You are considering investing $1,000 in a complete portfolio. The complete portf

Question

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%. To form a complete portfolio with an expected rate of return of 11%, you should invest __________ of your complete portfolio in Treasury bills.

50%

19%

36%

25%

Explanation / Answer

Risky Portfolio:

Weight of Stock X = 60%
Return on Stock X = 14%
Weight of Stock Y = 40%
Return on Stock Y = 10%

Expected Return = Weight of Stock X * Return on Stock X + Weight of Stock Y * Return on Stock Y
Expected Return = 60% * 14% + 40% * 10%
Expected Return = 12.40%

Complete Portfolio:

Let weight of treasury bills be x and weight of risky portfolio P be (1 - x)

Expected Return = Weight of Treasury Bills * Return on Treasury Bills + Weight of Risky Portfolio * Return on Risky Portfolio
11% = x * 5% + (1 - x) * 12.40%
0.11 = 0.05 * x + 0.124 - 0.124 * x
0.11 = 0.124 - 0.074 * x
0.074 * x = 0.014
x = 0.19 or 19%

So, weight of treasury bills is 19%

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