Question

2. You have $200,000 to invest in Stock D, Stock E, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 15 percent If D has an expected return of 18 percent and a beta of 1.50, E has an expected return of 15.2 percent and a beta of 1.15, and the risk-free rate is 6 percent, and if you invest $60,000 in Stock D, how much will you invest in Stock E?

Answer 1

Total Amount for investment = $200,000

Amount invested in Stock D = $60,000

Portion of Investment Amount invested in Stock D = 60,000/200,000 = 0.3

And,

Portion of Investment Amount invested in Stock E = W_E

Portion of Investment Amount invested in Risk free asset = (1-0.3-W_E)

Expected Return of Portfolio = 15%

Expected Return of Stock D = 18%

Expected return of Stock E = 15.2%

Expected return of risk free asset = 6%

$E(r_P) = r_D*w_D+r_E*w_E+r_f*w_f$

where,

p = portfolio

w = weight

r = expected return

f = risk free

putting the values

$0.15 = 0.18*0.3+0.152*w_E+0.06*(0.7-w_E)$

$0.15 = 0.054+0.152*w_E+0.042-0.06w_E$

$0.15 = 0.096+0.092*w_E$

$0.092*w_E = 0.15-0.096$

$0.092*w_E = 0.054$

$w_E = \frac{0.054}{0.092}$

$w_E = 0.5869565$

Thus, Amount invested in Stock E would be

$= 200,000*0.5869565$

$\bg_green \large = \$117,391.30$

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.