4. Evenl-Slwly Analysis

There can also be an upward bias in cumulative abnormal returns when these are calculated in the usual way. The bias arises from the observatiou-by-observation rebalancing to equal weights implicit in the calculation of the aggregate cumulative abnormal return combined with the use of trans-action prices which can represent both the bid and the ask side of the J£. market. Blume and Stambaugh (1983) analyze this bias and show that it can be important for studies using low-markcl-capiralization firms which 2L have, in percentage terms, wide bid-ask spreads. In these cases the bias can be eliminated by considering cumulative abnormal returns that represent 3c buy-and-hold strategies.

4.10 Conclusion

In clcsing, we briefly discuss examples of event-study successes and limitations. Perhaps the most successful applications have been in the area of corporate finance. Event studies dominate the empirical research in this area. Important examples include the wealth effects of mergers and acquisitions and the price effects of financing decisions by firms. Studies of these events- typically Tocus on the abnormal return around the dale of the first annul nccment.

In the 1960s there was a paucity of empirical evidence on the wealth effects? of mergers and acquisitions. For example, Manne (1965) discusses the various arguments for and against mergers. Al that time the debate centered On the extent lo which mergers should be regulaled in order to foster competition in the product markets. Marine argues that mergers represent a natural outcome in an efficiently operating market for corporate control and consequently provide protection for shareholders. He downplays the importance of the argument thai mergers reduce competition. At the conclusion of his article Manne suggests that the two competing hypotheses for mergers could be separated by studying the price effects of the involved corporations. He hypothesizes that if mergers created market power one-would observe price increases for both the target and acquirer. In contrast if the merger represented the acquiring corporation paying for control of the target, one would observe a price increase for the target only and not for the acquirer. However, at that time Manne concludes in reference to the price effects of mergers that ... no data arc presently available on this subject.

Since that time an enormous body of empirical evidence on mergers and acquisitions has developed which is dominated by the use of event studies. The general result is that, given a successful takeover, the abnormal returns of the targets are large and positive and the abnormal returns of the acquirer are close to zero. Jarrcll and Poulsen (1989) find that the average abnormal

4.10. Conclusion

return for target shareholders exceeds 20% for a sample of 663 successful takeovers from 1960 to 1985. In contrast die abnormal return for acquirers is close to zero at 1.14%, and even negative at - 1.10% in the 1980s.

Eckbo (1983) explicitly addresses the role of increased market power in explaining merger-related abnormal returns. He separates mergers of competing firms from other mergers and finds no evidence that the wealth effects for competing (inns are different. Further, he finds no evidence that rivals of firms merging horizontally experience negative abnormal returns. From this he concludes that reduced competition in the product market is not an important explanation Tor merger gains. This leaves competition for corporate control a more likely explanation. Much additional empirical work in the area of mergers and acquisitions has been conducted. Jensen and Ruback (1983) ami Jarrcll, Brickley.and Netler (1988) provide detailed

surveys of this work.

A number of robust results have been developed from event studies of financing decisions by corporations. When a corporation announces ifiqi it will raise capilal in external markets there is on average a negative abnormal return. The magnitude of the abnormal return depends on die source of external financing. Asquilh and Mullins (1986) study a sample of 266 firms announcing an equity issue in the period 1963 to 1981 and find that the two-day average abnormal return is -2.7%, while on a sample of 80 firms for the period 1972 to 1982 Mikkelson and Partch (1986) find that the two-day average abnormal return is -3.56%. In contrast, when linns decide lo use straight debt financing, the average abnormal return is closer lo zero. Mikkelson and Partch (1986) find ihe average abnormal return for debt issues to be -0.23% for a sample of 171 issues. Findings such as these provide the fuel for the development of new theories. For example, these external financing results motivate the pecking order theory of capital structure developed by Myers and Majltif (1984).

A major success related to those in the corporate finance area is the implicit acceptance of event-study methodology by the U.S. Supreme Court for determining materiality in insider trading cases and for determining appropriate disgorgement amounts in cases of fraud. This implicit acceptance in the 1988 Basic, Incorporated v. l.evinson case and its importance for securities law is discussed in Mitchell and Netler (1994).

