You want to create a $65,000 portfolio comprised of two stocks plus a risk-free security.Stock A has an expected return of 14.2 percent and Stock B has an expected return of 17.8 percent.You want to own $20,000 of Stock B.The risk-free rate is 4.8 percent and the expected return on the market is 13.1 percent.If you want the portfolio to have an expected return equal to that of the market,how much should you invest in the risk-free security?
A)$11,921
B)$13,509
C)$15,266
D)$17,315
E)$18,775

Question

Quizplus · Accepted Answer

Let X be the amount invested in Stock A.

Then, we have the following equation based on the expected return of the portfolio:

0.142X + 0.178($20,000) + 0.048($65,000 - X - $20,000) = 0.131($65,000)

Simplifying and solving for X, we get:

0.142X + 0.178($20,000) + 0.048($45,000 - X) = 0.131($65,000)
0.142X + $3,560 + $2,160 - 0.048X = $8,515.00
0.094X = $2,795.00
X = $29,680.85

Therefore, the amount invested in the risk-free security is:

$65,000 - $29,680.85 - $20,000 = $15,319.15

Rounding to the nearest dollar, the answer is $15,266.
The correct answer is (C).

You Want to Create a $65,000 Portfolio Comprised of Two