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 sure rate of 4.1%. The probability distributions of the risky funds are:   

	Expected Return		Standard Deviation
Stock fund (S)	11	%	33	%
Bond fund (B)	8	%	25	%

The correlation between the fund returns is .1560.

Suppose now that your portfolio must yield an expected return of 9% 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-bill 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.)

	Proportion Invested
Stocks	%
Bonds	%

Answer 1

	Stock Fund=Asset 1,Bond Fund=Asset 2
	Expected Return of asset1=R1=	11%
	ExpectednReturn of asset2=R2=	8%
	Standard deviation of asset 1=S1=	33%
	Standard deviation of asset 2=S2=	25%
	Correlation of asset 1 and 2=Corr(1,2)	0.1560
	Covariance(1,2)=Corr(1,2)*S1*S2=	128.7
	w1=Investment in asset 1
	w2=Investment in asset 2
	Portfolio Return
	w1*R1+w2*R2=w1*11+w2*8			……..Equation (1)
	Portfolio Variance=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov(1,2)
	Portfolio Variance=(w1^2)*(33^2)+(w2^2)*(25^2)+2*w1*w2*128.7
	Portfolio Variance=(w1^2)*1089+(w2^2)*625+w1*w2*257.4……………Equation (2)
	Portfolio Standard Deviation=Square root of Variance
	Standard Deviation for best Feasible CAL	22.7967432
	Weight of Stock	0.55
	Weight of Bond	0.45
	ALL POSSIBLE PORTFOLIOS			Equation(1)
		w1	w2	Rp=w1*11+w2*8	Vp(Using Equation (2)	Sp=Square root of Vp	SR=(Rp-4.1)/Sp
		Weight of	Weight of	Portfolio	Portfolio	Portfolio	SHARP
		STOCK	BOND	Return(%)	Variance	Std. Deviation(%)	RATIO
		0	1	8	625	25	0.156
		0.1	0.9	8.3	540.306	23.2445	0.18068804
		0.2	0.8	8.6	484.744	22.0169	0.20438842
		0.3	0.7	8.9	458.314	21.4083	0.22421242
		0.4	0.6	9.2	461.016	21.4713	0.23752656
		0.5	0.5	9.5	492.85	22.2002	0.24324078
		0.55	0.45	9.65	519.692	22.7967	0.24345583
		0.6	0.4	9.8	553.816	23.5333	0.24221002
		0.7	0.3	10.1	643.914	25.3755	0.23644891
		0.8	0.2	10.4	763.144	27.6251	0.22805379
		0.85	0.15	10.55	833.684	28.8736	0.22338763
		0.9	0.1	10.7	911.506	30.1912	0.21860705
		1	0	11	1089	33	0.20909091
	Portfolio Expected   Return	9.65	%
	Portfolio Standard Deviation	22.7967432	%
	SharpRatio for best feasible CAL	0.24345583
	w1=0.55, w2=0.45