The annual returns for three years for stock B were 0 percent, 10 percent, and 26...

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:)

Solutions

Expert Solution

B Return	Market Return
0%	6%
10%	18%
26%	24%

The formula to calculate beta for the stock B is:

β_B = Cov(B,M)/σ_M²

where Cov(B,M) is the covariance between the stock B return and the market portfolio return. And σ_M² 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[x_M] = (6%+18%+24%)/3 = 16%

Sample size = n =3

σ_M² = [(6%-16%)²+(18%-16%)²+(24%-16%)²]/(3-1) = (0.01+0.0004+0.0064)/2 = 0.0084

σ_M² = 0.0084

Covariance Calculation

Expected return on stock B = E[x_B] = (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, β_B = Cov(B,M)/σ_M²

β_B = 0.0114/0.0084 = 1.357143

Answer -> 1.36

jeff jeffy answered 1 year ago

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