placed. The first bets are placed at the ‘opening line’ which, for the NFL, is usually set by Monday morning. Bets can be placed up until kickoff, at which time the spread becomes the ‘closing line.’ A sample point spread in the NFL might be something like ‘New England minus four at Houston.’ In this case, New England would be the road favorite and is expected to beat Houston by four points.

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47 When a bettor believes that a team is undervalued relative to its competitor, she places a bet at a casino or through a bookie. If New England outscores Houston by more than four points, bets on New England win (cover). Those who bet on Houston receive nothing. If the result is that New England wins outright (straight-up) by exactly four points, wagers are declared to be a ‘push,’ and all bets are returned. Sometimes, no favorite exists (a closing line equal to zero), in which case the contest is referred to as a ‘pick-’em.’ In point spread betting, the role of the bookmaker (either a casino or a bookie) is in many ways similar to that of a stock exchange specialist. Both charge fees for matching buyers and sellers. The bookmaker’s profits come from a commission called the vigorish. Bettors decide which team to bet on and receive $10 for every $11 wager that wins. The portion of the loser’s bet that is not paid to the winner is the bookmaker’s vigorish. The bookmaker, like the specialist, usually prefers to avoid taking a naked position. 2 So, after she sets the initial price through her opening line, she adjusts the line over time to approximately match the dollar volume of bets placed on each side of the line. For instance, in the example above, if most of the money is initially bet on New England, then the bookmaker may move the line from ‘New England minus four’ to ‘New England minus four-and-a-half.’ If most of the new bets are again placed on New England, then the line is adjusted further in the same direction until all bets offset. However, when bets are placed in a point spread market, they immediately become 2 While the goal of the market specialist is strictly to match buyers and sellers, there is some evidence that the bookie may also intentionally take a position with respect to the outcome of the game if he is able to predict and capitalize on bettor biases (Jeffries and Oliver 2000 and Levitt 2002). However, even for the experts, predicting outcomes against the closing line is extremely difficult. Avery and Chevalier (1999) examine the historical success rate of sportswriters whose predictions of each game against the spread are published in newspapers. Of the 12 experts who made predictions for more than one season, only four correctly predict better than 50% of the outcomes and the highest success rate is only 51.1%.

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48 locked-in regardless of subsequent movements in the line. For instance, a bet placed on New England at minus four remains valid even if the closing line moves to minus five. Therefore, since betting lines move according to the dollar amount of wagers on each side of the bet, closing lines should reflect all public and private information as well as the biases of market participants. 3.2 Data and Methodology 3.2.1 Data The existence of statistical anomalies in the outcomes of NFL contests is central to our analysis. To fully examine inefficiency and predictability in sports betting markets, we compile a time-series data set that extends from the 1981 NFL season through the 2000 NFL season, and covers 4,688 games. The number of games varies by year because of two strike-shortened seasons (1983 and 1987), the addition of a single bye week and extra wild card game starting in 1990, the temporary addition of a second bye week in 1993, and league expansion in 1995. Team performance data and closing point spreads are obtained from Computer Sports World, which uses closing lines from the Stardust Sports book in Las Vegas. In addition, we obtain from the Nevada Gaming Control Board in Las Vegas, the dollar volume of football bets and resulting casino profits for the state of Nevada from 1988 to 2000. Finally, we gather daily weather data from the National Climactic Data Center (NCDC) for all NFL cities from 1981 to 2000. Table 3-1 provides a breakdown of closing lines, outcomes, and forecast errors defined with respect to home teams and underdogs. We assign negative closing lines to favorites, positive outcomes to teams that win outright, and positive forecast errors to teams that cover the spread. On average, underdogs (home underdogs) are predicted to lose by 5.63 (4.65) points, but actually lose by only 5.45 (3.76) points, so the resulting

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49 forecast error is 0.18 (0.89) points. This indicates that underdogs (home underdogs) perform better than expected in aggregate. The same is true for home teams, which are forecast to win outright by 2.67 points and actually win by 3.03 points. The largest forecast error occurs during the playoffs, when home teams are assigned a point spread of -5.37 points. The large negative spread is a result of the playoff format, which usually requires a weaker team to play on the road against a stronger opponent. In the playoffs, home playoff teams perform much better than expected, winning outright by 7.68 points, and beating the spread by 2.31 points on average. For each of the groups presented, we test the hypothesis that closing lines, outcomes, and forecast errors are distributed normally using a Kolmogorov-Smirnov test if N 2000, and a Shapiro-Wilk test otherwise. The p-Values shown in Table 3-1 (given as p-Value N ) indicate that the closing line, outcome, and forecast error for the vast majority of games are each distributed non-normally. Therefore, moving forward we will use non-parametric tests to establish whether the forecast error is biased. 3.2.2 Methodology We begin our examination with a statistical analysis designed to determine whether significant forecast errors exist and, if so, whether they follow a consistent pattern within seasons. If closing lines are not accurate reflections of actual outcomes, it may be possible to identify systematic mispricings. We then use regression analysis to confirm and extend our statistical results. In addition to examining various models and specifications, it important for us to account for potential time variation. There are at least four reasons that subsamples of various time lengths should be examined. First, because wager preferences of bettors

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50 may fluctuate throughout the season, it is reasonable to speculate that bookies will attempt to take advantage of bettor biases by manipulating the spread. For instance, Jeffries and Oliver (2000) state that as bettors take losses, they lose sight of the importance of the closing line and become more inclined to bet on teams that are expected to win straight-up. The authors advise bookmakers to increase the spread on Monday games because gamblers will try to make up for Sunday losses by betting on Monday favorites. They reason that bookies can make additional profits by taking a naked position on Monday night underdogs. Second, it is possible that market participants do not immediately process all of the relevant information needed to establish a rational price. In equities markets, information flow and price changes occur continuously. It can therefore be difficult to isolate how much time investors require to fully process new information. Information flow is more discrete in the NFL point spread market. All performance data from the prior period is usually revealed six days before final prices are set. If bettors rationally update their priors within this period, then closing lines should be an unbiased measure of outcomes. Alternatively, several betting periods may pass before bettors accurately update their priors. We examine the rate of information processing by observing how many weeks pass before all prior information is incorporated into bet price. Finally, financial investors may value certain descriptive characteristics more during one period than another (e.g., small cap vs. large cap in the 1980s). The analogy in sports betting markets is that, early in the season, gamblers may establish bet values based largely on venue, and discount information about recent offensive or defensive performance. Since teams go through many more significant changes during the off

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51 season (e.g., new players, coaches, and coordinators), the true strength of a team is likely to be less evident near the beginning of the season than near the end. We analyze whether bettors shift their perceptions of the value of different types of information over time. 3.3 Results 3.3.1 Summary Statistics The statistical summary shown in Table 3-2 demonstrates that gamblers significantly misvalue bets during particular months. 3 It also shows that the magnitude of the forecast error changes significantly over time. We further find that, in aggregate, bets on underdogs are significantly undervalued. The test statistic (given as p-Value FE ) obtained using a sign test, is sufficient to reject the hypothesis that underdogs do not perform better than expected (p-Value FE = 0.0120), though there does not appear to unfold a clear pattern of bet misvaluation as the season progresses. However, one problem created by examining data with respect to underdogs or favorites is that, by definition, the classification itself assumes that the closing line is efficient. That is, an underdog could actually be a favorite if the closing line is smaller than the forecast error. For instance, if we find that bets on home teams in January are underpriced by 4 points (that home teams beat expectations by 4 points), then there exists a group of teams playing at home in January that are classified as underdogs but that should be classified as favorites (if prices were perfectly efficient). Because of this 4-point bias, we would also expect to find that home teams and home underdogs win substantially more games than expected in January. Univariate tests performed with 3 August and September are combined throughout the analysis because few games are played in August.

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52 respect to underdogs, though, would misleadingly show that underdogs perform particularly well in January when the bias is actually caused by home teams exceeding expectations in January. Furthermore, as we discuss shortly, a sub-class of home teams, home open-air stadium teams, may be characterized by closing line biases that do not apply to home dome teams. We proceed under the assumption that inferences based on ‘underdog’ as a classification are less reliable than those based on ‘home,’ and interpret results accordingly. As expected, Table 3-2 shows that bets based on venue (Home) are more consistent than those based on spread (Underdog). While results indicate that bets on home teams are not mispriced in aggregate, a clear pattern of mispricing does occur. The performance of home teams against the spread improves linearly as the season progresses. The forecast error moves from -0.27 points in August and September, to 3.81 points in January. 4 In December, home team performance is significantly better than expected (p-Value FE = 0.0710), and in January home team over-performance is highly statistically significant (p-Value FE = 0.0009). Univariate statistics for the final category, home underdogs, are more difficult to interpret both because of the definitional problem discussed above and also because of the highly dependent relationship between home effects and underdog effects (68% of home teams in our sample are favorites). We delay our main discussion of home 4 In August and September, home teams perform worse that expected by 0.35 points. Although only marginally significant, it appears that early in the season, bettors tend to favor home teams, since bets on home teams perform relatively poorly. One potential explanation for this early-season bias is that, because more uncertainty exists about teams’ performance levels in the early part of the season, bettors overvalue the home team advantage. That is, in the absence of meaningful past performance data, the most significant remaining determinant of outcome is home field advantage. As a result, bettors may place a greater relative value on bets for home teams. They bid up the price, which causes these bets to lose more often.

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53 underdogs, then, until we present the results of our multivariate regression analysis, but below we briefly discuss home underdogs to illustrate the relationship between forecast errors and outcomes. Bets on home underdogs are highly statistically underpriced both in aggregate and within December and January individually. Playoff games typically occur in January, and we find that in the playoffs, home underdogs win outright by 8.66 points on average (not shown). Outliers do not drive this result. Home underdogs in the playoffs have 14 straight-up wins in 18 contests, with a median margin of victory of 7.50 points. Clearly, in the case of playoff home underdogs, forecast errors translate directly into the likelihood of bets winning against the spread. While the number of observations is low, this example illustrates the point that forecast errors contain information about market economic efficiency. However, it is equally important to directly examine whether statistical inefficiencies in point spreads significantly impact bet outcomes in the NFL point spread betting market. Table 3-3 shows the cover frequency of bets on underdogs, home teams, and home underdogs. To test whether the bet win percentage is statistically significant, we use a binomial test. A test statistic is given for each of two discrete levels. The first test statistic (p-Value 50% ) measures the likelihood that the bet win rate is greater than 50%, and the second (p-Value 52.38% ) tests whether the bet win rate is greater than 52.38%. 5 In the former, we are testing for statistical efficiency, and in the latter, we are testing for economic efficiency. Looking at game outcomes with respect to underdogs, Table 3-3 provides evidence that bets on underdogs are significantly underpriced in October, 5 Because of the 11 for 10 betting rule, any profitable strategy would need to beat the spread at a rate greater than 52.38%.

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54 November, and December, and highly significantly overpriced in January. Again, these results must be interpreted with caution, as efficiency is assumed when classifying teams as underdogs or favorites. The data in Table 3-3 describing the cover frequency of home teams confirms the conclusions obtained from the forecast error analysis presented in Table 3-2. That is, home teams increasingly outperform expectations as the season progresses, and cover at a significantly higher rate than predicted in December and January. In December the p-Value 50% is 0.0670, and in January the p-Value 50% is 0.0007. Additionally, the test statistic for economic efficiency reveals that the null hypothesis can be rejected with high confidence (p-Value 52.38% = 0.0052). That is, the bet win percentage reliably surpasses the 52.38% break-even rate. Bets on home underdogs also win at statistically significant rates in December and January individually, and in aggregate overall. The home underdog results shown in Tables 3-2 and 3-3 reveal that the timing of biases is critical to understanding the dynamics of bet mispricing. When December and January are removed from the sample, the mean forecast error drops from 0.89 (p-Value FE = 0.0103) to 0.20 (p-Value FE = 0.1907), and the cover frequency drops from 53.15% (p-Value 50% = 0.0096) to 51.42% (p-Value 50% = 0.1823). As we discuss shortly, the temperature conditions on game day play an important role in determining the forecast error, and game day temperatures in these months differ significantly from those in earlier months. However, it is difficult to interpret univariate statistics describing home underdog performance because of the relationship between the venue and the closing line. The multivariate analysis below will address the issue of economic

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55 efficiency of bets on home underdogs, and further make the connection between the home underdog effect and the home team temperature advantage. The findings presented thus far raise concerns about prior studies that test for NFL betting market efficiency using ‘season’ as the baseline time period (Gray and Gray 1997 and Dare and McDonald 1996). As we have shown, forecast errors change throughout each season, and therefore the dynamics of closing lines must be considered when examining market efficiency. Previous efficiency tests that utilize regression results from the first half of each NFL season to predict outcomes in the second half fail to consider the implications of these within-season biases (Zuber et al. 1985 and Sauer et al. 1988). While it is true that bets throughout the majority of the season appear to be priced efficiently, it is clear that information processing in this market is less than perfect. We next examine several potential explanations for this observation. 3.3.2 Temperature Conditions One potential source of a persistent seasonal bias is the failure of bettors to properly account for factors that alter team performance from one point to another within each season. A particularly relevant condition that differs from the start to the end of each season is the weather. Most NFL teams play in open-air stadiums. 6 Coaches, players, and sports writers argue that when away teams from mild regions play in cold environments late in the season, they are potentially at a large disadvantage both physically and mentally. 7 Furthermore, injuries accumulated throughout the season are likely to have a greater negative effect on performance when temperature is very low. 6 From 1981 to 2000, between four and six teams played in domed stadiums each season. 7 Hirshleifer and Shumway (2003) demonstrate the psychological relationship between weather and performance.