There have also been less successful applications of event-study methodology. An important characteristic of a successful event study is the ability to identify precisely the date of the event. In cases where die dale is difficult to identify or the event is partially anticipated, event studies have been less useful. For example, the wealth effects of regulatory changes for affected entities can be difficult lo delect using event-study methodology. The problem is that regulatory changes are often debated in the political arena over time and any accompanying wealth effects will be iueoiporatcd gradually into

/. Eveul-Sliuly Analysis

ihf value of a corporation as tin- probability of the change being adopted increases.

Dann and James (1982) discuss litis issue in their study of the impact of deposit interest tale ceilings on thrift institutions. They look, at changes in rale ceilings, bin decide not lo consider a change in 197.3 because il was due lo legislative action and hence was likely lo have been anticipated by the market. Schipper and Thompson (1083, 1085) also encounter this problem in a study of merger-ielated regulations. They attempt lo circumvent the problem of anticipated regulatory changes by identifying dates when the probability of a regulatory change increases or decreases. However, they find largely insignificant results, leaving open the possibility thai the absence of distinct event dates accounts for the lack of wealth effects.

Much has been learned from the body of research that uses event-study methodology. Most generally, event studies have shown that, as we would expect in a rational marketplace, prices do respond to new information. We expect thai even I studies will continue lo be a valuable and wirlely used tool in economics and finance.

IVoblcms-Chapter 4

4.1 Show that when using the market model lo measure abnormal returns, the sample abnormal returns from equation (4.4.7) are asymptotically independent as the length of ihe estimation window (/.) increases to infinity.

4.2 You are given the following information for an event. Abnormal returns are sampled at an interval of one day. The event-window length is three days. The mean abnormal return over the event window is 0.3% per day. You have a sample of 50 event observations. The abnormal returns are independent across the event observations as well as across event days for a given event observation. For 25 of the event observations lite daily standard deviation of the abnormal return is 3% and for the remaining 25 observations die daily standard deviation is 0%. (liven this information, what would be the power of the test for an event study using the cumulative abnormal return test statistic in equation (4.1.22)? What would be the power using the standardized ctimulalive abnormal return test statistic in equation (4.4.24)? For the power calculations, assume the standard deviation of the abnormal returns is known.

4.3 What would be the answers to question 4.2 if the mean abnormal return is 0.0% per day for the 25 linns wilh the larger standard deviation?

The Capital Asset Pricing Model

ONE OF THE IMPORTANT PROBLEMS of modern financial economics is [the quantification of the tradeoff between risk and expected return. Although common sense suggests that risky investments such as the stock market will generally yield higher returns than investments free of risk, it was only vjpth thedevelopmentof the Capital Asset PricingModel (CAPM) that economists were able to quantify risk and the reward for bearing it. The CAPM implies that the expected return of an asset must be linearly related to the covariance of its return with the return of the market portfolio. In this chapter we discuss the econometric analysis of this model.

The chapter is organized as follows. In Section 5.1 we briefly review the CAPM. Section 5.2 presents some results from efficient-set mathematics, including those that are important for understanding the intuition of econometric tests of the CAPM. The methodology for estimation and testing is presented in Section 5.3. Some tests are based on large-sample statistical theory making the size of the test an issue, as we discuss in Secdon 5.4. Section 5.5 considers the power of the tests, and Section 5.6 considers testing with weaker distributional assumptions. Implementation issues are covered in Section 5.7, and Section 5.8 considers alternative approaches to testing based on cross-sectional regressions.

5.1 Review of the CAPM

Markowitz (1959) laid the groundwork for the CAPM. In this seminal research, he cast the investors portfolio selection problem in terms of expected return and variance of return. He argued that investors would optimally hold a mean-variance efficient portfolio, that is, a portfolio with the highest expected return for a given level of variance. Sharpe (1964) and Limner (1965b) built on Markowitzs work to develop economy-wide implications. They showed that if investors have homogeneous expectations

5. The Capital Asset Pricing Model

avid optimally hold mean-variance efficient portfolios then, in the absence ormarkct frictions, the portfolio of all invested wealth, or the market portfolio, will itself be a mean-variance efficient portfolio. The usual CAPM equation is a direct implication of the mean-variance efficiency of the market portfolio.

