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 sure rate of 5.5%. The probability distributions of the risky funds are:
Expected Return Standard Deviation
Stock fund (S) 16% 34%
Bond fund (B) 10% 25%

The correlation between the fund returns is 0.11.

Required:
a. What would be the investment proportions of your portfolio if you were limited to only the stock and bond funds and the portfolio has to yield an expected return of 12%?
b. Calculate the standard deviation of the portfolio which yields an expected return of 12%.

Answer 1

Based on the probability distributions of the funds and the correlation, the following is true:

• Investment proportions would be 33% Equity and 67% debt.
• Standard deviation would be 21.16%.

What would be the Investment proportions?

The expected return can be found as:

= (Return on stock x Weight of stock) + (Return on debt x Weight of debt)

As we already have the return as 12%, we can solve the formula for weights :

12% = (16% x Weight of equity ) + (10% x Weight of debt)

12% = (16% x W of equity ) + (10% x (1 - W of equity))

12% = 0.16W + 10% - 0.1W

2% = 0.06W

W = 2% / 0.06

= 33%

Equity is 33% so Debt is 67%.

What would be the standard deviation?

= √(Weight of stock ² x Standard deviation of stock ² + Weight of debt ² x Standard deviation of debt² + 2 x standard deviation of stock x standard deviation of debt x Correlation x weight of stock x weight of debt )

= √(33%² x 34% ² + 67%² x 25%² + 2 x 34% x 25% x 0.11 x 0.33 x 0.67)

= 21.16%

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