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56 However, players who regularly practice and play in harsh weather conditions become better able to perform in those situations. In a perfectly efficient market, these factors should be fully reflected in closing lines. But, it is possible that closing lines do not properly account for these circumstances. If changes in weather conditions persistently result in bet mispricing, the implication is that bettors discount information from prior seasons. Otherwise, the weather bias would be expected and, therefore, incorporated into prices. We begin our weather analysis by assuming that players become accustomed to temperature conditions that are most similar to those near the city of their home venue. While not all players live in the cities where their home games are played, at a minimum, players spend several months in training camp near their home venue. They also have an opportunity to adjust more gradually to weekly and monthly changes in temperature than do players from visiting teams. To measure the baseline temperature at which players are accustomed, we calculate the mean annual temperature in each NFL host city in each year. We propose that the effect of temperature on player performance can be measured by the difference between this baseline temperature and the actual temperature on game day. So, for example, in December, 2000, the Miami Dolphins played in New England on December 24th. The mean yearly temperature for the Dolphins players in 2000 was 77F, and the game day temperature was 27F. So, if we are correct, then the Dolphin players were experiencing a disadvantage associated with playing in a temperature 50F less than their baseline. Earlier that season, on September 24th, New England (baseline temperature = 51F) played in Miami. The temperature that day was 84F, so the

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57 Patriots’ disadvantage is a function of the +33F difference. The Patriots’ visiting disadvantage can equivalently be viewed as the Dolphins’ home advantage. To be consistent throughout the paper, we construct all variables with respect to the home team, and model the temperature effect as a home advantage. Table 3-4 summarizes game day temperatures by month for NFL cities that host home games in open-air stadiums, and shows the mean temperature difference endured by the visiting team in each month. There is a change in mean temperature from 69.31F to 42.58F from the beginning to the end of each NFL season, and the temperature difference with respect to visiting teams ranges from 11.34F warmer than the team baseline in August and September, to 14.79F colder than the team baseline in January. We next analyze the relationship between game outcomes and differences in the visiting team’s baseline and the game day temperature to determine whether any potential temperature advantage is properly incorporated into closing lines. The correlation between temperature and outcome is illustrated in Table 3-5. Home teams experience a linear performance improvement relative to their opponents as temperature decreases and as the mean temperature difference increases. The increase in the temperature difference is also linearly associated with an improvement in the performance of the home team with respect to the closing line. The result is a significant mean forecast error for games played in months having the largest mean temperature differences. In December, home teams enjoy a 14.10F temperature advantage. They are projected to win outright by 2.83 points, but actually win outright by an average of 3.88 points, so the resulting mean forecast error is 1.06 points. The forecast error is

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58 statistically greater than zero (p-Value FE = 0.0745), and bets on home teams are relatively more likely to cover (p-Value 50% = 0.0699). This disparity is magnified in January, when the temperature advantage is 14.79F, the mean forecast error is 4.32 points (p-Value FE = 0.0004), and the cover rate of home teams is 63.82% (p-Value 50% = 0.0003). A binomial test for economic efficiency also reveals that the cover rate for home teams is reliably greater than the economic efficiency benchmark of 52.38% (p-Value 52.38% = 0.0024). The late-season results, when contrasted with the August and September outcomes, imply that home teams enjoy a cold-weather advantage, but not a hot-weather advantage. To examine the temperature/performance relationship further, we later present a multivariate analysis that separates cold game days from hot game days. First, however, we present an alternative behavioral theory that potentially explains why mispricing varies from the beginning of the season to the end. 3.3.3 Alternative Theories In the NFL point spread market, as in other betting markets, gamblers’ expected profits are negative because of the vigorish paid to bookmakers. As each season progresses, once bettors begin to experience losses, they may alter their strategies. It is possible that bettors shift from making rational bets, which ex post have cost them money, to making irrational bets in the hope that a change in betting strategy will reverse their misfortunes. 8, 9 According to Jeffries and Oliver (2000), bookmakers are well aware 8 Similar irrational decision-making mechanisms are identified in horse racetrack betting (e.g., Rachlin 1990 and Ritter 1994). Much like the bookmakers’ vigorish, the track-take in horse racing causes expected gambling returns to be negative. Rachlin (1990) argues that as bettors lose, their risk tolerance rises, and suggests that long shots are more overbet as a day progresses. That is, prior losses cause gamblers to subsequently overbet on outcomes that are less likely to occur. Since point spread markets do not offer bettors a higher payout for less likely outcomes, such behavior may be manifested instead in irrational movements of closing lines.

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59 of irrational tendencies of gamblers, and local bookies often extract wealth from gamblers by altering point spreads to exploit predictable misvaluation. The authors suggest that prior losses by their clients will bias their future bets towards favorites, and that therefore bookies should view Monday night games as particularly good opportunities to increase the point spread. This implies that Monday underdogs are underpriced while Sunday (and possibly Saturday) underdogs are not. A statistical analysis of Monday night games (not shown) reveals mixed evidence that casinos in Las Vegas seek to profit in this way. Excluding pushes, in 312 Monday night games between 1981 and 2000, underdogs cover 52.24% of the time, but the difference is not significantly greater than 50%. Monday night home underdogs, however, cover at a rate of 60.61%, which is significantly greater than 50% (p-Value 50% = 0.0174) and 52.38% (p-Value 52.38% = 0.0506). 10 In any case, it is not obvious that the line manipulation recommended by Jeffries and Oliver (2000) would occur in Las Vegas. To begin with, when bookies alter the spread to capitalize on gambler biases, the result is that their personal wealth covaries with game outcome. That is, bookies who move lines in this manner essentially become bettors who gamble on Monday night underdogs, and it is not necessarily the case that casinos are able or willing to do this. Furthermore, it is unlikely that casinos would be able to alter spreads to the same degree as bookies because they face more competition than do local bookmakers. Gamblers in Nevada have easy access to alternatives. 9 This type of behavior can also be explained by a change in reference point that alters the preference order for prospects (Kahneman and Tversky 1979). 10 It would be interesting to examine whether experts fare better or worse at predicting December, January, and Monday night games.

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60 Casinos are forced to compete and the result is that lines do not vary among sports books. So, in conclusion, it is unlikely that this behavioral theory explains the persistent mispricing of late season games. To bring this matter to closure, we instead focus our effort towards exploring the significant relationship between temperature and forecast error using multivariate regression analysis. 3.3.4 Regression Analysis 3.3.4.1 Model specification In past research, there has been a substantial amount of debate over the proper specification for modeling efficiency in point spread markets. To provide the reader with an understanding of the important issues, it is illustrative to briefly discuss past models and the literature’s progression to the models presented in this paper. In early research (Zuber et al. 1985 and Gandar et al.1988), tests for rationality take the form: E (OC i – CL i ) = 0, (1) where OC i is the outcome represented in terms of the number of points by which the favorite beats the closing line, CL i is the closing line, and is the set of all publicly available information. In linear form, the above model (1) is represented as: OC i = b 0 + b 1 CL i + i . (2) If rational expectations hold, b 0 = 0, b 1 = 1, and E( i ) = 0. However, tests of market efficiency using equation (2) are problematic. First, this model is able to pick up only aggregate biases. So, if an individual bias or combinations of biases cancel each other out over the selected time period, the result may be false acceptance of the null hypothesis. For instance, if home teams cover by an average of three points for the first 10 years of a 20 year sample, and away teams cover by three points during the final 10

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61 years, the test would show that b 0 = 0 and b 1 = 1. Therefore, an existing bias would fail to be identified. Second, the definition of the data can also affect the results. Measurement of the dependent variable OC i with respect to the underdog would capture only underdog bias, and measurement with respect to the home team would capture only home team bias. Accurate measurement of both biases requires an alternative specification. Since home teams have an advantage over visiting teams, the classification of teams as favorites or underdogs does not occur independently of venue. Throughout the 20 NFL seasons examined, over 2/3rds of away teams are underdogs. So, it is useful to disentangle potential home and underdog effects by re-specifying the model given by equation (2). Gray and Gray (1997) isolate the mispricing of these explanatory variables by using a binary regression of the form: Y i = b 0 +b 1 HOME i + b 2 FAV i + i . (3) where Y i = 1 if the team of record beats the closing line; Y i = 0 otherwise. 11 However, this specification fails to consider the interrelationships between categorizations. An unbiased specification requires restrictions on estimates such that, for instance, the home effect is the negative of the away effect. Dare and Holland (2003) extend the model originally developed by Dare and MacDonald (1996) and correctly isolate the mispricing of venue and closing line explanatory variables by using the specification: D i = HF HF i + VF VF i + ( – 1)CL i + i . (4) 11 The use of a randomly selected “team of record” was intended to eliminate a selection bias.

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62 Here, D i is the outcome (the actual difference in points scored between the favorite and the underdog) minus the closing line, HF i = 1 if the home team is the favorite; HF i = 0 otherwise, VF i = 1 if the visiting team is the favorite; VF i = 0 otherwise, and CL i is the closing line defined with respect to the favorite. However, it is unclear how much, if any, additional information is contained in the magnitude of the forecast error. If bettors view a particular outcome only in terms of success (failure), then the number of points by which a team covers (fails to cover) the closing line is irrelevant. In that case, a binary choice model is better suited for this analysis because an OLS regression may overweight outliers. Dare and Holland (2003) offer a specification similar to equation (4), except that now the left-hand-side variable, W i , is 1 if the home team covers and W i is 0 otherwise. We alter this model slightly in order to interpret biases with respect to home teams: W i = HF HF i + HU HU i + ( – 1)CL i + i . (5) We refer to this as our “Base Model.” As we explain shortly, one potential source of bias in closing lines is the mispricing of the home team advantage in games played in open-air stadiums on particularly cold game days. To measure the significance of the advantage, we use the Temperature-Augmented Model, which includes vector i to control for game day temperature conditions: W i = HF HF i + HU HU i + ( – 1)CL i + i + i . (6) We choose to employ a discrete choice regression as the benchmark for our analysis, but also compare the predictive accuracy of the linear and discrete approaches. If the discrete model is superior, then the implication is that bettors learn to price underlying bet components by repeated success/failure against the closing line. If the

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63 reverse is true, then the inference is that the magnitude of the forecast error contains valuable information. We intentionally omit performance statistics from our analysis. To exploit inefficiencies in the pricing of performance statistics and develop a practical out-of-sample betting strategy, one must be able to accurately predict future game statistics. For some teams and for some statistics, this may not be completely impossible. For instance, a team that relies primarily on rushing and has a running back that is relatively unlikely to fumble may be more likely to have a positive takeaway differential in future games. However, for practical purposes, it is essentially impossible to predict future game statistics. In the next section, we present the results of pooled multivariate regression models, and summarize how the statistical and regression analyses together reaffirm our stated hypotheses. Specifically, we demonstrate that home team performance significantly exceeds expectations during the latter portions of NFL seasons, that this bias exists because the effect of temperature conditions on game outcomes is mispriced, that a significant home underdog effect exists, and that persistent mispricing can be explained by the limits of arbitrage. 3.3.4.2 Regression results In the statistical analysis presented above, we provide evidence that bettors systematically misvalue the impact of temperature on game outcome, and that biases affecting home teams are dynamic in nature. However, because of interrelationships between the venue and the closing line, it is difficult to properly interpret our unconditional results. We next confirm that the proposed temperature mispricing exists, and quantify the importance of temperature as a predictor of bet outcome. Only open-air

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64 stadium games are examined in this section, and pick-’ems and pushes are also excluded. 12 We then compare the in-sample predictive accuracy of binary models with those of OLS models. Finally, we examine out-of-sample predictability to test whether pricing biases can be exploited via implementable betting strategies. Table 3-6 shows the results of regressions using the Base Model and the Temperature-Augmented Model. In the Base Model, coefficient estimates and p-Values for home favorites, home underdogs, and closing lines imply that no biases exist. A joint test of significance for HF and HU reveals a chi-square value of 3.01 (not shown) with a corresponding p-Value of 0.2221. This result indicates that there is insufficient evidence to reject the hypothesis that bets based on venue are mispriced. In Temperature-Augmented Model 1, we add variable TA HOME to control for the home team’s advantage resulting from the change in temperature that the visiting team experiences when traveling from its home city to the game venue. Since TA HOME is assumed to be an advantage, we model the absolute value of the difference between the visiting team baseline and the game day temperature. If we obtain a significantly positive (negative) coefficient estimate, it would indicate that there exists an unpriced advantage for home (visiting) teams. However, when modeled as a linear term, we find that the coefficient estimate for TA HOME is not significant (p-Value = 0.1338). But as demonstrated in Model 2, the squared term, (TA HOME ) 2 , is positive and highly significant (p-Value = 0.0078) indicating that home teams are much more likely to cover the spread 12 Our sample contains 3,877 open-air games, and 176 of these are classified as a pick-’em or result in a push.

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65 when visiting teams are unaccustomed to game day temperatures. 13 Together, these results suggest that large temperature differences between visiting team baselines and game day temperatures are much more influential in determining game outcomes against the spread than are small differences. Moving forward, we dissect our TA HOME into two separate effects, a hot advantage (likely to occur in August and September) and cold advantage (likely to occur in December and January), to examine the impact of each condition separately. When game day temperature is in the top quartile of all open-air game day observations, we assign a hot advantage, HA HOME , to the home team. Likewise, when the game day temperature is in the bottom quartile, we assign a cold advantage, CA HOME to the home team. HA HOME is calculated as the game day temperature minus the visiting team’s baseline, and CA HOME is calculated as the visiting team’s baseline minus the game day temperature. A positive (negative) and significant coefficient estimate for either term would indicate that home teams have an unpriced temperature advantage (disadvantage). Results for Model 3 show that there is a highly significant cold advantage (p-Value = 0.0051), but not a significant hot advantage (p-Value = 0.5678). In addition, coefficient estimates for Model 4 demonstrate again that squared temperature difference terms produce stronger results than do linear terms. In summary, there is evidence that the 13 Seminar participants often raise a sample selection bias objection – that cold weather teams, particularly the Bears, Bills, Broncos, and Giants were dominant from 1981 to 2000. They suggest that the proposed cold-weather effect is the result of these teams winning a relatively large proportion of their games by a relatively large margin. However, this inference is not supported by the data. First, our analysis examines team performance against the spread. It would be irrelevant were it true that these teams win outright more often and/or win by a relatively large margin straight-up. This is because the closing line incorporates team dominance (prior win/loss records), and no bias is shown to exist in the magnitude of the closing line (measured as – 1 in Tables V and VI). Furthermore, the winning percentage of warm-weather teams such as the 49ers, Dolphins, Cowboys, and Raiders surpasses those of the Broncos, Giants, Bills, and Bears respectively. Second, if bettors fail to properly account for the dominance of these teams, then a bias would exist from the beginning to the end of each season. However, we demonstrate that the bias in forecast error occurs at a particular point within each season.

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66 observed late-season overperformance of home teams is associated with particularly cold game day temperatures. 3.3.4.3 In-sample predictability To quantify the effect of weather mispricing on bet win frequency, we next use each model to predict game outcomes. Examining in-sample regression accuracy is not intended to test whether economic efficiency exists. Rather, it is a means to gain an understanding of the degree of mispricing ex post. Any discussion of an implementable betting strategy that is able to exploit mispricing must surpass the 52.38% threshold out-of-sample ex ante. To predict game outcomes in-sample, we perform a pooled cross-sectional regression and obtain coefficient estimates for each model. These estimates are then used to predict the outcomes of all games in the sample. At the bottom of Table 3-6, we present the accuracy and associated p-Value for each model. The Base Model is able to reliably predict over 50% of game outcomes (p-Value 50% = 0.0607), but is unable to surpass the 52.38% economic efficiency threshold. Similarly, the addition of the temperature control terms does not improve predictive accuracy beyond 52.38%. However, we again find that controlling for temperature is statistically important, as the addition of the vector i improves each model’s p-Value 50% to above the 1% significance level. As mentioned earlier, one advantage that discrete models have over linear models in analyzing forecast errors is that the results they produce are less likely to be driven by outliers. Furthermore, outcomes against the spread should be the sole concern of gamblers, and the number of points by which teams beat the spread should be irrelevant.

