Practice Question
You have observed the following annual returns for ABC Inc: 25%, 15%, -20%, 30% and -15%. What is the standard deviation of returns?
Step 1: Calculate the Mean Return
\[ \text{Mean} = \frac{25 + 15 + (-20) + 30 + (-15)}{5} = \frac{35}{5} = 7\% \]
Step 2: Compute Squared Deviations from the Mean
\[ (25 - 7)^2 = 324,\quad (15 - 7)^2 = 64,\quad (-20 - 7)^2 = 729,\\ (30 - 7)^2 = 529,\quad (-15 - 7)^2 = 484 \]
Step 3: Sum the Squared Deviations
\[ \text{Sum} = 324 + 64 + 729 + 529 + 484 = 2,130 \]
Step 4: Calculate the Variance
\[ \text{Variance} = \frac{2130}{5 - 1} = \frac{2130}{4} = 532.5 \]
Step 5: Calculate the Standard Deviation
\[ \text{Standard Deviation} = \sqrt{532.5} \approx 23.08\% \]
Conclusion: The standard deviation of ABC Inc.'s returns is approximately 23.08%.