Question

You have $300,000 to invest in two stocks and want an expected portfolio return of 12%. Stock A has an expected return of 5% and Stock B has an expected return of 16%. How much must you invest in each stock to reach your portfolio return goal?

A. $133,333 in Stock A and $166,667 in Stock B

B. $25,000 in Stock A and $275,000 in Stock B

C. $75,000 in Stock A and $225,000 in Stock B

D. $109,091 in Stock A and $190,909 in Stock B

Answer 1

Given

Total investment = $300,000

Expected portfolio return = 12%

Expected return of stock A = 5%

Expected return of stock B = 16%

Let investment in A be = W_A

Investment in B be = W_B

W_A + W_B = 1

W_B = 1 - W_A

Expected portfolio return = (Weight of stock A * Expected return of stock A) + (Weight of stock B * Expected return of stock B)

12%= W_A * 5% + W_B 16%

12%= W_A * 5% + (1 - W_A)* 16%

0.12 =0.05 W_A + 1*0.16 – 0.16 W_A

0.12 = -0.11 W_A + 0.16

0.11 W_A = 0.16 -0.12

0.11 W_A = 0.04

W_A = 0.04/0.11 = 4/11

W_B = 1- 4/11= 7/11

Weight of stock A = 4/11 * 300,000 = $109,090.9091

Weight of stock A = 7/11* 300,000 = $190,909.0909

Answer: option D. $109,091 in Stock A and $190,909 in Stock B