Question

You have the following data on (1) the average annual returns of the market for the past 5 years and (2) similar information on Stocks A and B. Which of the possible answers best describes the historical betas for A and B? Years Market Stock A Stock B 1 0.03 0.16 0.05 2 ?0.05 0.20 0.05 3 0.01 0.18 0.05 4 ?0.10 0.25 0.05 5 0.06 0.14 0.05

? bA > 0; bB = 1. bA > +1; bB = 0. bA = 0; bB = ?1. bA < 0; bB = 0. bA < ?1; bB = 1.

Answer 1

Beta is the volatility or movement of a stock in relation to the market. A positive beta denotes that the stock's return moves in the same direction the market moves . So, if market return goes up, then return of stock also goes up. Whereas neagitve beta denotes that the stock's return moves in the opposite direction the market return moves, i.e., when market goes up, stock goes down and when market goes down, the stock goes up.

In our current case, the return of stock B is constant and their is no volatility irrespective of the fact that market has a positive return or negative return. Therefore, beta of stock B, i.e., b_B is 0.

The correct option is either 2nd option or 4th option.

Now, if you observe the returns of stock A -

At market return of -0.05, return of stock A = 0.20

whereas at market return of 0.01, return of stock A = 0.18

So, stock A's return is going down when the market is going up. Therefore, it has a negative beta. Out of the two options (2nd and 4th), only option 4 has negative beta for stock A.

Therefore, correct option is option 4, b_A < 0 ; b_B = 0.