An empirical investigation into the behavior of options around merger and acquisition announcements

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An empirical investigation into the behavior of options around merger and acquisition announcements
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Yoder, James A., 1953-
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Consolidation and merger of corporations   ( lcsh )
Options (Finance)   ( lcsh )
Finance, Insurance, and Real Estate thesis Ph.D
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Thesis (Ph. D.)--University of Florida, 1988.
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Includes bibliographical references.
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Also available online.
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Typescript.
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Vita.
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by James A. Yoder.

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Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
    Abstract
        Page v
    Chapter 1. Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
    Chapter 2. Review of the literature
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
    Chapter 3. The behavior of options and option markets around merger and acquisition announcements
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
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    Chapter 4. Variance bias and non-synchronous prices in the Black-Scholes model
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
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    Chapter 5. Summary and conclusions
        Page 79
        Page 80
        Page 81
        Page 82
    References
        Page 83
        Page 84
        Page 85
        Page 86
    Biographical sketch
        Page 87
        Page 88
        Page 89
Full Text












AN EMPIRICAL INVESTIGATION INTO THE BEHAVIOR OF OPTIONS
AROUND MERGER AND ACQUISITION ANNOUNCEMENTS















By

JAMES A. YODER




















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA 1988





W F LIBRARIES

















ACKNOWLEDGEMENTS


I would like to express my special thanks to the chairman of my committee, Haim Levy, and to Drs. Roger Huang, Roy Crum and Sandy Berg. T would also like to express my appreciation to Drs. Andy McCollough, Craig Tapely, Robert Radcliffe, Dave Brown and Joel Houston for their encouragement and support.

I would also like to express my gratitude to my fellow students Young Hoon Byun, Lesa Nix, Bruce Kuhlman and Neil Sicherman for their suggestions and technical assistance. I would also like to acknowledge the computer programming assistance of Eric Olson.


































ii
















TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS . . . . . . . . . . . . ii

ABSTRACT . . . . . . . . . . . . . . v

CHAPTERS

I INTRODUCTION . . . . . . . . . . . I
The Behavior of Option Prices Around Merger Announcements 2
The Behavior of implied Standard Deviations Around Merger
Announcements . . . . . . . . . . 4
Does the Option Market React to Merger/Acquisition
Activity Differently than the Equity Market? . . . 5
How Does an Event Study in the Option Market Differ From
One in the Equity Market? . . . . . . . 8

2 REVIEW OF THE LITERATURE . . . . . . . . 12
Mergers . . . . . . . . . . . . 12
Options . . . . . . . . . . . . 16
Pricing . . . . . . . . . . . 16
Option Market Efficiency . . . . . . . 18
Variance Bias in the Black-Scholes Model . . . 19

3 THE BEHAVIOR OF OPTIONS AND OPTION MARKETS AROUND MERGER
AND ACQUISITION ANNOUNCEMENTS . . . . . . . 20
Data . . . . . . . . . . . . . 20
The Behavior of Options Around Merger and Acquisition
Announcements . . . . . . . . . . 22
The Behavior of ISDs Around Merger and Acquisition
Announcements . . . . . . . . . . . 24
Methodology . . . . . . . . . . 26
Interpretation Results . . . . . . . . 29
The Behavior of Call Option Prices Around Merger and
and Acquisition Announcements . . . . . . 34
Methodology and Results . . . . . . . 36
Interpretation Results . . . . . . . . 40
The Behavior of Options Around Merger and Acquisition
Announcements . . . . . . . . . . 43
Methods and Results . . . . . . . . . 47
Methods and Results . . . . . . . . . 50









4 VARIANCE BIAS AND NON-SYNCHRONOUS PRICES IN THE BLACKSCHOLES MODEL ........ ...................... 60
Variance Bias in the Black-Scholes Model .. ......... 61
Methodology and Results ..... ............... .. 64
Non-synchronous Prices and the Black-Scholes Model .... 71
Methodology and Results .... ............... .. 72
Conclusion ......... ........................ 77

5 SUMMARY AND CONCLUSIONS ..... ................. 79

REFERENCES ........... ........................... 83

BIOGRAPHICAL SKETCH ........ ....................... 87














































iv
















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


AN EMPIRICAL INVESTIGATION INTO THE BEHAVIOR OF OPTIONS
AROUND MERGER AND ACQUISITION ANNOUNCEMENTS By

James A. Yoder

December 1988


Chairman: Haim Levy
Major Department: Finance, Insurance, and Real Estate

This dissertation examines the behavior of options around merger and acquisition announcements. A variation of the traditional event study methodology was applied to the option market in order to measure the abnormal returns accruing to the bidding firm and target firm optionholders. The event study was extended to the equity market for comparison purposes. The behavior of ISDs was also examined in order to determine whether the option or equity market first reacted to the merger/acquisition announcement and to decompose the abnormal returns in the option market into a component due to changing stock prices and a component due to changing stock volatilities. Some methodological issues involving event studies were also examined.












v















CHAPTER 1
INTRODUCTION


Two of the most important developments in finance in recent years have been the growth of option markets and the high level of merger and acquisition activity. Not surprisingly, both of these areas have been subject to intense academic scrutiny. Literally hundreds of articles have been published on the theory and applications of options. There are also numerous papers concerned with the rationale for mergers and their impact on stockholders' wealth. This dissertation attempts to

relate these two subjects through an examination of op-- -ion and option market behavior around merger and acquisition announcements.

In order to accomplish this, four major issues will be addressed:

1. How do option prices react around merger/acquisition

announcements?

2. How do the Implied Standard Deviations (ISDs) of options

react around merger and acquisition announcements?

3. Does the option market react to merger and acquisition

activity differently than the equity market?

4. How does an event study in the option market differ from one

in the equity market?

Each of these issues will be discussed in turn.









I





2


The Behavior of Option Prices
Around Merger Announcements

Researchers in the equity market have sought to determine whether mergers and acquisitions produce economic gains and, if so, who reaps the benefits. Their findings have been relatively consistent. Dodd (1980), Asquith (1983) and Eckbo (1983), for example, have all presented evidence on the effects of mergers on shareholders' wealth. They conclude that most of the gains are captured by the stockholders of the target firm. Gains to the bidding firm shareholders are small and possibly non-existent. Their estimates of the abnormal returns accruing to -he bidding firm shareholders for the two days prior to the announcement range from a -1.09 percent loss to a paltry 0.20 percent gain. For the target firm shareholders, however, statistically significant gains ranging from 6.20 percent to 13.41 percent were obtained. The merger literature is discussed more thoroughly in Chapter 2.

These results in the equity market lead to empirically testable hypotheses for the expected behavior of options around merger and acquisition announcements. Under the assumption that the option market is efficient, option prices (and ISDs) can be expected to react prior to the formal merger announcement and stabilize immediately afterward. Merger negotiations involve many people such as investment bankers, lawyers, administrative personnel, etc. Word of impending mergers

-eaking to the financial market place has been amply demonstrated in the equity market. There is no reason why the same phenomenon should not occur in the option market.

A second hypothesis is that abnormal returns to the target firm optionholders should exceed those of the bidding firm optionholders. Theoretically, a call option can be duplicated by an appropriately





3



selected stock-bond portfolio. Because of this, the wealth effects of merger and acquisition announcements on optionholders can be expected to mirror that of the equityholders.

The wealth effects of merger and acquisition activity on optionholders is of interest for a number of reasons. In a recent survey article of the market for corporate control literature, Jensen and Ruback (1983) identified six key questions that have been addressed. At the top of the list is the following: "How large are the gains to ,.hareholders of bidding and target firms?" Options by their very nature afford superior leverage to the underlying equity. Consequently, optionholders, per dollar invested, have more reason to be concerned with potential merger and acquisition activity than the equityholders. An analysis of option prices around merger and acquisition announcements may also shed light on a puzzling question.

Merger activity is widespread but the rationale for it is not clear. As noted earlier, gains to the bidding firm shareholders are small and possibly negative. Why then do managers undertake merger and acquisition programs if they do not benefit the shareholders? An examination of bidding firm option prices may help to resolve this issue.

An option can be interpreted as a leveraged position in the equity. This leverage aspect of options may make them more sensitive to events than the underlying equity. Small abnormal returns in the equity market might result in much larger abnormal returns in the option market. Thus, it may be easier from a statistical standpoint to determine if bidding firm stockholders benefit from merger/acquisition activity by looking at the behavior of associated option prices.





4


Ihe Behavior of Implied Standard
Deviations Around Merger Ann uncements


The behavior of ISDs around merger announcements is important for two reasons. First, it is inseparable from the price behavior of

options. Stock volatility is one of the input variables for the BlackScholes model. By examining the ISD, it is possible to decompose

changes in option prices into a component due to price changes in the underlying stock and a component due to changes in the underlying volatility. Second, it provides an alternative measure of the information content associated with merger and acquisition announcements. Numerous studies have attempted to measure the information content of accounting announcements by showing that the expected return of the stock is affected. Patell and Wolfson (1979, i981) have pointed out that other moments of stock price distribution may also be affected by the announcement and thus serve as a measure of its significance. They proceeded to use ISDs as an ex-ante measure of the information content associated with earnings announcements whose disclosure date is known. This dissertation attempts to use ISDs to measure the expected impact of merger and acquisition announcements which are totally or at best partially anticipated events.

The hypotheses concerning the behavior of ISDs around merger and acquisition announcements parallels that of option prices. The first hypothesis is that ISDs should react prior to the formal announcement and stabilize immediately afterward. The second hypothesis is that the change in ISDs for the target firm should exceed that of the bidding 'irm options. Merger and acquisition activity has very little impact on the bidding firm shareholders. Thus, the distribution of stock





5


returns should not significantly change as a result of the announcement. The target firm shareholders, however, are greatly affected by the merger and acquisition activity. Increased volatility of the underlying stock returns can be generated by a multitude of factors. Uncertainty, for example, can arise over the anticipated terms of the agreement, whether a competing offer will be made or even whether the deal will be consummated.


Does the Option Market React to Merger and Acquisition
Activity Differently than the Equity Market?

The third major area of inquiry in this dissertation is the relationship between the option and equity markets around merger announcements. There are two independent arguments for hypothesizing that the merger activity will be more strongly manifested in the option rather than the equity market prior to the announcement.

Options represent leveraged positions in the underlying equity. The beta of an option in the Black-Scholes framework is always greater than that of the stock. Because of this, the option market may be more

sensitive to events than the equity market. Even though the two markets may be reacting to the same information, the signal may first be more apparent and stronger in the option market.

It is also possible that the option market contains information that is not incorporated in the equity market prior to mergers. As mentioned previously, a call or put option can be duplicated by an appropriate stock-bond portfolio. Because of this, options have been viewed as "derivative" assets whose prices are completely determined by the underlying equity. The possibility that the option market may influence the equity market has received little attention. It is





6


conceivable that information is first processed in the option market and then filters to the equity market. A similar issue has been studied by Manaster and Rendleman (1982). They have advanced the intriguing hypothesis that the option market may play a key role in determining equilibrium stock prices. They argue that some investors may prefer to invest in the option rather than the equity market because of reduced transaction costs, fewer short selling restrictions, and most importantly, superior leverage. These traders could push option prices out of equilibrium relative to the underlying stocks. Arbitrageurs would then intervene to restore equilibrium between the two markets.

Manaster and Rendleman attempted to test their theory. They

"inverted" the Black-Scholes model to solve for the implied stock price. The implied stock price was then used to predict future stock prices. They found some evidence that the option market contains information that is not incorporated in the equity market. Unfortunately, their results are very weak and fatally flawed by their reliance on non-synchronous data. The data used in this dissertation will avoid this problem.

In retrospect, Manaster and Rendlemans' lack of results is not surprising. Both the option and equity markets react to public information. Generally, one would expect both markets to adjust simultaneously to new public information. On any given day for any particular corporation there may not be and probably is not information that is not fully reflected in both markets.

