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 4.3%. The probability distributions of
the risky funds are:

Expected Return Standard Deviation

Stock fund (S) 13 % 34 %

Bond fund (B) 6 % 27 %

The correlation between the fund returns is .0630.

Suppose now that your portfolio must yield an expected return of
11% and be efficient, that is, on the best feasible CAL.

a. What is the standard deviation of your portfolio? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)

Standard deviation
%

b-1. What is the proportion invested in the T-bill fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Proportion invested in the T-bill fund
%

b-2. What is the proportion invested in each of the two risky
funds? (Do not round intermediate calculations. Round your answers
to 2 decimal places.)

Proportion Invested

Stocks %

Bonds %

Answer #1

a. The optimally risk portfolio is given by :

Ws = [(Ers - rf)Sb^2 -(Erb - rf)Corr*Sa*Sb] / [(Ers - rf)Sb^2 +(Erb - rf)Sa^2 -(Ers-rf + Erb-rf)Corr*Sa*Sb]

Ws = [(13-4.3)*27^2 - (6-4.3)*0.0630*27*34] /[(13-4.3)*27^2 + (6-4.3)*34^2 -(13-4.3+6-4.3)*0.0630*34*27]

Ws = 6243.9822/7706.0264 = 0.8103

Wb = 1- Ws = 0.1897

Expected return Erp = 0.8103*13 +0.1897*6 = 11.6721%

Std deviation = sqrt(0.8103^2*0.34^2 + 0.1897^2*0.27^2 +2*0.8103*0.1897*0.0630*0.34*0.27) = 0.2833 = 28.34%

**Standard deviation of your portfolio =
28.34%**

b. Erc = (1-y)*rf + y* Erp

GIven Erc =11, rf = 4.3 and Erp = 11.6721

11 = (1-y)*4.3 +y*11.6721

11 = 4.3 -4.3y+11.6721y

y = 0.9088

1-y = 0.0912

**Proportion invested in T-bill fund = 9.12%**

c. **Proportion invested in Stocks =** 0.9088
*0.8103 = 0.7364 **= 73.64%**

**Proportion invested in Bonds =** 0.9088*0.1897 =
0.1724 **= 17.24%**

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