Consider the following assumption about annual returns to two stock mutual funds \A" and \B." E(rA) = 8%A= 20% E(rB) = 12%B= 30% A,B= 0:2 In addition a one-year T-Bill with face value of $1000 is selling for $980.

(a) You have $1 million to invest. Although we know that diversi- _cation is important let's consider investments in just one risky security along with the T-Bill. Suppose that you have a target expected rate of return of 10% for your portfolio.

i. How could you achieve this target by investing in the T-Bill and mutual fundA? What percentage and dollar investment would be in the T-Bill and in the mutual fund? What is the standard deviation of your portfolio return? What is the Sharpe ratio of your portfolio? How does this compare to the Sharpe ratio of mutual fundA?

ii. Instead how could you achieve the target by investing in the T-Bill and mutual fundB? What percentage and dol- lar investment would be in the T-Bill and in the mutual fund? What is the standard deviation of your portfolio re- turn? What is the Sharpe ratio of your investment? How does this compare to the Sharpe ratio of mutual fundB?

(b) Both of the portfolios above achieve an expected return of 10%.

Which is preferred? Why?

(c) Suppose now that you can invest in a combination of the T-Bill, mutual fund A and mutual fund B. Once again your objective is achieve an expected return of 10%. How would you invest your money? Be speci_c (percentage investments and dollar invest- ments please). What is the Sharpe ratio of your portfolio? How does it compare to the Sharpe ratios of mutual funds A and B?

Answer rating: 100% (QA)

a i To achieve a target expected rate of return of 10 by investing in the TBill and mutual fund A Let x be the percentage invested in the TBill and 1x ... View the full answer