However, this may not be true prior to major announcements by corporations such as mergers. In the case of mergers, the option





7



market could be expected to be particularly influential in determining stock prices around merger announcements. Keown and Pinkerton (1981) have argued that information concerning impending mergers is susceptible to insider exploitation due to the large number of people typically involved in the negotiating process. They have attributed increased trading volume before the merger announcement to insider activity. An insider attempting to profit from knowledge of an impending merger would have an incentive to use options because of their leverage aspects. To quote Fischer Black (197"', p. 61), "Since an

investor can usually get more action from a given investment in options than he can by investing in the common stock, he may choose to deal with options when he feels he has an especially important piece of information." Option prices can be expected to contain more information than the equity market if nonpublic information is being exploited. If information regarding future mergers first reaches the financial markets through insider trading in options, merger activity may very well be reflected in the option market before the stock

market .

A separate issue raised by the above argument is that the option market may make the equity market more efficient If the option market serves to bring nonpublic information into the financial markets and options influence the prices of the underlying stock, then stocks with listed options should respond sooner to impending mergers than similar stocks without options.





8


How Does an Event Study in the Option Market
Differ From One in the Equity Market?


An event study attempts to measure the impact of some event on securityholders by comparing actual returns around the announcement to those predicted by some model. These predicted returns should be the returns that would have occurred if the event (merger and acquisitions in this case) had not taken place. The difference between the actual and predicted returns is the basic measure of the impact of the event. These residuals are then aggregated to measure the total impact of the event and provide statistics for tests of significance.

In the equity market, predicted returns are usually generated by one of two models:

a. Market model b. Mean returns

The market model assumes there is a linear relationship between individual security returns and market returns:


Rit ai iRmt


Where Rit return on company i for day t

Rmt = return on the market for day t


The coefficients a and 5 are obtained by regressing the company returns against the market returns over some base period prior to the merger activity. The base period should be selected so that the company returns are not affected by the event activity.

Another approach to generating predicted returns is to simply use the mean returns on the individual security computed over some base period





9



n
Ri 11N E Rit
t=1


where mean return on company i

Rit = return of company i for day t

N = number of observations in the base period


Again the base period should be selected so that the event activity has no effect.

Two implicit assumptions underlie the traditional event study methodology in the equity market. The first is that the return

generating process is linear. As long as predicted returns equal actual returns on average, the residuals should average out to zero over a large enough cross-sectional sample in the absence of some common disturbing event. The same reasoning justifies parameter estimation for the two models. The true beta is unknown and must be estimated. The estimated beta may lie above or below the true value. As long as an unbiased of beta is used, however, deviations from the true beta return will average out to zero. Since these models are linear, deviations from the true expected return will also offset and residuals should average out to zero in the absence of a common disturbance. The second assumption is that the return generating process is stationary. Specifically, beta is assumed to remain constant over time.

Call prices in a Black-Scholes framework are a function of five input variables. Two of these, the stock price and its volatility, are company specific and would be affected by an event such as a merger acquisition announcement. One implication of this is that there may be





10



a subtle but important difference between the interpretation of the results of an event study in the option and equity markets.

Xetger activity may not benefit t a stockholder even if abnormal returns are observed. These abnormal returns may be accompanied by increased risk. This increased risk may not be desired by an investor with a small portfolio even if it is compensated for by larger expected (not realized) returns.

If an investor holds a call option, the situation may be entirely different. An increase in the volatility of the underlying stock would definitely be preferred by all investors. Increased volatility would result in an actual (not expected) increase in the call price. The reason for this is that the return generating process underlying call prices is based on the formation of risk-less hedged portfolios.

The Black-Scholes formula is by far the most widely used option pricing model. Using it to generate predicted returns for an event study, however, presents some technical problems. The Black-Scholes model is highly non-linear. Consequently, using sample estimates for the input variables may result in a systematic bias. Errors in estimating the variables may offset in a large sample. Equal deviations from the true parameter estimate, however, will not result in equal deviations from the true call price. The most crucial variable is the stock volatility since the Black-Scholes model is most sensitive to it.

Because of this problem, the results of an event study utilizing the Black-Scholes model must be interpreted with care. A simulation analysis, however, provides some measure of the magnitude of this effect. The Black-Scholes formula was used to generate a theoretical option price assuming true values for the input parameters. Sample





11


estimates of the volatility were generated for input into the BlackScholes model. These sample call prices based on sample estimates for the volatility were compared to the theoretical call value. In

general, the difference was small (see chapter 4).
















CHAPTER 2
REVIEW OF THE LITERATURE


The literature on option theory and mergers, as mentioned previously, is immense. It is impossible to discuss in detail all the relevant studies in either of these fields. At best, the most important results can only be highlighted. This section will give a brief review of the work that directly affects this dissertation. The literature dealing with the impact of mergers on shareholders wealth, option pricing, option market efficiency, and variance bias in the Black-Scholes model will be addressed in turn.


Mergers

Two fundamental questions have been raised regarding merger activity. The first is why do mergers occur? In 1985 alone, merger activity involved over $120 billion in assets. Yet the economic justification for all this activity is not obvious. Levy and Sarnat (1970) have shown that given perfect capital markets, pure conglomerate mergers should not create value.

Agency theory provides one rationale for the continuous merger activity that has been observed over the past -few decades. Levy and Sarnat (1970), Lewellen (1971) and Gali and Masulis (1976) have argued that combining firms with less than perfectly correlated cash flows lowers the chances for bankruptcy. Thus, managers have an incentive to engage in merger activity so as to reduce their employment risk. Reid (1968) has argued that managers strive to maximize the size of the firm


12





13


rather than shareholder wealth. Jensen and Meckling (1976) have pointed that since managers are agents for the stockholders' their interests are not necessarily the same.

Others have sought to justify merger activity on the grounds that it produces real economic gains. Mergers may result in more efficient economic units. Weston and Chung (1983) have summarized possible sources of these efficiencies.

1. Differential Efficiency

2. Inefficient Management (target firm)

3. Operating Synergy 4. Financial Synergy

5. Strategic Realignment

b. Undervaluation (target firm)

of now, however, the exact rationale for mergers is still an

unresolved issue.

The second major issue that the merger literature has addressed is what are the effects of mergers on shareholders' wealth? Numerous studies concerned with this issue have appeared since Mandleker's (1974) seminal paper. Most of these have used the well known event study methodology.

Event studies in the equity market involving mergers have become relatively standardized. A base period prior to the event is selected, and data from this period are used to estimate predicted returns. The impact of the event is measured by calculating the difference between the actual and predicted returns during some period surrounding the event. The residuals are then aggregated and statistically analyzed,





14


usually using some form of a t-test, to determine if the excess returns are significantly different from zero.

Predicted returns in the equity market have usually been generated by one of two models. The first method is to use the market model.


Rjt = aj + Sj*Rmt


The estimates of aj and Bi are obtained by regressing the company returns against the market returns during some base period prior to and presumably untainted by the merger activity. The second method is to simply use the mean return computed over some base period.

Brown and Warner 0985) have shown that the event study methodoiogy is very robust to the method used to calculate excess returns. Using simulation analysis, thev showed that there is very little difference in the returns (or residuals) generated by the two methods. Because of this, mean adjusted returns will be used in this study.

Jensen and Ruback (1983) have summarized the results of the more important merger studies concentrating on announcement effects. These results are shown in the table below. The rop panel shows the results for the two days prior to the announcement. The bottom panel shows the results for the one month prior to the announcement. In each case, the total return during the event period, the number of observations and the t-statistic is given for both the bidding and target firms.

The results are very consistent. The gains to the acquiring firms are positive but small. The target firm stockholders reap much larger returns. This is true for both the short-term (2 day) and longterm (one month) event period. in addition, these results hold for

both successful (consummated) and ultimately unsuccessful mergers.





15



Table 2.1

Abnormal Returns Associated with Mergers; Sample Size and t-statistic


Study Sample Bidding firm Target firm
period


A. Two-day announcement effects

Dodd 70-77 -1.09" +13.41
(1980) (60 ,-2.98"*) (71,23.80)

Asquith 62-76 +0.20 +6.20
(1983) (196,0.78) (211,23.07)

Eckbo 63-78 +0.07 +6.24
(1983) (102,-0.12) (57,9.97)
...................------------------------------------------Weighted excess return -0.05 +7.72


B. One-month announcement effects

Dodd 70-77 +0.80 +21.78
(60,0.67) (71,11.93)

Asquith 62-76 +0.20 +13.30
(1983) (196,0.25) (211,15.65)

Eckbo 63-78 +1.58 +14.08
(1983) (102,1.48) (57,6.97)

Asquith et. 63-79 +3.48 +20.5
al. (1983) (170,5.30) (35,9.54)

Malatesta 69-74 +0.90 +16.8
(1983) (256,1.53) (83,17.57)
.............------------------------------------------------Weighted excess return +1.37 +15.90


*excess return
*number of observations
***t-statistic





16



The paper by Asquith, Bruner and Mullins deserves additional comment. Schipper and Thompson (1983) have shown that acquisition programs generate excess returns. If this is true, one might expect the impact of successive mergers to diminish. Asquith et. al. compare the abnormal returns associated with the first, second.. third, and fourth mergers. They find no evidence that abnormal returns are capitalized in the earlier mergers. They also found that the abnormal returns to the acqui ring firm is dependent on the size of the acquired

firm.


Options

Pri cing

The seminal work on option pricing is, of course, the BlackScholes option pricing model. Black and Scholes (1973) noted that a call and the underlying stock could be combined to form a risk-free hedged portfolio if continuous rebalancing was possible. This fact, combined with some appropriate assumptions

1. frictionless capital markets

2. risk-free interest rate is constant

3. stock pays no dividends

4. stock prices follow an Ito process with constant drift

5. no restrictions on short sales

allowed them to derive a differential equation relating call and stock prices. -Using stochastic calculus, they solved for the call price yielding the familiar Black-Scholes formula as a result


C = SN(dl) Xe-rTN(d?)


where





17



di= [ln(S X) + (r + O.5G2)T1/a7/T

d2= di T


The most limiting of the Black-Scholes restrictions is that the underlying stock pays no dividends. Modifying the model for dividends has two components. First, the stock price must be adjusted for the expected drop on the ex-dividend date. Second, the model must reflect that an American call has value due to its early exercise right. If a dividend is large enough, it may pay to exercise the option immediately before the stock goes ex-dividend. These problems can be dealt with simply by subtracting the present value of future dividends from the stock price as Black (1975) has suggested or assuming that dividends are paid continuously as Merton (1973) has done. Roll (1977), Geske (1979b), and Whaley (1981) have advanced more complex formulation that take both considerations into account. Whaley (1979) has empirically tested the different approaches to dividend adjustment and found the differences were slight.

A number of variants and extensions of the Black-Scholes model have appeared. Merton (1973) has relaxed the assumption of stationary interest rates. Thorpe (1973) has examined the effect of short sales restrictions. Geske (1979a) has developed a compound option formula.

The effects of different distributional assumptions regarding stock prices have also been investigated. Cox and Ross (1976) have developed a pure jump model that allows for discrete stock price movements. They have also developed a constant elasticity of variance model that allows for the variance to change with the stock price. Merton (1976) has developed a mixed diffusion-jump model that superimposes a jump process on a continuous return generating process.





18


Despite these advances, the Black-Scholes model with the stock prices adjusted for dividends is still the most widely used by far. Many of the models discussed above are difficult if not impossible to apply. Even if they can be applied, no model has yielded consistent, significantly better results for options near the money. While there are limitations to the Black-Scholes model, there is no strong reason to use any of the more esoteric alternatives in this study.


Motion Market Efficiency

A number of studies have been made of the efficiency of the Chicago Board of Options exchange. These studies are Joint tests of market efficiency and the Black-Scholes model. Galai (1977) conducted one of the earliest and most comprehensive studies using the BlackScholes model to identify mispriced options. He found that statistically (but not economic) significant excess returns could be earned.

