Question

A pension fund manager is consider ng three mutual unds. The s a stock un d the second is a ong-term government and corporate bond und, and the third is a T-bl money market f rd that yields a su erate o 4 4%, T epro ability distributions o rs the risky funds are 14% 5% Stock fund (S) Bond fund (B 34 28 % The correlation between the fund returns is.0214 Suppose now that your portfolio must yield an expected return of 13% 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-bil 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.) Stooks 36 36

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

0U

	Where
Stock fund	E[R(d)]=	14.00%
Bond fund	E[R(e)]=	5.00%
Stock fund	Stdev[R(d)]=	34.00%
Bond fund	Stdev[R(e)]=	28.00%
	Var[R(d)]=	0.11560
	Var[R(e)]=	0.07840
T bill	Rf=	4.40%
Correl	Corr(Re,Rd)=	0.0214
Covar	Cov(Re,Rd)=	0.0020
Stock fund	Therefore W(*d)=	0.9378
Bond fund	W(*e)=(1-W(*d))=	0.0622
	Expected return of risky portfolio=	13.44%
	Risky portfolio std dev=	31.97%

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)
0.13=0.044*Proportion invested in Tbill+0.1344*(1-Proportion invested in Tbill)
Proportion invested in Tbill (answer b-1) = (0.1344-0.13)/(0.1344-0.044)
=0.05
proportion invested in risky portfolio = 1-proportion invested in tbill
=0.95
Proportion invested in Bond fund (answer b-2) =proportion invested in risky portfolio *weight of Bond fund
=0.06
Proportion invested in Stock fund (answer b-2) =proportion invested in risky portfolio *weight of Stock fund
=0.891
std dev of portfolio (answer a) = std of risky portfolio*proportion invested in risky portfolio
0.95*0.3197=30.37%