A wavelet approach of investing behaviors and their effects on risk exposures

Roman Mestre

doi:10.1186/s40854-021-00239-z

Abstract

Exposure to market risk is a core objective of the Capital Asset Pricing Model (CAPM) with a focus on systematic risk. However, traditional OLS Beta model estimations (Ordinary Least Squares) are plagued with several statistical issues. Moreover, the CAPM considers only one source of risk and supposes that investors only engage in similar behaviors. In order to analyze short and long exposures to different sources of risk, we developed a Time–Frequency Multi-Betas Model with ARMA-EGARCH errors (Auto Regressive Moving Average Exponential AutoRegressive Conditional Heteroskedasticity). Our model considers gold, oil, and Fama–French factors as supplementary sources of risk and wavelets decompositions. We used 30 French stocks listed on the CAC40 (Cotations Assistées Continues 40) within a daily period from 2005 to 2015. The conjugation of the wavelet decompositions and the parameters estimates constitutes decision-making support for managers by multiplying the interpretive possibilities. In the short-run, (“Noise Trader” and “High-Frequency Trader”) only a few equities are insensitive to Oil and Gold fluctuations, and the estimated Market Betas parameters are scant different compared to the Model without wavelets. Oppositely, in the long-run, (fundamentalists investors), Oil and Gold affect all stocks but their impact varies according to the Beta (sensitivity to the market). We also observed significant differences between parameters estimated with and without wavelets.

Highlights

Markowitz (1952) Modern Portfolio Theory led the development of the Capital Asset Pricing Model (CAPM) which was created by Sharpe (1964), Lintner (1965) and Mossin (1966)
The Time–Frequency Multi-Betas Model effectively complements the different instruments used by stock investors to build their portfolios
It can substitute the CAPM by considering the residual anomalies by using Auto Regressive Moving Average (ARMA)-EGARCH processes to model the errors of the regression

Summary

Introduction

Markowitz (1952) Modern Portfolio Theory led the development of the Capital Asset Pricing Model (CAPM) which was created by Sharpe (1964), Lintner (1965) and Mossin (1966). In the short-run (D1), the CAPM is valid for only five stocks (16.66% of the sample) and results are similar to the previous estimate of the Standard Model This percentage decreases as the time horizon increase, so more stocks retain the Full Multi-Betas Model in the long-run. These results indicate that the initial tracker profile of Pf8 is only valid for short-run investments and so an adjustment of portfolio allocation is required if a long-run tracker profile is expected This portfolio has sensitives to oil and gold price variations in the long-run as this exposure is non-observed in the Standard Model. Concerning the Pf7, initially non sensitive to oil and gold, the insensitive characteristic is lost as the βo is significantly negative starting D3 bands even if βg is still equal to 0 To conserve this property for long-run investments, a new allocation is required. The results obtained by wavelet estimators of risks sensibilities are useful for investors to support their decision-making on portfolio allocation and could be completed by multiple criteria decisions making (MCDM) methods and clusters algorithms based on different risks measured in the assessment of financial risks or in predictions of variables (Kou et al 2014, 2021)

Conclusion

Findings

D5 D6 D1 D2 D3 D4 D5 D6 βm