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%. The dollar values of your positions in X, Y, and Treasury bills would be _________, __________, and __________, respectively, if you decide to hold a complete portfolio that has an expected return of 8%.

Answer 1

Weight of X = 0.6

Weight of Y = 0.4

Expected return of Optimal risky portfolio = Weight of X*Expected return of X+Weight of Y*Expected return of Y

Expected return of Optimal risky portfolio = 14*0.6+10*0.4

Expected return of Optimal risky portfolio = 12.4

Expected return of Complete portfolio = Weight of Optimal portfolio*Expected return of Optimal portfolio+Weight of Risk free asset*Expected return of Risk free asset

8 = 12.4*Weight of Optimal portfolio+5*(1-weight of Optimal portfolio)

Weight of Optimal portfolio = 0.4054

Risk free asset weight = 1-Weight of Optimal portfolio = 1-0.4054=0.5946

Weight of X = Weight of Optimal portfolio*weight of x in optimal portfolio = 0.4054*0.6=0.24324

Weight of Y = Weight of Optimal portfolio*weight of Y in optimal portfolio = 0.4054*0.4=0.16216

Amount in portfolio = portfolio value*weight

X = 1000*0.24324 = 243.24

Y = 1000*0.16216 = 162.16

Risk free asset = 1000*0.5946 = 594.6