You are considering investing $1000 in a complete portfolio. The complete portfo

Question

You are considering investing $1000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 38% and 62%, respectively X has an expected rate of return of 30%, and Y has an expected rate of return of 60%. The dollar values of your position in X would be if you decide to hold a complete portfolio that has an expected return of 40%. You are considering investing $1000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 38% and 62%, respectively. X has an expected rate of return of 30%, and Y has an expected rate of return of 60% The dollar values of your position in Y would be if you decide to hold a complete portfolio that has an expected return of 40%.

Explanation / Answer

a in treasury bills

(1-a) in risky portfolio

0.38x+0.62y = 1-a

expected return from (1-a)= 0.3*0.38+0.6*0.62 = 0.114 + 0.372 = 0.486

Expected return of portfolio = a*0.04+(1-a)0.486

0.4 = 0.486 - 0.486a+0.004a

0.482a = 0.086

a = 0.1784

1-a = 0.8216

x is 38% of (1-a) = 0.38*0.8216

x = 0.3121

In dollar terms x = 312.1

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