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.

A. 19% B. 25% C. 36% D. 50%

Answer 1

rate of return of treasury bills	5%
expected rate of return of Security X	14%
expected rate of return of Security Y	10%
Optimal weights of X is	60%
Optimal weights of Y is	40%
Expected rate of return is 11%
expected return= weight of tresury bills* expected return+weight of portfolio * expected return
11%=(W*0.05)+(1-W)*((0.6*0.14)+(0.4*0.10))
11%=0.05W+0.124-0.124w
w=0.014/0.074= 19%
Weight of portfolio invested in treasury bills is 19%
Answer A 19%