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67 To test whether this is the case, we re-estimate a pooled cross-sectional OLS regression using the specification given in equation (4). We find that probit models have a significantly higher accuracy rate (p-Value of difference = 0.0059, not shown) than comparable OLS models. This provides evidence that discrete regression models, which account for outcomes strictly as successes or failures, are more appropriate than OLS models in examining this particular market. However, our probit models still fail to explain the home underdog effect that has been identified in prior studies. We next propose a slight modification to the definition of game outcome that eliminates noise from the measurement of the forecast error. 3.3.4.5 Noise reduction In point spread betting, forecast errors are calculated by differencing the final score of the home team and the final score of the visiting team, and then comparing this difference to the closing line. If expectations are no different than outcomes then, by definition, the forecast error is zero. In this paper, we propose that the forecast error is biased because closing lines do not fully reflect the information content of game day temperature. Our regression results confirm that at least some information is mispriced, yet no home underdog effect is indicated. However, unnecessary noise is embedded within the forecast error for observations in which the home team’s score and the visiting team’s score are equal at the end of regulation play. This noise component can easily be eliminated. Suppose one were to know for certain that the difference in the relative strengths of opposing teams equals 0 where is insignificant, a bet would be fairly priced if the closing line were set near zero. If the actual outcome is that the teams are tied at the end of regulation, then the forecast error is essentially zero. However, NFL rules are such that most ties at the end

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68 of regulation are broken by playing until one team scores, and the wining margin is then calculated by adding the point value of the final play to the score of the victor. The result is that the outcome is measured either as three points or six points instead of as for these equivalently matched opponents. It would be more accurate to measure forecast errors, then, by replacing the difference between home and visiting team in such circumstances with . Zero is a good approximation for , and for the final portion of the analysis, we eliminate the noise term by setting the forecast error for these contests to zero. A total of 212 outcomes are affected. The results of the Adjusted Models, which are shown in Table 3-7, provide insight into the home underdog phenomenon that has been discussed in prior studies. The positive and significant coefficient (p-Value = 0.0131) for HU in the Base Model suggests that home underdogs are more likely to cover the spread than are road favorites. Furthermore, a joint test of HF and HU reveals a significant bias. The chi-square value of 6.19 (not shown) and corresponding test statistic (p-Value = 0.0453) are sufficient to reject the null hypothesis that bets based on venue are efficiently priced, and instead suggest that bets on home teams are significantly more likely to win than are bets on visiting teams. The addition of the vector i to the overtime-adjusted models demonstrates that the home underdog effect is robust in the presence of controls for game day temperature conditions. The positive and significant estimates for HU in models 2, 3, and 4 each confirm that bets on home underdogs are significantly underpriced (p-Values = 0.0915, 0.0503, and 0.0457 respectively). Furthermore, these models corroborate that the effect of extremely cold temperature conditions on bet outcome is mispriced.

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69 In aggregate, the overtime-adjusted models significantly outperform the unadjusted models (p-Value of difference = 0.0042, not shown). Test results also indicate that the Base Model and Temperature-Augmented Model 1 each perform significantly better when the overtime noise term is removed. The accuracy of the Base Model increases from 51.28% to 52.38% (p-Value of difference = 0.0895, not shown), and that of Temperature-Augmented Model 1 increases from 52.06% to 53.19% (p-Value of difference = 0.0846, not shown). 14 Although overtime adjustments successfully eliminate a noise component that was previously embedded in the measurement of forecast error, no adjusted model reliably surpasses the 52.38% economic efficiency threshold. The implications of the regression results presented thus far may be made clearer by quantifying the home and home underdog biases in a more intuitive manner. We can determine the marginal probability of home teams, underdogs, and home underdogs covering the spread by multiplying the appropriate coefficient estimate by a mean standardization factor. For instance, the mean standardization factor for the Adjusted Base Model is 0.3977. So, the marginal probability that a home team will cover the spread given that it is an underdog is 0.1157*0.3977 = 0.0460, or 4.60%. The equivalent marginal probabilities for home underdogs obtained from Adjusted Temperature-Augmented Models 1, 2, 3, and 4 are 3.33%, 3.27%, 3.85%, and 3.83% respectively. 15 Using i estimates from models 1, 2, 3, and 4 we can also determine the marginal effect of temperature. For example, a 30F difference between the visiting team’s baseline 14 Tests results also indicate that the adjusted probit models perform significantly better that their adjusted OLS counterparts. 15 Combining the coefficients for HF and HU, we can also estimate the marginal probability of a team covering the spread given that it is playing at home. For the Adjusted Base Model, the marginal probability is (-0.0467 + 0.1157) * 0.3977, or 2.74%.

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70 temperature and game day temperature translates into marginal probabilities of 2.57%, 3.51%, 5.39%, and 4.86% respectively. So, the marginal probability that a home team will cover the spread given that it is an underdog with a 30F cold advantage is 5.90%, 6.78%, 9.24%, and 8.69% respectively. The evidence presented above suggests that there is a significant home underdog bias, and it is compounded by a significant cold-weather bias. Gray and Gray (1997), despite using flawed methodology, document an aggregate home underdog bias in NFL betting from 1976 to 1994. However, their results also suggest that the home underdog bias has attenuated over time. The inference is that bettors have, albeit slowly, learned that mispricing exists and have adjusted their betting strategies accordingly. But as demonstrated in Table 3-8, the forecast error for home underdogs consistently increases in magnitude from the beginning to the end of our sample. 16 Furthermore, Table 3-9 shows that the home underdog effect in December and January has intensified. The mean forecast error increases from 1.58 points (1981 to 1985) to 5.83 points (1996 to 2000). Therefore, evidence suggests that neither the home underdog effect nor the cold-weather effect has attenuated over time. 3.3.4.6 Out-of-sample predictability The out-of-sample models are constructed by regressing outcomes in month m, and using the resulting coefficient estimates to predict outcomes in month m + 1. So, for example, we pool all October outcomes and use the resulting coefficient estimates to predict November’s outcomes. For comparison purposes, we also present the results of 16 It is not critical to test for significance within individual years. As discussed in Sauer, Brajer, Ferris, and Marr (1988), breaking the sample into small sub samples would unnecessarily increase sample variance. It is not our contention that this anomaly holds in each year, but rather that it is not driven by outlying observations.

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71 in-sample models, which are constructed such that coefficient estimates obtained by regressing outcomes in month m are used to predict month m’s outcomes. The top two rows in Table 3-10 show the results of the in-sample and the overtime-adjusted in-sample models, and the bottom two rows display results of the out-of-sample and the overtime-adjusted out-of-sample models. The figures shown represent the mean monthly accuracy for each respective model along with the associated binomial test statistics for each of the two standard hurdle rates, 50% and 52.38%. Test results indicate that monthly in-sample predictability significantly exceeds that of equivalent out-of-sample models, and that monthly overtime-adjusted models perform significantly better than their unadjusted counterparts. 17 In addition, several of the out-of-sample overtime-adjusted models surpass the 52.38% economic efficiency threshold, but not reliably. 18 The inability of regression models to surpass this barrier indicates that, while there is a mispriced weather advantage, bet prices are efficient much of the time. This implies that there are at least some informed bettors who are usually able to push prices towards their true values. Why, then, do prices exhibit efficiency one portion of each season yet deviate from underlying values in another? It may be instructive to draw on existing theories describing the relationship between noise traders and arbitrageurs in equities markets. Noise traders in financial markets sometimes move prices away from their rational values. Arbitrageurs, given unlimited capital, are able to earn abnormal profits by buying 17 The entire list of p-Values for tests comparing the base, adjusted, probit, OLS, in-sample, and out-of-sample model accuracies are available from the author upon request. 18 It is not surprising that that the accuracy of the out-of-sample Temperature-Augmented Models is insignificantly different than that of the Base Model. The out-of-sample models that control for the cold temperature advantage do not pick up the temperature bias until December, so only outcomes in January are affected (N =150) by the temperature controls.

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72 or selling misvalued equities until the transactions costs equal the marginal profits of additional trades. Any deviation from efficiency suggests that uninformed noise traders dominate the market. That is, market arbitrageurs are wealth-constrained and are unable to buy the volume of shares that is required to move prices to the associated true underlying values. As the playoffs approach, the NFL receives more media coverage and more attention from casual bettors. And, as Table 3-11 shows, the late-season weekly-dollar-volume of bets is much greater than that exhibited in earlier weeks. Given that potential arbitrageurs in the NFL point spread market have limited wealth, it appears that excessive bet volume of noise traders late in the season may overwhelm informed bettors’ ability to correct prices. Evidence, then, suggests that the limits of arbitrage enable late season prices to persistently remain biased even at the close of the line. The marginally significant mispricing of early season games becomes more difficult to explain, since the limits of arbitrage theory fails to explain inefficiencies during periods of low bet volume. One potential explanation is that more uncertainty exists about teams’ performance levels early in the season. Bettors may react to this uncertainty by relying heavily on home field advantage to predict outcomes. The result is that too much money is placed on bets for home teams, and thus these bets lose more often. Regardless of the mechanism by which pricing inefficiencies arise and persist, one reason that the empirical results presented above are significant is that the profitability of any betting strategy would be greatly improved if bets were timed to take advantage of the dynamic nature of biases. 19, 20 19 The results of a detailed economic analysis are available from the author upon request.

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73 3.4 Conclusions We demonstrate that bet prices in the NFL point spread market persistently deviate from their true underlying values in December and January over the 20-year period from 1981 to 2000. This anomaly occurs because gamblers undervalue the advantage gained by home teams playing in open-air stadiums on particularly cold game days. Our analysis indicates that these short-term but large price deviations from rationality are responsible for the existence of the enigmatic home underdog phenomenon. Evidence presented also suggests that arbitrage limits have enabled the home underdog effect to exist for decades. In addition, we show that noise created by overtime outcomes complicates regression analysis, and may have lead prior studies to erroneously conclude that the NFL point spread market is statistically efficient. While we demonstrate that out-of-sample predictability is reliably greater than 50%, there is no evidence that the 52.38% break-even threshold can be surpassed out-of-sample unless the cold-weather trend continues into the coming years. 20 Although research suggests that the Kelly Criterion enables bettors to determine optimal bet size, the Kelly Criterion assumes that the number of bets to be placed is known in advance. If game day temperature conditions are not fully incorporated into the closing line, and if temperature is difficult to forecast in advance, then the number of future bets to be placed is not known with certainty. Therefore, the Kelly Criterion may be impossible to employ, and a potential research opportunity exists.

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Table 3-1. NFL Closing Line Summary Statistics. This table contains summary statistics describing the closing spreads of all NFL games played between 1981 and 2000. The “underdogs” category includes only games in which there is a non-zero point spread, and the “home teams” and “home underdogs” categories exclude Superbowls. Closing Line describes the predicted difference in the number of points scored by the two teams in each category. Except for underdogs, the Closing Line is calculated with respect to the home team. Negative (positive) lines for home teams indicate that the home (visiting) team is favored on average. By definition, underdogs have a positive closing line and pick-’ems have a zero closing line. Outcome is the actual difference in points scored between the competing teams when the game is complete. A positive (negative) outcome indicates the mean number of points by which teams in a given category have won (lost) games. Forecast Error is the difference between the Closing Line and Outcome. A positive forecast error indicates that performance exceeds expectations. p-Value N is the test statistic obtained from testing the hypotheses that the distribution of the Closing Line, Outcome, and Forecast Error are normal using a Kolmogorov-Smirnov test if N 2000, and a Shapiro-Wilk test otherwise. Closing Line Outcome Forecast Error Category N Mean p-Value N Mean p-Value N Mean p-Value N Underdogs 4,596 5.63 0.0100 -5.45 0.0100 0.18 0.0100 Home Teams 4,668 -2.67 0.0100 3.03 0.0100 0.35 0.0100 Home Underdogs 1,423 4.65 0.0000 -3.76 0.0005 0.89 0.0424 Home Regular Season 4,480 -2.54 0.0100 2.79 0.0100 0.25 0.0100 Home Playoff Teams 208 -5.37 0.0000 7.68 0.5848 2.31 0.5003 Home Pick-’ems 92 0.00 0.28 0.3712 0.28 0.3712 Home Pushes 118 -1.66 0.0004 1.66 0.0004 0.00 74

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Table 3-2. NFL Game Outcomes. This table contains summary statistics describing the closing spreads of all NFL games played between 1981 and 2000. The Underdogs category includes only games in which there is a non-zero point spread. Home and Home Underdog categories exclude Superbowls. Mean FE is the mean forecast error, and is defined as the difference between the closing line and outcome. A positive forecast error indicates that performance exceeds expectations. p-Value is the test statistic obtained from a sign test of the hypothesis that the forecast error is not positive. 75 FE Underdog Months N FE N Mean FE FE Home Home Underdog Mean FE p-Value p-Value FE N Mean FE p-Value FE Aug. & Sept. 1,085 0.13 0.1698 1,103 -0.27 0.8948 337 -0.03 0.5221 October 0.1761 1,080 0.62 0.0445 1,105 -0.04 0.5966 346 0.65 November 1,168 -0.03 0.9087 1,194 0.06 0.3093 372 0.00 0.7356 December 1,066 0.31 0.0871 1,086 1.16 0.0710 340 2.39 0.0048 January 197 -1.37 0.9708 180 3.81 0.0009 28 8.66 0.0436 All Games 4,596 0.18 0.0120 4,668 0.35 0.3778 1,423 0.89 0.0103

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76 Table 3-3. NFL Cover Frequency. This table contains summary statistics describing the closing spreads of all NFL games played between 1981 and 2000. The Underdogs category includes only games in which there is a non-zero point spread. Home and Home Underdog categories exclude Superbowls. Cover % is the frequency at which bets on underdogs, home teams, and home underdogs cover the spread. p-Value 50% (p-Value 52.38% ) is the test statistic obtained from a binomial test of the hypothesis that the cover frequency is not greater than 50% (52.38%). Underdog Months N Cover % p-Value 50% p-Value 52.38% Aug. & Sept. 1,054 51.52% 0.1621 0.7124 October 1,046 52.68% 0.0417 0.4238 November 1,140 52.02% 0.0865 0.5968 December 1,049 52.14% 0.0824 0.5606 January 189 42.86% 0.9752 0.9956 All Games 4,478 51.70% 0.9884 1.0000 Home Months N Cover % p-Value 50% p-Value 52.38% Aug. & Sept. 1,072 48.04% 0.9002 0.9978 October 1,071 49.58% 0.6083 0.9667 November 1,166 49.23% 0.7010 0.9844 December 1,069 52.29% 0.0670 0.5230 January 174 62.07% 0.0007 0.0052 All Games 4,552 50.24% 0.3722 0.9981 Home Underdog Months N Cover % p-Value 50% p-Value 52.38% Aug. & Sept. 326 49.69% 0.5441 0.8343 October 334 52.69% 0.1623 0.4542 November 363 51.79% 0.2475 0.5889 December 330 57.27% 0.0041 0.0376 January 28 67.86% 0.0294 0.0505 All Games 1,381 53.15% 0.0096 0.2834

