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 5%. The probability distribution of the risky funds is as follows:

	Expected Return			Standard Deviation
Stock fund (S)		19	%		32	%
Bond fund (B)		12			15

The correlation between the fund returns is 0.11.

You require that your portfolio yield an expected return of 14%, and that it be efficient, on the best feasible CAL.

a. What is the standard deviation of your portfolio? (Round your answer to 2 decimal places.)

  

b. What is the proportion invested in the T-bill fund and each of the two risky funds? (Round your answers to 2 decimal places.)

T-bill funds :

Stocks:

Bonds:

Answer 1

To find the fraction of wealth to invest in Stock fund that will result in the risky portfolio with maximum Sharpe ratio the following formula to determine the weight of Stock fund in risky portfolio should be used

	Where
Stock fund	E[R(d)]=	19.00%
Bond fund	E[R(e)]=	12.00%
Stock fund	Stdev[R(d)]=	32.00%
Bond fund	Stdev[R(e)]=	15.00%
	Var[R(d)]=	0.10240
	Var[R(e)]=	0.02250
T bill	Rf=	5.00%
Correl	Corr(Re,Rd)=	0.11
Covar	Cov(Re,Rd)=	0.0053
Stock fund	Therefore W(*d)=	0.3019
Bond fund	W(*e)=(1-W(*d))=	0.6981
	Expected return of risky portfolio=	14.11%
	Risky portfolio std dev=	15.01%

Where
Var = std dev^2
Covariance = Correlation* Std dev (r)*Std dev (d)
Expected return of the risky portfolio = E[R(d)]*W(*d)+E[R(e)]*W(*e)
Risky portfolio standard deviation =( w2A*σ2(RA)+w2B*σ2(RB)+2*(wA)*(wB)*Cor(RA,RB)*σ(RA)*σ(RB))^0.5
Desired return = tbill return*proportion invested in tbill+risky portfolio return *proportion invested in risky portfolio
= tbill return*proportion invested in tbill+risky portfolio return *(1-proportion invested in tbill)
0.14=0.05*Proportion invested in Tbill+0.1411*(1-Proportion invested in Tbill)
Proportion invested in Tbill (answer b) = (0.1411-0.14)/(0.1411-0.05)
=0.0121
proportion invested in risky portfolio = 1-proportion invested in tbill
=0.9879
Proportion invested in Bond fund (answer b) =proportion invested in risky portfolio *weight of Bond fund
=0.6896
Proportion invested in Stock fund (answer b) =proportion invested in risky portfolio *weight of Stock fund
=0.2983
std dev of portfolio (answer a) = std of risky portfolio*proportion invested in risky portfolio
0.9879*0.1501=14.83%