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 4.1%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	17%	27%
Bond fund (B)	16%	19%

The correlation between the fund returns is 0.12.

What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected return	%
Standard deviation	%

Answer 1

step 1: Calculation of Covariance

Covariance = Correlation * SD of stock fund * SD of bond fund

= 0.12* 27 * 19

= 61.56

step 2: Calculation of proportion of portfolio at which risk is lower

Ws = ( SD_b² - Cov_sb) / (  SD_s² + SD_b² -2Cov_sb)

where

Ws - Weight of stock fund

SD_{b -} Standard Deviation of bond fund

SD_{s -} Standard Deviation of stock fund

Cov_sb - Covariance

Ws = ( SD_b² - Cov_sb) / (  SD_s² + SD_b² -2Cov_sb)

Ws = ( 19² - 61.56) / ( 27² + 19² -2*61.56₎

_{= (} 361 - 61.56) / (729+361-123.12)

= 299.44 / 966.88

=.3097

= 30.97% = 31%

Hance the minimum risk portfolio contains 31% stock fund and 69% bond fund.

step 3: Calculation of Expected return on portfolio

The return of a portfolio is the weighted average return of the securities which constitute the porfolio

	Weight	Expected Return (%)	Weight*Expected Return
Stock Fund	0.31	17	5.27
Bond Fund	0.69	16	11.04

Portfolio Return = 16.31% (5.27+11.04)

step 4: Calculation of portfolio standard deviation

(WS*SDS)² + (WB*SDB)² + (2*WS*WB*SDS*SDB*CorSB)

(.31 * .27)² + (.69*.19)² + (2*.31*.69*.27*.19*.12)

0.0268

=.1638

= 16.38%