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Do Multi-Factor Models Produce Robust Results? Econometric And Diagnostic Issues In Equity Risk Premia Study

Author

Listed:
  • Paweł Sakowski

    (Faculty of Economic Sciences, University of Warsaw)

  • Robert Ślepaczuk

    (Faculty of Economic Sciences, University of Warsaw; Union Investment TFI S.A.)

  • Mateusz Wywiał

    (Faculty of Economic Sciences, University of Warsaw; Quedex Derivatives Exchange)

Abstract

In recent decades numerous studies verified empirical validity of the CAPM model. Many of them showed that CAPM alone is not able to explain cross-sectional variation of stock returns. Researchers revealed various risk factors which explained outperformance of given groups of stocks or proposed modifcations to existing multi-factor models. Surprisingly, we hardly find any discussion in financial literature about potential drawbacks of applying standard OLS method to estimate parameters of such models. Yet, the question of robustness of OLS results to invalid assumptions shouldn't be ignored. This article aims to address diagnostic and econometric issues which can influence results of a time-series multifactor model. Based on the preliminary results of a five-factor model for 81 emerging and developed equity indices (Sakowski, Slepaczuk and Wywial, 2016a) obtained with OLS we check the robustness of these results to popular violations of OLS assumptions. We find autocorrelation of error term, heteroscedasticity and ARCH effects for most of 81 regressions and apply an AR-GARCH model using MLE to remove them. We also identify outliers and diagnose collinearity problems. Additionally, we apply GMM to avoid strong assumption of IID error term. Finally, we present comparison of parameters estimates and Rsquared values obtained by three different methods of estimation: OLS, MLE and GMM. We find that results do not differ substantially between these three methods and allow to draw the same conclusions from the investigated five-factor model.

Suggested Citation

  • Paweł Sakowski & Robert Ślepaczuk & Mateusz Wywiał, 2016. "Do Multi-Factor Models Produce Robust Results? Econometric And Diagnostic Issues In Equity Risk Premia Study," Working Papers 2016-08, Faculty of Economic Sciences, University of Warsaw.
    • Handle: RePEc:war:wpaper:2016-08
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    References listed on IDEAS

    as
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    5. Pawe³ Sakowski & Robert Œlepaczuk & Mateusz Wywia³, 2016. "Cross-Sectional Returns With Volatility Regimes From A Diverse Portfolio Of Emerging And Developed Equity Indices," "e-Finanse", University of Information Technology and Management, Institute of Financial Research and Analysis, vol. 12(2), pages 23-35, October.
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    More about this item

    Keywords

    multi-factor models; asset prising models; equity risk premia; OLS; MLE; GMM; autocorrelation; heteroscedasticity; outliers; collinearity; normality; econometric diagnostics;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • F30 - International Economics - - International Finance - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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