Chiras and Manaster (1978) adopted a different approach in analyzing option market efficiency. They weighted the ISD of each option on the stock by the option price elasticity to arrive at an overall measure of the stock's future volatility (WTSD). They then compared the WISD as an estimate of future stock volatility to estimates based on past stock returns. Having demonstrated the superiority of WISDs, they then proceed to compute implied option prices. Underpriced and overpriced options were then identified by comparing implied and actual prices. Risk-free hedges were then formed which earned substantial abnormal returns. These results are in agreement with a similar study by Trippi (1977) which used a simpler weighting scheme to arrive at WISDs. Kalay and Subrahmanyam (1984) have also provided some





19



evidence of option market inefficiency on the ex-dividend day of the equity.

Phillips and Smith (1980) have found fault with studies reporting inefficiencies in the option market. They argued that a close examination of trading costs (most notably the bid-ask spread) would account for the abnormal returns reported in earlier studies. Bhattacharya's (1980) study of CBOE (Chicago Board of Options Exchange) took these costs into consideration. In general, his results were consistent with market efficiency.


Variance Bias in the Black-Scholes Model

In order to apply the Black-Scholes model, five input variables must be obtained: the stock price, exercise price, time to maturity, risk-free rate of interest and the volatility of the underlying stock. Of these, four are directly observable. Only the variance of the underlying stock returns needs to be estimated.

Classical methods of estimating the variance will bias the model. Although unbiased estimators of the variance exist, the Black-Scholes model is highly non-linear. Equal deviations from the true variance will not result in equal deviations from the true call price as Ingersoll (1977) and Merton (1976) have observed. Boyle and Ananthanrayanan (1977) have used numerical integration to examine the magnitude of the expected error in a single case. Butler and Schachter (1986) trace the behavior of this bias to the second derivative of the cumulative normal density function.















CHAPTER 3
THE BEHAVIOR OF OPTIONS AND OPTION MARKETS
AROUND MERGER AND ACQUISITION ANNOUNCEMENTS


This chapter discusses the behavior of options and option markets around merger and acquisition announcements. The impact of merger and acquisition announcements will be studied by examining the behavior of option prices and ISDs around the announcement date. These results will be compared to those obtained from the underlying equity using the traditional event study methodology.

The organization of this chapter is as follows. First, the data is described and a po-Lential problem discussed. Next, the behavior of options around merger and acquisition announcements is analyzed. The return of an option is affected by two company specific variables: the stock price and stock volatility. Both of these variables are likely to be affected by merger and acquisition activity and thus influence call returns. An attempt is made to decompose the total impact of merger and acquisition activity into two components. First, the effect of changing !SDs is investigated and then the total impact due to both changing stock prices and stock volatility is analyzed. Finally, the traditional event study methodology is applied to the underlying stock in order to compare the behavior of the two markets.


Data

The merger and acquisitions selected for this study will be obtained from Mergers and Acquisitions. The mergers and acquisitions



20





21



selected will be confined to those involving at least $100 million in assets with either the acquiring or acquired firm having options listed on the CBOE between 1982 and 1985. The reason for this is to ensure the merger and acquisition is an event. Corporations listed on the CBE tend to be well established firms with large equity bases. The value of all the outstanding stock in firms such as General Motors, General Electric and International Business Machines, for example, is measured in the billions of dollars. The announcement date will come from the Wall Street Journal Index.

The Wall Street Journal will also be used to get the bid-asked spread on U.S. Treasury bills in order to calculate the risk-free rate. The risk-free rate for input into Black-Scholes formula will be the yield on the T-bill maturing closest to th~e expiration date of the option. The yield will be calculated according to the formula below from Cox and Rubinstein (1985, p. 255)


r =(P/10O )-/


where r =one plus the risk-free rate

P = price of a $10,000 T-bill
= 10,000 [1-0.0l(bid + asked)/2 (n/360)]

n = number of days to maturity

t = time to maturity expressed in years


The critical data for this thesis is the stock and option prices. Closing prices from the Wall Street Journal or similar sources can not be used because of the possibility of nonsynchronous trading between the two markets. Trading in the option market is significantly less active than in the equity market. It is quite likely that the last





22


option trade occurred prior to the last stock trade on any given day. The current stcck price for use in the Black-Scholes formula is the price existing at the time the option is being valued. Using the Black-Scholes model to generate predicted returns as in this study requires the stock price at the time of the last option trade. This problem, as Bookstaber (1981) has pointed out, casts doubt on much of the empirical work on options that has been done to date.

In order to avoid any problems with nonsynchronous trading, time-stamped data will be used. The Berkeley Options Tape will be the primary source of stock and option price information. Data from Francis Emory Fitch, Inc., although not machine readable, is also suitable.


The Behavior of Options Around Merger and Acquisition Announcements

The behavior of stocks around merger announcements has been extensively studied (see chapter 2). The results have been very consistent. Most of the gain due to merger activity is captured by the stockholders of the target firm. Gains to the bidding firm shareholders are small and possibly non-existent.

These results suggest empirically testable hypotheses for the expected behavior of options around merger and acquisition announcements. Market anticipation of formal merger announcements has been observed in the equity markets. Under the assumption that the option market is efficient, option prices and ISDs should react prior to the formal merger and acquisition announcement and stabilize immediately afterward. A second hypothesis is that the abnormal returns to the target firm optionholders should exceed those of the bidding firm





23



optionholders. Theoretically, a call option may be duplicated by an appropriately selected stock-bond portfolio. Because of this, the wealth effects of merger and acquisition announcements can be expected to mirror that of the equityholders. This assumes, however, that other factors such as the stock volatility are not affected by the merger and acquisition activity.

There are two main reasons why an analysis of the impact of merger and acquisition activity of optionholders wealth is of interest. First, the methodology used, the traditional event study, has never been applied to the option market. An event study in the option market presents new issues and sheds light, as will be discussed later, on event studies in the equity market. The second major reason why the wealth effects of merger and acquisition activity is important is that options afford superior leverage to the underlying equity by their very nature. Optionholders, per dollar invested, have more reason to be concerned with the effects of merger and acquisition activity than the equityholders.

These ideas will be more fully developed later on. At this point, the effect of merger and acquisition on option ISDs will be discussed. The behavior of ISDs around merger and acquisition announcements is not only a major determinant of call option returns and thus optionholders wealth but also has important implications for event studies in the equity market.

Event studies in the equity market implicitly assume that risk remains constant. Predicted returns are based on historical data from some base period. Increasing ISDs (i.e., stock volatility) would suggest that risk is increasing. More importantly, since ISDs can be





24


computed at a point in time and are correlated with stock betas, they can be used to adjust for increasing risk in the event period. This is discussed later on in this chapter.


The Behavior of ISDs Around Merger
andAcquisition Announcements

The behavior of option ISDs around merger and acquisition announcements is important for a variety of reasons. First, it is inseparable from the price behavior of options. Stock volatility is one of the input variables for the Black-Scholes model. By examining the behavior of the ISDs it is possible to decompose changes in option prices into a component due to price changes in the underlying stock and a component due to changes in the underlying volatility.

A second reason for examining the behavior of ISDs is that it provides an alternative measure of the information content associated with merger and acquisition announcements. The vast majority of event studies have attempted to measure the information content of some event by showing the expected return of the stock is affected. Patell and Wolfson (1979,1981) have pointed out that other moments of the stock price distribution may also be affected and thus serve as a measure of its significance. They used ISDs as an ex-ante measure of the information content associated with earnings announcements whose date is known.

This study will determine if the second moment (stock volatility) of the stock return distribution is affected by merger and acquisition activity. The behavior of ISDs will be tracked around the announcement date for both the bidding and target firms in order to determine if there is a difference in the impact of the activity between the two





25


categories. it should be noted that merger and acquisition announcements are unexpected or at best partially anticipated. This fact distinguishes this study from the ones by Patell an Wolfson which dealt with earnings announcements on known dates.

Another reason for examining the behavior of ISDs is that it may shed light on potential wealth shifts engendered by merger and acquisition activity. Option theory suggests that common stock can be interpreted as an option. Agency theory suggests that there is an incentive for stockholders (see Jensen and Meckling 1976) to shift wealth from the bondholders by undertaking risky investment projects. By undertaking investment projects which increase the variability of the firm's cash flows, the stockholders' can, in effect, gamble with the bondholder's money. This enriches the stockholders at the direct expense of the bondholders. Merger and acquisition activity can be regarded just like any other investment activity. Consequently, one might expect bidding firms to make acquisitions which tend to increase the variability of the firm's cash flows.

Others, however, have argued that the opposite occurs. Levy and Sarnat (1970), Lewellen (1971) and Galai and Masulis (1976) have argued that combining the cash flows of two independent companies may reduce the probability of default and increase the market value of debt at the stockholders' expense. Even if this occurs, it is possible that managers act to neutralize (issue more debt) any such wealth shift.

In any case, it is the variability of the firm's cash flow that is in question. A direct relationship, however, has been hypothesized in previous work (see Eger 1983). Consequently, the behavior of ISDs





26



around merger/acquisition announcements may be of value in analyzing whether these wealth shifts do, in fact, take place. Methodology

The methodology used for analyzing ISD behavior is as follows. First the sample was stratified into two groups. The first group was composed of 52 bidding firms involved in a merger or acquisition. The second group was composed of 21 target firms involved in a merger or divestment.

Base ISDs were obtained by "inverting" the Black-Scholes model using data forty days prior to the announcement date. it is assumed that the markets have not yet begun to reflect the merger and acquisition activity at this point. If the 40th day prior to the announcement is a holiday or weekend, the first trading day afterwards is used. Dividends are assumed to be paid continuously and are adjusted for as suggested by Merton'- (1973). The stock and option prices are the first prices from the Berkeley option tapes after the stock price has changed once. The opening trade is eliminated in order to ensure the market has stabilized. ISDs are calculated in a similar manner for each

company for each day in the event period. The event period ranges from five days prior to the announcement date to two days afterward. It should be noted that the announcement day is taken to be the date it first appeared in the Wall Street Journal. In many instances, the news was released during trading hours of the previous day.





'Dividends are adjusted for by using Merton's (1973) formula
C = Se2JtN(dl) Xe-rtN(d2)
where dl = [ln(S/X) + (r y 0.5G2)t]/GVt
d= dl avt
y = continuous dividend yield.





27


The impact of the merger and acquisition activity on option ISDs was measured by taking the difference between the ISD for each company for each day during the event period and the base ISD for each company


6ISDjt = ISDjt -ISDBj


where 6ISDjt Change in ISD for company j on day t.
(t = -5 to +2)

ISDt = ISD for company j on say t

ISDbj = Base ISD for company j


A t-test was run on the change in ISDs for each day in order to determine statistical significance:


t = 6ISDj/(S2/N)-1/2


The results are given in Table 3.1. For each day in the event period the mean change in the ISD is given, the t-statistic and the probability (if significant at the 10% level) of exceeding the absolute value of the t-statistic given there was no change in the distribution of ISDs between the base and event periods.

The effect of changing ISDs on call prices was also investigated. For each company, for each day during the event period, the closing price of the option closest to the money with at least 30 days to maturity was obtained. The Black-Scholes Model was used to compute a call price on the same option using the base ISD but actual (market) stock prices. The percentage difference between the actual (market) call price and the theoretical base price obtained using base period ISDs in the Black-Scholes model was calculated for each company for each day in the event period





28



Table 3. 1

Average Change in ISDs Between the Base and Event Period



Bidding Firms

Day Average t-Prob >
1513 Change Statistic /t/

-5 -0.010678 -1.41
-4 -0.009359 -1.46
-3 -0.002800 -0.39
-2 0.000765 0.12
-1 -0.001085 -0.17
0 -0.005835 -0.73
+1 -0.005354 -0.58
+2 0.000932 0.10



Target Firms

Day Average t- Prob >
ISD Change Statistic /t!

-5 0.025402 1.35
-4 0.021308 1.34
-3 0.033090 1.92 .0690
-2 0.034044 2.01 .0580
-1 0.048052 3.03 .0071
0 0.056132 2.39 .0266
+i 0.024384 1.53
+2 0.004447 0.24





29



Wit =(Cjt (Cbjt) / j

where WiCt = % Difference between the actual and the base call price for company j on day t

Cj Actual market call price for company j on day t

Cbjt =Base price obtained from using base ISD in the
Black-Scholes Model for company j on day t.


