Financial Risk Manager Part 1

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The following are the data on the financial analysis of a sales company's income over the last 200 months:

n = 200, \sum_{i=1}^{n} (x_i - \hat{\mu})^2 = 774,759.90 \quad \text{and} \quad \sum_{i=1}^{n} (x_i - \hat{\mu})^3 = -13,476.784

What is the value of skewness?

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TTanishq

-0.0002774

-0.00051738

-0.00031736

-0.00021733

Explanation:

The skewness is calculated using the formula:

\frac{\hat{\mu}^3}{\hat{\sigma}^3} = \frac{\frac{1}{n} \sum_{i=1}^{n} (x_i - \hat{\mu})^3}{\left[ \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \hat{\mu})^2 \right]^{3/2}} = \frac{\frac{1}{200}(-13,476.784)}{\left[ \frac{1}{200-1} \times 774,759.90 \right]^{3/2}} = -0.000274

Given:

n = 200
Sum of squared deviations = 774,759.90
Sum of cubed deviations = -13,476.784

The calculation shows the skewness is approximately -0.000274, which matches option A (-0.0002774) most closely. The slight negative value indicates the data is nearly symmetrical with a very small left skew.

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