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.

Note: the sectors names are abbreviated for readability. Refer to my earlier post for sectors names’ abbreviations.

Sector | Skewness vs 0 expected | Excess kurtosis vs 0 expected | Obs. below 99% CI vs 23 expected |
---|---|---|---|

TASI | -0.8486 | 9.903 | 55 |

TASI.BFS | -0.1863 | 8.269 | 46 |

TASI.PCI | -0.6701 | 7.078 | 52 |

TASI.CMT | -0.6123 | 13.622 | 45 |

TASI.RTL | -0.7570 | 9.699 | 48 |

TASI.EU | +0.0872 | 8.605 | 45 |

TASI.AFI | -0.6024 | 7.611 | 53 |

TASI.TIT | -0.4697 | 8.224 | 54 |

TASI.INS | -0.8096 | 4.082 | 60 |

TASI.MUI | -0.8107 | 6.041 | 62 |

TASI.INI | -0.9271 | 6.758 | 60 |

TASI.BDC | -1.0291 | 7.505 | 66 |

TASI.RED | -0.5750 | 6.827 | 59 |

TASI.TRA | -0.4645 | 6.138 | 57 |

TASI.MAP | -0.0686 | 4.439 | 67 |

TASI.HTT | +0.1061 | 7.969 | 51 |

Notice the following:

- 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.

Thank you.

## 2 thoughts on “TASI Sectors’ Normality Assumption”