Question

You have $20,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 8 percent.

  

If your goal is to create a portfolio with an expected return of 10 percent, how much money will you invest in Stock X?

• $6,667
• $33,333
• $7,000
• $6,334
• $6,934

  

If your goal is to create a portfolio with an expected return of 10 percent, how much money will you invest in Stock Y?

• $13,333
• $12,800
• $14,000
• $12,666
• $13,866

Answer 1

We know, expected return of a portfolio is equal to the weighted average of return from various stocks in that portfolio.

As per Question 1, let X be the amount to be invested in Stock X for getting a portfolio return of 10%. Therefore, amount invested in Stock Y= 20,000-X

Stock X return * (X/20,000) + (Stock Y return * ((20,000-X)/20,000) )= 10

Solving for X in the equation, we get X= $ 6667 (amount to be invested in stock X) Ans A

As per Question 2, amount to be invested in Y for a portfolio return of 10%= 20,000- 6667= $13,333

If we cross check by the above method, let Y be the amount to be invested in Stock Y for getting a portfolio return of 10%. Therefore, amount invested in Stock X= 20,000-Y

Stock X return * ((20,000-Y) /20,000) + (Stock Y return * Y/20,000 )= 10

Solving for Y in the equation, we get Y= $  13,333 (amount to be invested in stock Y) Ans A