5. (27pts) An insurance company collects 100 million USD from insurance premiums and needs to decide how to invest the money. Suppose there is a bond fund (B), a stock fund (S) and a risk-free asset to consider. Their statistics are given below. mean Table 3: Mean returns, volatilies, correlation and the risk-free rate (rf) volatility Bond 4% 10% Stock 12% 25% correlation 0.15 1% rf (1) (10pts) Find the optimal risky portfolio for the insurance company. (2) (7pts) Suppose the insurance company cannot invest more than 20% in the stock fund and it hopes to achieve a mean return as high as possible. What is the complete portfolio? (3) (5pts) Suppose the bond fund invests in two bonds: a 1-year zero coupon bond and a 4-year coupon bond (annual coupon with 5% coupon rate). The current YTM for both equals 6% and the pro- portions of the two bonds are 30% and 70%, respectively. What is the duration of the bond fund? (4) (5pts) Suppose the yield suddenly increases 1% and there is no change in the stock fund value and in the value of the risk-free asset. What is the approximate change in the value of the complete portfolio held by the insurance company? 5. (27pts) An insurance company collects 100 million USD from insurance premiums and needs to decide how to invest the money. Suppose there is a bond fund (B), a stock fund (S) and a risk-free asset to consider. Their statistics are given below. mean Table 3: Mean returns, volatilies, correlation and the risk-free rate (rf) volatility Bond 4% 10% Stock 12% 25% correlation 0.15 1% rf (1) (10pts) Find the optimal risky portfolio for the insurance company. (2) (7pts) Suppose the insurance company cannot invest more than 20% in the stock fund and it hopes to achieve a mean return as high as possible. What is the complete portfolio? (3) (5pts) Suppose the bond fund invests in two bonds: a 1-year zero coupon bond and a 4-year coupon bond (annual coupon with 5% coupon rate). The current YTM for both equals 6% and the pro- portions of the two bonds are 30% and 70%, respectively. What is the duration of the bond fund? (4) (5pts) Suppose the yield suddenly increases 1% and there is no change in the stock fund value and in the value of the risk-free asset. What is the approximate change in the value of the complete portfolio held by the insurance company