Assume that you manage a risky portfolio with an expected rate of return of 20%
ID: 2661033 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 20% and a standard deviation of 41%. The T-bill rate is 4%.
A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 30%.
What is the expected rate of return on the overall portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Assume that you manage a risky portfolio with an expected rate of return of 20% and a standard deviation of 41%. The T-bill rate is 4%.
Explanation / Answer
a)
standard deviation of T-bills, s2 = 0
Standard deviation of portfolio = sqrt( (w1*s1)^2 + (w2*s2)^2 + 2*w1*w2*r12*s1*s2 )
Let w1, w2 are proportions in risky portfolio and T bills respectively. s1, s2 are returns
w1= y, s1 = 41% ,
w2 =1-y and s2 = 0
Standard deviation of overall portfolio = y*41 + (1-y)*0 = 41y %
This can be maximum of 30%, so 30 = 41y
y = 30/41
y = 0.731707
b)
Return on portfolio = w1*r1 + w2*r2+...
w1=0.731707 , r1 = 20% ,
w2 =1-0.731707= 0.26829 and r2 = 4%
Return on portfolio = 0.26829*4 + 0.731707* 20
= 15.7073 %