Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
The returns generated by a sample of five stocks from the Karachi Stock Exchange are given in the exhibit below.
Exhibit: Karachi Stock Exchange Returns – Sample of 5 Stocks
| Stock | Return |
|---|---|
| A | 12% |
| B | 13% |
| C | 5% |
| D | 4% |
| E | 20% |
Using the data above, what is the sample standard deviation of returns?
Other
Community
NNikitesh
A
6.53%
B
5.84%
C
7.53%
D
8.34%
Explanation:
The correct answer is A (6.53%).
Calculation Steps:
-
Calculate the mean: Mean = (0.12 + 0.13 + 0.05 + 0.04 + 0.20) / 5 = 0.54 / 5 = 0.108 or 10.8%
-
Calculate squared deviations from the mean:
- Stock A: (0.12 - 0.108)² = (0.012)² = 0.000144
- Stock B: (0.13 - 0.108)² = (0.022)² = 0.000484
- Stock C: (0.05 - 0.108)² = (-0.058)² = 0.003364
- Stock D: (0.04 - 0.108)² = (-0.068)² = 0.004624
- Stock E: (0.20 - 0.108)² = (0.092)² = 0.008464
-
Sum of squared deviations: Total = 0.000144 + 0.000484 + 0.003364 + 0.004624 + 0.008464 = 0.017080
-
Calculate sample variance: Since this is a sample (not the entire population), we use n-1 in the denominator: Sample variance = 0.017080 / (5 - 1) = 0.017080 / 4 = 0.00427
-
Calculate sample standard deviation: Sample standard deviation = √0.00427 = 0.06534 or 6.534%
Key Concept: When calculating standard deviation from a sample (as opposed to the entire population), we use (n-1) in the denominator instead of n. This is called Bessel's correction, which provides an unbiased estimate of the population variance. The divisor (n-1) is known as degrees of freedom.
Comments
Loading comments...