Please show the math and how you got the answer so I can work through it myself.
ID: 2613126 • Letter: P
Question
Please show the math and how you got the answer so I can work through it myself.
Consider the following capital market: a risk-free asset yielding 1.00% per year and a mutual fund consisting of 65% stocks and 35% bonds. The expected return on stocks is 11.75% per year and the expected return on bonds is 4.25% per year. The standard deviation of stock returns is 36.00% and the standard deviation of bond returns 11.50%. The stock, bond and risk-free returns are all uncorrelated.
1. What is the expected return on the mutual fund?
2. What is the standard deviation of returns for the mutual fund?
Now, assume the correlation between stock and bond returns is 0.40 and the correlations between stock and risk-free returns and between the bond and risk-free returns are 0 (by construction, correlations with the risk-free asset are always zero).
3. What is the standard deviation of returns for the mutual fund? Is it higher or lower than the standard deviation found in part 2? Why?
Now, assume that the standard deviation of the mutual fund portfolio is exactly 26.50% per year and a potential customer has a risk-aversion coefficient of 2.50.
4. What correlation between the stock and bond returns is consistent with this portfolio standard deviation?
5. What is the optimal allocation to the risky mutual fund (the fund with exactly 26.50% standard deviation) for this investor?
6. What is the expected return on the complete portfolio?
7. What is the standard deviation of the complete portfolio?
8. What is the Sharpe ratio of the complete portfolio?
Explanation / Answer
1) A B C Mutual Fund Portfolio Weights Expected Return Expected mutual fund return (A x B) Stocks 65% 11.75% 7.637500% Bonds 35% 4.25% 1.487500% The expected return on the mutual fund is 9.125000% 2) Standard deviation of returns for the mutual fund A B C D E Mutual Fund Portfolio Weights Expected Return Deviation From mutual fund's expected Return; B- 9.125% Squared Deviation weights x Squared Deviation Stocks 65% 11.75% 2.625% 0.069% 0.045% Bonds 35% 4.25% -4.875% 0.238% 0.083% Variance 0.128% Standard Deviation 3.577%