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.

What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a portfolio that has an expected outcome of $1,120?

Answer 1

Expected outcome of the portfolio = $1120

T - bill rate = $ 1000

Expected return on complete portfolio = ( $1120 - $ 1000 ) / $ 1000 = 0.12 or 12%

= Weights of X ( Expected return of X) + Weights of Y (Expected return of Y )

= (0.6) * 0.14 + ( 0.40) * 0.01  

= 0.084 + 0.04

= 0.124 or 12.4 %

12% = W 5 % + 12.4 % ( 1 - W )

12 = 5 W + 12.4 - 12.4 W

0.4 = 7.4 W

W = 0.4 / 7.4

= 0.054

1 - W = 0.946

W = 0.054 ( $1000 ) = $ 54 T- bill

1 - W = 1 - 0.054 = 0.946

= 0.946 ( $ 1000) = $ 946

X = $946 * 0.6 = 567.6 or  $ 568

Y = $ 946 * 0.4 = $378.4 or $ 378