Question

(10. You own a portfolio with 50% invested in a risk-free asset, 30% in stock A with a beta of 1.5 and 20% in stock B. Your portfolio has the same expected return as the market portfolio. What is the beta of stock B? (The risk-free rate is 5%). a. 0.43 b. 1.00 c. 1.73 d. 1.85 0.20+1.50 e. 2.75

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Answer 1

Option (e) is correct

Portfolio beta is the weighted average beta of the stocks in portfolio. Here portfolio has the same expected return as that of market, so portfolio beta will also have same beta as that of market. Market has a beta of 1. So, portfolio beta is 1.

The weights of the betas in the stocks are:

Risk free asset: 50% or 0.50

Stock A: 30% or 0.30

Stock B: 20% or 0.20

In the next step, we will use the formula of portfolio beta or weighted average beta to calculate the beta of stock B.

Portfolio beta = w1 * b1 + w2 * b2 + w3 * b3

where, w1 is weight of risk free asset, w2 is weight of stock A, w3 is weight of stock B and b1 is beta of risk free asset, b2 is beta of stock A and b3 is beta of stock B, Portfolio beta = 1.

Risk free asset has zero beta. i.e. b1 = 0.

Putting the values in the above formula, we get,

1 = (0.50 * 0) + (0.3 * 1.5) + (0.2 * b3)

1 = 0 + 0.45 + b2 * 0.2

1 - 0.45 = b2 * 0.2

0.55 = b2 * 0.2

b2 = 0.55 / 0.2

b2 = 2.75

So, beta of stock B is 2.75