Since the observed (market) stock price is used to obtain the base call price (Cbjt), the difference between the actual and base call prices must be entirely due to the changing stock volatility.

A t-test was run on the percentage deviation from the actual call prices in order to determine statistical significance


t = %5C i / (S2 / N)-1/2


The results are given in Table 3. For each day in the event period, the mean percentage deviation is given, the t-statistic and the probability (if significant at the 10% level) of exceeding the absolute value of the t-statistic assuming there was no change between the base and actual market call prices.

T,. -ernretation of Results

As one might expect, the above two tables are very consistent. They may be regarded as opposite sides of the same coin. The change in ISDs for the bidding firm is small and statistically insignificant (at the 10% level) in all instances. Similarly, the percentage deviation of market prices from base prices is also small and statistically insignificant. The change in ISDs for the target firm are much larger than those of the bidding firm for corresponding days in the event period. Furthermore, the change is always positive and statistically





30


significant for days -3 through the announcement date (Day 0). The same observations hold for the percentage deviation in prices.

These results are consistent with the hypotheses of option market efficiency. For the bidding firm there is no evidence that the merger and acquisition activity has any effect on the volatility of the underlying stock. The change in ISDs are very small and do not result in large, statistically significant changes in the call prices. There does not appear to be any changes in the ISI)s or call prices before and after the merger and acquisition announcement. The target firms are definitely affected by the merger and acquisition activity. The average change in ISDs is over 5 percentage points in absolute terms on Day 0 and is responsible for call price increases of over 12%. The market, however, starts to anticipate the merger and acquisition announcement as early as three days ahead of time. The change in ISD from the base level jumps from roughly 0.021 on day -4 to 0.033 on day

-3.0 to -0.048 on day -1 to 0.056 on day 0. The percentage change in call prices follow a similar pattern. Immediately after the announcement is made public, however, ISDs and call prices quickly stabilize at close to their base levels. The deviation of the market from the base call price is only 0.009 for the target firms the day after the announcement.

The results in Tables 3.1 and 3.2 also support the hypothesis that TSI)s can be used to measure the information content of merger and acquisitions announcements. Studies in the equity market have shown that mergers do not greatly affect the expected return of the bidding firm stockholders. It would appear that the volatility of returns is





31



Table 3.2

Percentage Deviation Between Market and Base Call Prices



Bidding Firms

Day % Deviation t-Statistic Prob > /t/


-5 -0.009791 0.48
-4 -0.016577 -0.78
-3 -0.058152 -1.11
-2 0.002362 0.12
-1 -0.030124 -1.49
0 -0.021935 -1.05
1 -0.021193 -0.89
+2 -0.013851 -0.55


Target Firms

Day % Deviation t- Statistic Prob > /t/

-5 0.035339 0.76
-4 0.037151 0.85
-3 0.067024 1.66 0.1133
-2 0.085629 1.74 0.0966
-1 0.126755 3.14 0.0056
0 0.058533 1.65 0.1146
+1 0.008906 0.10
+2 -0.047437 -0.83





32


also unaffected. Changes in the bidding firm ISDs are very small and statistically insignificant.

Studies in the equity market have also shown that significant abnormal returns accrue to the target firm shareholders. The results here indicate these abnormal returns are accompanied by increased return volatility. it should be noted that the numbers in Table 3.1 are absolute changes from the base ISD. The percentage deviations from the base ISD would be much larger.

Why does merger and acquisition activity have such a major impact of the second moment (variance) of the return distribution of the target firms? As mentioned earlier, results in the equity market have shown that most of the gain from merger activity is captured by the target firm shareholders. The rationale for this is that the takeover market is competitive. If a company has some unique aspect that other companies can exploit, it will find or have the potential to find a number of bidders. Competition among the bidding firms will drive the net present value of the investment to zero (see Mandelker (1974) and Jensen and Ruback (1983)). Consequently, the gains from merger and acquisition activity will be reaped by the target firm shareholders.

Because of this, merger and acquisition activity could be expected to affect the volatility of the target firm's equity much more then that of the bidding firm's. Merger and acquisition activity is a more or less neutral event for the bidding firm shareholders. Target firm shareholders, however, are likely to be greatly affected. The importance of merger and acquisition activity to the target firm shareholders combined with uncertainty over the terms of the agreement, whether alternative bidders will appear, whether the agreement will be





33


consummated, etc., should result in higher ISDs for the target firm options.

Table 3.2 confirms this hypothesis. The average change for the bidding firms is negligible. The average change in ISD for the target firms is larger than that of the bidding firms for the corresponding day in all cases. In some instances, the change in the target firms' ISI)s exceeds those of the bidding firms by more than an order of magnitude.

This result warrants further comment. Event studies in the equity market have demonstrated time and time again that target firm shareholders reap abnormal returns as a result of merger activity. These abnormal returns, however, are accompanied by increased volatility as Table 3.2 shows. Thus, these "abnormal returns" may not truly be abnormal but merely reflect the increased uncertainty and riskiness engendered by the merger and acquisition activity. Instantaneous or short-term adjustments for risk are difficult in the equity market since beta requires historical time series to estimate. The ISD of an option, however, can be determined at a point in time. Thus, an event study in the option market may afford a better measure of excess return. This point is explored more deeply in the next section.

A final comment on the behavior of ISDs. It is interesting that the ISDs for both the bidding and target firms' revert back to their base level after the merger and acquisition announcement (see Table 3.2). It would appear that merger and acquisition activity does not result in permanent changes in the volatility of the underlying equity for either bidding or target firms. The evidence here does not support the hypotheses that wealth shifts between bondholders and stockholders





34


arises from merger and acquisition activity. This is counterintuitive. One would expect the post-announcement ISD to be function of the volatility of the underlying equity of both companies and their correlation. These results may be due to the sample selection process. Companies listed on the CBOE tend to be large companies. Thus, a merger and acquisition of $100 million may still be insignificant. In addition, large mergers or acquisitions are likely to take place between solid, established companies of relatively equal size. Thus, any conclusions concerning wealth shifts and merger and acquisition activity based on the data here must be interpreted with great care. The Behavior of Call Option Prices Around Merger and Acquisition Announcements

Many of the reasons for examining the behavior of option prices around merger and acquisition announcements have already been discussed earlier. First, it provides a test of option market efficiency. Merger (and acquisition) negotiations involve many people such as investment bankers, lawyers, administrative personnel, etc. Word of

impending mergers leaking to the financial market place has been amply demonstrated in the equity market (see Keown and Pinkerton, 1981). There is no reason why the same phenomenon should not occur in the option market.

The price behavior of options around merger and acquisition announcements is important to anyone who intends to invest or speculate in options. Merger and acquisition activity is a major economic factor in our economy and is likely to remain so for some time. Anyone involved in options may be confronted with an unanticipated merger or acquisition announcement. Options by their very nature afford superior leverage to the underlying equity. Optionholders, per dollar invested,





35



are more affected by merger and acquisition activity than the equityholders. In order to invest intelligently, potential optionholders (or sellers) need to have some idea of how merger and acquisition activity could potentially affect their wealth position.

Another reason for analyzing the behavior of option prices around merger and acquisition announcements is that it may help to determine if this type of activity is an "event" from the standpoint of the bidding firm. As noted earlier, gains to the bidding share holders are small, possibly negative and statistically insignificant (see Chapter 2). It also appears that merger and acquisition activity has no effect on the volatility (second moment of the return distribution) of the bidding firm's equity. It is possible, however, that the option

prices of the bidding firms might still measurably react to the merger and acquisition activity.

An option can be interpreted as a leveraged position in the equity. The leverage aspect of options may make them more sensitive to events than the underlying equity. A shock or event that provides an insignificant abnormal return in the equity market might be magnified into an identifiable, significant abnormal return in the option market. Thus, it might be easier from a statistical standpoint to determine if merger and acquisition activity is an event to the bidding firm security holders.

A final reason for examining the price behavior of call options is that this is the first study to apply the traditional event study methodology to the option market. The event analyzed here is merger and acquisition announcements. The methodology employed, however, has





36


general applicability. It can be applied to any event such as dividend or earning announcements.

Methodology and results

An event study attempts to measure the impact of some event on securityholders by comparing the actual, observed market returns to those predicted by some model. Ideally, these predicted returns should be the returns that would have occurred if the event (merger and acquisition activity) had not taken place. This study uses the BlackScholes model to generate predicted returns.

In a Black-Scholes framework, call option prices change when there is a change in the risk-free rate, the time to expiration, the exercise price, the stock price or stock volatility. In equilibrium, the actual, observed market price equals the theoretical, Black-Scholes price. Here the announcement effect is measured by the impact of the changing stock price and volatility on the option price. The observed call option price is compared to a predicted price generated by the Black-Scholes model that keeps the stock price and volatility constant.

An event study in the option market is fundamentally different from the one in the equity market. Event studies in the equity market assume the return generating process is linear and that the true beta remains constant over time. As long as predicted returns equal actual returns on average, residuals should average out to zero over a large enough cross-sectional sample in the absence of some common disturbing event. This also justifies using an estimate of beta. The true beta is unobservable and must be estimated. If an unbiased estimate of beta is used, deviations from the true expected return will also offset and





37


residuals should average out to zero in the absence of a common disturbance.

The return generating process in the option market, however, makes an event study inherently different from one in the equity market. A cursory examination of the Black-Scholes model shows it is highly non-linear. Even if unbiased estimators are used to obtain inputs for the model, equal deviations from the true parameters will not result in equal deviations from the true call price. Thus, residuals will be biased simply due to the estimation of the input variables. This issue has important implications for users of the Black-Scholes model and is analyzed at length in Chapter 4.

Another difference between an event study in the two markets is that the uncertainty of an option is an explicit function of time. The uncertainty of an option with a short time to maturity is greater than the same option with a longer life. The Black-Scholes model incorporates this time dependency and will be used for this study.

The methodology used to examine the behavior of call prices around merger and acquisition announcements is as follows. First, as before, the sample was divided into bidding and target firms. A number of options with different exercise prices and maturities exist for a company on a listed exchange. One option was selected to avoid statistical dependence in the returns. The exercise price selected was the closest price to the stock price forty days prior to the announcement. It is assumed that the impending announcement will not be reflected in option prices at this point. The maturity selected will be the first expiration date at least thirty days after the event period.





38


The reason for these particular choices of exercise price and maturity is to mitigate problems with using the Black-Scholes formula. The Black-Scholes formula has been found to be less accurate for deep in-the-money or out-of-the-money options. Thus, an option near-themoney is used. The reason for insisting the option have at least 30 days to expiration is that the Black-Scholes model has been shown (see Manaster and Rendleman 1982) to be sensitive to its underlying assumptions for options close to expiration.

Once an option is selected according to this criteria, returns will be computed for each day in the event period. These returns will be matched with predicted returns computed from prices generated by the Black-Scholes formula.

The predicted returns should be untainted by the merger and acquisition activity. Of the five input variables for the BlackScholes model, only the stock volatility and stock price are likely to be affected. The obvious approach to estimating the stock volatility is to use historical stock returns from some base period. Another method is to "solve" the Black-Scholes formula for the implied standard

deviation. ISDs reflect market expectations and should provide better estimates of future stock volatility than historical data. This has been confirmed by Latane and Rendelman (1976), Trippi (1977) and Chiras and Manaster (1978). Although a number of complex weighting schemes have been suggested, Beckers (1981) has demonstrated that using the ISD from the option nearest the money may work just as well. For this reason, the base ISDs computed in the previous section will be used to proxy the base volatility. The efficient market hypothesis suggests that the best estimate of tomorrow's stock price is today's stock





39


price. For this reason, the closing stock price 40 days prior to the announcement date (which is assumed to be unaffected by merger and acquisition activity) is used as the input stock price.

