1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a risk-free rate of 2%. The probability distributions of the risky funds are: I Stock funds (S) Bond funds (B) Expected Return 12% 5% Standard Deviation 15% 8% The correlation coefficient between the returns of stock funds and bond funds, Pes, is 0.1 a. You invest 50% in the T-bill money market fund and 50% in the bond fund. What is your expected return and standard deviation? b. You invest 50% in the stock fund and 50% in the bond fund. What is your expected return and standard deviation? c. You invest only in the stock fund and bond fund. You want an expected return of 8%. What is the standard deviation of your portfolio? d. You invest in all three funds. Use the formula below to compute the optimal portfolio weights. What is the sharp ratio of the best CAL? You manage $1000 for your client and your client wants an expected return of 8%. How much money do you invest in each of the three funds? [E (rp) - ry]o - [E(rs) roosPes [E(TB) r,]os + [E(rs) r, 10% - [E(rp) ry +E(rs) r; JOBOsPes Ws = 1-W e. Is the standard deviation of your complete portfolio from d) higher or lower than that in c). Show where your portfolios in c) and d) are on the expected return-standard deviation graph. 1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a risk-free rate of 2%. The probability distributions of the risky funds are: I Stock funds (S) Bond funds (B) Expected Return 12% 5% Standard Deviation 15% 8% The correlation coefficient between the returns of stock funds and bond funds, Pes, is 0.1 a. You invest 50% in the T-bill money market fund and 50% in the bond fund. What is your expected return and standard deviation? b. You invest 50% in the stock fund and 50% in the bond fund. What is your expected return and standard deviation? c. You invest only in the stock fund and bond fund. You want an expected return of 8%. What is the standard deviation of your portfolio? d. You invest in all three funds. Use the formula below to compute the optimal portfolio weights. What is the sharp ratio of the best CAL? You manage $1000 for your client and your client wants an expected return of 8%. How much money do you invest in each of the three funds? [E (rp) - ry]o - [E(rs) roosPes [E(TB) r,]os + [E(rs) r, 10% - [E(rp) ry +E(rs) r; JOBOsPes Ws = 1-W e. Is the standard deviation of your complete portfolio from d) higher or lower than that in c). Show where your portfolios in c) and d) are on the expected return-standard deviation graph
