Question

#4. You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40%, respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. The risky portfolio, P, has a standard deviation of 0.7. Assuming you decide to hold a complete portfolio that has an expected return of 8%.

a. What is the expected return of your risky portfolio? (Round your answer to the first decimal place)

Continue from the previous problem, and use your answer from #4 for the following question:

What is the weight you invested in Treasury bills? What is the weight you invested in the risky portfolio?

hint: rc = wp*rp + wf*rf; and wf = 1-wp

0.08 = wp*rp + (1-wp) *0.05 (where rp is your answer from #4)

Answer 1

Ans A)

Return on treasury bills=5%

Lets assume that we invest "w" portion of $1000 in treasury bill and (1-w) in risky portfolio

We need expected return on complete portfolio =8%

w(5%)+0.6(1-w)(14%)+0.4(1-w)(10%)=8%

5w+8.4(1-w)+4(1-w)=8

12.4(1-w)+5w=8

12.4-7.4w=8

4.4=7.4w

4.4/7.4=w=0.5945%

hence we invest 59.45% in Treasury Bills and 40.55% in Risky Portfolio

Expected Return in Risky Portfolio=0.4055*0.6(14%)+0.4055*0.4(10%)=5.0282%

Ans B)

Weight invested in trasury bills is (4.4/7.4)=0.5946%

Weight invested in the risky portfolio 0.4054%