A portfolio has an expected return of 13.4 percent.This portfolio contains two stocks and one risk-free security.The expected return on Stock X is 12.2 percent and on Stock Y it is 19.3 percent.The risk-free rate is 4.1 percent.The portfolio value is $48,000 of which $10,000 is the risk-free security.How much is invested in Stock X?
A)$21,548.19
B)$19,514.14
C)$18,478.87
D)$22,200.14
E)$16,904.72

Question

Quizplus · Accepted Answer

To find the amount invested in Stock X, we first calculate the weights of the risk-free security and the stocks in the portfolio. The weight of the risk-free security is $10,000 / $48,000 = 0.2083. The expected return of the portfolio is 13.4%, and the risk-free rate is 4.1%. Let wX be the weight of Stock X and wY be the weight of Stock Y. We have: 0.2083 * 4.1% + wX * 12.2% + wY * 19.3% = 13.4%. Also, wX + wY = 1 - 0.2083 = 0.7917. Solving these equations gives wX = 0.3841. Therefore, the amount invested in Stock X is 0.3841 * $48,000 = $18,478.87.

A Portfolio Has an Expected Return of 13