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 5.3%. The probability distributions of the risky funds are:   

	Expected Return		Standard Deviation
Stock fund (S)	14	%	43	%
Bond fund (B)	7	%	37	%

The correlation between the fund returns is .0459.

Suppose now that your portfolio must yield an expected return of 12% 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

To find the fraction of wealth to invest in stock 1 that will result in the risky portfolio with

the maximum Sharpe ratio the following formula to determine the weight of debt in risky portfolio should be used

	Where
Bond	E[R(d)]=	7.00%
Stock	E[R(e)]=	14.00%
Bond	Stdev[R(d)]=	37.00%
Stock	Stdev[R(e)]=	43.00%
	Var[R(d)]=	0.1369
	Var[R(e)]=	0.1849
T bil	Rf=	5.30%
Correl	Corr(Re,Rd)=	0.0459
Covar	Cov(Re,Rd)=	0.0073
	Therefore W(*d)=	0.1755
	W(*e)=(1-W(*d))=	0.8245
	Expected return of risky portfolio=	12.77%
	Risky portfolio std dev =	36.34%

Desired return=

12%

= tbill return*proportion invested in tbill+risky portfolio return *(1-return*proportion invested in tbill)

0.12=0.053*Proportion invested in Tbill+0.1277*(1-Proportion invested in Tbill)

Proportion invested in Tbill (answer b.1)= (0.1277-0.12)/(0.1277-0.053)

=0.1

proportion invested in risky portfolio = 1-*proportion invested in tbill

=0.9

Proportion invested in stock fund (answer b.2)=proportion invested in risky portfolio *weight of stock fund

=0.74

Proportion invested in bond fund (answer b.2)=proportion invested in risky portfolio *weight of bond fund

=0.1579

std dev of portfolio (answer a) = std of risky portfolio*proportion invested in risky portfolio

0.9*0.3634=32.71%