Question

You are considering investing $1,000 in a complete portfolio. The complete portfolio is comprised of treasury bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The weight 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.

A. 19%

B. 25%

C. 50%

D. 65%

Answer 1

Calculate the expected return of the portfolio X and Y as follows:

Expected return = (Rate of X * Weight of X) +(Rate of Y * Weight of Y)

= (60%*14%) +(40%*10%)

= 12.40%

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Let X be the weight of the risk free asset invested. weight of portfolio will be (1-X). Both the weights will be equal to 1. That is (Weight of Portfolio +  Weight of risk free asset =1)

Calculate the proportion of risk free asset as follows:

Current Expected return = (Expected return* Weight of Portfolio) +(Risk free rate * Weight of risk free asset)

11% = (12.40%*(1- X) + (5%*X)

7.4% X = 1.4%  

X = 19%

Therefore, the weight of risk free asset is 19%.

Option A is correct.