Question

A portfolio has a beta of 1.27. the portfolio consists of 25 percent u.s. treasury bills, 38 percent stock x, and 37 percent stock y. stock x has a risk level equivalent to that of the overall market. what is the beta of stock y?

a. 1.49
b. 1.54
c. 2.41
d. 2.02
e. 1.79

Answer 1

The beta of stock Y in the portfolio is calculated as the remaining weight after accounting for the known betas and weights of the other components. After performing the necessary calculations, the beta of stock Y is determined to be 2.41.

Step-by-step explanation:

To calculate the beta of stock Y, we first need to understand the concept of portfolio beta. The beta of a portfolio is the weighted average of the betas of all the securities in the portfolio. Since we know the portfolio's beta, the weight of each security in the portfolio, and the beta of Stock X and U.S. Treasury bills (which is zero), we can solve for the beta of Stock Y.

The portfolio beta (P) is given by:

P = (Weight of Treasury bills × Beta of Treasury bills) + (Weight of Stock X × Beta of Stock X) + (Weight of Stock Y × Beta of Stock Y)

P = (0.25 × 0) + (0.38 × 1) + (0.37 × Beta of Stock Y)

1.27 = (0) + (0.38) + (0.37 × Beta of Stock Y)

We can now solve for the beta of Stock Y:

1.27 = 0.38 + (0.37 × Beta of Stock Y)

Beta of Stock Y = (1.27 - 0.38) / 0.37

Beta of Stock Y = 2.41

Therefore, the correct answer is 2.41, which corresponds to option c.