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Two risky assets have return rates r1, r2 that are random variables with expected values r_bar1 and r_bar2, respectively. Let [sigma_1,1 sigma_1,2; sigma_2,1 sigma_2,2] be the matrix of covariances. Because sigma_1,2 = E[(r1 - r_bar1)(r2 - r_bar2)] and sigma_2,1 = E[(r2 - r_bar2)(r1 - r_bar1)], (1) sigma_2,1 = sigma_1,2. Consider the portfolio composed of these two assets with weights w1, w2. Then the variance of the portfolio is (2) sigma_P^2 = ?_{i=1}^2 ?_{j=1}^2 sigma_{i,j} w_i w_j = (Use (1) to replace sigma_2,1 with sigma_1,2, so your answer should not involve sigma_2,1. Type sigma_1,1 as sg11, sigma_1,2 as sg12, sigma_2,2 as sg22, w1 as w1, w2 as w2. ) The expected return rate for the portfolio is (3) r_bar_P = (Type r_bar1 as rb1, r_bar2 as rb2.) Let rf be the return rate for a risk-free asset. The portfolio F of the one fund theorem, is the combination of risky assets that maximizes (4) (r_bar_P - rf) / sigma_P subject to the constraint

          Two risky assets have return rates r1, r2 that are random variables with expected values r_bar1 and r_bar2, respectively. Let [sigma_1,1 sigma_1,2; sigma_2,1 sigma_2,2] be the matrix of covariances. Because sigma_1,2 = E[(r1 - r_bar1)(r2 - r_bar2)] and sigma_2,1 = E[(r2 - r_bar2)(r1 - r_bar1)], (1) sigma_2,1 = sigma_1,2. Consider the portfolio composed of these two assets with weights w1, w2. Then the variance of the portfolio is (2) sigma_P^2 = ?_{i=1}^2 ?_{j=1}^2 sigma_{i,j} w_i w_j = (Use (1) to replace sigma_2,1 with sigma_1,2, so your answer should not involve sigma_2,1. Type sigma_1,1 as sg11, sigma_1,2 as sg12, sigma_2,2 as sg22, w1 as w1, w2 as w2. ) The expected return rate for the portfolio is (3) r_bar_P = (Type r_bar1 as rb1, r_bar2 as rb2.) Let rf be the return rate for a risk-free asset. The portfolio F of the one fund theorem, is the combination of risky assets that maximizes (4) (r_bar_P - rf) / sigma_P subject to the constraint

Two risky assets have return rates r1, r2 that are random variables with expected values rbar1 and rbar2, respectively. Let [sigma1,1 sigma1,2; sigma2,1 sigma2,2] be the matrix of covariances. Because sigma1,2 = E[(r1 - rbar1)(r2 - rbar2)] and sigma2,1 = E[(r2 - rbar2)(r1 - rbar1)], (1) sigma2,1 = sigma1,2. Consider the portfolio composed of these two assets with weights w1, w2. Then the variance of the portfolio is (2) sigmaP^2 = ?i=1^2 ?j=1^2 sigmai,j wi wj = (Use (1) to replace sigma2,1 with sigma1,2, so your answer should not involve sigma2,1. Type sigma1,1 as sg11, sigma1,2 as sg12, sigma2,2 as sg22, w1 as w1, w2 as w2. ) The expected return rate for the portfolio is (3) rbarP = (Type rbar1 as rb1, rbar2 as rb2.) Let rf be the return rate for a risk-free asset. The portfolio F of the one fund theorem, is the combination of risky assets that maximizes (4) (rbarP - rf) / sigmaP subject to the constraint

Added by Kathryn P.

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