to the market will still be a useful risk measure. In fact, several authors have shown that modified versions of the CAPM will hold true even if we consider differences among individuals leading them to hold different portfo- lios. For example, Brennan9 examined the impact of differences in investors personal tax rates on market equilibrium, and Mayers10 looked at the impact of nontraded assets such as human capital (earning power). Both found that although the market portfolio is no longer each investors optimal risky portfolio, the expected return-beta relationship should still hold in a somewhat modified form. If the expected return-beta relationship holds for any individual asset, it must hold for any combination of assets. Suppose that some portfolio P has weight wk for stock k, where k takes on values 1, . . . , n. Writing out the CAPM equation 9.7 for each stock, and multi- plying each equation by the weight of the stock in the portfolio, we obtain these equations, one for each stock:   w1E(r1) w1rf w1 1[E(rM) rf]   w2E(r2) w2rf w2 2[E(rM) rf] . . . . . .   wnE(rn) wnrf wn n[E(rM) rf]   E(rP) rf P[E(rM) rf]   Summing each column shows that the CAPM holds for the overall portfolio because E(rP) wk E(rk) is the expected return on the portfolio, and P wk k is the portfolio beta. k k Incidentally, this result has to be true for the market portfolio itself,   E(rM) rf M[E(rM) rf]   Indeed, this is a tautology because M 1, as we can verify by noting that     M   Cov(rM, rM) 2 2 2 M M   This also establishes 1 as the weighted average value of beta across all assets. If the market beta is 1, and the market is a portfolio of all assets in the economy, the weighted average     9 Michael J. Brennan, "Taxes, Market Valuation, and Corporate Finance Policy," National Tax Journal, December 1973. 10 David Mayers, "Nonmarketable Assets and Capital Market Equilibrium under