Question

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%

Answer 1

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.