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)	15%	32%
Bond fund (B)	9	23

The correlation between the fund returns is .15.

Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of 0% to 100% in increments of 20%. What expected return and standard deviation does your graph show for the minimum-variance portfolio? Draw a tangent from the risk-free rate to the opportunity set.

Answer 1

First let us tabulate the required information:

Fund	EXPECTED RETURN	STANDARD DEVIATION
S	15.00%	32.00%
B	9.00%	23.00%
PORTFOLIO	WEIGHT OF S	WEIGHT OF B	WEIGHTED PORTFOLIO RETURN	WEIGHTED PORTFOLIO STANDARD DEVIATION
1	0.000%	100.000%	9.000%	23.000%
2	20.000%	80.000%	10.200%	20.368%
3	40.000%	60.000%	11.400%	20.181%
4	60.000%	40.000%	12.600%	22.500%
5	80.000%	20.000%	13.800%	26.680%
6	100.000%	0.000%	15.000%	32.000%

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We can see from the above table that the standard deviation goes on decreasing till portfolio 3 when it is 20.181% at expected return of 11.400% and then starts to increase from there so portfolio 3 is the minimum variance portfolio