Question

You are considering investing $1,300 in a complete portfolio. The complete portfolio is composed of Treasury bills 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 65% and 35% respectively. X has an expected rate of return of 17%, and Y has an expected rate of return of 12%. 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.

Multiple Choice

• 0%; 65%; 35%

• 29%; 19%; 10%

• 50%; 33%; 18%

• 29%; 48%; 23%

Answer 1

Given that,

The optimal weights of X and Y in P are 65% and 35% respectively. X has an expected rate of return of 17%, and Y has an expected rate of return of 12%.

So, Wx = 0.65

Wy = 0.35

E(x) = 17%

E(y) = 12%

So, expected return of this risky portfolio is Wx*E(x) + Wy*E(y) = 0.65*17 + 0.35*12 = 15.25%

required return of complete portfolio = 8%

let weight of risk asset rate is w and weight of risky portfolio is 1-w

risk free rate = 5%

So, 8% = 5*w + (1-w)*15.25

=> w = 0.71

So investment in risky portfolio = 1-0.71 = 0.29 or 29%

investment in X is 65% of 0.29 = 0.19 or 19%

investment in Y is 35% of 0.29 = 0.10 or 10%

So, to form a complete portfolio with an expected rate of return of 8%, you should invest approximately 29% in the risky portfolio. This will mean you will also invest approximately 19% and 10% of your complete portfolio in security X and Y, respectively.