M) will be a combination of T and S, with weights determined by the relative wealth and degrees of risk aversion of the two investors. Since T and S are each on the efficient frontier, so is M (from Property 1). From Property 2, M has a companion zero-beta portfolio on the minimum-variance frontier, Z(M), shown in Figure 9.8. Moreover, by Property 3 we can express the return on any security in terms of M and Z(M) as in equation 9.8. But, since by construction Cov[rM,rZ(M)] 0, the expression simplifies to   E(ri) E[rZ(M)] E[rM rZ(M)] Cov(ri, rM) 2 M   (9.9)   where P from equation 9.8 has been replaced by M and Q has been replaced by Z(M). Equation 9.9 may be interpreted as a variant of the simple CAPM, in which rf has been re- placed with E[rZ(M)]. The more realistic scenario, where investors lend at the risk-free rate and borrow at a higher rate, was considered in Chapter 8. The same arguments that we have just employed can also be used to establish the zero-beta CAPM in this situation. Problem 18 at the end of this chapter asks you to fill in the details of the argument for this situation.     CONCEPT C H E C K ☞ QUESTION 6 Suppose that the zero-beta portfolio exhibits returns that are, on average, greater than the rate on T-bills. Is this fact relevant to the question of the validity of the CAPM?     Lifetime Consumption and the CAPM   One of the restrictive assumptions for the simple version of the CAPM is that investors are myopic-they plan for one common holding period. Investors actually may be concerned III. Equilibrium In Capital Markets 9. The Capital Asset Pricing Model The McGraw−Hill