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

Question

Quizplus · Accepted Answer

To calculate the beta of stock A, we first need to calculate its average nominal return and the average nominal return of the market portfolio. 
Average nominal return of stock A = (-8% + 10% + 22%) / 3 = 8%
Average nominal return of market portfolio = (6% + 18% + 24%) / 3 = 16%
Next, we need to calculate the covariance between stock A and the market portfolio, as well as the variance of the market portfolio. 
Covariance between stock A and market portfolio = [(8% - 16%) x (6% - 16%) + (10% - 16%) x (18% - 16%) + (22% - 16%) x (24% - 16%)] / 2 = 35.2%
Variance of market portfolio = [(6% - 16%)^2 + (18% - 16%)^2 + (24% - 16%)^2] / 3 = 38.67%
Finally, we can calculate the beta of stock A using the formula:
Beta of stock A = Covariance / Variance of market portfolio = 0.91

Therefore, the closest answer choice is A) 1.64 (which is off by about 0.73).

The Historical Nominal Returns for Stock a Were -8%,+10%,and +22