You are considering investing $1000 in a complete portfolio. The complete portfolio is composed of Treasury notes 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%. 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

Using the formula for the expected rate of return of a complete portfolio:
Expected Return = Weight of Treasury Notes * Risk-free Rate + Weight of Risky Portfolio * Expected Return of Risky Portfolio
8% = 0.05 * (1) + Weight of Risky Portfolio * [(0.60)(0.14) + (0.40)(0.10)]
8% = 0.05 + 0.088
Weight of Risky Portfolio = 0.40 or 40%
Therefore, you should invest $400 of your complete portfolio in the risky portfolio. This means you should invest $240 and $160 of your complete portfolio in securities X and Y, respectively. So the answer is C.

You Are Considering Investing $1000 in a Complete Portfolio