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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 two 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 10% what percentage of your complete portfolio should you invest in treasury bills?

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Answer:

34.78% should be invested.

Explanation:

Expected return of portfolio constructed with stock X and Y

= Rate of return on stock X * Weight of stock X + Rate of return on stock Y + Weight of stock Y

= 18*0.40 + 10*0.60 i.e 13.20

Calculation of percentage to be invested in treaury bill

10% = 4% * X + 13.20% ( 1-X)

0.10 = 0.04X + 0.1320 - 0.1320X

0.10-0.1320 = -0.092X

X = 34.7826%

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