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Seven & Eight Holdings Co Ltd has an expected rate of return of 26%, and a standard deviation of 21%
Seven & Eight Holdings Co Ltd has an expected rate of return of 26%, and a standard deviation of 21%. The risk-free rate is 3%, and assume investors use the utility function we have studied all semester.
You are the advisor for several clients, for whom you have determined the following values of risk aversion, A:
| Investor | Aversion level |
| Millie | 10.4 |
| Olivia | 5.2 |
| Oliver | 0.5 |
| Benjamin | 8.4 |
| Zoe | 2.2 |
Which client is indifferent between Seven & Eight Holdings Co Ltd and the risk-free asset?
Select one:
a. Oliver
b. Benjamin
c. Olivia
d. Zoe
e. Millie
Expert Solution
For utility of the portfolio we have following equation -
U = E(r) – 0.5A * σ^2
Where E(r) = expected return of Seven & Eight Holdings Co Ltd = 26%
And σ is the standard deviation of Seven & Eight Holdings Co Ltd = 21%
For Millie, risk aversion, A = 10.4
U = 0.26 - 0.5 * 10.4*(0.21) ^2 = 0.03068 or 3.068%
For Olivia, risk aversion, A = 5.2
U = 0.26 - 0.5 * 5.2*(0.21) ^2 = 0.14534 or 14.534%
For Oliver, risk aversion, A = 0.5
U = 0.26 - 0.5 * 0.5*(0.21) ^2 = 0.24898 or 24.898%
For Benjamin, risk aversion, A = 8.4
U = 0.26 - 0.5 * 8.4*(0.21) ^2 = 0.07478 or 7.478%
For Zoe, risk aversion, A = 2.2
U = 0.26 - 0.5 * 2.2*(0.21) ^2 = 0.21149 or 21.149%
The risk-free are is 3.0% and the utility for Millie is very close to 3.0% (3.068%); therefore Millie is indifferent between Seven & Eight Holdings Co Ltd and the risk-free asset.
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