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?
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.
A. $568; $378; $54
B. $568; $54; $378
C. $378; $54; $568
D. $108; $514; $378
E. Cannot be determined.
A. $568; $378; $54
($1,120 – $1,000)/$1,000 = 12%; (0.6)14% + (0.4)10% = 12.4%; 12% = w5% + 12.4%(1 – w);w = 0.054; 1-w = 0.946; w = 0.054($1,000) = $54 (T-bills); 1 – w = 1 – 0.054 = 0.946($1,000) = $946; $946 × 0.6 = $568 in X; $946 × 0.4 = $378 in Y.
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