Question

you have $100,000 to invest in either stock D, Stock F, or a risk-free asset. ou must invest all your money. Your goal is to create a portfolio that has an expected return of 9.9 percent. Assume D has an expected return of 12.8 percent, F has an expected return of 9.3 percent, and the risk-free rate is 3.8 percent. Required: If you invest $50,000 in Stock D, how much will you invest in Stock F?

Answer 1

Required Return on Portfolio = 9.9 %

Total Investment = $ 100,000

Return on Stock D = 12.8 %

Return on Stock F = 9.3 %

Risk Free Rate = 3.8 %

Weight of Stock D = $ 50,000 / $ 100,000 = 0.5

Let Weight of Stock F = x , then weight of risk free security = ( 0.5 - x ) as weight of portfolio = 1

9.9 % = ( Weight of Stock D * Return on Stock D ) +( Weight of Stock F * Return on Stock F ) + ( Weight of Risk Free Security * Risk Free Rate )

9.9 % = ( 0.5 * 12.8 % ) + ( x * 9.3 % ) + ( ( 0.5 - x ) * 3.8 % )

9.9 = 6.4 + 9.3x + 1.9 - 3.8x

9.9 - 6.4 - 1.9 = 9.3 x - 3.8 x

1.6 = 5.5 x

x = 1.6 / 5.5

= 0.290909

29% will be invested in stock F

Total amount invested in stock F = 0.290909 * $ 100,000 = $ 29090.90