Problem
Stock X provides 10% rate of return and the standard deviation of the rate of return is 30%. Stock Y provides 15% return but is riskier as its standard deviation is greater at 45%. The correlation coefficient between X and Y is known to be -0.4. Investors can also borrow at the interest rate of 4% with no limit.
I. Using EXCEL find the optimal portfolio of X and Y (and the risk-free asset) that provides the best return per risk-taken for the investors. Calculate the Sharpe Ratio at that optimal portfolio and explain what it means.
II. If an investor borrows money at 4% interest rate and invests in the market portfolio, what is the rate of return and risk of the investment. Please assume that the borrowed money is twice the size of own investment.
Now armed with this information, you can help the following two people. Provide advice.
I. Mr. Ash is very risk-averse but he is not totally happy with 4% return from the safe asset he owns. He is willing to take some risk to increase the return of his portfolio to 7%. What would be your advice to Mr. Ash?
II. Ms. Bee is risk-averse but he is not afraid of taking some risk as long as his risk-taking is rewarded handsomely. Right now, he is trying to find a way to get 16% return with minimum possible risk. Explain in detail how Ms. Bee can achieve 16% return while minimizing the risk.