Question

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. If you want to form a portfolio with an expected rate of return of 0.10, what percentages of your money must you invest in the T-bill, X, and Y, respectively if you keep X and Y in the same proportions to each other as in portfolio P

Answer 1

Answer:

% in T bills = 18.92%, % in P = 81.08%

Explanation:

Portfolio return = Weighted average return

Return of portfolio P = 0.14*0.6 + 0.10*0.4

Return of portfolio P = 0.124

Let % money in T bills be x

0.11 = 0.05*x + 0.124*(1-x)

0.11 = 0.05x + 0.124 - 0.124x

0.014 = 0.074x

x = 18.92%

Hence, % in T bills = 18.92%, % in P = 81.08%