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 2 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%.
-To form a complete portfolio with an expected rate of return of 8%,you should invest approximately __________ in the risky portfolio.This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y respectively.
A) 0%, 60%, 40%
B) 25%, 45%, 30%
C) 40%, 24%, 16%
D) 50%, 30%, 20%

Question

Quizplus · Accepted Answer

To achieve an 8% expected return, calculate the proportion to invest in the risky portfolio (P) using the formula: 0.05(1-w) + 0.12w = 0.08, where w is the weight in P. Solving gives w = 0.4 or 40%. In P, invest 60% in X and 40% in Y, so 0.4 * 0.6 = 24% in X and 0.4 * 0.4 = 16% in Y.

You Are Considering Investing $1,000 in a Complete Portfolio