Question

Problem 5-13 Assume that you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 47%. The T-bill rate is 4%. Your risky portfolio includes the following investments in the given proportions: Stock A 31 % Stock B 31 % Stock C 38 % Your client decides to invest in your risky portfolio a proportion (y) of his total investment budget with the remainder in a T-bill money market fund so that his overall portfolio will have an expected rate of return of 10%. a. What is the proportion y? (Round your answer to 2 decimal places.) Proportion y b. What are your client's investment proportions in your three stocks and the T-bill fund? (Round your intermediate calculations and final answers to 2 decimal places.) Security Investment Proportions T-Bills % Stock A % Stock B % Stock C % c. What is the standard deviation of the rate of return on your client's portfolio? (Round your intermediate calculations and final answer to 2 decimal places.) Standard deviation % per year

Answer 1

	w1	Weight of investment in risky portfolio	y
	w2	Weight of investment in T-bill	1-y
	R1	Expected Return of risky portfolio	12%
	R2	Expected Return of T-Bill	4%
		Expected Return of Client =w1*R1+w2*R2
		Expected Return =10%
		y*12+(1-y)*4=10
		12y-4y+4=10
		8y=10-4=6
		y=6/8=	0.75
	w1	Weight of investment in risky portfolio	0.75
	w2	Weight of investment in T-bill	0.25	(1-0.75)
		Proportion of y=0.75=75%
		Proportion of investment in T bill fund=	25%
		Proportion of investment in Stock A	23.25%	(0.75*31)	%
		Proportion of investment in Stock B	23.25%	(0.75*31)	%
		Proportion of investment in Stock C	28.50%	(0.75*38)	%
		Variance of Client Portfolio Return:
		(w1^2)*((Portfolio Standard Deviation)^2)+(w2^2)*((T-bill Standard Deviation)^2)=2w1*w2* Covariance (Portfolio,T-bill)
		T - Standard Deviation=0
		Covariance(Portfolio, T-bill)=0
		Variance of Client Portfolio Return:
		(w1^2)*((Portfolio Standard Deviatio)^2)
		(0.75^2)*(47^2)%%=		1242.563	%%
		Standard Deviation =Square Root (Variance)
		Standard Deviation =(1242.563^(1/2))		35.25	%