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.

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

Solution-

T- Bill Yield (T)= 5.5%

ER(S)= 15%

ER(B) = 9%

SD (S)= 32%

SD (B)= 23%

Cor(S,B) = 0.15

Covariance (B,S)= Cor(S,B)*SD(S)*SD(B)

Covariance (B,S)= 0.15*32%*23%

Covariance (B,S)= 0.01104

Computation of portfolio invested in stock fund (S)

Weight of Stock Fund (WS)= [ER(S) - (T)]* (SD(B))^2 - [ER(B) - (T)]*Cov(B,S)/ [ER(S) - (T)]* SD(B)^2 + [ER(B) - (T)]*SD(S)^2 - [ER(S) - (T) + ER(B) - (T)]* Cov(B,S)

WS= [15% - 5.5%]*23%^2 - [9%-5.5%]*0.01104 / [15%- 5.5%]*23%^2 + [9% - 5.5%]*32%^2 - [15%-5.5%+9%-5.5%]*0.01104

WS= 9.5%*0.0529 - 3.5%*0.01104 / 9.5%* 0.0529 +3.5%*0.1024 - 13%*0.01104

WS= 0.004639/ 0.0071743

WS= 0.6466 = 64.66%

WB= 1- WS

WB= 1-0.6466

WB= 0.3534 = 35.34%

Calculation of Expected Return

ER(S,B) = WS * ER(S) + WB* ER(B)

ER(S,B) = 64.66%* 15% +35.34% *9% =

ER(S,B) = 12.88%

Calculation of Standard Deviation

SD(S,B) = [(WS^2 * SD(S)^2 + WB^2 * SD(B)^2 + 2*WS*WB*Cov(B,S)]^1/2

SD(S,B) = [(64.66%)^2*(32%)^2 + (35.34%)^2*(23%)^2 +(2*64.66%*35.34%*0.01104)]^1/2

SD(S,B) = 23.34%