You own a portfolio equally invested in a risk-free asset and two stocks (If one of the stocks has a beta of 0.66 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio? (Hint: Remember that the market has a Beta=1; also remember that equally invested means that each asset has the same weight - since there are 3 assets, each asset's weight is 1/3 or 0.3333). Enter the answer with 4 decimals (e. g. 1.1234)

Question

Business

Adolfo Mcknight

22 June, 11:46

You own a portfolio equally invested in a risk-free asset and two stocks (If one of the stocks has a beta of 0.66 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio? (Hint: Remember that the market has a Beta=1; also remember that equally invested means that each asset has the same weight - since there are 3 assets, each asset's weight is 1/3 or 0.3333). Enter the answer with 4 decimals (e. g. 1.1234)

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Kinsley George · Answer 1

The beta of the other stock or stock B is 2.34

Explanation:

The beta of the portfolio is the weighted average of the individual stock betas that form up the portfolio. To calculate the beta for the portfolio, we use the following formula,

Portfolio beta = wA * Beta of A + wB * Beta of B + ... + wN * Beta of N

Where,

w represents the weight of each stock in the portfolio

As the portfolio is equally as risky as the market, the portfolio beta is assumed to be the same as that of the market and the beta is 1.

The beta is the measure of systematic risk and a risk free asset does not have risk and has a beta of 0.

To calculate the Beta of stock B in the portfolio, we simply put the available values in the formula for the portfolio beta,

1 = 1/3 * 0 + 1/3 * 0.66 + 1/3 * Beta of B

1 = 0 + 0.22 + 1/3 * Beta of B

1 - 0.22 = 1/3 * Beta of B

0.78 * 3 = 1 * Beta of B

2.34 = Beta of B

Thus, the beta of the other stock or stock B is 2.34