Investments, tenth edition

  The Risk Premium of the Market Portfolio 

 In Chapter 6 we discussed how individual investors go about deciding capital allocation. 

If all investors choose to invest in portfolio  M  and the risk-free asset, what can we deduce 

about the equilibrium risk premium of portfolio  M  ?

 Recall that each individual investor chooses a proportion  y,  allocated to the optimal 

portfolio  M,  such that

 

   y

5

E

 

(

 

r

M

 

)

2 r

f

As

M

2

 

 (9.1)  

where  E ( r  

 M 

 )   2     r  

 f 

      5     E ( R  

 M 

 ) is the risk premium (expected excess return) on the market 

portfolio. 

 If there are only a few investors who perform 

security analysis, and all others hold the market 

portfolio,  M,  would the CML still be the efficient 

CAL for investors who do not engage in security 

analysis? Why or why not? 

 CONCEPT CHECK 

9.1 

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6/21/13   3:39 PM

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 In the simplified CAPM economy, risk-free investments involve borrowing and lend-

ing among investors. Any borrowing position must be offset by the lending position of 

the creditor. This means that net borrowing and lending across all investors must be zero, 

and therefore, substituting the representative investor’s risk aversion, A, for  A,  the average 

position in the risky portfolio is 100%, or    y

5 1.  Setting  y   5  1 in Equation 9.1 and rear-

ranging, we find that the risk premium on the market portfolio is related to its variance by 

the average degree of risk aversion:

 

   E

 

(

 

R

M

 

)

5 As

M

2

 

 (9.2)