Question

You are considering investing $1,000 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 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 11%, you should invest __________ of your complete portfolio in Treasury bills.

Answer 1

First we must calculate the expected return of the P portfolio: 0,60 x 0,14 + 0,40 x 0,10 =  0,124 = 12,4%.

The weight of the T banknotes in the total portfolio will be equal to the total weight less, the portfolio P. If the weight of the portfolio p is "w"

T = 1 - w

The expected return of the entire portfolio must be 11%

0.11 = w x 0.124 + (1 - w) x 0.05

w = 0,81.

Then, the amount invested in the Portfolio P = 0.81 * $ 1000 = $ 810

Then, the amount invested in banknotes T = 0.19% of $ 1000 = $ 190

you should invest 19% of your complete portfolio in Treasury bills