Residuals will be computed for each company for each day in the event period


Ujt = Rjt R*j,t


where Uj,t = residual for company j on day t

Rjpt = actual (observed) option return for company
j on day t

R'j,t = predicted option return for company j on day t


Next daily average residuals will be computed to measure the impact of the merger and acquisition announcement for each day in the event period


n
Ut = 1/N iUj't


where Ut = average daily residual for day t

N = number of observations


Finally, cumulative average residuals (CARs) will be calculated to measure the total abnormal return accruing to the optionholders.


t
CARt = E Ut
t=-4


The statistical significance will be measured by a t-test on the daily residuals





40




U J N

Vn (U U)2

j=t



Residuals for the bidding and target firm will, of course, be treated separately. The results are given in Table 3.3. For each day in the

event period, the daily average residual, t-st~atistic, probability (if significant) of exceeding the absolute value of the t-statistic and CAR are given.

Triterpretation of results

It is interesting to note that with the possible exception of the bidding firms' behavior on day-2, the results in Table 3.3 are consistent with the results in Tables 3.1 and 3.2. Merger and acquisition activity has a much larger impact on the target firm option holders than the bidding firm optionholders. The cumulative average residual is about 7.5% through the announcement day for the bidding firm options versus about 39% for the target firm. Abnormal returns for the target firm options are statistically significant two days and the day before the announcement.

It would seem, however, that merger and acquisition activity is an event for the bidding firm option holders. The excess return of 6.4%

two days before the announcement is highly significant. This is consistent with the ISD behavior of the bidding firms' options on day2. Although not statistically significant, the ISD does change sign and become positive (see Table 3.1). The issue of whether merger or acquisition, should be regarded as an event (having measurable impact)





41



Table 3.3

Abnormal Returns in the Option Market
Around Merger and Acquisition Announcements



Bidding Firms

Daily
Day Average t- Prob > Car
Residual Statistic /t/

Day-4 0.004993 0.21 0.004993
Day-3 0.007201 0.37 0.012194
Day-2 0.064110 2.87 0.0059 0.076304
Day-i 0.015931 0.40 0.092235
Day 0 -0.017628 -0.62 0.074607
Day+l 0.019649 0.74 0.094256
Day+2 0.022679 0.92 0.116935


Target Firms

Daily
Day Average t- Prob > Car
Residual Statistic /t/

Day-4 -0.015935 -0.52 -0.015935
Day-3 0.033639 0.69 0.017704
Day-2 0.128971 1.75 0.0956 0.146675
Day-i 0.210493 2.68 0.0152 0.357168
Day 0 0.031266 0.45 0.388374
Day+1 0.017990 0.51 0.406364
Day+2 0.025705 -0.90 0.380659





42



on the bidding firm optionholders will be returned to in the next section.

The above results, as might be expected, are consistent with the hypothesis of market efficiency. For both the bidding and target firms, the formal announcement is anticipated.
After the merger and acquisition is made public, there are no excess returns.

The "abnormal returns" in Table 4 are based upon the traditional event study methodology that has been used in the equity market. That is, the parameter(s) (beta in the equity market) for the model generating the predicted returns are estimated using data -from some base period free from the disturbing effects of the event (merger and acquisition) activity. The difference between the actual, observed market returns and the predicted returns is defined to be the excess or abnormal return.

This excess return assumes that the risk (beta) does not change. In actuality, merger and acquisition activity may not benefit a stockholder even if abnormal returns are observed. These abnormal returns may be accompanied by increased risk engendered by the merger and acquisition activity. If risk were compensated for on a continuous basis, it is possible that the abnormal returns reported would disappear. This has not been done in the equity market since estimating beta requires time series data over a relatively lengthy period of time. The issue is explored more fully in the next section.

For an event study in the option market, it is not necessary to estimate beta. The relevant counterpart is the stock volatility for which the ISD can be used as a proxy. The ISD, however, unlike beta, can be computed at a point in time. This allows for a more complete





43



current estimate of predicted returns for event studies in the option market than in the equity market.

In order to demonstrate this, the event study above was rerun for the target firms on Day -2 and Day -1 (which yielded abnormal returns). The only difference is that ISDs from the previous day (rather than 40 days prior to the announcement date) were used in the Black-Scholes model to generate predicted returns. That is, prices for day-3 were based on ISDs from day-4, prices for day-2 were based on prices from day-3 and prices for day-i were based on ISns from day-2. All other aspects of the study are identical. The results are shown in Table

3.4.

The implication of these results is that abnormal returns reported in event studies to date may be overstated. Using the previous day's ISDs to reflect a more current measure of the stock volatility reduced the excess return on day-2 by almost three percentage points. Although there is no direct relation between a stock's volatility and beta, it would seem logical that merger and acquisition activity could have short run effects. If beta could be observed on a continuous basis so that equity returns could be properly adjusted for risk, abnormal returns might be substantially reduced or even eliminated. This is discussed in more detail in the next section. The behavior of option markets around merger and acquisition announcements

This section extends the event study in the option market

to the underlying equity. The reason for doing this is to compare the behavior of the two markets around the announcement of merger and acquisitions. There are two major reasons for doing this.





44



Table 3.4

Target Firm Option Abnormal Returns
Based On Previous Day ISDs



Daily
Day Average t- Prob >
Residual Statistic t

Day-2 0.099975 1.45 0.1617
Day-i 0.208600 2.49 0.0288





45


The first is that it places the option market results in perspective. While the absolute level of abnormal returns is of interest in itself, it is important to compare the level of excess returns in the option and equity markets. An investor concerned with merger and acquisition activity would need to know the relative effects before he could properly allocate his resources between the two markets.

The second reason for extending the event study to the underlying stocks is that the two markets may behave differently. There are two independent arguments for the hypothesis that merger and acquisition activity will be first manifested in the option (rather than equity) market.

Options can be interpreted as leveraged positions in the underlying equity. The beta of an option is always greater than that of the underlying asset (stock). Thus, it is possible that the option market may be more sensitive to events than the equity market. In other words, although both markets may have received the same bit of information, the signal may be "magnified" and first apparent in the option market.

It is also possible that the option market contains information that is not incorporated in the equity market prior to major corporate announcements. As mentioned previously, a call or put option can be duplicated by an appropriate stock-bond portfolio. Because of this, options have been viewed as "derivative" assets whose prices are completely determined by the underlying equity. The possibility that the option market may influence the equity market has received little attention. Information may first be processed in the option market and then filter to the equity market.





46



This issue has been investigated by Manaster and Rendleman (1932). They advanced the intriguing hypothesis that the option market may play a key role in determining equilibrium stock prices. They argue that some investors may prefer to invest in the option rather than the equity market because of reduced transaction costs, fewer short selling restrictions and most importantly, superior leverage. These traders could push option prices out of equilibrium relative to the underlying stocks. Arbitragers would then intervene to restore equilibrium between the two markets.

Manaster and Rendleman attempted to test their theory. They "inverted" the Black-Scholes model to solve for the implied stock price. The implied stock price was then used to predict future stock prices. They found some evidence that the option market contains information that is not incorporated in the equity market. Unfortunately, their results are very weak and fatally flawed by their reliance on non-synchronous data. The data used in this dissertation avoids this problem.

In retrospect, Manaster and Rendlemans' lack of results is

not surprising. Both the option and equity markets react to public information. Generally, one would expect both markets to adjust simultaneously to new public information. On any given day for any particular corporation there may not be and probably is not information that is not fully reflected in both markets.

However, this may not be true prior to major announcements by corporations such as mergers or acquisitions. In this case, the option market could be expected to be particularly influential in determining stock prices. Keown and Pinkerton (1981) have argued that information





47


concerning impending mergers is susceptible to insider exploitation due to the large number of people typically involved in the negotiating process. They have attributed increased trading volume before the merger announcement to insider activity. An insider attempting to

profit from knowledge of an impending merger would have an incentive to use options because of their leverage aspects. To quote Fischer Black (1975, p. 61), "Since an investor can usually get more action from a given investment in options than he can be investing in the common stock, he may choose to deal with options when he feels he has an especially important piece of information." Option prices can be expected to contain more information than the equity market if nonpublic information is being exploited. If information regarding future mergers first reaches the financial markets through insider trading in options, merger activity may very well be reflected in the option market before the stock market.

Methodology and results

The standard event study methodology was applied to the equity market. Daily returns for each day in the event period were obtained from the Center for Security Price Research (CRSP) tapes. These observed market returns were then compared to mean returns. Mean returns were computed using returns for the sixty trading days prior to the base date forty days prior to the announcement date.

Residual computation and analysis is as before. Residuals are calculated for each company for each day in the event period



Upt = Rjt R j


where Ujt = residual for company j on day t





48


where Uj,t = residual for company j on day t

Rjit = actual equity return for company j on day t

Rj mean return for company j


Next daily average residuals are computed to measure the impact of the merger or acquisition announcement for each day in the event period


n
Ut = i/n Z Uj
j=i


Cumulative average residuals are also calculated to measure the total excess return accruing to the equityholder.

Statistical significance of the residuals is measured as before by a t-test on the daily residuals.


U t n

n (U. t)2
^4 n I
j=1
The results are given in Table 3.5. For each day in the event period, the daily average residual, t-statistic and probability of exceeding the absolute value of the t-statistic, if significant, is given.

Table 3.5 is consistent with other merger studies done in the equity market. Merger and acquisition activity has very little impact on the bidding firms. The largest daily average residual, although statistically significant at the 10% level is only 0.0044. For the target firms, a statistically significant daily average return of almost 0.04 was observed on day-i.

The abnormal returns for the target firm equityholders is a

little low compared to returns obtained in other merger studies. This





49


Table 3.5

Abnormal Returns In The Equity Market
Around Merger and Acquisition Announcements



Bidding Firms

Daily
Day Average t- Prob >
Residual Statistic /t/ Car

Day-4 -0.001457 -0.65 -0.001457
Day-3 0.001275 0.50 -0.000182
Day-2 0.004015 1.71 0.0926 0.003833
Day-i -0.002133 -0.52 0.001700
Day 0 -0.007647 -2.15 0.0362 -0.005947
Day+1 -0.003259 1.26 -0.009206
Day+2 0.000562 0.22 -0.008694


Target

Daily
Average t- Prob >
Day Residual Statistic /t/ Car

Dz-4 -0.006512 -1.68 -0.006512
Day-3 -0.002720 -0.50 -0.008932
Day-2 0.007597 1.07 -0.001335
Day-I 0.039875 +2.44 0.0240 0.038540
Day 0 0.000620 0.08 0.039160
Day+1 -0.002300 -0.36 0.036860
Day+2 0.000402 0.08 0.037262





50



concerning impending mergers is susceptible to insider exploitation due to the large number of people typically involved in the negotiating process. They have attributed increased trading volume before the merger announcement to insider activity. An insider attempting to

profit from knowledge of an impending merger would have an incentive to use options because of their leverage aspects. To quote Fischer Black (1975, p. 61), "Since an investor can usually get more action from a given investment in options than he can be investing in the common stock, he may choose to deal with options when he feels he has an especially important piece of information." Option prices can be expected to contain more information than the equity market if nonpublic information is being exploited. if information regarding future mergers first reaches the financial markets through insider trading in options, merger activity may very well be reflected in the option market before the stock market.

Methodology and results

The standard event study methodology was applied to the equity market. Daily returns for each day in the event period were obtained from the Center for Security Price Research (CRSP) tapes. These observed market returns were then compared to mean returns. Mean returns were computed using returns for the sixty trading days prior to the base date forty days prior to the announcement date.

Residual computation and analysis is as before. Residuals are

calculated for each company for each day in the event period



uj3,t = Rj t R i





51


is probably due to the sample. Companies listed on the CBOE tend to be large, established companies. The takeover market may not be as efficient for firms of this size. Relatively few companies have the resources to undertake an acquisition of this scope. This fact is reflected in the sample. Of the 21 target firms in the sample, seven are mergers. For the divestitures, abnormal returns may also be

comparatively small due to the size of the firms involved. Although large in absolute terms, a $100 million divestiture for a company such as General Electric is likely to have very little impact.

