Question

Problem 11-23 Calculating Portfolio Weights [LO 1]

Stock J has a beta of 1.22 and an expected return of 13.26 percent, while Stock K has a beta of .77 and an expected return of 10.2 percent. You want a portfolio with the same risk as the market.

What is the portfolio weight of each stock? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

Answer 1

Market or market beta is considered to be 1.

Let weight of Stock j be "W". Then weight of Stock K is (1 - W).

Beta of portfolio = Weight of Stock J x Beta of Stock J + Weight of Stock K x Beta of Stock K

or, 1 = W x 1.22 + (1 - W) x 0.77

or, 1 = 1.22 W + 0.77 - 0.77 W

or, 0.45 W = 0.23

or, W = 0.23 / 0.45 = 0.5111

Therefore, Weight of Stock J = 0.5111

Weight of Stock K = 1 - 0.5111 = 0.4889