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 7%. The probability distribution of the risky funds is as follows: Expected Return 220 Standard Deviation Stock Fund (S) Bond fund (B) The correlation between the fund returns is 0.11 You require that your portfolio yield an expected return of 11%, 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.) Standard deviation b. What is the proportion invested in the T-billfund and each of the two risky funds? (Round your answers to 2 decimal places.) Proportion Invested T-bil fund Stocks Bonds Prev 1 of 4 Next >

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)]=	22.00%
bond fund	E[R(e)]=	12.00%
Stock fund	Stdev[R(d)]=	32.00%
bond fund	Stdev[R(e)]=	19.00%
	Var[R(d)]=	0.10240
	Var[R(e)]=	0.03610
T bill	Rf=	7.00%
Correl	Corr(Re,Rd)=	0.11
Covar	Cov(Re,Rd)=	0.0067
Stock fund	Therefore W(*d)=	0.5524
bond fund	W(*e)=(1-W(*d))=	0.4476
	Expected return of risky portfolio=	17.52%
	Risky portfolio std dev (answer )=	20.44%
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)
0.11=0.07*Proportion invested in Tbill+0.1752*(1-Proportion invested in Tbill)
Proportion invested in Tbill (answer b) = (0.1752-0.11)/(0.1752-0.07)
=0.6198 (61.98%)
proportion invested in risky portfolio = 1-proportion invested in tbill
=0.3802 (38.02%)
Proportion invested in bond fund (answer proportion invested in bond fund) =proportion invested in risky portfolio *weight of bond fund
=0.1702 (17.02%)
Proportion invested in Stock fund (answer b) =proportion invested in risky portfolio *weight of Stock fund
=0.21 (21%)
std dev of portfolio (answer a) = std of risky portfolio*proportion invested in risky portfolio
0.3802*0.2044=7.77%