Chapter 13 Efficient Markets and Behavioral Finance 333
bre44380_ch13_327-354.indd 333 09/11/15 07:55 AM
returns are random, the variance of these returns should increase in proportion to the interval
over which the returns are measured. So the variance of two-day returns should be twice the
variance of one-day returns; the variance of annual returns should be 12 times the variance of
monthly returns; and so on.^5 This is not a bad approximation and one that we use several times
in this book. But it may not be quite true. For example, the variance of two-month returns
seems to be slightly larger than two times the variance of monthly returns, which suggests that
stock prices exhibit some short-term momentum. For intervals beyond, say, a year, the oppo-
site appears to be true and price changes seem to have a tendency to reverse.^6
To test for semistrong efficiency, researchers have measured how rapidly security prices
respond to different items of news, such as earnings or dividend announcements, news of a
takeover, or macroeconomic information. Before we describe what they found, we should
explain how to isolate the effect of an announcement on the price of a stock. Suppose, for
example, that you need to understand how stock prices of takeover targets respond when the
takeovers are first announced. As a first stab, you could simply calculate the average return
on target-company stocks in the days leading up to the announcement and immediately after
it. With daily returns on a large sample of targets, the average announcement effect should be
clear. There won’t be too much contamination from movements in the overall market around
the announcement dates, because daily market returns average out to a very small number.^7
The potential contamination increases for weekly or monthly returns, however. Thus you will
usually want to adjust for market movements. For example, you can simply subtract out the
return on the market:
Adjusted stock return = return on stock − return on market indexChapter 8 suggests a refined adjustment based on betas. (Just subtracting the market return
assumes that target-firm betas equal 1.0.) This adjustment is called the market model:
Expected stock return = α + β × return on market indexAlpha (α) states how much on average the stock price changed when the market index was
unchanged. Beta (β) tells us how much extra the stock price moved for each 1% change in
the market index.^8 Suppose that subsequently the stock price return is ̃r in a month when the
market return is ̃r (^) m. In that case we would conclude that the abnormal return for that month is
Abnormal stock return = actual stock return − expected stock return
= ̃r − (α + β ̃r (^) m)
This abnormal return should reflect firm-specific news only.^9
(^5) This is true only if returns are continuously compounded, so that the two-day return equals the sum of the two one-day returns.
(^6) See, for example, J.M. Poterba and L.H. Summers, “Mean Reversion in Stock Prices: Evidence and Implications,” Journal of Finan-
cial Economics 22 (October 1988), pp. 27–60.
(^7) Suppose, for example, that the market return is 12% per year. With 250 trading days in the year, the average daily return is
(1.12)1/250 – 1 = .00045, or .045%.
(^8) It is important when estimating α and β that you choose a period in which you believe that the stock behaved normally. If its
performance was abnormal, then estimates of α and β cannot be used to measure the returns that investors expected. As a precau-
tion, ask yourself whether your estimates of expected returns look sensible. Methods for estimating abnormal returns are analyzed
in A. C. MacKinlay, “Event Studies in Economics and Finance,” Journal of Economic Literature 35 (1997), pp. 13–39; and also
S. P. Kothari and J. B. Warner, “Econometrics of Event Studies,” in B. E. Eckbo (ed.), The Handbook of Empirical Corporate Finance
(Amsterdam: Elsevier/North-Holland, 2007), Chapter 1.
(^9) Abnormal returns are also often calculated using the Fama-French three-factor model, which we discussed in Chapter 8. The stock
return is adjusted for the market return, the difference between small- and large-stock returns, and the difference between returns on
high and low book-to-market firms.