The annual returns for three years for stock B were 0 percent, 10 percent, and 26 percent. Annual returns for three years for the market portfolio were +6 percent, 18 percent, and 24 percent. Calculate the beta for the stock.
A)0.75
B)1.36
C)1.00
D)0.74

Question

Quizplus · Accepted Answer

To calculate beta, we need to first calculate the average returns for both the stock and the market:

Stock B: (0% + 10% + 26%) / 3 = 12%
Market: (+6% + 18% + 24%) / 3 = 16%

Next, we calculate the covariance between the stock and the market:

Covariance = [(0-12) x (6-16) + (10-12) x (18-16) + (26-12) x (24-16)] / 2

Covariance = -240/2 = -120

Finally, we calculate beta:

Beta = Covariance / Variance of the market
Variance of the market = [(6-16)^2 + (18-16)^2 + (24-16)^2] / 3 = 64

Beta = -120/64 = -1.875

Therefore, the answer is not one of the choices given. However, if we take the absolute value of beta to make it positive, the answer becomes 1.875. This is closest to choice B, 1.36. But we must remember that we should not take the absolute value of beta in reality.

The Annual Returns for Three Years for Stock B Were