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77 Table 3-4. Open-Air Stadium Game Day Temperature. This table contains summary statistics for the temperature at home teams’ venues on game days. Games played in a dome are excluded. Mean Game Day Temperature is the average temperature at the site of the game. Mean Temperature Difference is the average difference between visiting teams’ mean yearly temperature and the game day temperature. Months N Mean Game Day Temperature (F) Mean Temperature Difference (F) Aug. & Sept. 906 69.31 -11.34 October 925 60.37 -2.68 November 968 50.34 7.36 December 903 43.00 14.10 January 157 42.58 14.79 All Games 3,859 55.17 1.35

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Table 3-5. Open-Air Stadium Game Outcomes. This table contains summary statistics with respect to home teams in games played in open-air stadiums. N is the number of games played, CL is the mean closing line, OC is the mean outcome, and FE is the mean forecast error. A positive forecast error indicates that performance exceeds expectations. p-Value FE is the test statistic obtained from a sign test of the hypothesis that the forecast error is not positive. Cover % is the proportion of outcomes that result in the home team covering the spread. p-Value 50% (p-Value 52.38% ) is the test statistic obtained from a binomial test of the hypothesis that Cover % is not greater than 50% (52.38%). 78 Months N CL OC FE p-Value FE Cover % p-Value 50% p-Value 52.38% Aug. & Sept. 906 -2.84 2.49 -0.35 0.9215 47.56% 0.9263 0.9979 October 925 -2.59 2.57 -0.01 0.5400 49.78% 0.5532 0.9405 November 968 -2.75 2.80 0.05 0.5000 50.05% 0.4870 0.9238 December 903 -2.83 3.88 1.06 0.0745 52.48% 0.0699 0.4768 January 157 -5.05 9.38 4.32 0.0004 63.82% 0.0003 0.0024 All Games 3,859 -2.84 3.19 0.35 0.2623 50.53% 0.2570 0.9883

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79 Table 3-6. Base Model and Temperature-Augmented Models. The Base Model is W i = HF HF i + HU HU i + ( – 1)CL i + i , where HF is 1 if the home team is favored; HF is 0 otherwise, HU is 1 if the home team is an underdog; HU is 0 otherwise, and CL i is the closing line defined with respect to the home team. The Temperature-Augmented Models are W i = HF HF i + HU HU i + ( – 1)CL i + i + i , where i is a vector of weather variables. Base Model Temperature-Augmented Models (N = 3,684) (N = 3,684) Model 1 Model 2 Model 3 Model 4 0.0089 -0.0317 -0.0291 -0.0143 -0.0142 HF (0.8408) (0.5420) (0.5336) (0.7616) (0.7584) 0.0656 0.0241 0.0268 0.0423 0.0423 HU (0.1601) (0.6568) (0.5834) (0.3937) (0.3833) 0.0042 0.0043 0.0043 0.0044 0.0045 ( – 1) (0.4825) (0.4764) (0.4701) (0.4636) (0.4555) 0.0028 TA HOME (0.1338) 0.0001 (TA HOME ) 2 (0.0078) 0.0049 CA HOME (0.0051) -0.0013 HA HOME (0.5678) 0.0002 (CA HOME ) 2 (0.0007) 0.0000 (HA HOME ) 2 (0.6954) Model Predictive Accuracy 51.28% 52.06% 52.25% 52.04% 52.01% p-Value 50% (0.0607) (0.0061) (0.0031) (0.0067) (0.0074) p-Value 52.38% (0.9102) (0.6500) (0.5613) (0.6621) (0.6741)

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80 Table. 3-7 Adjusted Base Model and Adjusted Temperature-Augmented Models. This table shows the results of the Adjusted Base Model and Temperature-Augmented Models. The models and definitions are identical to those in Table 2-5 except that outcome is defined as the difference in score between the home team and visiting team at the end of regulation play rather than at the end of overtime. Adjusted Base Model Adjusted Temperature-Augmented Models (N = 3,696) (N = 3,696) Model 1 Model 2 Model 3 Model 4 -0.0467 -0.0783 -0.0800 -0.0661 -0.0667 HF (0.2928) (0.1319) (0.0859) (0.1609) (0.1478) 0.1157 0.0835 0.0823 0.0969 0.0966 HU (0.0131) (0.1229) (0.0915) (0.0503) (0.0457) -0.0013 -0.0013 -0.0013 -0.0012 -0.0012 ( – 1) (0.8211) (0.8258) (0.8295) (0.8412) (0.8461) 0.0022 TA HOME (0.2429) 0.0001 (TA HOME ) 2 (0.0193) 0.0045 CA HOME (0.0097) -0.0018 HA HOME (0.4516) 0.0001 (CA HOME ) 2 (0.0017) 0.0000 (HA HOME ) 2 (0.5897) Adjusted Model Predictive Accuracy 52.38% 53.19% 52.95% 52.54% 52.95% p-Value 50% (0.0019) (0.0001) (0.0002) (0.0010) (0.0002) p-Value 52.38% (0.4995) (0.1613) (0.2442) (0.4212) (0.2442)

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Table 3-8. Home Underdog Attenuation. This table contains summary statistics with respect to home underdogs. N is the number of games played excluding pushes, CL is the mean closing line, OC is the mean outcome, and FE is the mean forecast error. A positive forecast error indicates that performance exceeds expectations. p-Value FE is the test statistic obtained from a sign test of the hypothesis that the forecast error is not positive. Cover % is the proportion of outcomes that result in the home team covering the spread. p-Value 50% (p-Value 52.38% ) is the test statistic obtained from a binomial test of the hypothesis that Cover % is not greater than 50% (52.38%). 81 Seasons N CL OC FE p-Value FE Cover % p-Value 50% p-Value 52.38% 1981 1985 324 4.15 -3.53 0.61 0.1433 53.14% 0.1310 0.3924 1986 1990 344 4.60 -3.91 0.69 0.3315 51.34% 0.3120 0.6495 1991 1995 377 4.91 -4.00 0.91 0.1241 53.17% 0.1137 0.3818 1996 2000 378 4.86 -3.56 1.30 0.0371 54.82% 0.0331 0.1759 All Years 1,423 4.65 -3.76 0.89 0.0103 53.15% 0.0096 0.2834 Table 3-9. December and January Home Underdog Attenuation. This table contains summary statistics with respect to home teams in games played in open-air stadiums. N is the number of games played excluding pushes, CL is the mean closing line, OC is the mean outcome, and FE is the mean forecast error. A positive forecast error indicates that performance exceeds expectations. p-Value FE is the test statistic obtained from a sign test for hypothesis that the forecast error is not positive. Cover % is the proportion of outcomes that result in the home team covering the spread. p-Value 50% (p-Value 52.38% ) is the test statistic obtained from a binomial test of the hypothesis that Cover % is not greater than 50% (52.38%). Seasons N CL OC FE p-Value FE Cover % p-Value 50% p-Value 52.38% 1981 1985 91 4.64 -3.05 1.58 0.1983 55.06% 0.1700 0.3066 1986 1990 75 4.55 -2.68 1.87 0.3638 52.70% 0.3210 0.4778 1991 1995 101 5.01 -3.21 1.80 0.1332 56.12% 0.1127 0.2291 1996 2000 101 5.05 0.77 5.83 0.0005 67.01% 0.0004 0.0020 All Years 368 4.84 -1.97 2.87 0.0013 58.10% 0.0011 0.0151

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Table 3-10. NFL Monthly Outcome Predictability. This table shows the success rate of both the standard and the adjusted Base and Temperature-Augmented Models in correctly predicting outcomes of NFL games from 1981 to 2000. Coefficient estimates are recalculated each month. For in-sample predictions, each month’s estimates are used to predict outcomes in that same month. For out-of-sample predictions, each month’s estimates are used to predict the following month’s outcomes. Model accuracy is presented along with binomial test statistics for each of the two standard hurdle rates, 50% and 52.38%. 82 Temperature-AugmentedModels Base Model Model 1 Model 2 Model 3 Model 4 Predictive Accuracy 53.34% 53.26% 53.80% 53.34% 53.42% p-Value 50% (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) In-Sample (N = 3,684) p-Value 52.38% (0.1220) (0.1432) (0.0422) (0.1220) (0.1031) Predictive Accuracy 53.90% 53.73% 53.98% 53.79% 54.25% p-Value 50% (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) Adjusted In-Sample (N = 3,696 ) p-Value 52.38% (0.0325) (0.0497) (0.0259) (0.0433) (0.0115) Predictive Accuracy 51.63% 51.31% 51.56% 50.71% 51.28% p-Value 50% (0.0416) (0.0817) (0.0487) (0.2257) (0.0876) Out-of-Sample (N = 2,820) p-Value 52.38% (0.7870) (0.8719) (0.8083) (0.9622) (0.8796) Predictive Accuracy 52.67% 52.24% 52.31% 52.49% 52.42% p-Value 50% (0.0023) (0.0085) (0.0069) (0.0040) (0.0050) Adjusted Out-of-Sample (N = 2,831) p-Value 52.38% (0.3799) (0.5580) (0.5282) (0.4532) (0.4832)

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Table 3-11. Nevada Football Betting. This table shows the number of football games and bet volume by month from September, 1988 to January, 2001. The number of games shown represents college football (CFB) and National Football League games listed on betting boards in Las Vegas. Mean Bet/Game is total casino handle per game in Nevada, and Mean Profitability is the mean hold per game divided by the mean handle per game. Because the Nevada Gaming Control Board pools its CFB and NFL betting data for accounting purposes, the dollar volume of football bets cannot be broken down into college vs. professional games. Months CFB Games NFL Games Total Games Mean Bet/Game Mean Profitability Aug. & Sept. 3,021 726 3,747 $567,532 7.91% October 3,007 754 3,761 $580,764 4.78% November 2,325 786 3,111 $700,072 2.59% December 350 758 1,108 $1,487,142 6.02% January 0 142 142 $12,820,228 8.26% 83

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84 CHAPTER 4 ALLOCATION OF SCARCE FINANCIAL RESOURCES: INSIGHT FROM THE NFL SALARY CAP An extensive body of financial literature links corporate executive pay with firm performance. One reason that principal-agent issues are so often studied using executive compensation is that firms, in accordance with SEC requirement s, publicly release compensation data. These data are read ily available through sources such as ExecuComp. While such data can be useful in examin ing agency problems and optimal contract design, there remain unsolved issues regarding performance measurement. For instance, if salary and bonus are tied to accounting benc hmarks, there is both an incentive and an opportunity for corporate offi cers to manipulate accounting da ta over the short run to cash in at the expense of the stockholders . Studies on incentive-based pay, then, sometimes depend on measures that may not be accurate indicators of firm success. Therefore, it is instructive to study incentive stru cture in an environment where the link between pay and performance can be meas ured with a high degree of accuracy. Pay structures in the NFL are similar to those in corporations. Firms’ executives agree to base salary terms a nd also receive bonus compensa tion once their performance is revealed. For executives, bonus pay is often su bstantially greater than salary. In the NFL, top players often receive more comp ensation through signing bonuses that through base salary.

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85 To some extent, all organizations possess a limited pool of wealth that they distribute among members. The existence of NFL salary cap creates an opportunity to examine the relationship between organizational performance and the distribution of limited resources. For instance, one issue that has received attention recently is the growing disparity between top executive pay and mid-level manager pay. Firms characterized by this inequity may suffer from low morale, increased turnover, and decreased productivity. The same is true in the NFL, where top players earn more than ten times that of their teammates. A question that remains to be answered is how this pay disparity affects team success in the NFL. This paper addresses the above issues and suggests several potential avenues for future research. 4.1 The Collective Bargaining Agreement The NFL is the most popular team sport in America. Television rights contracts for the 1998 through 2005 seasons are projected to be worth over $2.2B per season. TV revenue, which represents the largest source of league revenue, topped $4.5B in the 2001 season. The players’ share including salaries and benefits was over $3.1B. Currently, the average NFL salary is over $1MM and the players’ guaranteed share of league revenues is projected to result in average salaries doubling by 2005. The average starter would then be making around $2.3MM per season. However, until the 1980s, players held little bargaining power during contract negotiations. Beginning in 1982, the USFL provided a source of competition for players’ services. The USFL folded in 1985. After two player strikes (1982 and 1987) years of antitrust litigation, the Collective Bargaining Agreement was signed in 1993. The NFL team salary cap was triggered following the 1993 season, when player compensation surpassed a pre-determined proportion of league revenues.

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86 Beginning in 1994, the NFL’s Collective Bargaining Agreement set the rules that govern player compensation. The two cornerstones of the CBA are the salary cap and free agency. One of the stated goals of the CBA was to settle the team owners’ fears that bidding wars for players would result in excessive salaries or another player strike. To prevent these scenarios from occurring and to ensure that teams located in small markets are able to put a competitive team on the field, the CBA mandates that a pre-determined percentage of league revenues be allocated to players. 1 The players also benefit from the CBA. First, it ensures an equitable distribution of wealth between players and owners because players share in the financial success of the NFL. Second, the agreement implements a free-agency system which enables market forces to determine players’ salaries. Free agents are not bound by contract and therefore are able to negotiate and sign contracts with any team. The ability of players to move freely between teams gives them increased bargaining power during contract negotiations, and results in owners paying more than the nominal team salary cap allows. While the salary cap increased from $34.6MM in 1994 to $71.1MM in 2002, actual team spending exceeded the stated cap by over $4.5MM per season per team during this time. So, players have actually received $1.2B more compensation than nominal cap figures imply. This can be achieved because various forms of compensation are applied to the cap differently. Teams can, to a certain extent, spend more than the nominal salary cap by accruing compensation to future seasons. For instance, a signing bonus of $X paid today to entice a player to sign a contract with a duration of Y seasons costs the team 1 The split has historically been around 64% for owners and 36% for players.

