Assume that you manage a risky portfolio with an expected rate of return of 14%
ID: 2661029 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 29%. The T-bill rate is 4.5%.
Suppose a 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 11.15%.
What are your client's investment proportions in your three stocks and the T-bill fund? (Round your answers to 2 decimal places. Omit the "%" sign in your response.)
What is the standard deviation of the rate of return on your client's portfolio? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 29%. The T-bill rate is 4.5%.
Explanation / Answer
a) Return on portfolio = w1*r1 + w2*r2+...
11.15 = 4.5*(1-y) + (y)* 14 = 4.5 + (14-4.5)*y = 4.5 + 9.5y
y = (11.15-4.5)/9.5
y = 6.65/9.5
y = 0.7
So he should 70% in portfolio and remaining 30 % in T bills
b) proportions in stock:
T-bills: 30%
Stock A: 0.7* 27= 18.9 %
Stock B: 0.7*41= 28.7%
Stock C: 0.7*32 = 22.4 %
c) standard deviation of T-bills, s2 = 0
Standard deviation of portfolio = sqrt( (w1*s1)^2 + (w2*s2)^2 + 2*w1*w2*r12*s1*s2 )
w1= 0.7, s1 = 29% ,
w2 = 0.3 and s2 = 0
So,
standard deviation of portfolio, Sp = 0.7*29 = 20.3 %