Question

You are considering investing $1,000 in a portfolio. The 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 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 portfolio with an expected rate of return of 11%, you should invest __________ percent of your portfolio in Treasury bills.

Answer 1

First we need to calculate the expected returns from portfolio P.

The return from P can be calculated as

Rp = (Wx * Rx) + (Wy * Ry)

where Wx = percentage of P invested in X = 60%

Rx = Return of portfolio X = 14%

Wy = percentage of P invested in Y = 40%

Ry = Return of portfolio Y = 10%

Rp = (0.6*14%) + (0.4*10%) = 12.4%

For main Portfolio, the return is calculated same way

R = (Wt * Rt) + (Wp * Rp)

where Wt = percentage of Portfolio invested in Treasury Bill

Rt = Return from Treasury Bill = 5%

Wp = percentage of Portfolio invested in P

Rp = Return of portfolio P = 12.4%

Wp can also be written as (1-Wt)

Hence

11% = (Wt * 5%) +((1-Wt)*12.4%)

1.4% = 7.4% * Wt

Wt = 0.189

Hence, 18.9% of $ 1000 should be invested in treasury bills