You have $136,000 to invest in a portfolio containing Stock X and Stock Y. Your

Question

You have $136,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 18 percent. Stock X has an expected return of 16 percent and a beta of 1.38, and Stock Y has an expected return of 11.0 percent and a beta of 1.14. How much money will you invest in stock Y? (Do not round intermediate calculations. A negative amount should be indicated by a minus sign.) Investment in Stock Y $ 143017.60 What is the beta of your portfolio? (Do not round intermediate calculations. Round your answer to 3 decimal places, e.g., 32.161.) Beta of the portfolio 1.0516

Explanation / Answer

Answer a:

Expected Portfolio Return = 18%
Total Weight of Portfolio = 1
Let the Weight of Stock X = x
Therefore Weight of Stock Y = 1- x

Portfolio Return = (Weight of Stock X * Return on Stock X) + (Weight of Stock Y * Return on Stock Y)
0.18 = (x * 0.16) + (1-x) * 0.11
0.18 = 0.16x + 0.11 - 0.11x
0.07 = 0.05x
x = 1.4
Weight of Stock X = 1.4
Weight of Stock Y = 1 - 1.4 = -0.4

Investment in Stock X = 136,000 * 1.4 = $190,400
Investment in Stock Y = 136,000 - 194,000 = -$54,400

Answer b:

Weight of Stock X = 1.40
Weight of Stock Y = -0.40

Portfolio Beta = Weight of Stock X * Beta of Stock X + Weight of Stock Y * Beta of Stock Y
Portfolio Beta = 1.40 * 1.38 + (-0.40) * 1.14
Portfolio Beta = 1.48

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