PROBLEM 2. (a) (8 Points) After examining years of daily data on hundreds of US equities, you discover the following relationship between the monthly returns of 3 stocks, S1, S2, and S3: 1 Ri 3 7 R2 + -R3 4 8 200 Find a risk-free portfolio of the three stocks. What should the effective annual risk free rate be? Why? (b) (16 Points) Let R and Rbe the daily return of two equities, and let M1, M2, o and oz be the mean and variance of the returns. If the returns are perfectly correlated, then determine the relationship that governs R and R2. If there are no arbitrage opportunities in the market, determine the risk free rate. Hint: Recall that two random variables R and R2 are perfectly correlated if and only if R1 = ax R2+b, for some constants a + ( and b. Based on the information you have, determine the unknowns a,b. Consider only the cases "a # 1. PROBLEM 2. (a) (8 Points) After examining years of daily data on hundreds of US equities, you discover the following relationship between the monthly returns of 3 stocks, S1, S2, and S3: 1 Ri 3 7 R2 + -R3 4 8 200 Find a risk-free portfolio of the three stocks. What should the effective annual risk free rate be? Why? (b) (16 Points) Let R and Rbe the daily return of two equities, and let M1, M2, o and oz be the mean and variance of the returns. If the returns are perfectly correlated, then determine the relationship that governs R and R2. If there are no arbitrage opportunities in the market, determine the risk free rate. Hint: Recall that two random variables R and R2 are perfectly correlated if and only if R1 = ax R2+b, for some constants a + ( and b. Based on the information you have, determine the unknowns a,b. Consider only the cases "a # 1