Question

You decided to create a $100,000 portfolio comprised of two stocks and a risk-free security. Stock X has an expected return of 13.6 percent and Stock Y has an expected return of 14.7 percent. You want to put 25% in Stock B. The risk-free rate is 3.6 percent and the expected return on the market is 12.1 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?

Answer 1

Expected Return = 12.1%

Weight of Stock B = 0.25

Let the Weight of Stock A = X

Weight of Risk Free Security = 1 - 0.25 - X

12.1% = Return of Stock A * Weight of Stock A + Return of Stock B * Weight of Stock B + Return of Risk Free Security * Weight of Risk Free Security

12.1% = 13.6% * X + 14.7% * 0.25 + 3.6% * (1 - 0.25 - X)

12.1% = 13.6% * X + 14.7% * 0.25 + 3.6% * (0.75 - X)

12.1% = 13.6% * X + 3.675% + 2.7% - 3.6% X

12.1% = 10% * X + 6.375%

X = (12.1% - 6.375%) / 10%

X = 57.25%

Investment in Risk Free Security = 1- 0.25 - 0.5725 = 0.1775 OR 17.75%

Amount to be invested in Risk Free Security = 17.75% * 100,000 = $ 17,750