Question

Show steps and work as u solve it please

you are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.65 and 0.35, respectively. X has an expected rate of return of 0.15 and variance of 0.04, and Y has an expected rate of return of 0.20 and a variance of 0.0081. If you want to form a portfolio with an expected rate of return of 0.13, what percentages of your money must you invest in the T-bill and P, respectively?

Answer 1

Weight of X = 0.65

Weight of Y = 0.35

Expected return of Portfolio P = Weight of X*Expected return of X+Weight of Y*Expected return of Y

Expected return of Portfolio P = 15*0.65+20*0.35

Expected return of Portfolio P = 16.75

Expected return of Portfolio P = Weight of Portfolio P*Expected return of Portfolio P+Weight of Risk free asset*Expected return of Risk free asset

13 = 16.75*Weight of Portfolio P+5*(1-weight of Portfolio P)

Weight of Portfolio P = 0.68085

Investment in portfolio P = weight in P *portfolio value = 0.68085*1000 = 680.85

Investment in Risk free asset = 1000-680.85=319.15