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87 only $X/Y against this year’s cap allowance. Many player contracts include such complexities designed to circumvent cap restrictions. 2,3 The role of player incentive is central to our analysis. Therefore, it is important to provide an understanding of the relationship between free agency, the salary cap, and type of compensation (base salary vs. bonuses). Base salary is not guaranteed. If a player is cut, he will not receive the base salary that has been agreed to in his contract. However, signing bonuses represent guaranteed compensation. Player incentives, then, can be broken into two categories. First, a player has an incentive to perform well each season to ensure that he is placed on the roster the following season. Second, a player has an incentive to play well enough over the long term (throughout the course of his contract) to be worthy of a large signing bonus when he negotiates his next contract. Interestingly, then, player performance within the season does not affect his concurrent base salary or bonus, so compensation is always determined in advance of performance. Within-season incentive pay exists, but represents an insignificant portion of pay in player contracts. NFLPA documents indicate that in 2001, base salary and signing bonuses amounted to 55% and 40% of total compensation respectively, while incentive bonuses combine amounted to less than 1% of player compensation (2002 Mid Season Salary Averages and Analysis, NFLPA). Furthermore, only 72 of 1890 players in 2001 received performance bonuses. So, the vast majority of compensation is predictive in nature. That is, all base salary and the vast majority of bonus salary are decided before 2 See Appendix C for a detailed example. 3 From the day free agency begins (March 1) up until opening day, only the top 51 players’ salaries, bonuses, and incentives count against the cap. Any money paid to players with salaries below that of the 51 st highest-paid player do not affect the team’s cap figure. Upon completion of training camp and exhibition games, each player to make the final 53-man roster counts towards the salary cap, as does the money appropriated to players who are injured or have been cut.

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88 the player ever sets foot on the field. Therefore, if pay is commensurate with performance, then NFL teams are good at predicting performance and set pay to match expected performance. Signing bonuses in the NFL are effectively the only guaranteed portion of players’ salaries. Since the inception of the CBA, major changes have occurred in the amount of guarantees offered to players. Before 1993, signing bonuses accounted for only around an average 20% of player salaries. However, between 1999 and 2000, approximately $1 of every $2 that players earned was guaranteed. In the pre-CBA environment, there were a total of 4,023 signing bonuses awarded to players, and the average bonus was $125,000. Since 1993, the more than 8,000 signing bonuses have averaged almost $700,000. Signing bonuses are prorated over the life of the contract because of salary cap implications. If a player fails to make the team roster at the beginning of the season, he receives in full the remaining unpaid portion of his singing bonus, but does not receive any salary. Therefore, the incentive structure in the NFL is such that a player is motivated to perform well enough during the course of his contract to later be offered a signing bonus. Ironically, once a player surpassed this performance hurdle and is offered a signing bonus, there intuitively seems to be a reduced incentive to perform. Because teams can push the accrual of signing bonuses into future season, they have an incentive to substitute guaranteed bonus pay for (unguaranteed) base salary pay. Teams typically entice the best free agents by offering them signing bonuses. Signing bonuses are valuable to players because they are, for practical purposes, the only guaranteed for of compensation that teams can offer. However, teams take on risk when paying signing bonuses because if the player is cut or traded before the end of the

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89 contract, the unaccrued portion of the signing bonus is applied entirely to the following season’s cap figure. So, teams are often forced to keep unwanted or overpaid players to avoid an unmanageable cap hit. The incentive structure created by the CBA enables us to test several hypotheses. First, we determine whether teams are good at predicting player performance. Since pay is set in advance of performance, if teams are good at evaluating talent/productivity, then we expect to see that player compensation is a good predictor or player performance. Second, we can examine whether each team’s relative distribution of compensation among positions is important in determining its relative statistical performance. We do this by examining the correlation between the amount of total salary allocated to each position and the resulting performance of team units (e.g., rushing and passing defense and offense). If variations in unit rankings are explained by variations in compensation, then the distribution of scarce resources is an important factor. Third, we can test whether base pay or bonus pay is more effective at providing players with an incentive to perform. If base pay provides a better incentive than bonus pay, we would expect a stronger correlation between base pay and player and/or team unit performance. Fourth, we examine the relative value of the resources allocated to each position. If teams efficiently allocate scarce resources, we would expect to see an equal tradeoff in per-dollar win productivity amongst all positions. 4.2 Analysis 4.2.1 Data We utilize team and individual player compensation data and performance statistics from the 1994 NFL season (the first season governed by the CBA’s salary cap) to the 2002 NFL season using base and bonus compensation data for 16,213 player-years. The

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90 main sources for player salaries are USA Today Library and Research Service and the website of the NFL Players’ Association (NFLPA.org). Specific documents for each are listed in the References section. Player and team performance statistics are obtained from Stats, Inc. and Pro Football Edge respectively. Player data consists of name, age, passing, rushing, receiving, and defensive statistics for 17,123 player-years from the 1994 NFL season to the 2002 NFL season. Team performance statistics include game scores and numerous offensive and defensive statistics covering 2,184 NFL regular season games from the 1994 season to the 2002 season. Table 4-1 provides summary statistics describing how players were acquired and detailing player experience. The first column indicates the mean overall pick position that players were taken within the draft. The decrease over time likely occurs because the NFL draft was shortened from 12 rounds to 8 in 1993, and then to 7 beginning in 1994. The trend in the second column shows that team rosters spots are increasingly occupied by undrafted players since the CBA went into effect in 1994. This indicates that NFL teams have increasingly found value in utilizing players with less talent and, in all likelihood, lower salary expectation. Newly-drafted players and experienced free-agents have well-defined salary and signing bonus expectations during each of their first three or four years. Furthermore, the NFL imposes a minimum salary requirement that increases in relation to the number of years players have been in the NFL. Teams are often forced to make a keep-or-cut decision since renegotiation is unlikely. Undrafted free-agents, though, are likely to be willing to sign 1-year deals, and therefore provide valuable flexibility in team caps. The reduction in salary and associated reduction in on-field performance is evidently a valuable tradeoff that teams are willing to make.

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91 The number of 1 st year players that become part of team rosters fluctuates over time as demonstrated in the 3 rd column. It appears that rookies played less of a role in the years immediately following the implementation of the CBA, and then became more important after the transitional years. This may have occurred because teams needed to rid themselves of high-priced players early-on in the salary-cap era, and then again after the earliest free-agent contracts expired in the late 1990s. Mean player age has remained relatively steady over time, as has game experience. Game experience is measured by previous games started (prior to the beginning of each season), previous games played (games in which the player played at least one snap), and previous number of Pro Bowls (calculated as player-games played per team). 4 Figure 4-1 provides a perspective of changes in base and bonus compensation over time. The vertical line marks the institution of CBA salary cap restrictions. Bonus compensation has become a much larger portion of player salary than was the case in pre-CBA years. In 1993, the mean player salary consisted of 73% base salary and 16% signing bonus. By 2002, compensation consisted of 48% base salary and 42% signing bonus. As discussed earlier, teams are able to spend more, but also bear more risk when they pay large signing bonuses instead of high base salaries. Players prefer large signing bonuses, but are only able to command such bonuses through superior long-term performance. The upward trend suggests an increasing risk tolerance of teams and/or increased negotiating power of players between 1994 and 2002. Although not shown, evidence indicates that, as a percentage of total compensation, reporting bonuses and 4 For instance, if a team had 5 players with Pro Bowl experience, and those players had 1, 2, 3, 4, and 5 prior Pro Bowl games respectively, then the number of previous Pro Bowls played for that team is calculated as 15.

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92 roster bonuses have decreased (p-Values = 0.04972 and 0.0001), and compensation falling under the “other” category has increased (p-Value <0.0001). 5 4.2.2 Methodology 4.2.2.1 The Lorenz curve and Gini coefficient The Lorenz curve has been used extensively in research involving income distribution within societies. It also has applications in microeconomic environments such as the NFL. A Lorenz curve is a plot of cumulative wealth vs. cumulative population that enables one to determine, for instance, that the bottom X% of the population earns Y% of the total compensation. To study the distribution of player salaries in the NFL, we quantify compensation inequality using the Gini coefficient. This value is calculated by dividing the area between a Lorenz curve and the 45 equality line by 0.5. A perfectly uniform distribution of player salary would result in a Gini coefficient of 0, as the Lorenz curve would be a 45straight line. At the other extreme, a Gini coefficient of 1 represents total inequality. That is, a sole individual possesses all existing wealth. An analysis of the properties of the Lorenz curve of each NFL team will enable us to determine the relationship between compensation distribution and organizational success (measured as the number of wins in a season). If we see that teams with low Gini coefficients have significantly greater win rates than those with high coefficients, the implication would be that a relatively equal compensation distribution is more efficient given limited resources. Winning teams, then, would be characterized by few players at extreme ends of the compensation spectrum (star players and undrafted rookies, for 5 A roster bonus is a guaranteed sum of money that must be paid to a player if he is included on the team’s roster at the beginning of a season.

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93 instance). If we find that the Gini coefficients for the best teams are significantly higher than those of the worst teams, then results would imply that star players are a valuable commodity and/or that low-paid players are a good value. 4.2.2.2 Regression analysis We begin our analysis by testing whether player compensation is a good predictor of performance. We do this by regressing a group of productivity variables on total player compensation while correcting for age and experience. Any positive and significant coefficient estimates for the productivity variables would imply that teams have successfully predicted players’ performance levels. We then test for differences in predictive power between base salary and bonus salary. This provides us with an indication of the relative difficulty of predicting short-term vs. long-term player performance. The length of time between the point at which compensation level is determined and the point at which performance level is revealed is shorter for base salary than it is for signing bonuses. Therefore, if base salary explains player performance better than does bonus salary, then it is likely that teams have more difficulty predicting player performance in the long term. On the other hand, if bonus pay is more closely associated with player performance, the implication is that bonus pay is a good indicator of player talent, and that additional incentives created by base salary produce no significant improvements in player performance. We then extend this test to determine whether compensation allocation is correlated with team unit performance (e.g., pass offense or rush defense). We do this by measuring the performance rank of each team’s units against its peers. So, for example, we test whether teams that spend relatively more on the running back position have higher

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94 rushing output relative to other teams. In each set of relationships, we again contrast the correlation between unit performance and type of compensation (base vs. bonus). To determine whether positional pay translates into unit performance, we use the following specification: R i = + d POS POS i + d CV CV i + d GINI GINI i + i , (1) where R i is team i’s rank in one of 6 categories: pass defense, rush defense, overall defense, pass offense rush offense, and overall offense. is an intercept, and POS i is a vector of team i’s positional salaries. All position variables are defined as the difference between team i’s compensation allocated to each position and the average league-wide compensation allocated to each position. Likewise, CV i is the difference between team i’s salary coefficient of variation and the average league-wide coefficient of variation, and GINI i is the difference between team i’s Gini coefficient and the average league-wide Gini coefficient. A negative estimate indicates a decrease in rank (towards 1) and implies that a relative increase in spending, CV, or Gini results in improved performance relative to the league average. To examine the relationship between salary allocation and organizational success, we estimate a pooled cross-sectional OLS regression with specification dW i = d POS POS i + d CV CV i + d GINI GINI i + i , (2) where dW i is the difference between team i’s number of wins and the league-wide number of wins, POS i is a vector describing the difference between team i’s salary and the mean league salary in each of 14 different positions, CV i is team i’s salary coefficient of variation, and GINI i is team i’s Gini coefficient. The vector POS i is defined in two

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95 ways. The first definition measures positional compensation, and the second measures player compensation. So, for instance, under the first measure the term d C within POS i is defined as the difference between the total salary of all of the centers on a team roster and the mean league-wide per-team total salary allocated to the center position. Under the second measure, d C within POS i is the difference between the mean salary of all centers on a team roster and the league-wide per-team mean center salary. The first definition measures both the quality and depth of each team’s roster in a particular position while the second measures quality without regard to depth. 4.3 Results 4.3.1 Compensation Distribution Figures 4-2, 4-3, and 4-4 illustrate the inequity among NFL players in base, bonus, and total compensation. If base salary were perfectly evenly distributed among all players, each of these figures would be characterized by a 45 straight line. Instead, the cumulative compensation plot for all players from 1994 to 2002 reveals a convex curve for each of the categories – offense, defense, and special teams (kickers and punters). For the 8,157 offensive player-years in our data set, the Gini coefficients for base, bonus, and total compensation are calculated to be 0.47, 0.76, and 0.54 respectively. The plot of the 7,472 defensive player-years results in base, bonus, and total compensation Gini coefficients of 0.46, 0.74, and 0.53 respectively. Finally, the 602 special teams player-years results in base, bonus, and total compensation Gini coefficients of 0.28, 0.65, and 0.33 respectively. For each of the three forms of compensation, offensive and defensive team Gini coefficients are quite similar to each other. Special teams player Gini

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96 coefficients are typically higher than offensive and defensive players, indicating that compensation is distributed less equitably. Evidence indicates that, since the triggering of the CBA’s salary cap in 1994, the yearly offensive, defensive, and special teams total compensation Gini coefficients have remained very stable. From 1994 to 2002, the respectively coefficients have moved from 0.53, 0.52, and 0.72 to 0.54, 0.45, and 0.72 (not shown). In 1994, the overall Gini coefficient for all positions was 0.52, and moved to 0.54 by 2002. Therefore, the middle class in the NFL has been reduced slightly, but has not disappeared as some envisioned early-on in the salary cap era. Anecdotal evidence indicates that some teams have pursued an unbalanced strategy, attempting to overload some parts of their rosters with impact players and make due by filling out the remaining portion with bargain players. In 1998, the Minnesota Vikings broke the all-time record for most points scored. That season, the Vikings had three offensive backups with larger cap values than eight of their defensive starters. Two years later, the Baltimore Ravens broke the all-time NFL record for fewest points allowed. In that season, the combined salary cap values for the Ravens' 11 defensive starters doubled those of the offensive starters. On the other hand, players at the bottom end of the salary spectrum become very important under the CBA. In 2000, the New England Patriots won only 5 of 16 games and finished last in their division. The next season, they signed 20 free agents, six of whom were starters in their Superbowl XXXVI victory. However, an examination of the mean distribution of positional salary over time indicates that teams have not generally pursued unbalanced strategies between 1990 and

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97 2002. The mean coefficient of variation across positions for all teams from 1990 to 1993 was 0.38. The same measure is 0.33 from 1994 to 2002. If teams were attempting to become more specialized, the coefficient of variation would have instead increased significantly over this period. 4.3.2 Player Performance and Compensation Table 4-2 shows the results of a pooled cross-sectional OLS regression with total player compensation (base salary plus bonus salary) in thousands of dollars as the LHSV. The explanatory variables are broken into player age, experience, and productivity measures. Tables 4-2 and 4-3 detail defensive positions and offensive positions respectively. Examination of the age group of variables indicates that cornerbacks (CB), defensive ends (DE), defensive tackles (DT), linebackers (LB), and safeties (S) are at the peak of their earning potential when they are in the middle age classification. For cornerbacks, a position that arguably requires the most speed and agility, salary significantly decreases after 30 years of age. Regular season experience and Pro Bowl experience matter for all defensive positions except the defensive end position. In terms of productivity, compensation is generally correlated with the number of tackles, sacks matter for all positions except cornerbacks, passes defense are significant all positions except defensive tackles and linebackers, and interceptions are important in explaining pay for cornerbacks, defensive tackles, and linebackers. Table4-3 confirms that teams account for age, experience, and likely productivity in determining compensation. Centers (C), guards (G), and tackles (T) have few measurable productivity indicators. However, age and experience explain 71.51%, 66.28%, and 66.72% of the variation in total compensation respectively. Again, we observe that compensation is highest for these positions when player age is between 25

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98 and 30 years. The number of prior starts and the number of prior pro-bowls are also significantly related to compensation. For running backs (RB), tight ends (TE), and wide receivers (WR), we include productivity variables. The performance measurements used are rushes, yards per rush, number of receptions, and yards per reception. We find that for running backs, the number of rushes is important, but not productivity as measured by yards per carry. For wide receivers and tight ends, after controlling for the number of catches, yards per reception are not significantly related to compensation. The low p-values for running backs receptions and for wide receivers rushes indicate that versatility is valued. We perform the same type of analysis for quarterbacks and kickers (not shown). Quarterback performance in the NFL is often measured by the passer rating system. The formulas used to determine the quarterback’s rating consists of four components: percentage completions per attempt, average yards gained per attempt, percentage of touchdown passes per attempt, and percentage of interceptions per attempt (The Official NFL Record and Fact Book, 1999). We test two specifications. The first breaks the rating system to examine the individual components. The second tests the rating formula as a whole. Evidence from the first specification indicates that the first and fourth components are significantly positively related to quarterback pay (p-Values = 0.0087 and 0.0237 respectively). However, the second specification shows that passer rating system in aggregate, is not a good indicator of salary (p-Value = 0.1595). Both specifications show that the ability to rush is positively correlated with compensation (p-Values 0.0080 and 0.0167 respectively) as are game experience (p-Values 0.0001 and 0.0008 respectively) and prior Pro Bowls (p-Values 0.0001 and 0.0143 respectively).

