In: Finance
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
please do not use excel ti solve the answer, thx:)
B Return | Market Return |
0% | 6% |
10% | 18% |
26% | 24% |
The formula to calculate beta for the stock B is:
βB = Cov(B,M)/σM2
where Cov(B,M) is the covariance between the stock B return and the market portfolio return. And σM2 is the variance of the market return
Variance Calculation
We will first calculate the sample variance (sample size-n) on Market return using the formula:
Expected return on market portfolio = E[xM] = (6%+18%+24%)/3 = 16%
Sample size = n =3
σM2 = [(6%-16%)2+(18%-16%)2+(24%-16%)2]/(3-1) = (0.01+0.0004+0.0064)/2 = 0.0084
σM2 = 0.0084
Covariance Calculation
Expected return on stock B = E[xB] = (0%+10%+26%)/3 = 12%
Sample covariance between random variables X and Y (sample size = n) is calculated using the formula:
Now, we can calculate covariance between market return and stock B return using the formula:
Cov(B,M) = [(0%-12%)*(6%-16%)+(10%-12%)*(18%-16%)+(26%-12%)*(24%-16%)]/2
Cov(B,M) = [0.012+(-0.0004)+0.0112]/2 = 0.0114
Therefore, βB = Cov(B,M)/σM2
βB = 0.0114/0.0084 = 1.357143
Answer -> 1.36