. Lintner's Derivation Lintner (1965) presented another derivation of the CAPM. Given the investment opportunity set (un

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Lintner S Derivation Lintner 1965 Presented Another Derivation Of The Capm Given The Investment Opportunity Set Un 1 (82.69 KiB) Viewed 60 times

. Lintner's Derivation Lintner (1965) presented another derivation of the CAPM. Given the investment opportunity set (under the curve ABF) containing all risky assets, and, the risk-free asset illustrated in Figure A12.1, wealth-maximizing investors will want to maximize the slope of the straight line passing through the risk-free rate of return, rf. Elp) F m Slopen > Slopes > Slopes B FIGURE A12.1 Combining the Risk-free Asset with Risky Assets Given that the objective function is given by Maximize 0 = E ["p] - ri op a) Show that the covariance between portfolio p and security i can be written as P 72 Oip = w;8? + W; j = 1 ji b) Show that the solution to the maximization problem is equivalent to finding the simultaneous solution of the following n simultaneous equations 72 --- ཙ བདས ་ 1 Ә0, dwi = 0, for i = 1,2,...,n, Op E [ra] – ry-wio? + W;dij j = 1 iti where [E["p]=r;] c) Show that if the portfolio p equals the market portfolio m, then we have E [r:] - r;= B; CE [Nm] – rj] where Bi 0