Question

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 0.60 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?

A) 0.25; 0.45; 0.30

B) Cannot be determined

C) 0.50; 0.30; 0.20

D) 0.19; 0.49; 0.32

E) 0.32; 0.41; 0.27

Answer 1

Hence, the correct answer is the last option i.e. option E) 0.32; 0.41; 0.27

For the risky portfoio P,

Rp = w1 x R1 + w2 x R2 = 0.60 x 0.14 + 0.40 x 0.1 = 0.1240

Let w be the proportion invested in T bill then,

E(R) = w x Rf + (1 - W) x R_p

Or, 0.10 = w x 0.05 + (1 - w) x 0.1240

Hence, w = (0.1240 - 0.1) /(0.124 - 0.05) = 0.32

Hence, proportion invested in X = (1 - w) x w₁ = (1 - 0.32) x 0.6 = 0.41

and that in Y = (1 - w) x w₂ = (1 - 0.32) x 0.4 = 0.27

Hence, the correct answer is the last option i.e. option E) 0.32; 0.41; 0.27