Question

10.      You are considering investing $1,000 in a complete portfolio. The complete portfolio is comprised of treasury bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The weight 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 10%, you should invest __________, __________ and __________ of your complete portfolio in the treasury bill, X, and Y respectively.

A.       19%, 49%, 32%

B.       25%, 45%, 30%

C.       32%, 41%, 27%

D.       50%, 30%, 20%      

The answer is c, I am just unaware of the steps to find the weight of the T-Bill. I don't know what to do to get the Wf after this.

.1 = Wf(.05) + (1 - Wf)(.6)(.14) + (1-Wf)(.4)(.1)

Answer 1

The final equation what you mentioned is

.1 = Wf(.05) + (1 - Wf)(.6)(.14) + (1-Wf)(.4)(.1)

0.1 = 0.05 Wf + 0.084 - 0.084 Wf + 0.04 - 0.04 Wf

0.1 = 0.124 - 0.074 Wf

0.074 Wf = 0.024

Wf = 32% Approximately

So

1 - Wf

= 1 - 0.32

= 0.68

Investment in X is computed as follows:

= 0.68 x 60%

= 41% Approximately

Investment in Y is computed as follows:

= 0.68 x 40%

= 27% Approximately

So the correct answer as you have already said is option c i.e. 32%, 41%, 27%

Feel free to ask in case of any query relating to this question