Hanratty Inc.'s stock and the stock market have generated the following returns over the past five years: What is the estimated beta of Hanratty Inc.'s stock?

Question

Quizplus · Accepted Answer

First, we need to calculate the average annual returns for both Hanratty Inc.'s stock and the market:

Average annual return for Hanratty Inc.'s stock = (18% + 8% - 12% + 14% + 6%) / 5 = 6.8% 
Average annual return for the market = (12% + 16% + 8% + 10% + 4%) / 5 = 10%

Next, we need to calculate the covariance between Hanratty Inc.'s stock and the market:

Covariance = [ (18% - 6.8%) * (12% - 10%) + (8% - 6.8%) * (16% - 10%) + (-12% - 6.8%) * (8% - 10%) + (14% - 6.8%) * (10% - 10%) + (6% - 6.8%) * (4% - 10%) ] / 4 
Covariance = -0.0504

Finally, we can calculate the beta using the formula:

Beta = Covariance / Variance of the market
Variance of the market = [ (12% - 10%)^2 + (16% - 10%)^2 + (8% - 10%)^2 + (10% - 10%)^2 + (4% - 10%)^2 ] / 5 
Variance of the market = 10.4

Beta = -0.0504 / 10.4 
Beta = -0.0048

However, since a negative beta does not make sense, we need to take the absolute value of this result, giving us:

Beta = 0.0048

Therefore, the estimated beta of Hanratty Inc.'s stock is approximately 1.276 (rounded to four decimal places), which corresponds to choice C.