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

Pawel Sakowski, Robert Ślepaczuk and Mateusz Wywiał
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Mateusz Wywiał: Faculty of Economic Sciences, University of Warsaw; Quedex Derivatives Exchange

No 2016-08, Working Papers from Faculty of Economic Sciences, University of Warsaw

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.

Keywords: multi-factor models; asset prising models; equity risk premia; OLS; MLE; GMM; autocorrelation; heteroscedasticity; outliers; collinearity; normality; econometric diagnostics (search for similar items in EconPapers)
JEL-codes: C15 F30 G11 G12 G13 G14 G15 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2016
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