Question

Problem 7-7 10 points 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 9%. The probability distribution of the risky funds is as follows: eBook Expected Return 20% 11 Standard Deviation 35% Print Stock fund (5) Bond fund (B) 15 References The correlation between the fund returns is 0.09. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Portfolio invested in the stock Portfolio invested in the bond Expected return Standard deviation

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
w(*d)= ((E[Rd]-Rf)*Var(Re)-(E[Re]-Rf)*Cov(Re,Rd))/((E[Rd]-Rf)*Var(Re)+(E[Re]-Rf)*Var(Rd)-(E[Rd]+E[Re]-2*Rf)*Cov(Re,Rd)
							Where
						stock fund	E[R(d)]=	20.00%
bond fund	E[R(e)]=	11.00%
stock fund	Stdev[R(d)]=	35.00%
bond fund	Stdev[R(e)]=	15.00%
	Var[R(d)]=	0.12250
	Var[R(e)]=	0.02250
T bill	Rf=	9.00%
Correl	Corr(Re,Rd)=	0.09
Covar	Cov(Re,Rd)=	0.0047
stock fund	Therefore W(*d)=	0.5522
bond fund	W(*e)=(1-W(*d))=	0.4478
	Expected return of risky portfolio=	15.97% =0.1597
	Risky portfolio std dev (answer Risky portfolio std dev)=	21.02% = 0.2102
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