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, resp

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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?

\$568; \$378; \$54

\$108; \$514; \$378

\$568; \$54; \$378

\$378; \$54; \$568

Cannot be determined

Giải thích

Chọn đáp án A

Giải thích: (\$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.