Although the pattern of abnormal returns is similar for both markets, the residuals in the option market tend to be much larger. For the bidding firms, cumulative average residuals were 0.074607 through the announcement day for the options vice -0.005947 for the equity. For the target firms, cumulative average residuals were

0.388374 and 0.039160 for the options and equity, respectively.

The only puzzling feature in the above tables is the statistically significant excess return for the bidding firms options observed two days prior to the announcement date. The results in the equity market, however, are consistent. The average residual for day2, although small in absolute terms, is large compared to those of other days and is statistically significant. It should be noted that the data source used in the option and equity markets are independent. The Berkeley option tapes served as the basis for the option event study and the CRSP tapes for the equity.

The results for day-2 are also not due to low priced options. A small price change on an option priced at less than a dollar could result in large returns that might not actually be realizable. This





52



possibility was checked for by redoing the analysis for the bidding firm options on day-2 and the target firm options on day-1. This time, however, returns based on prices less than one dollar are eliminated. The results are given in Table 3.6. The daily average residual for the bidding firm does decline from about 6.4% to roughly 4%. it is, however, still statistically significant. Eliminating the low priced options from the target firms actually increases the daily average residual.

The results from this study support the hypotheses that merger and acquisition activity is first manifested in the option market. For the bidding firms in the equity market, the daily average residual is uniformly small. In the option market, however, there is a large jump between the daily average residual of 0.007201 on day-3 and 0.064110 on day-2. For the target firms, the evidence is more pronounced. In the equity market, the merger and acquisition activity is not evident until day-1. in the option market, the merger activity is definitely reflected by the excess returns on day-2 and arguably on day-3. The target firm iSDs, however, have started to react three days prior to the announcement.

As noted earlier, abnormal returns were obtained for the target firms in the equity market (see Table 3.5). These abnormal returns, however, were based on historical data. Thus, an underlying assumption is that the risk (beta) does not change. In reality, merger and acquisition activity may be accompanied by increased risk that is not reflected in the base beta. If beta could be observed on a continuous basis so that equity returns could be properly adjusted for risk, abnormal returns might be substantially reduced or even eliminated.





53


Table 3.6

Selected Abnormal Returns with Call Prices Under $1.00 Eliminated



Bidding Firms Target Firms
Day-2 Day-i

Daily Daily
Average t- Prob > Average t- Prob >
Residual Statistic /t/ Residual Statistic /t/

0.039593 1.98 0.0536 0.248540 2.76 0.0147





54


A number of attempts were made to adjust for risk in the equity market by exploiting the high correlation between a stocks volatility and beta. Unlike beta which requires time-series data, the ISD can be calculated at a point in time. Although there is no theoretical relationship between the ISD and a stock's beta, empirical relationships can be established. These relationships can then be used to adjust for the increasing risk due to the impending merger or acquisition announcement.

The methodology used to adjust the level of risk in the equity market during the event period involves regressing stock betas against their volatility. Daily returns for the target firms were regressed against the market (CRSP value weighted) index for the six months prior to the base (40 days prior to the announcement) date. This

yielded the intercept for the market model and an unadjusted beta to conduct an event study in the equity market. Stock volatilities based on the daily returns were also calculated. The target firm betas were regressed against the volatilities to obtain the following relation


B = 0.866764 + 19.48914* a R2 = 0.098


A similar relationship was obtained using annual data. Annual returns for the target firm were regressed against the market (CRSP value weighted) index for the thirty years 1952 to 1981. Stock volatilities based on this annual data were also computed. The annual betas were then regressed against the stock volatilities to obtain


B = -0-061901 + 3.669232* u RZ = 0.714





55


These relationships were used to adjust the beta for each day in the event period. The 'LSD was plugged into the equations above to obtain an adjusted beta. These adjusted betas were then plugged into the market model (based on the daily returns) to generate predicted returns. The standard event study methodology was then used to obtain the results shown in Table 3.7. The first column is the residuals and associated t-statistics obtained from using an unadjusted beta, that is, the beta based on the six months of daily data. The second column shows the results obtained when the ISD is used to adjust the beta using the relationship between beta and a based on the annual data. The third column shows the results when the ISD for each day in the event period is used to adjust the beta using the relationship based on the daily data.

These results indicate the adjustments for risk were not successful. On day-1, the abnormal return are almost identical regardless of whether the unadjusted beta, adjusted beta based on annual return data or daily return data is used. Either the adjustment procedure is

flawed or the level of risk did not change during the event period. An analysis of the data reveals a technical reason why the adjustment procedure did not work.

In a CAPM framework, stocks must have an expected return greater than the risk-free rate. Ex-post, however, negative returns do occur. Many of the market returns on the day prior to the announcement date (day-1) were negative in this sample. The average market return is

-0.000808. The practical effect of this is that adjusting beta upwards can result in larger abnormal returns (residuals) because of the data. If the market return is negative, increasing beta will only result in a





56



Table 3.7

Abnormal Returns for the Target Firms
for Various Beta Adjustments



Day Unadjusted Annually Daily
Beta Adjusted Adjusted
Beta Beta

-4 -0.002448 -0.003664 -0.003431
(t = -0.59) A = -0.89) (t = -0.81)

-3 -0.002102 -0.001601 -0.001539
A = -0.51) (t = -0.41) (t = -0.39)

-2 0.005530 0.005232 0.005516
(t = 0.84) (t = 0.79) (t = 0.82)

-1 0.032000 0.033300 0.033147
(t = 2.34) (t = 2.35) (t = 2.34)

0 0.001017 0.001048 0.001032
(t = 0.13) (t = 0.14) (t = 0.14) +1 -0-002665 -0.002597 -0.002729
(t = -0.66) (t = -0.64) (t = 0.26)

+2 0.001301 0.000929 0.001190
(t = 0.28) (t = 0.19) (t = 0.26)






57



lower predicted return. This illustrated by the abnormal returns that result from the following adjustment to beta for day-!


B a = B[(ISD(-1) ISDb)/ISDb) + 1.0] k where B a = adjusted beta

B = base beta obtained from six months daily data

ISD(-1) = ISD on day-i

ISDb = base I.SD

k =an arbitrary scaler


The results for k =1, 1.3, 1.5, and 2.0 are shown in Table 3.8. Here we see that increasing beta has very little impact on the residuals. A larger beta results in a larger predicted return (smaller residual) impact for those companies for which the market return was positive. This is offset, however, by those companies for which the market return is negative.

The magnitude by which beta would have to be increased in order to eliminated the abnormal returns can still be calculated. Adding 0.015 to the market returns on day-i to make them positive and B*.015 to the company returns does not change the residuals but makes the adjustment process conform to theoretical expectations. The above regressions were rerun with the indicated adjustment. The results are given in Table 3.9. These results show that adjusting the base beta by the percentage change in the ISDs times a scaler of 1.40 reduces the abnormal returns to statistical insignificance. This suggests that the basic methodology used to adjust beta above is sound but needs to be applied to a larger sample where the average market return is positive.





58



Table 3. 8

Abnormal Returns Obtained by Adjusting Beta by the
Percentage Change in ISDs Times a Scaler (K)



K = 1.0 K = 1.3 K = 1.5 K = 2.0


Day -1 0.033378 0.033793 0.034070 0.034761
(t = 2.34) (t = 2.35) (t = 2.35) (t = 2.33)






59




Table 3. 9

Abnormal Returns Obtained by Adjusting beta by the
Percentage Change in the ISD and a Scaler (K) After Adding 0.015 to the Market Returns and B*.015 to the Company Returns



K =1.0 K = 1.10 K = 1.20 K = 1.30 K = 1.40

Day-i 0.029318 0.027321 0.025323 0.023325 0.021327
(t = 2.19) (t = 2.05) (t = 1.91) (t = 1.77) (t = 1.62)
(0.0422) (0.0552) (0.0720) (0.0939) (12.17)
















CHAPTER 4
VARIANCE BIAS AND NON-SYNCHRONOUS PRICES IN THE BLACK-SCHOLES MODEL



One of the underlying assumptions of an event study in the equity market is that the return generating process is linear. As long as predicted returns equal observed (actual market) returns on average, residuals (abnormal returns) should also average out to zero. it is the common disturbance (event) that generates abnormal returns.

This linearity of the return generating process also justifies using an estimate of beta. If an unbiased estimator of beta is used, errors will tend to offset. The estimates of beta may be high or low but will average out in a large sample. Furthermore, the error in estimated returns and thus residuals will also average out to zero.

The Black-Scholes model, however, is highly nonlinear. Thus, using an estimate for the input variables may result in a systematic bias. Even if an unbiased estimator is used for the input variables (most notably the stock volatility), errors from the true call price will not offset even in a large sample. The reason for this is that equal deviations from the true input parameters will not result in eaual deviations from the true call price.

This has implications far beyond that of conducting an event study in the options market. Applying the Black-Scholes model has an

inherent bias due to the fact that the formula is non-linear and input variables must be estimated. The magnitude and direction of these



60





61



biases is of interest to any user of the Black-Scholes model. For this reason, the issue of bias in the Black-Scholes model arising from these sources is considered in a broader context rather than as a technical issue concerning event study methodology.

This chapter has two sections. The first section deals with the bias that results in the Black-Scholes model from using a sample estimate of the variance with all other input parameters assumed to be known. The following section extends the analysis to uncertainty in the underlying stock price due to non-synchronous trading (or price quotes) between the option and equity markets.


Variance Bias in the Black-Scholes Model

The Black-Scholes model is by far the most widely used option pricing formula. In order to apply it, five input variables must be obtained: the stock price, exercise price, time to maturity, risk-free rate of interest and the volatility of the underlying stock. Of these

variables, four are directly observable. Only the variance of the underlying stock returns needs to be estimated. Hull and White (1987) have analyzed the impact of a2 itself being stochastic on the call option value. In this paper, however, we assume that u2 is constant but its estimate, 2, is a random variable.

Classical methods of estimating the variance will bias the BlackScholes model as Ingersoll (1976) and Merton (1976) have pointed out. To see this, define 2t= Ln(1 +t where Rtis the rate of return on

the underlying stock in period t and assume that 2t is an independent, normally distributed random variable. The unbiased estimate, 02, of the variance of the stock returns is given by





62


n
S(2t- Z)2
t=i
g2 = (4.1)
N 1


where N is the number of observations


n
Z = Z 2tN
t=1


While it is well known that g2 is an unbiased estimate of 02, it is not true that E(C) = C where C is the value derived from the Black-Scholes formula with the true but unknown 02 and C is a random variable calculated by employing the Black-Scholes formula with the random variable g2.

Let us elaborate this point. The Black-Scholes model is given by


C = SON(dl) Ee-rtN(d2) 4.2


where d = [ln(S0/E) + (r + 0.5a2)t]/at

d2 = dl ot


and the sample estimate of C is given by C


C = SoN(dI) Ee-rtN(d2) 4.3


where dl = [ln(S0/E) + (r + 0.5S2)t]/S2 t

d2 = di S/t


(recall that S is a random variable) It is obvious that R(C) # C for the following reasons. First, even if E(S2) = G2, R(S) # a and a is one of the inputs into the BlackScholes formula. Second, even if E(S) = a (which it does not), E(C) #





63


since a appears in the denominator of the formula and E(1/S) # 1/o.

Even if E(S) = a and E(1/S) = 1/a, the model would still be biased due to its non-linearity. Equal deviations from the the true a2 would not result in equal deviations from the true option price.

Analyzing the gap between E(C) and C is difficult. One has to evaluate the following difference


Ln(S0/E) + (r+0.5g2)/St Ln(S0/E) + (r-0.5S)t/2It


-0.5Z2 -rt -0.5Z2
E(C) c = so i/l27 e dz -Ee f 2/ e dz




Ln(S0/E) + (r+0.5a2)t/ajt Ln(S0/E) + (r-0.5a2)t/JIt


-0.5Z2 -rt -0.5Z2
-so f I/V27 e dz + Ee d z/V?7 e am



A closed-form solution to the first two integrals is extremely complex since S, a random variable, appears in the upper bound. Boyle and Anathanarayanan (1977) used numerical integration to approximate the above integrals and investigated the case of an option expiring in 90 days.

