Question

Suppose you have a portfolio that has $280 in stock A with a beta of 1.03, $1,120 in stock B with a beta of 1.33, and $840 in the risk-free asset. You have another $560 to invest. You wish to achieve a beta for your whole portfolio to be the same as the market beta. What is the beta of the added security?

A) 0.83

B) 1.00

C) 1.20

D) 1.33

Answer 1

The beta of the added security is calculated as the weighted average of the betas of the individual securities in the portfolio.

Step-by-step explanation:

To achieve the same beta as the market, we need to calculate the beta of the added security. The formula for the beta of a portfolio is the weighted average of the betas of the individual securities in the portfolio.

Given the investments in stock A, stock B, and the risk-free asset, the beta of the added security can be calculated as follows:

Beta of added security = (Total investment in stock A x Beta of stock A + Total investment in stock B x Beta of stock B) / Total investment in portfolio

Using the given values, the beta of the added security is calculated as follows:

Beta of added security = (280 x 1.03 + 1120 x 1.33) / (280 + 1120 + 840) = 1.24

Therefore, the beta of the added security is approximately 1.24, which is not one of the given options.