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? Group of answer choices a.$568; $54; b.$378 $108; c.$514; $378 d.$378; $54; e.$568 $568; f.$378; $54

Answer 1

c)$568; $378; $54

Step-by-step explanation:

($1,120 - $1,000)/$1,000 = 12%

(0.6)14% + (0.4)10% = 12.4%

12% = w5% + 12.4%(1 - w)

w = .054

1-w = .946

w = 0.054($1,000)

= $54 (T-bills)

1 - w = 1 - 0.054 = 0.946

0.946($1,000) = $946

$946 x 0.6 = $568 in X

$946 x 0.4 = $378 in Y.