In this paper, we provide an alternative approach by using

simulation. Sample estimates, S2, of the stock volatility, a2, are generated and used to compute option prices using the BlackScholes formula. These prices are then compared to the theoretical value determined by using the true a2 in the Black-Scholes formula in order to measure the bias induced. This is repeated for options with





64


various maturities. The dispersion of sample call prices from the

theoretical value is also investigated.


Methodology and Results

The effect of using a sample estimate of the variance in the Black-Scholes model was analyzed using simulation analysis. For this purpose, an option with the following characteristics was chosen. These parameters were representative of IBM options in the early 1980's. Note that the true stock volatility is assumed known.


Stock price = $68.125

Risk-Free Rate = 0.1325
of Interest

True Standard = 0.4472
Deviation of Stock Returns

Time to Maturity = Various Exercise Price = Various


The simulation is based on the well known relationship

the sample and true variance

2
2 2 4.4
N 1

2 is distributed as a Chi-square with N-1 degrees of freedom which for this analysis is assumed to be fifty-nine. This implies that the sample variance was estimated using sixty observations. One thousand Chi-square deviates were obtained using the International Mathematical and Statistical Library (IMSL) computer program. The sample variance was then computed for each Chi-square observation for input into the Black-Scholes formula. For each exercise price, one thousand call






65


prices using the sample variances obtained from simulation were calculated and the average computed. Options with five, sixty, and two hundred seventy days to maturity were examined.

The results are given in Table 1. The theoretical price assuming the true variance is known is given for each exercise price. The exercise price changes in five percent increments from the given stock price of $68.125. The average simulation price is the mean of the thousand generated call prices. The percentage bias is calculated by


% bias = (theoretical__price-average simulation price) 100 theoretical price

Note that a positive bias is associated with average simulation prices less than the theoretical Black-Scholes prices.

These results show a definite bias exists. While mean simulated prices do deviate from theoretical Black-Scholes prices, however, the differences are small. In most cases, the average simulation price is within a few cents of the theoretical price. The largest difference is approximately eight cents. The percentage bias is also small. For the options with 60 and 270 days to expiration, it is always under one percent. While biases over one percent do occur for the option with five days to maturity, they are at prices so low as to be economically meaningless.

A few observations on the nature of the bias between the average simulation value and the theoretical value should be made. First, A downward bias exists in most cases. The average value obtained from simulation is less than the theoretical value for all nine exercise prices for the options with sixty and two hundred seventy days to expiration. For the five day option, the theoretical price exceeds the





66


Table 4. 1

Theoretical Call Price and Average Simulation Call Price


T = 5 Days to Maturity

Exercise Theoretical Average Simu- Percent
Price Price lation Price Bias

54.500 13.7178 13.7157 0.01523
57.906 10.3184 10.3175 0.00872
61.313 6.9418 6.9427 -0.01253
64.719 3.7987 3.7966 0.05503
68.125 1.4799 1.4701 0,66084
71.531 0.3669 0.3636 0.89129
74.938 0.0549 0.0568 -3.49790
78.344 0.0050 0.0060 -20.16123
81.730 0.0003 0.0005 -60.71423

----------------------------------------------------------T = 60 Days to Maturity

Exercise Theoretical Average Simu- Percent
Price Price lation Price Bias

54.500 15.1807 15.1806 0.00040
57.906 12.3118 12.3038 0.06482
61.313 9.7241 9.7056 0.19035
64.719 7.4747 7.4468 0.37366
68.125 5.5917 5.5583 0.59802
71.531 4.0735 4.0402 0.81773
74.938 2.8926 2.8639 0.99112
78.344 2.0055 1.9846 1.04311
81.750 1.3596 1.3474 0.90314

---------------------------------------------------------T = 270 Days to Maturity

Exercise Theoretical Average Simu- Percent
Price Price lation Price Bias

54.500 20.9884 20.9614 0.12868
57.906 18.7896 18.7513 0.20132
61.313 16.7597 16.7107 0.29198
64.719 14.9000 14.8419 0.39013
68.125 13.2070 13.1416 0.49526
71.531 11.6748 11.6044 0.60293
74.938 10.2950 10.2220 0.70870
78.344 9.0591 8.9858 0.80924
81.750 7.9562 7.8849 0.89591





67


average simulation price for five exercise prices. In the other four cases, the bias is extremely small amounting to less than one cent.

The bias is largest in absolute terms for the options with longer maturities. However, there is no systematic relationship when the bias is expressed in percentage terms. When the bias is expressed in percentage terms, the bias for the sixty day option is smaller than that of the two hundred seventy day option at low exercise prices but larger at high relative exercise prices.

For an option of a given maturity, the bias is more pronounced at high exercise prices. This holds true regardless of whether the bias is expressed in absolute or percentage terms. This makes intuitive sense. At low exercise prices most of an option's value is due to its intrinsic worth. At high exercise prices more of the option's value can be attributed to the volatility of the underlying stock. Consequently, the estimate of the variance becomes more important.

The results in Table 4.1 are encouraging to users of the BlackScholes model. The bias in a large sample is small. This does not guarantee, however, that using a sample estimate of the variance will not severely degrade the applicability of the Black-Scholes model. Sample call prices might each differ from the theoretical price by a great amount. in a large sample these individual errors might offset so that the average error was small. The dispersion of the sample call prices from the theoretical value is also crucial.

For this reason, average simulated prices were generated on the same IBM option as before only using 4, 6, 8, 10, 15 and 30 runs instead of a thousand. The results are given in Table 4.2. As before, options with 5, 60 and 270 days to expiration were examined. For each





68



Table 4.2

Average Simulated Values and Bias for Various Sample Sizes



Maturity = 5 Days
Exercise Price = $54.50
Theoretical Price = $13.7178

Number of Average Percent
Simulations Simulation Price Bias

4 13.7178 0.0000
6 13.7178 0.0000
8 13.7178 0.0000
10 13.7178 0.0000
15 13.7178 0.0000
30 13.7178 0.0000


Maturity = 5 Days
Exercise Price = $68.125
Theoretical Price = $1.4799

Number of Average Percent
Simulations Simulation Price Bias

4 1.5181 -2.5812
6 1.4626 1.1690
8 1.4516 1.9123
10 1.4526 1.8448
15 1.4608 1.2906
30 1.4669 0.8785


Maturity = 5 Days
Exercise Price = $81.750
Theoretical Price = $.0003

Number of Average Percent
Simulations Simulation Price Bias

4 0.0005 -66.6667
6 0.0004 -33.3333
8 0.0003 0.0000
10 0.0003 0.0000
15 0.0003 0.0000
30 0.0004 -33.3333

- - - - - - - - - - - - - - -





69



Table 4.2 (continued)


Maturity = 60 Days
Exercise Price = $54.50
Theoretical Price = $15.1807

Number of Average Percent
Simulations Simulation Price Bias

4 15.2367 -0.3689
6 15.1680 0.0837
8 15.1528 0.1838
10 15.1526 0.1851
15 15-1618 0.1245
30 15-1742 0.0428


Maturity = 60 Days
Exercise Price = $68.125 Theoretical Price = $5.5917

Number of Average Percent
Simulations Simulation Price Bias

4 .5.7214 -2.3195
6 5.5328 1.0533
8 5.4955 1.7204
10 5.4980 1.6578
15 5.5266 1.1642
30 5.5473 0.7940


Maturity = 60 Days
Exercise Price = $81.75
Theoretical Price = $1.3596

Number of Average Percent
Simulations Simulation Bias
Price

4 1.4633 -7.6272
6 1.3239 2.6258
8 1.2949 4.7588
10 1.2962 4.6632
15 1.3159 3.2142
30 1.3355 1.7726

- - - - - - - - - - - - - - -





70


Table 4.2 (continued)


Maturity = 270 Days
Exercise Price = $54.50
Theoretical Price = $20.9884

Number of Average Percent
Simulations Simulation Price Bias

4 21.1675 3.9112
6 20.9231 0.3112
8 20.8727 0.5513
10 20.8753 0.5389
15 20.9101 0.3731
30 20.9429 0.2168


Maturity = 270 Days
Exercise Price = $68.125
Theoretical Price = $13.2070

Number of Average Percent
Simulations Simulation Price Bias

4 13.4635 -1.9421
6 13.0913 0.8760
8 13.0177 1.4333
10 13.0244 1.3826
15 13.0789 0.9699
30 13.1198 0.6603


Maturity = 270 Days
Exercise Price = $81.75
Theoretical Price = $7.9562

Number of Average Percent
Simulations Simulation Price Bias

4 8.2374 -3.5344
6 7.8293 1.5950
8 7.7485 2.6105
10 7.7559 2.5175
15 7.8157 1.7671
30 7.8606 1.2016






71


of these maturities, exercise prices of $54.50, $68.125 and $81.75 were selected. The percent bias is calculated as before 5. The theoretical Black-Scholes price is also given for each option.

These results show that the dispersion of option prices from their theoretical values due to using the sample variance is not great. The largest absolute difference is about $0.25. I-n general, the percentage bias is usually less than 2%. The major exception is for the out-ofthe-money option with five days to maturity. This is due to the insignificant theoretical call prices (less than $0.01) associated with this option.

The same observations concerning the behavior of the bias for the large sample (1000 runs) experiments apply to the small sample experiments. The bias is generally positive (theoretical price exceeds average simulated price). When the bias is negative, it is almost always associated with the smallest number of simulations (4). Again, the percentage bias is usually smallest at low exercise prices and becomes larger as the exercise price is increased.


Non-synchronous Prices and the Black-Scholes Model

Many investment decisions involving options are based on closing stock and option prices or other non-sychronous sources of data. Since the option market is much thinner than the stock market, these prices are often based on trades from different times of the day. The stock price prevailing at the time of the last option trade may be significantly different from the closing price at the end of the day. Consequently, using this stock price in the Black-Scholes model may cause options to appear mispriced as Trippi (1977), Chiras and Manaster (1978), Galai (1977) and Bookstaber (1981) have pointed out.






72



Here the mispricing of options that can occur due to the nonsimultaneity of stock and option quotations and using a sample estimate for the variance of the underlying stock returns in the Black-Scholes model is examined. An option is constructed for analysis and its theoretical value is calculated assuming the input variables including the relevant stock price and true volatility a2, are known. This value is compared to call prices generated with the same parameters (including the true assumed volatility) only varying the input stock price from the assumed true stock price in order to measure the effects of nonsimultaneous stock and option quotations.

The additional bias resulting from using a sample estimate of the variance is measured by simulation analysis. For each stock price, sample estimates, 17, of the stock volatility, 02, are generated and used to compute option prices using the Black-Scholes formula. These prices are then compared to the theoretical price determined by using the true variance, o2, and true (synchronous) stock price in order measure the bias due to the combination of the two factors. The methodology and results are describe below.


Methodology and Results

Simulation analysis was used to measure the effects in the Black-Scholes model of using a sample estimate of the variance in conjunction with nonsimultaneous stock and option quotations. For this purpose, an option with the following characteristics was chosen. These parameters are representative of a typical option traded on the Chicago Board Option Exchange in the mid 1980's. Note that the true stock volatility and stock price are known.






73



Stock Price =$50.000

Risk-Free Rate = 0.1000
of Interest

True Standard = 0.3500
Deviation of
Stock Returns

Time to Maturity =Various Exercise Price = $50.000


The effect of nonsimultaneous stock and option prices alone on the Black-Scholes model was measured by varying input stock price in 1/8 increments from the true stock price of $50.000. For each stock price between $49.000 and $51.000 the Black-Scholes value was computed using the parameters listed above including the true assumed variance of

0.3500.

