Question

Time Remaining 35 minutes 30 seconds

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Item 8

Item 8

Time Remaining 35 minutes 30 seconds

00:35:30

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 5%. The probability distribution of the risky funds is as follows:

	Expected Return			Standard Deviation
Stock fund (S)		20	%		35	%
Bond fund (B)		11			15

The correlation between the fund returns is 0.09.

What is the Sharpe ratio of the best feasible CAL?

Answer 1

Solution

Risk premium on stock = 20 – 5 = 15%, and its SD = 35%

Risk premium on bond = 11 – 5 = 6%, and its SD = 15%

Cov = 0.09*0.35*0.15 = 0.004725

W1 = (0.15*0.15^2 – 0.06*0.004725) / (0.15*0.15^2 + 0.06*0.35^2 – 0.21*0.004725) = 0.3176389

W2 = 0.6823611

Variance of risk portfolio = 0.3176389^2*0.35^2 + 0.6823611^2*0.15^2 + 2*0.3176389*0.6823611*0.004725

Variance of risk portfolio = 0.024884183 = 0.157747211^2

Standard deviation of risk portfolio = 0.157747211

Expected return on the risk portfolio = 0.3176389*0.20 + 0.6823611*0.11 = 0.138587501

Sharpe Ratio = (0.138587501 – 0.05) / 0.157747211 = 0.5616