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Problem 5-13 Assume that you manage a risky portfolio with an expected rate of return of...

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Finance

Problem 5-13 Assume that you manage a risky portfolio with anexpected rate of return of 12% and a standard deviation of 47%. TheT-bill rate is 4%. Your risky portfolio includes the followinginvestments in the given proportions: Stock A 31 % Stock B 31 %Stock C 38 % Your client decides to invest in your risky portfolioa proportion (y) of his total investment budget with the remainderin a T-bill money market fund so that his overall portfolio willhave an expected rate of return of 10%. a. What is the proportiony? (Round your answer to 2 decimal places.) Proportion y b. Whatare your client's investment proportions in your three stocks andthe T-bill fund? (Round your intermediate calculations and finalanswers to 2 decimal places.) Security Investment ProportionsT-Bills % Stock A % Stock B % Stock C % c. What is the standarddeviation of the rate of return on your client's portfolio? (Roundyour intermediate calculations and final answer to 2 decimalplaces.) Standard deviation % per year

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3.6 Ratings (399 Votes)

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 %

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