A pension fund manager is considering three mutual funds. The first is a stock f
ID: 2731816 • Letter: A
Question
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 8%. The probability distribution of the risky funds is as follows:
Expected Return Standard Deviation
Stock fund (S) 20% 30%
Bond fund (B) 12% 15%
The correlation between the fund returns is 0.10.
Tabulate the investment opportunity set of the two risky funds. (Round your answers to 2 decimal places. Omit the "%" sign in your response.)
Proportionin Stock Fund Proportion
in Bond Fund Expected
Return Standard
Deviation 0.00% 100.00% % % 17.39 82.61 20.00 80.00 40.00 60.00 45.16 54.84 60.00 40.00 80.00 20.00 100.00 0.00
Explanation / Answer
The expected return and standard deviation are calculated with the use of following formula:
Expected Return = Proportion in Stock Fund*Expected Return Stock Fund + Proportion in Stock Fund*Expected Return Bond Fund
Standard Deviation = [(Proportion in Stock Fund)^2*(Standard Deviation Stock Fund)^2 + (Proportion in Bond Fund)^2*(Standard Deviation Bond Fund)^2 + 2*Proportion in Stock Fund*Proportion in Bond Fund*Standard Deviation Stock Fund*Standard Deviation Bond Fund*Correlation Coefficient]^(1/2)
_______
The completed table is given below:
Proportionin Stock Fund Proportion
in Bond Fund Expected
Return Standard
Deviation 0.00% 100.00% 12.00% 15.00% 17.39% 82.61% 13.39% 13.92% 20.00% 80.00% 13.60% 13.94% 40.00% 60.00% 15.20% 15.70% 45.16% 54.84% 15.61% 16.54% 60.00% 40.00% 16.80% 19.53% 80.00% 20.00% 18.40% 24.48% 100.00% 0.00% 20.00% 30.00%
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