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

Question

Quizplus · Accepted Answer

First, we need to calculate the average annual return for both stock B and the market portfolio.

Stock B:
(0 + 10 + 26)/3 = 12%

Market Portfolio: 
(6 + 18 + 24)/3 = 16%

Next, we need to calculate the covariance between stock B and the market portfolio.

Covariance = [(0-12)(6-16) + (10-12)(18-16) + (26-12)(24-16)]/2
= (-12)(-10) + (-2)(2) + (14)(8)
= 120 + (-4) + 112
= 228

Finally, we can calculate the beta for stock B using the formula:

Beta = Covariance / Variance of the market portfolio

To calculate the variance of the market portfolio, we need to first calculate the standard deviation:

σ = sqrt[((6-16)^2 + (18-16)^2 + (24-16)^2)/3] = sqrt[128/3] ≈ 7.21

Variance = σ^2 = (7.21)^2 = 51.96

Therefore, the beta for stock B is:

Beta = Covariance / Variance = 228 / 51.96 ≈ 4.39

The correct answer is not among the choices.

The Annual Returns for Three Years for Stock B Were