Capital Allocation
Problem
Consider the following capital market: a risk-free asset
yielding 1.50% per year and a mutual fund consisting of 60% stocks and 40%
bonds. The expected return on stocks is 9.50% per year and the expected return
on bonds is 3.25% per year. The standard deviation of stock returns is 28.00%
and the standard deviation of bond returns 8.00%. 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 0.55 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 15.00% per year and a potential customer has a
risk-aversion coefficient of 3.0.
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 15.00% 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?
Problem is
solved in Excel.
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