Investments, tenth edition

  SOLUTIONS TO CONCEPT CHECKS 

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13 

1

 P

AR

T III 

  IN THIS CHAPTER, 

we turn to the vast liter-

ature testing models of risk and return. The 

very existence of such a vast literature sug-

gests a serious problem is involved— testing 

these models is not trivial. Indeed, an impor-

tant part of the work here is to understand 

the challenges in doing so. 

 All models of capital asset pricing have two 

parts. First, they derive the optimal portfo-

lio of an individual investor, conditional on 

a utility function (describing how an investor 

trades off risk against expected return) and 

an input list that includes estimates of port-

folio expected returns and risk. Second, they 

derive predictions about expected returns on 

capital assets in equilibrium, when investors 

complete the trades necessary to arrive at 

their personal optimal portfolios. 

 Obviously, the flow of new information 

alone will change input lists and thus desired 

portfolios. Here is where the efficient mar-

ket hypothesis (EMH) kicks in. If asset prices 

reflect all available information, then  changes

of asset prices resulting from new informa-

tion will have zero means, that is, prices will 

follow random walks.  

1

   The response to new 

information will introduce noise around the 

predictions of the model, but by itself this 

should not cause any difficulty that cannot be 

overcome with appropriate statistical meth-

ods and lots of data. But when the EMH is 

off, even temporarily, by economically signifi-

cant margins, changes in prices and expected 

returns will not change randomly and model 

predictions can be affected. This is why a test 

of an asset pricing model is of necessity a joint 

test of the EMH.  

 The single-factor CAPM has one key impli-

cation that can be expressed in either of two 

ways: The market portfolio is mean-variance 

efficient, and (equivalently) the risk premium 

(expected excess return) on each individual 

asset is proportional to its beta,  E ( R  

 i 

 )  5   b  

 i 

  E ( R  

 M 

 ). 

The first statement is, in practice, untestable 

because we do not observe the market port-

folio. However, if a broad index is sufficiently 

well diversified, even if not mean-variance 

efficient, it may nevertheless support the 

mean-beta relationship (the SML) using the 

arguments of the APT. 

 Testing the ex-ante mean-variance effi-

ciency of a particular market index can never 

 CHAPTER THIRTEEN