The historical nominal returns for stock A were -8 percent, +10 percent, and +22 percent. The nominal returns for the market portfolio were +6 percent, +18 percent, and 24 percent during this same time. Calculate the beta for stock A.
A)1.64
B)0.61
C)1.00
D)0.50

Question

Quizplus · Accepted Answer

Using the formula for beta:

Beta = Covariance(stock A, market) / Variance(market)

We first need to calculate the covariance between stock A and the market:

Covariance = [(-8%-6%)(10%+18%)+(10%-6%)(22%+18%)+(22%-6%)(24%+18%)] / 3
Covariance = 293/3

Next, we need to calculate the variance of the market:

Variance = [(6%-12.67%)^2 + (18%-12.67%)^2 + (24%-12.67%)^2] / 3
Variance = 46.22%

Beta = Covariance / Variance = (293/3) / 0.4622 = 1.64

Therefore, the answer is A) 1.64.

The Historical Nominal Returns for Stock a Were -8 Percent