Question

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 12 percent. Assume D has an expected return of 15.5 percent, F has an expected return of 11.4 percent, and the risk-free rate is 6.25 percent. If you invest $50,000 in Stock D, how much will you invest in Stock F? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Amount of Stock F to buy

Answer 1

Expected Return from D = R_D = 15.5%

Expected Return from F = R_F = 11.4%

Expected Return from Risk free = R_R = 6.25%

Proportion invested in D = w_D = 50000/100000 = 0.50

Let Proportion invested in F = w_F = x

Proportion invested in risk free = w_R = 1 - 0.50 - x = 0.50 - x

Portfolio Return = 12% = w_DR_D + w_FR_F + w_RR_R

=> 12 = 0.50*15.5 + x*11.4 + (0.50 -x)*6.25

=> 12 = 0.50*15.5 + x*11.4 + 0.50*6.25 - x*6.25

=> x = (12 - 0.50*15.5 - 0.50*6.25) / (11.4 - 6.25) = 0.2184466

Hence Amount of F = 0.2184466*100000 = $21,844.66