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.
The market line estimation implicitly assumes that its parameters are constant over time supposing whatever the investment horizon, the investors have a similar behaviour. In this paper, we discuss this hypothesis using the technique of wavelets. First, we verify the expected result concerning the statistical weaknesses of market line and the high volatility of its parameters. Second, we use the wavelets to estimate the frequency betas. We show that the classic beta (estimated with ols) considers a short-run beta. We propose a methodology based on time-frequency analysis that leads to an overview of equities characteristics useful to portfolio managers.
This study proposes a wavelets approach to estimating time–frequency-varying betas in the capital asset pricing model (CAPM) framework. The dynamic of systematic risk across time and frequency is analyzed to investigate stock risk-profile robustness. Furthermore, we emphasize the effect of an investor’s investment horizon on the robustness of portfolio characteristics. We use a daily panel of French stocks from 2012 to 2022. Results show that varying systematic risk varies in time and frequency, and that its short and long-run evolutions differ. We observe differences in short and long dynamics, indicating that a stock’s betas differently fluctuate to early announcements or signs of events. However, short-run and long-run betas exhibit similar dynamics during persistent shocks. Betas are more volatile during times of crisis, resulting in greater or lesser robustness of risk profiles. Significant differences exist in short-run and long-run risk profiles, implying a different asset allocation. We conclude that the standard CAPM assumes short-run investment. Then, investors should consider time–frequency CAPM to perform systematic risk analysis and portfolio allocation.
This paper empirically investigates the differences between the systematic risk estimated by OLS and it simultaneous estimation with a GARCH errors. The systematic risk of an asset is estimated by the beta coefficient of the market line. According to the OLS hypothesis, the estimators are robust and residuals are white noise process. However various papers show the existence of statistical anomalies (stylized facts) in residuals (heteroskedasticity, autocorrelation and non‐normality) rejecting the BLUE properties of estimators. In order to considerate these anomalies to modelize the hazard in residuals regression, we use ARCH processes class that has proved it efficiency in finance. We estimate simultaneously the parameters of the market line and those of the GARCH process for the 30 perennial equities listed in CAC40 for the daily period 2005 to 2015 and we compare them each other. We select the E‐GARCH model providing the best residuals characteristics and we note significant differences with the OLS Betas particularly for equities with betas greater than 1. On this base, we estimate a linear relationship between the OLS Betas and the E‐GARCH Betas considering this break to modelize the differences between these two kinds of Betas. By this way, Investors can quickly adjust the Beta with this tool without completely reestimating them with GARCH.
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