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The Risk Premia from the European Equity Market: An application of the Three-Pass Estimation Methodology

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  • Elisa Ossola
  • Irina Trifan

Abstract

We develop an empirical application on a large dataset of European stock returns, in order to estimate the risk premia. We propose an application of the Three-Pass Estimation Method (3PEM) by Xiu and Giglio (2021) as a multipurpose tool in asset pricing. By assuming the Fama–French Five-Factor model (Fama and French (2015)) as baseline model, we show that the 3PEM yields risk premium estimates that are more economically plausible and statistically robust than those obtained using the traditional two-pass estimation method (2PEM). Moreover, we extend the results by Xiu and Giglio (2021) showing that the 3PEM is able to detect noise in tradable factors. Furthermore, the method is used to denoise the observed factors, providing purified versions that better capture the systematic components of risk. We also identify noisy factors, and yield denoised factor series that improve the estimation of stock-level exposures and expected returns.

Suggested Citation

  • Elisa Ossola & Irina Trifan, 2025. "The Risk Premia from the European Equity Market: An application of the Three-Pass Estimation Methodology," Working Papers 565, University of Milano-Bicocca, Department of Economics.
    • Handle: RePEc:mib:wpaper:565
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    References listed on IDEAS

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    1. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    2. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    3. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    4. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    5. 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.
    6. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2020. "Estimation of large dimensional conditional factor models in finance," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 219-282, Elsevier.
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    Keywords

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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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