A portfolio has an expected return of 12.3 percent.This portfolio contains two stocks and one risk-free security.The expected return on Stock X is 9.7 percent and on Stock Y it is 17.7 percent.The risk-free rate is 3.8 percent.The portfolio value is $78,000 of which $18,000 is the risk-free security.How much is invested in Stock X?
A)$18,600
B)$19,667
C)$21,375
D)$22,204
E)$24,800

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 $18,000 / $78,000 = 0.2308. The expected return of the portfolio is 12.3%, so we set up the equation: 0.2308 * 3.8% + (1 - 0.2308) * (wX * 9.7% + (1 - wX) * 17.7%) = 12.3%. Solving for wX gives the weight of Stock X, which is then multiplied by the total stock investment ($78,000 - $18,000) to find the dollar amount invested in Stock X.

A Portfolio Has an Expected Return of 12