TASI’s Normality Assumption

In this post, I explore normality assumption of the Saudi stock market; i.e. Tadawul. Mainly, I attempt to answer the question, “Is it valid to assume that Tadawul shows characteristics of normality in its returns?” The short answer is a resounding NO. Why? You need to continue reading this post.

Normality assumption is a choice made by financial analysts and risk managers to simplify their understanding of the financial markets.

Normality assumption implies that each stock/portfolio return is an independent realization from the same normal distribution; i.e. returns are i.i.d normal. It also implies that the returns distribution can be completely characterized by only two parameters: the mean and the variance. The skewness and (excess) kurtosis should be zero. However, this is rarely the case in financial markets.

Now let us consider the daily returns of TASI index for the period from 7-Jan-2007 to 27-Dec-2015 (illustrated and described below).

Daily log returns on TASI index from 7-Jan-2007 to 27-Dec-2015. Notice the extreme volatility in 2007 and 2008.

Analysis of TASI index returns, 7-Jan-2007 to 27-Dec-2015

Observations 2241
Mean return -6.123602e-05
Standard deviation per day 1.46%
Volatility 23.06%
Skewness -0.8486 vs. 0 expected
Excess kurtosis 9.903 vs. 0 expected
Observations below the lower bound of 99% CI 55 vs. 23 expected

As shown in the last line in the above table, the number of observations below the lower bound of 99% confidence interval (marked red in the plot below) is more than expected due mainly to the negative skewness and positive excess kurtosis.

Observations below the lower bound of 99% CI are marked red. Notice the clustering and calendar dates of these observations.

Conclusion: this analysis demonstrated that TASI violates the assumption of normality.

In the next blog, I’ll explore the normality assumption of all the sectors in TASI.

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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