IDEAS home Printed from https://ideas.repec.org/p/war/wpaper/2016-08.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://www.wne.uw.edu.pl/index.php/download_file/2552/
    File Function: First version, 2016
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Ruzita Abdul Rahim & Abu Hassan Shaari Mohd. Nor, 2006. "A Comparison Between Fama and French Model and Liquidity-Based Three Factor Models in Predicting Portfolio Returns," Asian Academy of Management Journal of Accounting and Finance (AAMJAF), Penerbit Universiti Sains Malaysia, vol. 2(2), pages 43-60.
    3. Frazzini, Andrea & Pedersen, Lasse Heje, 2014. "Betting against beta," Journal of Financial Economics, Elsevier, vol. 111(1), pages 1-25.
    4. Sakowski Paweł & Ślepaczuk Robert & Wywiał Mateusz, 2016. "Cross-Sectional Returns with Volatility Regimes from a Diverse Portfolio of Emerging and Developed Equity Indices," Financial Internet Quarterly (formerly e-Finanse), Sciendo, vol. 12(2), pages 23-35.
    5. Fama, Eugene F. & French, Kenneth R., 2012. "Size, value, and momentum in international stock returns," Journal of Financial Economics, Elsevier, vol. 105(3), pages 457-472.
    6. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    7. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    8. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    9. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cakici, Nusret & Zaremba, Adam, 2022. "Salience theory and the cross-section of stock returns: International and further evidence," Journal of Financial Economics, Elsevier, vol. 146(2), pages 689-725.
    2. Adam Zaremba & Jacob Koby Shemer, 2018. "Price-Based Investment Strategies," Springer Books, Springer, number 978-3-319-91530-2, December.
    3. Hanauer, Matthias X. & Lauterbach, Jochim G., 2019. "The cross-section of emerging market stock returns," Emerging Markets Review, Elsevier, vol. 38(C), pages 265-286.
    4. Thomas Nitschka, 2016. "Is There a Too-Big-to-Fail Discount in Excess Returns on German Banks’ Stocks?," International Finance, Wiley Blackwell, vol. 19(3), pages 292-310, December.
    5. Zaremba, Adam & Szyszka, Adam & Karathanasopoulos, Andreas & Mikutowski, Mateusz, 2021. "Herding for profits: Market breadth and the cross-section of global equity returns," Economic Modelling, Elsevier, vol. 97(C), pages 348-364.
    6. Cakici, Nusret & Zaremba, Adam, 2021. "Who should be afraid of infections? Pandemic exposure and the cross-section of stock returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 72(C).
    7. Qiao, Zhuo & Wang, Yan & Lam, Keith S.K., 2022. "New evidence on Bayesian tests of global factor pricing models," Journal of Empirical Finance, Elsevier, vol. 68(C), pages 160-172.
    8. Sakowski Paweł & Ślepaczuk Robert & Wywiał Mateusz, 2016. "Cross-Sectional Returns with Volatility Regimes from a Diverse Portfolio of Emerging and Developed Equity Indices," Financial Internet Quarterly (formerly e-Finanse), Sciendo, vol. 12(2), pages 23-35.
    9. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "Estimation of large dimensional conditional factor models in finance," Working Papers unige:125031, University of Geneva, Geneva School of Economics and Management.
    10. Cakici, Nusret & Zaremba, Adam, 2023. "Recency bias and the cross-section of international stock returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 84(C).
    11. Dahlquist, Magnus & Odegaard, Bernt Arne, 2018. "A Review of Norges Bank's Active Management of the Government Pension Fund Global," UiS Working Papers in Economics and Finance 2018/1, University of Stavanger.
    12. Zaremba, Adam & Czapkiewicz, Anna, 2017. "Digesting anomalies in emerging European markets: A comparison of factor pricing models," Emerging Markets Review, Elsevier, vol. 31(C), pages 1-15.
    13. Bradrania, Reza & Veron, Jose Francisco, 2023. "The beta anomaly in the Australian stock market and the lottery demand," Pacific-Basin Finance Journal, Elsevier, vol. 77(C).
    14. Ciciretti, Rocco & Dalò, Ambrogio & Dam, Lammertjan, 2023. "The contributions of betas versus characteristics to the ESG premium," Journal of Empirical Finance, Elsevier, vol. 71(C), pages 104-124.
    15. Sara Kelly Anzinger & Chinmoy Ghosh & Milena Petrova, 2017. "The Other Side of Value: The Effect of Quality on Price and Return in Real Estate," The Journal of Real Estate Finance and Economics, Springer, vol. 54(3), pages 429-457, April.
    16. Shiyang Huang & Xin Liu & Dong Lou & Christopher Polk, 2024. "The Booms and Busts of Beta Arbitrage," Management Science, INFORMS, vol. 70(8), pages 5367-5385, August.
    17. Ruanmin Cao & Lajos Horváth & Zhenya Liu & Yuqian Zhao, 2020. "A study of data-driven momentum and disposition effects in the Chinese stock market by functional data analysis," Review of Quantitative Finance and Accounting, Springer, vol. 54(1), pages 335-358, January.
    18. Christian Fieberg & Daniel Metko & Thorsten Poddig & Thomas Loy, 2023. "Machine learning techniques for cross-sectional equity returns’ prediction," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 289-323, March.
    19. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    20. Lu Zhang, 2017. "The Investment CAPM," European Financial Management, European Financial Management Association, vol. 23(4), pages 545-603, September.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:war:wpaper:2016-08. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Marcin Bąba (email available below). General contact details of provider: https://edirc.repec.org/data/fesuwpl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.