If the correlation is.5. the 0252-0.5×0.15×0.25 0.152+0252-2×0.5×0.15×0 therefore the minimum variance portfolio consists of 92. 1% aT&T stock and 7.9% Microsoft stock b. Expected return of the minimum variance portfolios: 10.87% Variance of the minimum variance portfolios: 0.2222 c. The weight of investment in AT&T (asset 1)of the optimal portfolio is calculated using -rk2-(k- -2+-2-(-+-1 If the correlation is 0.5. then (0.10-0045)×0.252-(0.21-0045)×0.5×0.15×025 (0.10-0045)×0252+(021-045)×0.152-(010+021-2×0045)×005×0.5×025 =114% therefore the optimal portfolio consists of 11. 4% at&T stock and 88.6% Microsoft stock d. Variance of the optimal portfolios: 0.0531 Expected returns of the optimal portfolios: 19.75 e. Risk-return(reward) trade-off line for optimal portfolio with correlation equal to 0.5 F=0.045+0.1975-0045 05310,=0045+066p and the extra expected return for an extra unit of risk(1% standard deviation) is 0.66% Question 4 a. Impossible. Since the expected risk premium on the market portfolio is positive, a security with a higher beta must have a higher expected return ◎徐信忠 MBA公司财务学© 徐信忠 MBA 公司财务学 4 If the correlation is 0.5, then 92.1% 0.15 0.25 2 0.5 0.15 0.25 0.25 0.5 0.15 0.25 2 2 2 min = + −    −   w = , therefore the minimum variance portfolio consists of 92.1% AT&T stock and 7.9% Microsoft stock. b. Expected return of the minimum variance portfolios: 10.87% Variance of the minimum variance portfolios: 0.2222 c. The weight of investment in AT&T (asset 1) of the optimal portfolio is calculated using: ( ) ( ) ( ) ( ) ( ) 1 2 12 1 2 2 2 1 2 1 2 2 12 1 2 2 1 2 1          f f f f f f r r r r r r r r r r r r w − + − − − + − − − − = If the correlation is 0.5, then ( ) ( ) ( ) ( ) ( ) 11.4% 0.10 0.045 0.25 0.21 0.045 0.15 0.10 0.21 2 0.045 0.05 0.15 0.25 0.10 0.045 0.25 0.21 0.045 0.5 0.15 0.25 2 2 2 1 = −  + −  − + −     −  − −    w = , therefore the optimal portfolio consists of 11.4% AT&T stock and 88.6% Microsoft stock. d. Variance of the optimal portfolios: 0.0531 Expected returns of the optimal portfolios: 19.75 e. Risk-return(reward) trade-off line for optimal portfolio with correlation equal to 0.5 is: P P P r  0.045 0.66 0.0531 0.1975 0.045 0.045 = + − = + and the extra expected return for an extra unit of risk (1% standard deviation) is 0.66%. Question 4 a. Impossible. Since the expected risk premium on the market portfolio is positive, a security with a higher beta must have a higher expected return. b. Possible