Assume that you manage a risky portfolio with an expected rate of return of 15%
ID: 2819498 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 25%. The T-bill rate is 3% . Suppose your risky portfolio includes the following investments in the given proportions.
Dell 50%
Apple 30%
HP 20%
What are the investment proportions of your client’s overall portfolio, including the position in T-bills, if your client's risk aversion coefficient is 3?
___ Dell A. 32%
___ Apple B. 19.2%
___ HP C. 12.8%
___ T Bill D. 36%
Which of the following assets would be best to combine with a T-bill yielding 3%?
E(r) = 6%; std=10%
E(r) = 19%; std=42%
E(r)=12%; std=25%
E(r)= 9%; std=15%
E(r) = 6%; std=10%
E(r) = 19%; std=42%
E(r)=12%; std=25%
E(r)= 9%; std=15%
Explanation / Answer
U=E(r)-0.5*3*variance=(y*15%+(1-y)*3%-0.5*3*(y*25%)^2)
=0.12y+0.03-0.09375y^2
Maximization of utility occurs at
y=0.12/(2*0.09375)=0.64
Hence, investment proprtion:
Dell=50%*0.64=32%
Apple=30%*0.64=19.2%
HP=20%*0.64=12.8%
TBill=36%
Max Utility in Option A=(6%-3%)*(6%-3%)/(2*0.5*3*0.1*0.1)+3%-0.5*3*(10%)^2*((6%-3%)/(2*0.5*3*0.1*0.1))^2=4.5%
Max Utility in Option B=(19%-3%)*(19%-3%)/(2*0.5*3*0.42*0.42)+3%-0.5*3*(42%)^2*((19%-3%)/(2*0.5*3*0.42*0.42))^2=5.42%
Max Utility in Option C=(12%-3%)*(12%-3%)/(2*0.5*3*0.25*0.25)+3%-0.5*3*(25%)^2*((12%-3%)/(2*0.5*3*0.25*0.25))^2=5.16%
Max Utility in Option D=(9%-3%)*(9%-3%)/(2*0.5*3*0.15*0.15)+3%-0.5*3*(15%)^2*((9%-3%)/(2*0.5*3*0.15*0.15))^2=5.67%
Option D should be utilised