You have $100,000 to invest in either Stock D, Stock F, or a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 10.6 percent. Assume D has an expected return of 14.1 percent, F has an expected return of 10 percent, and the risk-free rate is 5.55 percent. If you invest $50,000 in Stock D, how much will you invest in Stock F

Amount of Stock F to buy $17,420

Explanation:

The risk-free asset is one minus the weight of the other two assets. Therefore Mathematically, the expected return of the portfolio will be:

E[Rp] = 0.106 = 0.50 (0.141) + wF (0.100) + (1 - 0.50 - wF) (0.0555)

0.106 = 0.50 (0.141) + wF (0.100) + 0.0555 - 0.02775 - 0.0555wF = 0.1742

Hence, the weight of the risk-free asset is:

wRf = 1 - 0.50 - 0.1742 = 0.3258

And the amount of Stock F to buy is:

Amount of stock F to buy = 0.1742 ($100,000) = $17,420