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 rate of 8 percent. The probability distribution of the risky funds is as follows:

	Expected Return	Standard Deviation
Stock fund (S)	.20	.30
Bond fund (B)	.12	.15

The correlation between the fund returns is 0.10.

1. What is the reward-to-variability ratio of the best feasible CAL?
2. You require that your portfolio yield an expected return of 14 percent and be efficient on the best feasible CAL.
   1. What is the standard deviation of your portfolio?
   2. What is the proportion invested in the T-bill fund and each of the two risky funds?
3. If you were to use only the two risky funds and will require an expected return of 14 percent, what must be the investment proportions of your portfolio? (Compare its standard deviation to that of the optimized portfolio in question 2.)

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)]=	12.00%
Stock	E[R(e)]=	20.00%
Bond	Stdev[R(d)]=	15.00%
Stock	Stdev[R(e)]=	30.00%
	Var[R(d)]=	0.0225
	Var[R(e)]=	0.09
T bil	Rf=	8.00%
Correl	Corr(Re,Rd)=	0.1
Covar	Cov(Re,Rd)=	0.0045
	Therefore W(*d)=	0.5484
	W(*e)=(1-W(*d))=	0.4516
	Expected return of risky portfolio=	15.61%
answer b	Risky portfolio std dev =	16.54%

reward to variability=

= (

Expected return of risky portfolio-Rf)/Risky portfolio std dev = (15.61-8)/16.54 = 0.46

Desired return=

14%

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

0.14=0.08*Proportion invested in Tbill+0.1561*(1-Proportion invested in Tbill)

Proportion invested in Tbill = (0.1561-0.14)/(0.1561-0.08)

=0.21

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

=0.79

Proportion invested in stock fund =proportion invested in risky portfolio *weight of stock fund

=0.36

Proportion invested in bond fund =proportion invested in risky portfolio *weight of bond fund

=0.4332

std dev of portfolio = std of risky portfolio*proportion invested in risky portfolio

0.79*0.1654=13.07% : answer a