The Sharpe and 1 .miner derivations of the CAPM assume the existence of lending and borrowing at a riskfree rate of interest. For ibis version of the CAPM we have for the expected return of asset i,

E[Kj] = Rj + fiWJ -Rj)

(5.1.1)

Cov[/i /{, Var[/(, ]

(5.1.2)

where Rn is the return on the market portfolio, and R, is the return on the ris dree asset. The Sharpe-Lintner version can be most compactly expressed in terms of returns in excess of this riskfree rate or in terms of excess returns. Щ represent the return on the jth asset in excess of the riskfree rate, Zi t= It, - Rj. Then for the Sharpe-I.intner CAPM we have

E[Z,1 = pimE[/.m} Cov[/ /.,

Pim =

Yar[Z, ]

(5.1.3) (5.1.4)

where Z is the excess return on the market portfolio of assets. Because the riskfree rale is treated as being nonstochastic, equations (5.1.2) and (5.1.4) are equivalent. In empirical implementations, proxies for the riskfree rale are stochastic and thus the betas can difTcr. Most empirical work relating to the Sharpe-Lintner version employs excess returns and thus uses (5.1.4).

Empirical tests of the Sharpe-Lintner CAPM have focused on three implications of (5.1.3): (1) The intercept is zero; (2) Beta completely captures the cross-sectional variation of expected excess returns; and (3) The market risk premium, E[Zm] is positive. In much of this chapter we will focus on the first implication; the last two implications will be considered later, in Section 5.8.

ln the absence of a riskfree asset, Black (1972) derived a more general version of the CAPM. In this version, known as ihe Black version, the expected return of asset i in excess of the zero-beta return is linearly related to its beta. Specifically, for the expected return of asset i, Е[Л,1, we have

= E[/t,J-f-A (E[ ]-E[/<,j).

(5.1.5)

R is the return on the market portfolio, and R is the return on the zero-beta portfolio associated with m. This portfolio is defined to be the portfolio that has the minimum variance of all portfolios uncorrelated with m. (Any

5.1. Review of Ihe CAPM

other uncorrelated portfolio would have the same expected return, but a higher variance.) Since il is wealth in real terms that is relevant, for the Black model, returns are generally staled on an inllalion-adjusted basis and /), , is defined in terms of real returns,

Cov/<,. H, \

P, = ---- (5.1.(i)

Var [R, \

Econometric analysis of the Black version of the (АРМ treats the zero-beta portfolio return as an unobserved quantity, making the analysis more complicated than that of the Sharpe-Lintner version, flic Black version can be tested as a restriction on the real-return market model. For the real-return market model we have

VARA = c + fi Y.[IU. V5-1-7)

and the implication of the Black version is

ot,m = Kl/Ud -P.. ) V i. (5.1.8)

In words, the Black model restricts the asset-specific intercept of the real-return market model to be equal to the expected zero-beta portfolio return times one minus the assets beta.

The CAPM is a single-period model; hence (5.1.3) and (5.1.5) do not have a lime dimension. For econometric analysis ol the model, it is necessary to add an assumption concerning the time-series behavior of returns and estimate the model over time. We assume that returns are independently and identically distributed (IID) through time and jointly multivariate normal. This assumption applies to excess returns for the Sharpe-Lintner version and to real returns for ihe Black version. While the assumption is strong, it has the benefit of being theoretically consistent with the CAPM holding period by period; il is also a good empirical approximation for a monthly observation interval. Wc will discuss relaxing this assumption in Section 5.(3.

The CAPM can be useful for applications requiring a measure of expected slock returns. Some applications include cost of capital estimation, portfolio performance evaluation, and cvenl-sludy analysis. As an example, we briefly discuss ils use for estimating the cost of capilal. The cost ol equity capital is required for use in corporate capilal budgeting decisions and in the determination of a fair rate ol return for regulated utilities. Implementation of the model requires three inputs: the stocks beta, the market risk premium, and the riskfree return. The usual estimator of beta ol die equity is the OLS estimator of the slope coefficient in the excess-return market model, that is, the beta in the regression equation

/.il = II + P /-ml + f

(5.1.9)