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You are considering investing $1,000 in a T-bill that pays a rate of return of 0
You are considering investing $1,000 in a T-bill that pays a rate of return of 0.05 and a risky portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.17 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 0.10, 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*(0.60*0.17+0.40*0.10)+(1-w)*0.05=0.11
=>w=(0.10-0.05)/(0.60*0.17+0.40*0.10-0.05)
=>w=0.543478261
Tbills=1-0.543478261=45.6522%
Stock X=0.543478261*0.60=32.6087%
Stock Y=0.543478261*0.40=21.7391%
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