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Seven & Eight Holdings Co Ltd has an expected rate of return of 26%, and a standard deviation of 21%

Finance Nov 13, 2020

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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