There are two asset classes: stocks and bonds. The expected return to stocks is 12% with...
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There are two asset classes: stocks and bonds. The expected return to stocks is 12% with a standard deviation of 22%. The expected return to bonds is 5% with a standard deviation of 8%. The correlation between stocks and bonds is 0.80. Assume your utility function is given by: U = E(r) – 2.5σ2. Given no constraints on investing in stocks or bonds, your utility is highest in which of the following portfolios?
Homework Answers
Solution
Given : return from stock =12%
Standard deviation of stock = 22%
Return from bonds = 5%
Standard deviation of bond = 8%
utility = E(r) -2.5 variance
1) when only stock in the portfolio
Utility = E(r) - 2.5 variance
= 0.12 - 2.5 ( 0.22)^2
= 0.12 - 2.5 (0.0484)
= 0.12 - 0.121
= -0.001 or -0.1%
2) when only bond is used in portfolio
Utility = E(r) - 2.5 variance
= 0.05 - 2.5 (0.08)^2
= 0.05 - 2.5 (0.0064)
= 0.05 - 0.016
= 0.034 or 3.4%
Therefore the utility is highest when the portfolio consists only of bonds.
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