You are considering investing $1,000 in a T-bill that pays a rate of return of 0

Finance Jan 14, 2021

You are considering investing $1,000 in a T-bill that pays a rate of return of 0.06 and a risky portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.70 and 0.30, respectively. X has an expected rate of return of 0.14 and a variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. If you want to form a portfolio with an expected rate of return of 0.11, what percentages of your money must you invest in the T-bill, X, and Y, respectively if you keep X and Y in the same proportions to each other as in portfolio P?

Expert Solution

w*(0.70*0.14+0.30*0.10)+(1-w)*0.06=0.11

=>w=(0.11-0.06)/(0.70*0.14+0.30*0.10-0.06)

=>w=0.735294118

Tbills=1-0.735294118=26.4706%

Stock X=0.735294118*0.70=51.4706%

Stock Y=0.735294118*0.30=22.0588%

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