Stock J has a beta of 1.38 and an expected return of 14.11 percent, white Stock

Question

Stock J has a beta of 1.38 and an expected return of 14.11 percent, white Stock K has a beta of 0.94 and an expected return of 11.05 percent. You want a portfolio with the same risk as the market. Requirement 1: What is the portfolio weight of each stock? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).) Requirement 2: What is the expected return of your portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected return of the portfolio percentage

Explanation / Answer

To get the same risk as market, portfolio should have a beta of 1.
Let’s assume that weight of stock J in the portfolio is W. So, weight of stock K will be (1-W).

Beta of portfolio = (weight of stock J x Beta of stock J) + (weight of stock K x Beta of stock K)

1 = (Wx1.39) + [(1-W)x0.94]
1 = (1.39W) + (0.94 – 0.94W)
1-0.94 = 1.39W – 0.94W
W = 0.06/0.45 = 0.1333 or 13.33%

So, to have a beta of 1, weight of stock J should be 13.33% and weight of stock K should be (1-0.1333) = 86.67%

Expected Return of portfolio:

E(RP) = [E(RJ) x WJ] + [E(RK) x WK]
= (0.1411 x 0.1333) + (0.1105 x 0.8667) = 0.114579 or 11.46%

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