Sun Corporation has had returns of -6 percent, 16 percent, 18 percent, and 28 percent for the past four years. Calculate the standard deviation of the returns using the correction for the loss of a degree of freedom shown below.
When variance is estimated from a sample of observed returns, we add the squared deviations and divide by N -1, where N is the number of observations. We divide by N -1 rather than N to correct for a loss of a degree of freedom. The formula is
Variance(

_m) =

Where

_mis the market return in period t and r_m is the mean of the values of r_mt.

Question

Sun Corporation has had returns of -6 percent, 16 percent, 18 percent, and 28 percent for the past four years. Calculate the standard deviation of the returns using the correction for the loss of a degree of freedom shown below.
When variance is estimated from a sample of observed returns, we add the squared deviations and divide by N -1, where N is the number of observations. We divide by N -1 rather than N to correct for a loss of a degree of freedom. The formula is
Variance(

_m) =

Where

_mis the market return in period t and r_m is the mean of the values of r_mt.

Quizplus · Accepted Answer

Step 1: Find the mean return.

Mean return = (-6% + 16% + 18% + 28%) / 4 = 14%

Step 2: Calculate the squared deviations from the mean.

Squared deviation from mean = (return - mean return)^2

Deviation from mean for -6% = (-6% - 14%) = -20%
Squared deviation from mean for -6% = (-20%)^2 = 400%

Deviation from mean for 16% = (16% - 14%) = 2%
Squared deviation from mean for 16% = (2%)^2 = 4%

Deviation from mean for 18% = (18% - 14%) = 4%
Squared deviation from mean for 18% = (4%)^2 = 16%

Deviation from mean for 28% = (28% - 14%) = 14%
Squared deviation from mean for 28% = (14%)^2 = 196%

Step 3: Calculate the sum of squared deviations.

Sum of squared deviations = 400% + 4% + 16% + 196% = 616%

Step 4: Calculate the variance.

Variance = sum of squared deviations / (number of observations - 1)
Variance = 616% / (4 - 1) = 205.33%

Step 5: Calculate the standard deviation.

Standard deviation = square root of variance
Standard deviation = sqrt(205.33%) = 14.3%

Therefore, the standard deviation of returns for Sun Corporation using the correction for the loss of a degree of freedom is 14.3%. The best choice is B.

Sun Corporation Has Had Returns of -6 Percent, 16 Percent