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 2 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 12%. To form a complete portfolio with an expected rate of return of 11%, you should invest of your complete portfolio in treasury bills. 19% 26.8% 36% 50%

You should invest 26.8% of your complete portfolio in treasury bills to earn an expected rate of return of 11% on a complete portfolio.

Explanation:

To begin with, first we have to calculate the return of P portfolio consisting of X and Y securities.

Expected Return (ER) = (Weight of X*Return of X) + ( Weight of Y*Return of Y)

ER = (0.6*0.14) + (0.4*0.12)

ER = 0.084 + 0.048

ER = 0.132 or 13.2%

Now, we have to compute the weight of treasury bills in complete portfolio:

ER = (Weight of TB*Return of TB) + (Weight of P*Return of P)

ER = (wTB * rTB) + (wP * rP)

ER= (wTB * rTB) + rP * (1-wTB)

0.11 = (wTB * 0.05) + 0.132*(1-wTB)

0.11= 0.05wTB + 0.132 - 0.132wTB

0.11 = -0.082wTB + 0.132

Let's make the Weight of Treasury Bills subject:

0.082wTB = 0.132 - 0.11

0.082wTB = 0.022

wTB = 0.022/0.082

Weight of Treasury Bills = 0.268 or 26.8%

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