Question

You have $20,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 11 percent and Stock Y with an expected return of 12 percent. If your goal is to create a portfolio with an expected return of 11.39 percent, how much money will you invest in Stock X and Stock Y? (Do not round intermediate calculations and round your answer to the nearest dollar, e.g., 32.)

Answer 1

Investment in stock X $12200

Investment in stock Y $7800

Step-by-step explanation:

The portfolio return is made up of individual stock returns multiplied by their weight in the portfolio. Thus, the formula for portfolio return is,

Portfolio Return = Weight of Stock X * rX + Weight of Stock Y * rY

Where rX and rY are returns of stock X and stock Y.

To calclate weight, we plug in numbers in the formula,

Let x be the investment in stock X, then investment in stock Y is 1-x.

0.1139 = x * 0.11 + (1-x) * 0.12

0.1139 = 0.11x + 0.12 - 0.12x

0.1139 - 0.12 = -0.01x

x = -0.0061 / -0.01

x = 0.61

Then 1 - x is 1 -0.61 = 0.39

So investment in stock X is 20000 * 0.61 = $12200

Investment in stock Y is 20000 * 0.39 = $7800