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 2 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 the risky portfolio P.

		25%
		81%
		36%
		50%

Answer 1

Risky portfolio optimal weights of X = 60%

expected rate of return of X = 14%

Risky portfolio optimal weights of Y= 40%

expected rate of return of Y= 10%

Expected return of Risky portfolio = (Exp. return of X * weight of X)+(Exp. return of Y * weight of Y)

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

=0.124 or 12.40%

complete portfolio required expected return =11%

Risk free rate = 5%

Assume Risky portfolio weight = x

Riskfree weight will be 1-x

Expected return of complete portfolio = (Exp. return of risky portfolio * weight of risky)+(Exp. return of riskfree* weight of riskfree)

11% =(12.4%*x)+(5%*(1-x))

0.11 = 0.124x + 0.05 - 0.05x

0.11-0.05 = 0.074x

x = 0.06/0.074

=0.8108108108 or 81%

So we should invest _____81%_____ of complete portfolio in the risky portfolio P