Question

need answers asap please

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 4.0%. The probability distributions of the risky funds are: Stock fund (S) Bond fund (3) Expected Return 100 Standard deviation 320 241 The correlation between the fund returns is 1250 Suppose now that your portfolio must yield an expected return of 8% 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.) ht ces 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.) Proportion Invested Stocks Bonds

Answer 1

			STOCK Fund =Asset 1, Bond Fund =Asset 2, T-Bill=Asset3
			Expected Return of asset1=R1	10.0%	0.1
			Expected Return of asset2=R2	7.0%	0.7
			Expected Return of asset 3=R3	4.0%	0.04
			Standard deviation of asset 1=S1	32%	0.32
			Standard deviation of asset 2=S2	24%	0.24
			Correlation between asset 1 and 2=Corr(1,2)	0.1250
			Covariance(1,2)=Cov(1,2)=Corr(1,2)*S1*S2	96.0000	%%	0.00960
			w1=Investment in asset 1
			w2=Investment in asset 2
			Portfolio Return=Rp(Percentage)
			w1*R1+w2*R2=w1*10+w2*7			……..Equation (1)
			Vp=Portfolio Variance=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov(1,2)
1024			Vp=Portfolio Variance=(w1^2)*1024+(w2^2)*576+2*w1*w2*96….Equation(2)
			Sp=Portfolio Standard Deviation=Square root of Variance=SQRT(Vp)
			Risk Free Rate	4%	0.04
		(b)	ALL POSSIBLE PORTFOLIOS
			STOCK A AND STOCKB	w1	w2	Rp=w1*10+w2*7	Vp(Using Equation (2)	Sp=Square root of Vp
				Weight of	Weight of	Portfolio	Portfolio	Portfolio
				STOCK FUND	BOND FUND	Return(%)	Variance(%%)	Std. Deviation(%)
				0	1	7	576	24
				0.1	0.9	7.3	494.08	22.2279
				0.2	0.8	7.6	440.32	20.9838
				0.3	0.7	7.9	414.72	20.3647
				0.35	0.65	8.05	412.48	20.3096
				0.4	0.6	8.2	417.28	20.4274
				0.45	0.55	8.35	429.12	20.7152
				0.5	0.5	8.5	448	21.166
				0.6	0.4	8.8	506.88	22.514
				0.7	0.3	9.1	593.92	24.3705
				0.8	0.2	9.4	709.12	26.6293
				0.9	0.1	9.7	852.48	29.1973
				1	0	10	1024	32
									Highest possible Return to Volatility (OptimumRisky Portfolio) 20.7152 Portfolio Expected Return Portfolio Variance Portfolio Standard Deviation StockA StockB 8.35% 429.12 %% 20.715212 % 45% 55% 0.083 0.04291 0.20715 4% COMBINATION OF THIS PORTFOLIO WITH T-BILL Return of T-Bill Standard Deviatio Covariance w1 Weight of Weight of Vp=(w1" Sp=Squ R=w1*8.32)*429. are root 5+w2*4 12 of Vp NewPortf New New olio Portfolio Portfolio Std. Return(% Varianc Deviatio n(%) Portfolio T-Bill 0.8 4.871 17.166 4.1432 Standard Deviatior Covariance Vp=(wt Sp=Squ R=w18.3 21*429.1 are root 5+w2'4 12 of Vp Weight New Porto New New Weight of of lio Portfolio Portfolio Std. Varianc Deviatio Portfolio T-Bill Return()e 61%) 40 0.2 0. 8 4 .87 17.166 4.1432 0.41 0.6 5.74 68.664 8.2864 0.6 0. 4 6 .61 154.49 12.43 0.81 0. 2 7 .481 274.661 16.573 0.92 0.08 8.002 363.23 19.059 0.95 0.05 8.13251 387.31 19.68 1 0 8 .35 429.15 20.716 For 8%. Return, Weight of Portfolio =w1= Weight of T-Bill=w2= Weight of Stock Fund=0.92'0.45 Weight of Bond Fund =0.92 0.55= Standard Deviation of the Portfolio Standard Deviation 0.92 0.08 8% 0.414 41.40% 0.506 50.602 19.058661 % 19.06% Proportion invested in T-bill Fund 82 b-1 b2 Proportion Invested Stocks Bonds 41.407 50.602