Determine the following capital market: a risk-free asset yielding of 0.75% per year and a mutual fund consisting of the 30% bonds and 70% stocks. The expected return on the stocks is 10.75% per year and expected return on bonds is 3.25% per year. The standard deviation of the stock returns is 30.00% and standard deviation of the bond returns 8.75%. The stock, bond and risk-free returns are all uncorrelated.
1. Determine the expected return on the mutual fund?
2. Determine the standard deviation of returns for the mutual fund?
Now, assume the correlation among bond and stock returns is 0.45 and the correlations among stock and the risk-free returns and among the bond and the risk-free returns are 0 (by construction, correlations with the risk-free asset are always zero).
3. Determine the standard deviation of returns for 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 20.25% per year and a potential customer has a risk-aversion coefficient of 2.25.
4. Explain what correlation among the stock and the bond returns is consistent with this portfolio standard deviation?
5. Determine the optimal allocation to the risky mutual fund (the fund with exactly 20.25% standard deviation) for this investor?
6. Determine the expected return on the complete portfolio?