Assume that the CAPM holds, in which case, the return on any asset i can be written

as: ri = rf + i(rm - rf) + i

where rf is the risk-free rate, rm is the return on the market portfolio, and i is the

idiosyncratic (i.e. firm-specific) return, with E(i) = 0. Assume that the risk-free rate is

constant, and that the firm-specific return is uncorrelated with both the market return

and the firm-specific return of any other asset. There are N risky assets in the

economy. Denote by and 2 the expected excess return and the variance of the

excess return of the market portfolio.

a) Show that the expected return and the systematic risk of any portfolio in this economy depends only on three variables: its market beta , and 2 . Also, If P is an efficient frontier portfolio with market beta equal to , explain why P has the least idiosyncratic risk among all portfolios with market beta equal to .