Standard Deviation Calculation for Stock Returns

What is the sample standard deviation if stock returns followed this historical distribution: +15%, -5%, -20%, 12%, and +15%?

A. 15.5% B. 18.5% C. 19.0% D. 20.1%

Answer:

The sample standard deviation of the stock returns is approximately 15.43%.

To calculate the sample standard deviation, we follow these steps:

  1. Calculate the mean of the data set.
  2. Calculate the squared difference between each data point and the mean.
  3. Sum the squared differences.
  4. Divide the sum by (n-1), where n is the number of data points.
  5. Take the square root of the result.

We know the stock returns of +15%, -5%, -20%, 12%, and +15%, let's calculate the sample standard deviation:

  1. Calculate the mean: (15 - 5 - 20 + 12 + 15) / 5 = 17 / 5 = 3.4%
  2. Calculate the squared difference for each data point:
    • (15 - 3.4)² = 136.9%
    • (-5 - 3.4)² = 73.96%
    • (-20 - 3.4)² = 529.64%
    • (12 - 3.4)² = 73.96%
    • (15 - 3.4)² = 136.9%
  3. Sum the squared differences: 136.9 + 73.96 + 529.64 + 73.96 + 136.9 = 951.36%
  4. Divide by (n-1): 951.36 / (5-1) = 237.84%
  5. Take the square root: √237.84% ≈ 15.43%

Therefore, the sample standard deviation of the stock returns is approximately 15.43%.

In conclusion, the correct answer is not provided in the options. The closest option is A. 15.5%, which is a reasonable approximation of the calculated sample standard deviation.

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