Question

Portfolio Expected ReturnYou have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 12.7 percent and Stock Y with an expected return of 9.1 percent. If your goal is to create a portfolio with an expected return of 11.2 percent, how much money will you invest in Stock X? In Stock Y?

Answer #1

Let the weight invested in stock X be w_{X} = x

Hence, investment in Stock Y = w_{Y} = 1-x

Hence, expected return of the portfolio =
ER_{X}*w_{X} + ER_{Y}*w_{Y}

where, ER_{X} is the expected return for Stock X =
12.7&%

ER_{Y} is the expected return for Stock Y = 9.1%

w_{X} is the weight invested in Stock X and
w_{Y} is the weight invested in Stock Y

Hence, portfolio return = 12.7*x + 9.1*(1-x)

This is equal to 11.2%

=> 11.2 = 12.7*x + 9.1*(1-x)

=> 11.2 = 12.7 x + 9.1 - 9.1x

=> 3.6x = 2.1

=> x = 0.5833

Hence, investment in Stock X = 0.5833*10000 = $5833

Investment in Stock Y = (1 - 0.5833)*10000 = $4167

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