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99 For kickers, prior experience and age variables are unimportant in determining salary. We also include two controls for kicking accuracy. One measures accuracy rate for kicks of less than 40 yards, and the other for kicks 40 yards an longer. Results indicate that only the accuracy of shorter kicks is related to salary (p-Value = 0.0119). So far, the LHSV in the regressions has been total compensation. One of our goals is to examine the incentive differences between base salary and bonus compensation. If base pay provides a better incentive than bonus pay, we would expect a stronger correlation between base pay and player and/or team unit performance. We next look at the relationship between the salary components and performance. At the bottom of Table 4-2, the r-squares of each model (total compensation, base salary, signing bonuses) are given. Age, experience, and productivity measures do not explain variations in bonus salary as well as they do variations in base salary or total compensation. For bonus salaries, though, pay has a significantly negative relationship with the highest age category in each of the defensive positions (not shown). The highest age category also has negative and significant coefficient estimates for kickers, quarterbacks, running backs, and tackles (not shown) when regressing on bonus pay. The implication is that teams are less willing to pay guaranteed money to older players in these positions. On the other hand, base salaries for all offensive and defensive positions are positively correlated with the highest age category, the only exceptions being cornerbacks and kickers. This is potentially due to NFL rules regarding minimum salary requirements for veteran players. 4.3.3 Positional Compensation and Statistical Rank Tables 4-4 and 4-5 demonstrate that each team’s relative distribution of compensation (in millions of dollars) is important in determining its relative statistical

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100 performance. For instance, in Table 4-4, the coefficient for safeties vs. pass is -0.9897 and significantly different from zero (p-Value = 0.0352). The implication is that if a team that pays $1MM more to its safeties than the league average, it is likely that its overall defense will rank 15.68 1.4876, or 14 th , ceteris paribus. The more negative the coefficient, the more value is created by allocating resources to the position. That is, it would create value to reallocate compensation from linebackers to safeties because defensive performance is relatively less strongly correlated with the amount of compensation allocated to linebackers (-0.3980 vs. -1.4876). Positive coefficient estimates, such as cornerbacks in rush defense, imply that because resources are limited, sometimes resources allocated to one position cause shortages in funding for other positions. For instance, teams that spend a relatively large amount of money on cornerbacks have less money to pay safeties. The bottom of Table 4-4 shows that, in aggregate, a relatively small portion of the each team’s defensive performance can be explained by the allocation of compensation among defensive positions. It is likely that the performance of each unit is interrelated with the performance of other units. For instance, if a team has a highly ranked rushing unit, it is also likely to have a highly ranked total defense because the rushing game reduces opponents’ time of possession. The result is that the opponent runs fewer plays, and therefore the defense gives up fewer yards. Interestingly, the relative distribution of compensation is better at explaining the performance of rushing defense than the passing defense. This is possibly because there is more randomness to pass defense (or opposing pass offense) than rush defense (or opposing rush offense). Further evidence is provided by the estimates for the coefficient of variation and Gini coefficient. Comparing

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101 coefficient estimates describing compensation distribution for passing defense vs. rushing defense, it is clear that the ranking of the rush defense is much more affected by salary allocation than is that of the pass defense. Table 4-5 shows the results of a similar set of regressions for offensive players. Evidence indicates that compensation differences among positions are more closely related to offensive performance than to defensive performance. The r-squares for the base, bonus, and total compensation regressions are each higher for the set of offensive regressions than for the set of defensive regressions. Interestingly, bonus pay is substantially better than base salary at explaining the relative performance of the offensive unit. Although not shown, the p-Values for coefficient estimates of offensive unit bonus pay indicate that bonus pay for quarterbacks and running backs are highly significant (p-Values = 0.0070 and 0.0062). The bonus regression produces an estimate of -1.1658 for d QB , so spending $1MM more than the league average on signing bonuses for quarterbacks results in an offensive ranking likely to be one rank higher than average. Similarly, the estimate of -1.6020 for d RB indicates that spending $1MM more than the league average on signing bonuses for running backs is likely to result in overall offensive rank that is better than average. Offensive performance, then, is more closely related to bonus salary than is defensive performance. This may be because an offense can be successful if a team can acquire two players a highly accomplished quarterback and running back. The defensive performance, however, relies on many more players to be successful. This may also explain why defensive rushing performance is better explained by compensation than is passing defense. Pass defense may be a function of a greater number of positions.

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102 For instance, a good defensive line can stop the run, but to stop the pass, but a team needs a good defensive line to apply pressure to the quarterback plus linebackers and defensive backs with good pass coverage skills. If a weak link exists, it may be much easier to exploit by passing into the weak spot. 4.3.4 Positional Compensation and Team Wins In this section, we analyze how teams distribute limited funds among the various positions. One of the difficulties with regressing positional pay on unit ranking is that there is less constraint in total compensation. Money can be diverted from the offensive unit to the defensive unit and vice versa, so the concept of limited resources is less applicable to individual team units. Regressing positional spending on team success mitigates this problem, and also provides a more direct test of the effect of compensation allocation on team performance. If teams efficiently allocate resources, we would expect to see an equal tradeoff in per dollar productivity amongst all positions. If teams systematically underestimate the value of a position, then we would expect to see significant coefficient estimate(s). The intuition is that a diversion in resources from a position that is not significantly related to wins to another position that is strongly related to wins would benefit the team. Two specifications are used in this analysis: the Positional Regression and the Player Regression. The Positional Regression provides a perspective on the relative value added by each position and implicitly measures the contribution of position depth. The RHSVs in this specification measure differences between each team’s allocation and the league-wide average allocation of compensation to each position (in millions of dollars). The player regression instead measures differences in mean player salary in

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103 each position and the league average. So, the latter provides insight into the value of compensation allocated to players without regard to positional depth. Table 4-6 illustrates the relationship between total positional compensation and team performance. The significant coefficient estimates indicate that the impact of particular positions on wins is systematically misvalued by teams. For instance, the coefficient estimate for the difference in running back compensation is 0.3393 (p-Value = 0.0049). This indicates that a team can expect to win one more game on average if it spends (1/0.3393), or $2.95MM more than the league average on its running back position, ceteris paribus. The additional money allocated to its running backs, though, must be taken away from another position, so a tradeoff occurs. For example, we would expect that a team spending $2.95MM less than the league average on its quarterbacks and $2.95MM more on its running backs would win an extra 2.95 * (0.3393 0.2347), or 0.38 games each season. The coefficient estimates, then, provide an indication of the relative value of positions. The higher the coefficient estimate, the more expected wins per dollar allocated. Evidence, then, suggests that the most value is generated by spending limited resources on the positions of safety, center, and running back, while the least value is created by allocating scarce resources on punters, receivers, and kickers. However, this regression makes no distinction whether money is spent to increase depth (add an additional player) or to increase the average quality of the players (replace a poor player with a good one). The Player Regression, presented in the final two columns, provides insight into the value of compensation allocated to players without regard to positional depth. For

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104 instance, if a team with two running backs pays one $5MM more than the league average and pays one $1MM less than the league average, the expected result is that the team would win (1.3835 * $2MM) = 2.8 games more than the league average, ceteris paribus. The same result would hold if it paid each running back $2MM more than the league average. As in Table 4-3, coefficient estimates for d CV and d GINI in Table 4-6 suggest that a team having an optimal compensation distribution would be characterized by a relatively high coefficient of variation and relatively low Gini coefficient. While the two terms are generally positively correlated, the relationship between them depends on the skewness of the salary distribution. Figure 4-5 illustrates the Lorenz curves of two teams with equal mean salaries, equal Gini coefficients, and unequal coefficients of variation. The curve that begins relatively flat and then becomes relatively steep is generated by plotting the Lorenz curve of a team on which a small group of players earn salaries that are significantly below the team average, and a large group of players earn salaries that are slightly above the team average. In contrast, the Lorenz curve that begins more steeply is generated by a team that pays the majority of its players an amount below the team average, and pays a few players much greater salaries than the team average. Evidence suggests, then, that a team consisting mostly of slightly below-average players that are complimented by a very small group of star players is likely to win more games, ceteris paribus. 4.3.5 Parity In implementing the CBA, one goal of the NFL was to facilitate parity. The salary cap was predicted to encourage fan support because small-market teams would be able to compete on an economically-level playing field with big-market teams. In contrast,

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105 baseball teams operating in larger markets have a nearly insurmountable advantage. Has the NFL has successfully avoided an MLB-like split into the haves and have-nots? If the CBA has created parity among NFL teams, we would expect that the difference between each team’s win total for each season has moved closer to 8. Because less separates good teams from bad teams, it is also likely that teams are more likely to experience a greater shift in the number of wins from one season to the next. For instance, if all teams are equal in strength, then a team at the bottom of its division one year has as much of a chance as any other team to win the Superbowl the next year. Figure 4-6 describes the distribution of wins and the changes in team seasonal success in the pre-CBA era vs. the post-CBA era. Between 1983 and 1993, the standard deviation of the number of wins for all teams is 3.05, and the average change in wins from one season to the next is 2.55. Following the 1993 season, the standard deviation falls slightly to 2.95, and the mean change in wins increases to 2.65. Evidence, then, indicates that the institution of the CBA has lead to a slight increase in league parity. Disparities in won/loss records among teams are marginally less extreme within individual seasons, and teams are also more able to move up or down in wins from one season to the next. This trend indicates that because differences in salary have narrowed, the talent level between teams has become narrower, and small improvements in team quality are more likely to result in larger improvements in wins. 4.3.6 Salary Components and Team Performance As a robustness check, we run a regression of each type of compensation on the difference between the league average and team wins per season. 6 We further break the 6 Reporting bonuses and workout bonuses reward players for attending team training camps and participating in fitness programs, and usually have negligible salary cap implications.

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106 sample into preand post-CBA eras. Negative coefficient estimates suggest that a team is likely to win fewer games than the average team, and positive coefficients imply that a team is likely to win more games than the league average. Table 4-7 shows that between 1981 and 1993, the percentage of compensation paid as base salary is positively correlated with performance. On the other hand, from 1994 to 2002, the number of wins is negatively correlated with percentage base salary. The implication is that in the salary-cap environment the best teams are willing to accept the risks associated with paying signing bonuses. There has been a fundamental change in the form of compensation required for organizational success. 4.4 Conclusions Since the inception of the CBA, major changes in salary structure have occurred. In 1993, the mean player salary consisted of 73% base salary and 16% signing bonus. By 2002, average player compensation was of 48% base salary and 42% signing bonus. Since the triggering of the CBA’s salary cap in 1994, the distribution of compensation among league players has remained steady. Evidence also shows that teams have remained balanced in allocating compensation among positions. We further demonstrate that each team’s relative distribution of compensation among positions is important in determining the relative statistical performance of offensive and defensive units. We find that that teams account for age, experience, and likely productivity in determining compensation. Base salary and total compensation are better predictors of performance than is bonus salary. Evidence also suggests that quarterbacks and running backs are undervalued. That is, teams would create more value if they were to redirect compensation away from other positions and into their quarterbacks and running backs, ceteris paribus. Evidence further suggests that a team consisting of slightly below

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107 average players that are complimented by a very small group of star players is likely to win more games, ceteris paribus. The institution of the CBA has lead to a modest increase in league parity. Disparities in won/loss records are marginally less extreme within individual seasons, and teams are also a bit more able to move up or down in standings from one season to the next. This trend indicates that because differences in salary have narrowed, the talent level between teams has become narrower, and small improvements in team quality are more likely to result in larger improvements in wins. One important factor that we have not accounted for is the effect of coaches on maximizing player value. For instance, some head coaches and coordinators install complex offensive and defensive systems. New players provide less value to their teams in the short-term because of the learning curve associated with mastering the system. An important component of team success, then, becomes retaining or acquiring players that are already familiar with this system.

