As observed in the previous post, the normality assumption in TASI index is not valid. In this post, I’ll explore the normality assumption in all the sectors in Saudi stock market. As you’ll see, all the sectors violate the normality assumption.
The normality assumption is not valid due to the presence of skewness and large positive excess kurtosis. This causes the number of observations below the lower bound of 99% confidence interval to be higher than expected. For example, TASI index has a skewness of -0.8486 (expected zero) and an excess kurtosis of 9.903 (expected zero) which results in 55 observation (expected 23) below the the lower bound of 99% confidence internal.
In the table below, I show the skewness, kurtosis and number of observation belows the lower bound of 99% CI for all the sectors.
Building and Construction (TASI.BDC) has the highest negative skewness.
Only two sectors show positive skewness; i.e. Energy & Utilities (TASI.EU) and Hotels & Tourism (TASI.HTT). But despite that, the same two sectors show high positive kurtosis and this result in having large number of observations below the lower bound of 99% CI; i.e. 45 and 51, respectively.
All sectors show high excess kurtosis resulting in large number of observations below the lower bound of 99% CI.
Conclusion: analysis demonstrated that all sectors in the Saudi stock market violate the assumption of normality.
To visualize the skewed returns in the distribution of the sectors, I made the following box plots. A box plot consists of a box and whiskers. The box starts from the 25th percentile to the 75th percentile of the data, known as the inter-quartile range (IQR). In the box, the line in the middle indicates the median (i.e., the 50th percentile) and the diamond shape indicates the mean. The whiskers start from from the edge of the box and extend to the furthest data point that is 1.5 times the IQR. If there are any data points that are farther than the end of the whiskers, they are considered outliers and indicated with dots.
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).
Analysis of TASI index returns, 7-Jan-2007 to 27-Dec-2015
Standard deviation per day
-0.8486 vs. 0 expected
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.
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.
In this post, I explore the correlations between the different sectors in the Saudi stock market, TASI. The data set used is from 6-Jan-2007 to 27-Dec-2015.
First, some explanation about the above correlation matrix is in order. For readability, I have abbreviated the long sectors names; for example, TASI.BFS is the Banks & Financial Services sector. The full list of the sectors names and their abbreviations is listed at the end of this post.
Correlation is a number between -1 (negative correlation) and +1 (positive correlation). For readability, I use a scale between 1 (weak correlation) to 10 (strong correlation) to represent the strength of correlation between two sectors. Note that in the Saudi stock market the correlation between sectors are all positive.
As mentioned above, correlations between sectors in the Saudi stock market are all observed to be positive correlations (i.e. not negative correlations between sectors).
The strongest positive correlation (around .85) is observed between the sector Industrial Investment (TASI.INI) and the sector Building & Construction (TASI.BDC). Below is a plot of the correlation between the daily log returns of both sectors. As you can see, the points in the plot are very close to each other.
The weakest positive correlation (around 0.35) is observed between the sector Energy & Utilities (TASI.EU) and the sector Media and Publishing (TASI.MAP). Below is a plot of the correlation between the daily log returns of both sectors. As you can see, the points in the plot are very dispersed. However, regardless of the weak correlation, extreme price changes happens at the same time.
That’s it for now. I’ll present more observations in the next post.
The purpose of this blog is to publish quantitative research on the GCC countries’ stock markets as well as the Forex market. I have access to enormous quantities of data and I will use power methods for extracting quantitative information, particularly about volatility and risk. I am using R for computations and graphics. I am planning to cover advanced topics such as multivariate distribution, copulas, Bayesian computations, VaR, expected shortfall and cointegration.
The prerequisites to understand the subject I am going to blog present are basic statistics and probability, matrices and linear algebra, and calculus. Some exposure to finance is helpful.