Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky funds are as follows:

	Expected Return				Standard Deviation
Stock fund (S)		17	%			30	%
Bond fund (B)		11				22

The correlation between the fund returns is 0.10.

a-1. What are the investment proportions in the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

a-2. What are the expected value and standard deviation of its rate of return? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Answer 1

A) We need to calculate the investment proportions in the two risky funds

Weight in Bond Fund = [Variance of Stock- {Std Dev. Stock * Std Dev. Bond * Correlation}] / [Variance of Stock + Variance of Bond - (2* Std Dev. Stock * Std. Dev. bond * Correlation)]

Numerator = (30%)^2 - (30%*22%*.1) = .0834

Denominator = (30%)^2 + (22%)^2 - (2*30%*22%*.1) = 0.1252

Weight in Bond Fund = .0834/.1252 = 66.61%

Weight in Stock Fund = 1- 66.61% = 33.39%

B) We need to calculate expected return and portfolio variance of this portfolio.

Expected Return of Portfolio = Expected Return on Stock * Weight of Stock Fund + Expected Return on Bond * Weight of Bond Fund  

= (17% * 33.39%) + (11%*66.61%)

= 5.6757% + 7.3275%

=13.0032%

Portfolio Std Dev. = SQUARE ROOT OF [ (Weight of Stock)^2 * (Std Dev. of Stock)^2 + (Weight of Bond)^2 * (Std Dev. of Bond) ^2 + (2* Std Dev. of stock * Std Dev. of bond * weight of bond * weight of stock * correlation) ]

=

(33.39%)^2 * (30%)^2 + (66.61%)^2 * (22%)^2 +(2*33.39%*30%*66.61%*22%.1)

=Square root of 3.4444%= 18.5592%