Investments, tenth edition

 Empirical  Evidence 

on Security Returns 

1

 Actually, prices will show an upward drift since expected rates of return are positive. But over short time horizons, this drift is 

trivial compared to volatility. For example, at a daily horizon, the expected rate of return is around 5 basis points (corresponding to 

an annual return of 12%). The daily standard deviation of stock prices is an order of magnitude higher, typically exceeding 2% for 

individual stocks. 

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     13.1 

The Index Model and the Single-Factor APT 

be a conclusive test of the CAPM. In any sample, 

there always is an ex-post efficient portfolio 

that will never be identical to the index. How 

do we measure “distance from efficiency,” and 

what would constitute a rejection of the model? 

Given these difficulties, the mean-beta equa-

tion has been the test arena of most research. 

However, most of these tests are better inter-

preted as tests of the APT (rather than the 

CAPM) since we know from the outset that the 

index may not be mean-variance efficient but 

may nevertheless be well-diversified. 

 We begin with tests of the single-factor security 

market line, the theater where the basic meth-

odologies have been developed, and then pro-

ceed to multifactor models with emphasis on the 

empirically motivated Fama-French three-factor 

model. We show how this research may be inter-

preted as tests of Merton’s multifactor ICAPM. We 

end this part of the chapter with a section that 

brings liquidity into the empirical framework. We 

devote a section to the theoretically appealing 

consumption CAPM in order to present the equity 

premium puzzle, and end with an assessment of 

where research into asset  pricing is headed.