Financial Risk Manager Part 1

The skewness is calculated using the formula:

Given:

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

Step-by-step calculation:

1. Calculate the numerator: $\frac{1}{200} \times (-13,476.784) = -67.38392`$2`. Calculate the denominator:
   • First, compute $\frac{1}{200} \times 774,759.90 = 3,873.7995$
   • Then raise to the power of 3/2: $(3,873.7995)^{3/2} = (3,873.7995)^{1.5}$
   • Since $3,873.7995^{1.5} = 3,873.7995 \times \sqrt{3,873.7995}$
   • $\sqrt{3,873.7995} \approx 62.239$
   • So $3,873.7995 \times 62.239 \approx 241,000$3. Final calculation: $\frac{-67.38392}{241,000} \approx -0.0002795$

The value of the skewness is slightly negative and not far from 0, implying the data is symmetrical.