The combined effects of nonsimultaneous price quotations and using a sample estimate of the variance was analyzed by simulation. The simulation is based on the relationship between the sample and true variance didcusssed earlier

2
N-2 S 2 4.4


gis distributed as a Chi-square with N-i degrees of freedom which for this analysis is assumed to be twenty-nine. This implies that the sample variance was estimated using thirty observations. One thousand Chi-square deviates were obtained using the International Mathematical and Statistical Library (IMSL) computer program. The sample variance was then computed for each Chi-square observation for input into the Black-Scholes formula. For each exercise price, one thousand call

prices using the sample variances obtained from simulation were






74



calculated and the average computed. Options with five, sixty, and two hundred seventy days to maturity were examined.

The results are given in Table 4.3. For each stock price, the Black-Scholes value is given based on the true variance of 0.3500. This gives a measure of the mispricing that can occur to nonsiinultaneous price quotations. For each of these stock prices, the average simulation price is also given. The average simulated price is the mean of the thousand generated call prices obtained with that exercise price and estimates of the variance.

The percentage bias of these values from the theoretical value is also given. The percentage bias is calculated by


% bias = (theoretical price-average simulation price) 100 theoretical price

Note that a positive bias is associated with average simulation prices less than the theoretical Black-Scholes prices.

These results indicate that making investment decisions involving options on the basis of nonsynchronous price data must be made with great care. Even when the stock price is off by only an eighth the observed call price will deviate from its theoretical price by over one percent. For short maturities, using a stock price that deviates from the true stock price by one dollar can results in call prices that are over 50% off from the true value. The error due to using a sample estimate of the true variance is small in comparison to that caused by using noncontemparenous stock prices. For stock prices above the true value, the two errors are offsetting. For stock prices below the true stock value, the two errors reinforce one another.





75



Table 4. 3

Mispricing in the Black-Scholes Model Due to Nonsimultaneous
Stock and Option Quotations and Using a Sample Estimate
for the Variance of the Underlying Stock Returns



T = 5 Days to Maturity
Theoretical Price =0.843231

Stock Black-Scholes Average Percent Bias Percent
Price Price With Simulation Due to Non- Bias Due to
True Variance Price Simultaneous Both Effects
Quotations

51.000 1.455809 1.452143 -72.6465 -72.2117
50.875 1.369338 1.365278 -62.3918 -61.9103
50.750 1.285629 1.281119 -52.4646 -51.9298
50.625 1.204605 1.199766 -42.8558 -42.2820
50.500 1.126509 1.121297 -33.5944 -32.9762
50.375 1.051239 1.045770 -24.6679 -24.0193
50.250 0.978912 0.973244 -16.0906 -15.4184
50.125 0.909561 0.903781 -7.8662 -7.1807
50.000 0.843231 0.837410 0.0000 -0.6903
49.875 0.779953 0.774134 7.5042 8.1943
49.750 0.719757 0.713988 14.6430 15.3271
49.625 0.662537 0.656968 21.4288 22.0892
49.500 0.608398 0.603052 27.8492 28.4832
49.375 0.557251 0.552217 33.9148 34.5117
49.250 0.509110 0.504414 39.6240 40.1809
49.125 0.463882 0,459599 44.9875 45.4954
49.000 0.417516 0.500117 50.0117 50.4644

------------------------ ------ ---- -- -- -- -





76


Table 4.3 (continued)
T = 60 Days to Maturity
Theoretical Price 3.135864

Stock Black-Scholes Average Percent Bias Percent
Price Price With Simulation Due to Non- Bias Due to
True Variance Price Simultaneous Both Effects
Quotations

51.000 3.726805 3.708286 -18.8446 -18.2540
50.875 3.649992 3.631251 -16.3951 -15.7975
50.750 3.574020 3.555066 -13.9724 -13.3680
50.625 3.498869 3.479729 -11.5759 -10.9655
50.500 3.424468 3.405258 -9.2033 -8.5907
50.375 3.351058 3.331654 -6.8623 -6.2436
50.250 3.278503 3.258919 -4.5486 -3.9241
50.125 3.187067 3.187067 -2.2607 -1.6328
50.000 3.135864 3.116100 0.0000 0.6303
49.875 3.065887 3.046021 2.2315 2.8650
49.750 2.996780 2.976843 4.4353 5.0711
49.625 2.928482 2.908547 6.6132 7.2489
49.500 2.861113 2.841156 8.7617 9.3980
49.375 2.794615 2.774673 10.8821 11.5181
49.250 2.728973 2.709085 12.9754 13.6096
49.125 2.664169 2.644415 15.0419 15.6719
49.000 2.600462 2.580659 17.0735 17.7050


T 270 Days to Maturity
Theoretical Value 7.302824

Stock Black-Scholes Average Percent Bias Percent
Price Price With Simulation Due to Non- Bias Due to
True Variance Price Simultaneous Both Effects
Quotations

51.000 7.948135 7.909295 -8.8364 -8.3046
50.875 7.866165 7.827100 -7.7140 -7.1791
50.750 7.784515 7.745256 -6.5959 -6.0584
50.625 7.703323 7.663871 -5.4842 -4.9439
50.500 7.622467 7.582793 -4.3677 -3.8337
50.375 7.541931 7.502134 -3.2742 -2.7292
50.250 7.461836 7.421933 -2.1774 -1.6310
50.125 7.3821.85 7.342033 -1.0867 -0.5369
50.000 7.302824 7.262574 0.0000 0.5512
49.875 7.223953 7.183511 1.0800 1.6338
49.750 7.145445 7.104862 2.1550 2.7108
49.625 7.067305 7.026569 3.2250 3.7829
49.500 6.989562 6.948733 4.2896 4.8487
49.375 6.912291 6.871284 5.3477 5.9092
49.250 6.835295 6.794231 6.4020 6.9643
49.125 6,758818 6.717631 7.4493 8.0132
49.000 6.682646 6.641387 8.4923 9.0573





77



Conclusion

In empirical tests of the black-Scholes model, one normally employs ex-post estimates of cY2 since a2 itself is unknown. While the sample variance is an unbiased estimate of o2, the derived option value (which is a random variable) is a biased estimate of the true BlackScholes value.

The effects of this bias were analyzed by simulation. The true variance was assumed to be known and sample estimates generated by using a Chi-square distribution. One thousand sample variances and their associated call prices were obtained in each case. The average call price was calculated and compared to the theoretical Black-Scholes value. This process was performed on options with various maturities and exercise prices.

The results show that using a sample estimate for the variance in the Black-Scholes model results in a downward bias. The average simulation price was less than the theoretical price for all options with 60 and 270 days to maturity. For the 5 day option, the average simulation price was less than the theoretical price for 5 of the 8 exercise prices. When an upward bias was observed, it was not economically significant. The downward bias was also evident in the small sample experiments. Sample call prices were generated in the same

manner previously described only using fewer trials. Average simulation prices were computed using 4, 6, 8, 10, 15 and 30 runs. The average call prices generated by simulation were usually less than the theoretical Black-Scholes price for six or more runs. The differences between the average call prices generated by simulation and the





78


theoretical values were small. The percentage biases were also small except for deep-out-of-the-money options close to expiration.

The effect of non-synchronous prices was also investigated. if the input stock prices deviate from the true stock price by only 1/8, the mispricing ranged from roughly 1% for the 270 day option to approximately 7% for the 5 day option. The additional error due to using an estimate of the variance was relatively small.
















CHAPTER 5
SUMMARY AND CONCLUSIONS


This dissertation investigated the behavior of options around merger and acquisition announcements. A variation of the traditional event study methodology was applied to the option market in order to determine the abnormal returns accruing to the bidding firm and target firm optionholders. The event study was then extended to the underlying equity and the results between the two markets compared.

In both the equity and option market, the effect of merger and acquisition activity was most pronounced for the target firms. The cumulative average residuals for the bidding firms in the equity market through the announcement date were close to zero. For the target firms, they were close to 4%. The corresponding CARs in the option market were 7.5% and 38.8%, respectively.

The abnormal returns for the target firms in the option market are surprisingly large. Abnormal returns accruing to the optionholder are over 10 times as large as those accruing to the equityholders. The is due is not only the leverage effect in options but the fact that the stock volatility is increasing as well.

Merger and acquisition activity can be expected to have a larger impact on the volatility (second moment of the return generating function) of the target firms than of the equity firms. Event studies in the equity market have shown that most of the gains from merger activity are captured by the target firm shareholders. The rationale



79





80


for this is that the takeover market is competitive. If a company has some unique aspect to exploit, it will find or have the potential to find a number of bidders. Competition among the bidding firms will drive the net present value of the investment to zero.

Because of this, merger and acquisition activity should be expected to affect the volatility of the target firms' much more than the bidding firms'. Merger and acquisition activity is a more or less neutral event for the bidding firm shareholders. Target firm

shareholders are much more likely to be greatly affected. The

importance of merger and acquisition activity combined with uncertainty over the terms of the agreement, whether alternative bidders will appear, whether the agreement will be consummated, etc., should result in higher ISDs for the target firms.

This hypothesis was confirmed. The change in the ISDs between the event period and base date for the bidding firms was not significant. The changes were small and statistically insignificant. The target firms, however, had large statistically significant changes in the ISDs.

The effect of changing stock volatility on option prices was also examined. Option prices in the event period were compared to those using the Black-Scholes model using the current stock price but the base TSD. The results showed that changing stock volatility was an important factor in the abnormal returns reaped by the target firm ODtionholders.

The results of this study also suggest that merger and acquisition activity is first reflected in the option market. The target firm ISDs started to increase and were statistically significant 3 days





81


before the announcement. Target firm option returns had started to increase and were statistically significant 2 days before the announcement. Target firm stock returns, however, did not significantly increase until the day prior to the announcement. Bidding firm option returns were economically and statistically significant two days before the announcement. Bidding firm stock returns were very small through the announcement date although they were statistically significant 2 days before the announcement.

These results have practical implications for investors. if

someone anticipates a company is about to announce a merger or acquisition, they would reap much greater returns by purchasing options rather than the stock. Furthermore, they would be substantially better off by purchasing the target firm option rather than that of the bidding firm.

This dissertation analyzed two issues involving the event study methodology. The first was the proper adjustment for risk in the equity market. Predicted returns have usually been based on data from some base period. The traditional event study methodology, thus,

implicitly assumes that risk remains constant. It is far more likely that risk is actually changing due to the event (merger and acquisition activity). Abnormal returns would thus be overstated. Empirical

relationships between the ISD (stock volatility) and beta were developed. These relationships were then used to adjust beta during the event period. Although conceptually sound, the results were

disappointing due to a technical factor. The market return for many of the companies was negative. This resulted in smaller predicted returns (larger residuals) when larger betas were plugged into the market model.





82


The second major issue involves event studies in the option market. The Black-Scholes model is non-linear. Unbiased estimators for the input variables will still bias the results since equal deviations from the true input parameter value will not result in equal deviations from the true call price. Simulation analysis was used to measure the magnitude of this effect. The results indicate that although caution must be used in interpreting the results of an event study that uses the Black-Scholes model to generate predicted returns, the error is usually small.
















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87









BIOGRAPHICAL SKETCH


James A. Yoder was born on June 18, 1953, at Fort Monmouth, New Jersey. He received his Bachelor of Science degree in mathematics in 1974 from the State University of New York at Albany. He then went on to obtain an M.A. in economics in 1975 from the same university.

Mr. Yoder entered the Navy in the Nuclear Power Program. He

served on board the U.S.S. Dwight D. Eisenhower and made one

Mediterranean deployment. After leaving the Navy, he completed his MBA at the State University of New York at Albany before entering the Ph.D. program at the University of Florida.
















I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy.




Haimn Levy, Chairman-/ Walter J. Matherly Professor of Finance

T :e ftify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a diss-ertation for the degree of Doctor of Philosophy.




Roy Cium
Professor of Finance, Insurance, and Real Estate

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of

Doctor of Philosophy.

7- ~2j?;v

Sanfor V. Berg 1Profe sor of Economics

This dissertation was submitted to the Graduate Faculty of the Department of Finance, Insurance, and Real Estate in the College of Business Administration and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy.





Dean, Graduate School

December 1988