Financial Risk Manager Part 1

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The returns generated by a sample of five stocks from the Karachi Stock Exchange are given in the exhibit below.

What is the standard deviation of this sample?

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6.53%

5.84%

7.53%

8.34%

Explanation:

Calculation Explanation

Step 1: Calculate the Mean

\text{Mean} = \frac{(0.12 + 0.13 + 0.05 + 0.04 + 0.20)}{5} = \frac{0.54}{5} = 0.108 \text{ or } 10.8\%

Step 2: Calculate Deviations and Squared Deviations

Stock	Return	X – Mean	(X – Mean)²
A	12%	1.2%	0.000144
B	13%	2.2%	0.000484
C	5%	–5.8%	0.003364
D	4%	–6.8%	0.004624
E	20%	9.2%	0.008464
Total			0.017080

Step 3: Calculate Sample Standard Deviation

\text{Sample Standard Deviation} = \sqrt{\frac{\sum(X - \text{Mean})^2}{n - 1}} = \sqrt{\frac{0.017080}{4}} = \sqrt{0.00427} = 0.0653 \text{ or } 6.53\%

Key Points:

We use n-1 in the denominator because this is a sample standard deviation (not population)
The sample standard deviation is an unbiased estimator of the population standard deviation
The calculation follows the formula: $s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$

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