You are considering investing $1,700 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 75% and 25% respectively. X has an expected rate of return of 13%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 7%, 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.
Multiple Choice
50%; 38%; 13%
23%; 62%; 15%
36%; 27%; 9%
0%; 75%; 25%
Given that,
The optimal weights of X and Y in P are 75% and 25% respectively. X has an expected rate of return of 13%, and Y has an expected rate of return of 10%.
So, Wx = 0.75
Wy = 0.25
E(x) = 13%
E(y) = 10%
So, expected return of this risky portfolio is Wx*E(x) + Wy*E(y) = 0.75*13 + 0.25*10 = 12.25%
required return of complete portfolio = 7%
let weight of risk asset rate is w and weight of risky portfolio is 1-w
risk free rate = 4%
So, 7% = 4*w + (1-w)*12.25
=> w = 0.64
So investment in risky portfolio = 1-0.64 = 0.36 or 36%
investment in X is 75% of 0.36 = 0.27 or 27%
investment in Y is 25% of 0.36 = 0.09 or 9%
So, to form a complete portfolio with an expected rate of return of 7%, you should invest approximately 36% in the risky portfolio. This will mean you will also invest approximately 27% and 9% of your complete portfolio in security X and Y, respectively.
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