Using Heavy-Tailed Distributions with TASI: Pareto Distribution

As established in a previous post, Tadawul All Shares Index (TASI) of the Saudi stock market has high excess kurtosis (9.903). The high kurtosis indicates that TASI has heavy tails. This means that the probability of extremely large negative returns is higher compared to a normal distribution. In this post, I use Pareto distribution to model TASI’s left tail.

Pareto distribution is used in modeling excesses over a predefined threshold. Pareto distribution is characterized by two parameters: a minimum value (scale parameter) and the tail index α (shape parameter). For the minimum value parameter, I decided to use the daily normal value-at-risk (VaR) at 95% confidence level (note: normal VaR was computed using the normal distribution). The tail index α is estimated to be 0.2637. The smaller the value of the tail index α, the heavier the tail. The value of the tail index α must be larger than 0.

In the plot below, I fit returns from TASI’s left tail using Pareto distribution using the minimum threshold value at -0.0244 and the tail index α at 0.2637.

TASI Pareto
Using Pareto distribution to model the left tail of TASI returns

Conclusion: Returns from TASI’s left tail fit Pareto distribution. This clearly indicates that TASI has heavy tails; i.e. large negative returns have high probability.

Thank you.

Author: Thamir K. AlHashemi

Practitioner in the fields of quantitative finance and risk management. A lifetime learner. Reading is the only hobby that I haven't failed in ;)

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