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Table 4-1. NFL Player Summary Statistics. This table provides summary statistics for all NFL players from 1994 to 2002. Draft Position is the mean overall draft pick position of all players in the NFL. Undrafted Players per Team is the number of players per team that are signed as undrafted free agents. Rookies per Team is the mean number of players per team who have no prior NFL experience. Age is the mean age of all players in the league. Previous Games Started and Previous Games Played represent the mean game experience of all players in the NFL. Previous Pro Bowls is the average number of Pro Bowl player-seasons for each team. 108 Season Draft Position Undrafted Players per Team Rookies per Team Age Previous Games Started Previous Games Played Previous Pro Bowls 1994 111.0 15.4 17.4 26.5 24.4 43.0 19.9 1995 109.7 15.0 17.4 26.7 24.7 44.0 18.7 1996 107.2 14.6 14.2 26.7 25.6 45.5 19.1 1997 104.8 14.6 13.0 26.8 25.8 46.4 19.9 1998 105.3 15.6 12.9 26.8 25.5 46.4 20.1 1999 105.8 18.9 17.4 26.7 23.8 43.3 19.9 2000 105.7 17.2 15.4 26.7 25.0 44.6 19.5 2001 103.6 18.1 15.5 26.6 24.0 43.0 17.9 2002 105.6 19.6 16.1 26.6 23.5 42.7 17.7

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109 Table 4-2. Determinants of Compensation by Defensive Position. This table contains results for a pooled cross-sectional OLS regression with total player compensation (base salary plus bonus compensation) as the LHSV. The explanatory variables are grouped into age, experience, and productivity. Coefficient estimates are given along with their associated p-Values (in parenthesis). R-squares for the regressions on total salary, base salary, and bonus salary are listed at the bottom of the table. Position Variable CB DE DT LB S 142.30 118.99 189.58 162.49 144.12 < 25 (0.0000) (0.0066) (0.0000) (0.0000) (0.0000) 316.41 205.29 283.98 295.55 275.92 25 30 (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) -241.21 137.54 12.71 4.51 97.53 Age > 30 (0.0016) (0.1188) (0.8811) (0.9298) (0.0403) 10.69 9.44 10.99 7.49 5.66 Starts (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) 148.47 10.01 301.23 169.45 114.59 Experience Pro Bowls (0.0000) (0.6514) (0.0000) (0.0000) (0.0000) 5.86 7.87 3.63 5.11 3.89 Tackles (0.0000) (0.0000) (0.0144) (0.0000) (0.0000) -24.02 70.54 71.44 61.17 75.84 Sacks (0.4408) (0.0000) (0.0000) (0.0000) (0.0000) 12.57 25.53 25.80 13.52 15.10 Passes Defensed (0.0394) (0.0816) (0.1110) (0.1076) (0.0113) 46.28 -48.80 148.43 -38.52 -10.58 Productivity Interceptions (0.0044) (0.5199) (0.0598) (0.0821) (0.3844) N 1,484 1,302 1,242 2,086 1,354 RSQ Total Compensation 0.6788 0.6761 0.7078 0.7197 0.7371 RSQ Base Salary 0.6338 0.6529 0.6659 0.6815 0.7317 RSQ Signing Bonus 0.4678 0.4794 0.5244 0.5039 0.4981

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Table 4-3. Determinants of Compensation by Defensive Position. This table contains results for a pooled cross-sectional OLS regression with total player compensation (base salary plus bonus compensation) as the LHSV. The explanatory variables are grouped into age, experience, and productivity. Coefficient estimates are given along with their associated p-Values (in parenthesis). R-squares for the regressions on total salary, base salary, and bonus salary are listed at the bottom of the table. 110 Position Variable C G RB T TE WR 250.84 283.28 214.13 369.62 194.47 205.71 < 25 (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) 485.34 472.32 310.86 590.06 287.93 314.67 25 30 (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) 313.40 148.17 59.97 88.17 216.57 50.93 Age > 30 (0.0000) (0.0365) (0.3551) (0.3733) (0.0000) (0.4315) 9.41 10.79 6.82 13.93 6.85 10.62 Starts (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) 53.47 80.96 290.23 100.23 33.29 9.38 Experience Pro Bowls (0.0135) (0.0000) (0.0000) (0.0001) (0.0455) (0.5523)

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Table 4-3. Continued. 111 Position Variable C G RB T TE WR 0.65 3.25 Rushes (0.0000) (0.0000) -1.96 Yards/Rush (0.8141) 0.40 0.97 0.75 Receptions (0.0013) (0.0000) (0.0000) -2.45 -3.16 Productivity Yards/Reception (0.3284) (0.2042) N 670 1,132 1,602 1,149 1,005 1,700 RSQ Total Compensation 0.7151 0.6628 0.7032 0.6672 0.7544 0.7086 RSQ Base Salary 0.7067 0.6730 0.6779 0.6221 0.7419 0.6687 RSQ Signing Bonus 0.4536 0.4083 0.5039 0.4273 0.4949 0.4968

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112 Table 4-4. Team Defensive Performance. This table contains coefficient estimates and associated p-Values for a pooled cross-sectional OLS regression with specification R i = d POS POS i + d CV CV i + d GINI GINI i + i where R i is team i’s rank in either pass defense, rush defense, or overall defense. Coefficient estimates are shown along with associated p-Values (in parentheses). POS i is a vector of team i’s positional salaries. All position variables are defined as the difference between team i’s salary total salary allocated to each position and the average league-wide salary allocated to each position. Likewise, CV i is the difference between team i’s salary coefficient of variation and the average league-wide coefficient of variation, and GINI i is the difference between team i’s Gini coefficient and the average league-wide Gini coefficient. R-squares for the regressions on total salary, base salary, and bonus salary are listed at the bottom of the table. Defensive Rank Variable vs. Pass vs. Rush Overall 15.68 15.68 15.68 Intercept (0.0000) (0.0000) (0.0000) -0.4305 0.6894 0.0727 d CB (0.1476) (0.0167) (0.8041) -0.3390 -0.3899 -0.4715 d DE (0.2224) (0.1463) (0.0860) -0.2463 0.3367 0.0361 d DT (0.4485) (0.2835) (0.9104) -0.3929 -0.0974 -0.3980 d LB (0.1625) (0.7193) (0.1518) -0.9897 -1.2619 -1.4876 Compensation Differences d S (0.0352) (0.0056) (0.0014) -2.16 -16.49 -13.04 d CV (0.7876) (0.0337) (0.0981) -4.44 83.00 51.45 Distribution Differences d GINI (0.8994) (0.0150) (0.1390) N 273 273 273 RSQ Total Compensation 0.0340 0.1004 0.0596 RSQ Base Salary 0.0198 0.0973 0.0594 RSQ Signing Bonus 0.0274 0.1195 0.0502

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113 Table 4-5. Team Offensive Performance. This table contains coefficient estimates and associated p-Values for a pooled cross-sectional OLS regression with specification R i = d POS POS i + d CV CV i + d GINI GINI i + i where R i is team i’s rank in either pass offense, rush offense, or overall offense. Offensive Rank Pass Rush Overall 15.6754 15.6726 15.6921 Intercept (0.0000) (0.0000) (0.0000) 1.0236 -0.8565 0.6181 d C (0.0502) (0.1032) (0.2295) -0.3202 -0.2642 -0.5863 d G (0.4087) (0.4983) (0.1258) -1.3111 -0.0506 -1.3495 d QB (0.0000) (0.8728) (0.0000) -0.5683 -1.3125 -0.8984 d RB (0.1110) (0.0003) (0.0110) 0.1325 -0.2006 -0.1651 d T (0.7131) (0.5803) (0.6423) 0.8222 -0.5414 0.7024 d TE (0.2700) (0.4704) (0.3394) -0.3629 0.1126 -0.2825 Compensation Differences d WR (0.3282) (0.7629) (0.4402) -7.86 -9.19 -11.18 d CV (0.3246) (0.2528) (0.1559) 70.60 77.26 105.99 Distribution Differences d GINI (0.0455) (0.0298) (0.0025) N 273 273 273 RSQ Total Compensation 0.0997 0.0859 0.1236 RSQ Base Salary 0.0624 0.0878 0.0559 RSQ Signing Bonus 0.0966 0.0862 0.1444

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114 Table 4-6. Team Positional Spending and Wins. This table contains coefficient estimates and associated p-Values for pooled cross-sectional OLS regressions with specification dW i = d POS POS i + d CV CV i + d GINI GINI i + i where dW i is the difference between team i’s number of wins and the league-wide number of wins, POS i is a vector of team i’s positional salaries, CV i is team i’s salary coefficient of variation, and GINI i is team i’s Gini coefficient. In the Positional Regression, all position variables are defined as the difference between team i’s salary total salary allocated to each position and the average league-wide salary allocated to each position. In the Player Regression, all position variables are defined as the difference between team i’s mean player salary for each position and the average league-wide mean player salary for each position. R-squares for the regressions on total salary, base salary, and bonus salary are listed at the bottom of the table. Positional Regression Player Regression Variable Estimate p-Value Estimate p-Value d C 0.4197 0.0219 0.5445 0.1733 d CB 0.1135 0.2505 0.9113 0.0762 d DE 0.1792 0.0681 0.8816 0.0371 d DT 0.1652 0.1261 0.7495 0.0920 d G 0.1798 0.1873 1.2170 0.0349 d K 0.3314 0.5956 0.6662 0.2814 d LB 0.0915 0.3736 1.3832 0.0645 d P -0.7978 0.3168 -0.6117 0.4544 d QB 0.2347 0.0289 0.8700 0.0037 d RB 0.3393 0.0049 1.3835 0.0260 d S 0.5827 0.0002 2.7620 0.0001 d T 0.1493 0.2250 0.8695 0.0390 d TE 0.4303 0.0883 1.3943 0.1184 Compensation Differences d WR -0.0065 0.9598 0.8443 0.2062 d CV 7.23 0.0130 8.66 0.0016 Distribution Differences d GINI -38.20 0.0032 -42.58 0.0003 N 273 273 RSQ Total Compensation 0.1360 0.1743 RSQ Base Salary 0.0862 0.0992 RSQ Signing Bonus 0.1498 0.1596

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115 Table 4-7. Salary Components and Wins. This table contains coefficient estimates and associated p-Values for pooled cross-sectional OLS regressions for NFL teams from 1981 – 2002. The dependent variable is the difference between team wins and the mean number of wins each season. % Base is the proportion of team salary allocated to player base salary. An equivalent definition holds for % Signing Bonus, %Report Bonus, % Roster Bonus, and % Misc. % Misc. consists of workout bonuses, loans, and injury settlements. Total is the total team salary allocated among all players on a team in 000s. Season 1981 – 1993 1994 – 2002 1981 2002 0.9307 -1.8055 0.4158 % Base (0.0658) (0.0719) (0.1971) -3.6892 -1.5620 -2.1791 % Signing Bonus (0.0758) (0.5825) (0.1402) -10.8674 19.7122 -2.8864 % Report Bonus (0.2564) (0.1807) (0.7136) -10.5172 -14.7046 -9.5164 % Roster Bonus (0.2601) (0.0867) (0.1088) -8.6806 13.3442 -5.4725 % Misc. (0.1179) (0.1995) (0.2510) 0.0216 0.0270 0.0198 Total (0.2221) (0.3111) (0.0846) N 350 208 558 RSQ 0.0314 0.0339 0.0121

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116 $0$5,000$10,000$15,000$20,000$25,000$30,000$35,000$40,00019811986199119962001SeasonCompensation Base SalaryOther CompensationSigning Bonus Figure 4-1. NFL Compensation Trends (1981 – 2002). This figure summarizes mean per-team base and bonus salaries (in 000s) for 37,346 NFL player-seasons from 1981 – 2002. Base Salary and Signing Bonus Salary represent mean team expenditures each season. Other Salary includes signing bonuses, report bonuses, roster bonuses, workout bonuses, loans, and injury settlements. The vertical line marks the institution of CBA salary cap restrictions in 1994.

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117 0%25%50%75%100%0%25%50%75%100%Cumulative % PlayersCumulative % Base CompensationSpecial TeamsOffenseDefense Figure 4-2. NFL Player Base Salary Lorenz Curve (1994 – 2002). The figure below plots the Lorenz curve of all defensive, offensive, and special teams players in the NFL. The closer each plot is to a 45 straight line, the more equitable the base salary is distributed among players.

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118 0%25%50%75%100%0%25%50%75%100%Cumulative % PlayersCumulative % Bonus CompensationSpecial TeamsDefenseOffense Figure 4-3. NFL Player Bonus Salary Lorenz Curve (1994 – 2002). The figure below plots the Lorenz curve of all defensive, offensive, and special teams players in the NFL. The closer each plot is to a 45 straight line, the more equitable the bonus pay is distributed among players.

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119 0%25%50%75%100%0%25%50%75%100%Cumulative % PlayersCumulative % Total CompensationOffenseDefenseSpecial Teams Figure 4-4. NFL Player Total Salary Lorenz Curve (1994 – 2000). The figure below plots the Lorenz curve of all defensive, offensive, and special teams players in the NFL. The closer each plot is to a 45 straight line, the more equitable the total compensation is distributed among players.

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120 0%25%50%75%100%0%25%50%75%100%Cumulative % PlayersCumulative % CompensationLow CVPerfect Equality High CV Figure 4-5. Total Equality vs. Ideal Distribution. This figure contrasts the hypothetical total salary distributions of two teams, and contrasts each to the case of perfectly equal compensation. If all players on a team are paid the same compensation, the Lorenz curve is represented by a 45 Lorenz curve. Despite having identical Gini coefficients, the Lorenz curves depicted below (in dashed lines) differ from each other in coefficient of variation. Regression results indicate that teams with high coefficients of variation and low Gini coefficients have are likely to be more successful than otherwise.

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121 0.00.51.01.52.02.53.03.54.01983198819931998SeasonStandard DeviationMean Change Figure 4-6. Parity in the NFL (1983 – 2002). This figure shows the standard deviation of wins per team for each NFL season from 1983 – 2002. Standard Deviation measures the difference in wins between all team in each season. Mean Change measures the average difference in wins for each team from one season to the next. The 1982 season is omitted because of the strike-shortened season. The vertical line marks the institution of the team salary cap in 1994.

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CHAPTER 5 CONCLUSION In this analysis, we begin by describing the impact of corporate diversification decisions on market valuation. We then offer a test of market efficiency using a proxy market. Finally, we examine allocation decisions in an environment in which financial resources are artificially bounded. We now conclude by reviewing the main results from each chapter. In chapter 2, we confirm that the transition from specialized firm into conglomerate is associated with a significant reduction in market valuation. However, results of our analysis indicate that age is an important explanatory variable in the relationship between organizational structure and firm value. We find that young single segment firms are an appropriate benchmark when calculating the relative value of young diversified firms, but that results can be misleading when using young focused firms to evaluate diversification discounts associated with old diversified firms. That is, differences in growth rates between old and young firms must be carefully accounted for when calculating excess value. In addition, we show that firms follow a life cycle in which they begin as specialized entities, and then gradually expand into new industries as existing business lines experience diminishing growth. Evidence also suggests that old firms in stagnant industries have the most to gain from diversification, since these firms are the most likely to capitalize on the benefits of diversification, and are also more likely than young firms to be experiencing decreasing returns to scale. We propose that particularly productive firms have little to gain from 122

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123 pursuing new businesses, and our results confirm that young firms are less likely to add value by diversifying. Findings suggest that young diversified firms trade at the largest discount relative to their age-matched focused peers. It is likely that these firms are sacrificing good existing projects for diversification efforts. We suggest that diversification increases the likelihood of survival and therefore enables firms to explore new opportunities and potentially capitalize on finding a better match between business lines and organizational abilities. However, the incentive for managers to ensure firm survival potentially misaligns managers’ and shareholders’ interests. If a firm has few or no positive NPV opportunities, then the risk/return tradeoff of using remaining funds to explore new business ventures is likely too high, and it would instead be optimal for the firm to return cash to shareholders. In chapter 3, we supplement our diversification analysis with an efficiency test using the NFL point spread betting market as a proxy for equities markets. We find that not all available information is fully reflected in prices. Specifically, evidence presented shows that the home underdog phenomenon exists because bettors undervalue the advantage gained by home teams playing in open-air stadiums on particularly cold game days. In addition, we show that noise created by overtime outcomes complicates regression analysis, and may have led prior studies to erroneously conclude that the NFL point spread market is statistically efficient. In chapter 4, we extend the premise that the NFL is a useful proxy market and demonstrate that salary distribution is a significant determinant of organizational performance. Further, we find evidence that since the inception of the NFL’s Collective Bargaining Agreement, major changes in salary structure have occurred. In recent years,

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124 guaranteed pay has become a much larger portion of total player compensation than was the case in prior years. The creation of a free agency system has forced teams to offer large signing bonuses in order to entice the best players. Evidence also shows that teams have remained balanced in allocating compensation among positions. We further demonstrate that each team’s relative distribution of compensation among positions is significantly correlated with its performance.

