The Systematic Risk at the Crisis—A Multifractal Non-Uniform Wavelet Systematic Risk Estimation

Mounir Sarraj,Anouar Ben Mabrouk

doi:10.3390/fractalfract5040135

Abstract

In the last decade, many factors, such as socio-political and econo-environmental ones, have led to a perturbation in the timeline of the worldwide development, and especially in countries and regions having political changes. This led us to introduce a new idea of risk estimation taking into account the non-uniform changes in markets by introducing a non-uniform wavelet analysis. We aim to explain the econo-political situation of Arab spring countries and the effect of the revolutions on the market beta. The main novelty is first the construction of a dynamic backward-forward model for missing data, and next the application of random non-uniform wavelets. The proposed procedure will be acted empirically on a sample corresponding to TUNINDEX stock as a representative index of the Tunisian market actively traded over the period from 14 January 2016 to 13 January 2021. The chosen 5-year period is important as it constitutes the first five years after the revolution and depends strongly on the socio-econo-political stability in the revolutionary countries. The results showed the efficiency of non-uniform wavelets in explaining the dynamics of the market well. They therefore may be good tools to explore important phenomena in the market such as the non-stationary aspect of financial series, non-constancy, and time-varying parameters. These facts in turn will have positive implications for investors as well as politicians in front of the evolution of the market. Besides, recommendations to extend the present method for other types of wavelets and markets will be of interest.

Highlights

Introduction and MotivationsIt is well known that economies are based to a large extent on the corresponding financial markets, local as well as external
Our new idea consists first in applying a backwardforward method to reconstruct missing data, and a non-uniform time scaling in the evaluation of the wavelet CAPM by means of a set of non uniformly-timed samples corresponding to the so-called non-uniform wavelets instead of classical wavelets
We proposed a wavelet multifractal procedure to estimate the systematic risk beta via the so-called CAPM

Summary

Introduction

Introduction and MotivationsIt is well known that economies are based to a large extent on the corresponding financial markets, local as well as external. Local markets explain or reflect the internal policies of governments and the internal laws that govern the movement of money locally such as local prices, internal laws of economics and finance, production, development, etc. The interaction with foreign markets explains and reflects first of all the effectiveness of foreign affairs policy, import–export movements, the quality of the export, etc. To control the situation of the market, controllers such as governments usually apply qualitative and quantitative measurements such as purses and/or indices. This permits econo-financial agents such as financial markets to reconcile the antagonistic objectives of their clientele such as profitability, security, and liquidity.

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