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APPENDIX A SFAS131 SEGMENT DATA ISSUES Aggregated firm-level data are reported in the Compustat Industry File. Disaggregated segment-level data are contained in the Combined CRSP/Compustat Segment File. The date in which a particular segment accounting report was submitted to Standard and Poor’s is called the “Source Year.” The fiscal year to which the segment report pertains is the “Data Year.” A problem arises because segment data are often restated for Data Years 1997 and later due to new SFAS regulations. Because both sets of numbers appear in the raw segment file, the sum of segment sales by Data Year often differs from aggregate firm sales or assets reported in the COMPUSTAT Industry File. For instance, in 1999, the AAR Corp. (GVKEY 1004) reported one segment (SID 7) having $1024.333MM in sales. So, in this case, Source Year is 1999 and Data Year is 1999. In 2000, the firm re-stated segment figures, and reported SIDs 8, 9, 10, and 11. The total sales for these segments also totaled $1024.333MM. Summing solely by Data Year figures would result in double counting segment figures. So, the sum of segment sales would be twice the aggregate figure obtained from the Compustat Industry File. If only one Source Year were chosen, Herf would either be 1.00 (using Source Year 1999) or 0.41 (using Source Year 2000). So, depending on the Source Year selected, this firm would either appear as focused or as diversified. Additionally, selecting a single Source Year to use for calculations is problematic because the reporting standard is not consistent over the 1981-1996 and 1997-2000 sample periods. For instance, in 1998, Ceco Environmental Corp. (GVKEY 1050) 125

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126 reported one segment (SID 7) having $5.083MM in sales. This figure is inaccurate, as total firm sales were actually $26.382MM. In 2000, the firm re-stated the segment figures, and reported four segments SIDs 5, 6, 8, and 99. The total sales for these segments is only $21.299MM (still not accurate). The only way the data can be made consistent is to take SID 7 from Source Year 1998 and add it to the figures from Source Year 2000. Together, sales from Source Years 1998 and 2000 (SIDs 5, 6, 7, 8, and 99) add to $26.382MM, and therefore match the aggregate sales figure from the Compustat Industry File. To solve these problems, we select the combination of Source Years that make the total segment sales figures closest to the aggregate sales reported by firms. However, a complication arises when segment data are consistent with aggregate firm-level data in more than one Source Year or combination of Source Years. The GVKEY 1004 example above illustrates this case. When this issue arises, we use the most recent Source Year(s) that combine to make segment accounting data consistent. Because later Source Years are more likely to contain more highly disaggregated segment information than are earlier years, this approach best captures the effect of SFAS 131.

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APPENDIX B EXCESS VALUE CALCULATIONS To calculate imputed firm values, we use an approach similar to that of Berger and Ofek (1995): )(ln)(1VIVEXVALSVIndSVInimfii where )(VI = imputed value of the sum of a firm’s segments as stand-alone firms, iS = sales in segment in the valuation multiple, mfiSVInd = multiple of total capital to sales for the median focused firm in segment i’s industry, EXVAL = the diversified firm’s excess value, V = firm’s total capital (market value of common equity plus book value of debt), and n = total number of segments in segment i’s firm. To calculate our age and ownership multiples, we use a weighted average approach: 127

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128 )(ln)(1 IIndwInimfii where mfiInd = the ratio of the variable for the median focused firm in segment i’s industry )( I = the imputed value of the variable, iw = the proportion of the firm’s sales in industry i, = age or ownership, = the imputed age or ownership.

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APPENDIX C SALARY CAP EXAMPLE While bonuses are typically paid in one lump sum, they are prorated over the life of the contract for salary cap calculations. Teams attempt to take advantage of the cap intricacies by creative accounting. For example, say a player is signed to a five-year contract with a $5MM signing bonus and a base salary of $5MM per year. The cap number for the player is determined as in Table C-1. If the team restructures the deal in the second year, it can reduce its cap exposure in the short-term. For instance, say the team offers the player a new deal in year 2. The contract calls for a signing bonus of $4MM. Instead of receiving a $5MM salary in year 2, the player receives a bonus check for $4MM and a salary check for $1MM. As shown in Table C-2, the new arrangement saves the team $3MM in cap space in year 2, but sacrifices future cap availability because the contract is back-loaded. The team is, in effect, trying to stay ahead of the cap. Since the cap is likely to increase each year, this can be an effective strategy. 129

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130 Table C-1. Initial Player Contract. Contract Year 1 2 3 4 5 Total Base (MM) $5 $5 $5 $5 $5 $25 Pro-Rated Bonus (MM) $1 $1 $1 $1 $1 $5 Cap Figure (MM) $6 $6 $6 $6 $6 $30 Actual Expenditure (MM) $10 $5 $5 $5 $5 $30 Table C-2. Modified Player Contract. Contract Year 1 2 3 4 5 Total Base (MM) $5 $1 $5 $5 $5 $16 Pro-Rated Bonus 1 (MM) $1 $1 $1 $1 $1 $4 Pro-Rated Bonus 2 (MM) N/A $1 $1 $1 $1 $4 Cap Figure (MM) $6 $3 $7 $7 $7 $30 Actual Expenditure (MM) $10 $5 $5 $5 $5 $30

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LIST OF REFERENCES Amihud, Yakov, and Baruch Lev, 1981, Risk reduction as a managerial motive for conglomerate mergers, Bell Journal of Economics, Vol. 12, 605-617. Amoako-Adu, Ben, Harry Marmer, and Joseph Yagil, 1985, The efficiency of certain speculative markets and gambler behavior, Journal of Economics and Business 37, 365-378. Avery, Christopher, and Judith Chevalier, 1999, Identifying investor sentiment from price paths: The case of football betting, Journal of Business 72, 493-521. Berger, Philip, and Rebecca Hahn, 2003, The impact of SFAS no. 131 on information and monitoring, Journal of Accounting Research, Vol. 41, 163-223. Berger, Philip, and Eli Ofek, 1995, Diversification’s effect on firm value, Journal of Financial Economics, Vol. 37, 39-65. Bevelander, Jeffrey, 2002, Tobin’s q, corporate diversification, and firm age, Working paper, Massachusetts Institute of Technology. Brown, William O., and Raymond D. Sauer, 1989, Does the basketball market believe in the ‘hot hand?’ Comment, American Economic Review 83, 1377-1386. Burch, Timothy, Vikram Nanda, and M.P. Narayanan, 2003, Industry structure and value-motivated conglomeration, Working paper, University of Miami. Camerer, Colin F., 1989, Does the basketball market believe in the “hot hand,”? American Economic Review 79, 1257-1261. Campa, Jos, Manuel, and Simi Kedia, 2002, Explaining the diversification discount, Journal of Finance, Vol. 57, 1731-1762. Cox, D.R., 1972, Regression models and life-tables, Journal of the Royal Statistical Society, Series B (Methodological), Vol. 34, 187-220. Dare, William H., and A. Steven Holland, 2003, Efficiency in the NFL betting market: Modifying and consolidating research methods, Applied Economics 36, 2004, 9-15. Dare, William H., and S. Scott MacDonald, 1996, A generalized model for testing the home and favorite team advantage in point spread markets, Journal of Financial Economics, 1996, 295-318. 131

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132 Denis, David, Diane Denis, and Atulya Sarin, 1997, Agency problems, equity ownership, and corporate diversification, Journal of Finance, Vol. 52, 135-160. Fama, Eugene, and Kenneth French, 1992, The cross-section of expected stock returns, Journal of Finance, Vol. 67, 427-465. Fama, Eugene, and Kenneth French, 2003, New lists and seasoned firms: Fundamentals and survival rates, Working paper, University of Chicago. Gandar, John, Richard Zuber, Thomas O’Brien, and Ben Russo, 1988, Testing rationality in the point spread betting market, Journal of Finance 43, 995-1008. Golec, Joseph, and Maurry Tomarkin, 1991, The degree of inefficiency in the football betting market, Journal of Financial Economics 30, 311-323. Gomes, Joao, and Dmitry Livdan, 2004, Optimal diversification: Reconciling theory and evidence, Journal of Finance, Vol. 59, 507-535. Graham, John, Michael Lemmon, and Jack Wolf, 2002, Does corporate diversification destroy value?, Journal of Finance, Vol. 57, 695-720. Gray, Philip, and Stephen Gray, 1997, Testing market efficiency: Evidence from the NFL sports betting market, Journal of Finance 52, 1725-1737. Harville, David, 1980, Predictions for National Football League games via linear-model methodology, Journal of the American Statistical Association 75, 516-524. Jeffries, James, and Charles Oliver, 2000, The Book on Bookies: An Inside Look at a Successful Sports Gambling Operation (Paladin Press, Boulder, Colorado). Jensen, Michael, 1986, Agency costs of free cash flow, corporate finance, and takeovers, American Economic Review, Vol. 76, 323-329. Kahneman, Daniel, and Amos Tversky, 1979, Prospect Theory: An analysis of decision under risk, Econometrica 47, 263-291. Khoroshilov, Yuri, 2003, A dynamic model of diversification and divestiture, Working paper, University of Michigan. Lang, Larry, and Ren Stulz, 1994, Tobin’s q, corporate diversification, and firm performance, Journal of Political Economy, Vol. 102, 1248-1280. Levitt, Steven D., 2002, How do markets function? An empirical analysis of gambling on the National Football League, NBER Paper. Matsusaka, John, 2001, Corporate diversification, value maximization, and organizational capabilities, Journal of Business, Vol. 74, 409-431.

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133 May, Don, 1995, Do managerial motives influence firm risk reduction strategies?, Journal of Finance, Vol. 50, 1291-1308. NFL Players’ Association, 2002 mid-season salary averages and analysis, 2002, 4. NFL Players’ Association, NFL economics primer 2002, 2002, 31-52. The Official National Football League 2001 Record and Fact Book, Workman Publishing Co., New York, 2001. Overberg, Paul, American Football Conference Team by Team Salaries, USA Today, May 7, 1997, 11C. Overberg, Paul, National Football Conference Team by Team Salaries, USA Today, May 8, 1997, 6C. Overberg, Paul, Special report: AFC team by team salaries, USA Today, January 18, 1995, 11C. Overberg, Paul, Special report: NFC team by team salaries, USA Today, January 19, 1995, 4C. Pearson, Barbara, NFL: AFC team by team salaries, USA Today, January 22, 1996, 8C. Pearson, Barbara, NFL: NFC team by team salaries, USA Today, January 23, 1996, 8C. Rachlin, Howard, 1990, Why do people gamble and keep gambling despite heavy losses?, Psychological Science 1, 294-297. Ritter, Jay R., 1994, Racetrack betting – An example of a market with efficient arbitrage, in Efficiency of Racetrack Betting Markets (Academic Press, Inc., San Diego), 431-441. Romer, David, 2002, It’s fourth down and what does the Bellman equation say? A dynamic-programming analysis of football strategy, Working paper, University of California, Berkeley. Roper, Andrew, 2003, Leverage in young public companies: Evidence of life cycle in capital structure, Working paper, University of Wisconsin, Madison. Sauer, Raymond D., Vic Brajer, Stephen P. Ferris, and M. Wayne Marr, 1988, Hold your bets: Another look at the efficiency of the gambling market for National Football League games, Journal of Political Economy 96, 206-213. Scharfstein, David, and Jeremy Stein, 2000, The dark side of internal capital markets: Divisional rent-seeking and inefficient investment, Journal of Finance, Vol. 55, 2537-2564.

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134 Schleifer, Andrei and Robert Vishny, 1989, Managerial entrenchment, The case of manager-specific investments, Journal of Finance, Vol. 25, 123-139. Simonoff, Jeffrey S., and Lan Ma, 2003, An empirical study of factors relating to the success of Broadway shows, Journal of Business, Vol. 76, 135-150. Villalonga, Beln, 1999, Does diversification cause the “diversification discount,”? Working paper, University of California, Los Angeles. Weisman, Larry, 2002 NFL salaries, USA Today.com, July 29, 2003, 14C. Weisman, Larry, and Barbara Pearson, AFC salary list, USA Today, June 15, 1999, 14C. Weisman, Larry, and Barbara Pearson, American Football Conference salaries, USA Today, June 23, 1998, 8C. Weisman, Larry, and Barbara Pearson, National Football Conference salaries, USA Today, June 24, 1998, 9C. Weisman, Larry, and Barbara Pearson, NFC salary report, USA Today, June 16, 1999, 12C. Weisman, Larry, and Cheryl Philips, National Football League 1999 salaries: AFC, USA Today, May 23, 2000, 14C. Weisman, Larry, and Cheryl Philips, National Football League 1999 salaries: NFC, USA Today, May 23, 2000, 15C. Weisman, Larry, Cheryl Philips, and Scott Boeck, 2000 AFC salaries, USA Today, June 8, 2001, 13C. Weisman, Larry, Cheryl Philips, and Scott Boeck, NFC salaries, USA Today, June 8, 2001, 14C. Weisman, Larry, Cheryl Philips, and Scott Boeck, 2001 NFL salaries, USA Today.com, July 12, 2002, 13C. Whited, Toni, 1999, Is it inefficient investment that causes the diversification discount? New evidence from BITS establishment-level data, Journal of Finance, Vol. 56, 1667-1691. Zuber, Richard A., John M. Gandar, and Benny D. Bowers, 1985, Beating the spread: Testing the efficiency of the gambling market for National Football League games, Journal of Political Economy 93, 800-806.

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BIOGRAPHICAL SKETCH Rick Borghesi has a BS in civil engineering from the University of Hartford and an MBA from Loyola University Chicago. Before beginning Florida's finance program in 1999, he worked as a product manager for a broadband telecommunications firm. His research interests include organizational structure, behavioral finance, and betting markets. 135