IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.02521.html
   My bibliography  Save this paper

Fundamental properties of linear factor models

Author

Listed:
  • Damir Filipovic
  • Paul Schneider

Abstract

We study conditional linear factor models in the context of asset pricing panels. Our analysis focuses on conditional means and covariances to characterize the cross-sectional and inter-temporal properties of returns and factors as well as their interrelationships. We also review the conditions outlined in Kozak and Nagel (2024) and show how the conditional mean-variance efficient portfolio of an unbalanced panel can be spanned by low-dimensional factor portfolios, even without assuming invertibility of the conditional covariance matrices. Our analysis provides a comprehensive foundation for the specification and estimation of conditional linear factor models.

Suggested Citation

  • Damir Filipovic & Paul Schneider, 2024. "Fundamental properties of linear factor models," Papers 2409.02521, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2409.02521
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.02521
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kelly, Bryan T. & Pruitt, Seth & Su, Yinan, 2019. "Characteristics are covariances: A unified model of risk and return," Journal of Financial Economics, Elsevier, vol. 134(3), pages 501-524.
    2. 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..
    3. Olivier Ledoit & Michael Wolf, 2019. "The power of (non-)linear shrinking: a review and guide to covariance matrix estimation," ECON - Working Papers 323, Department of Economics - University of Zurich, revised Feb 2020.
    4. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," Review of Finance, European Finance Association, vol. 33(5), pages 2223-2273.
    5. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2223-2273.
    6. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    7. Joachim Freyberger & Andreas Neuhierl & Michael Weber, 2020. "Dissecting Characteristics Nonparametrically," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2326-2377.
    8. 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.
    9. Alain-Philippe Fortin & Patrick Gagliardini & Olivier Scaillet, 2023. "Latent Factor Analysis in Short Panels," Swiss Finance Institute Research Paper Series 23-44, Swiss Finance Institute.
    10. Joachim Freyberger & Andreas Neuhierl & Michael Weber & Andrew KarolyiEditor, 2020. "Dissecting Characteristics Nonparametrically," Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2326-2377.
    11. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-1323, September.
    12. Robert F. Engle & Olivier Ledoit & Michael Wolf, 2019. "Large Dynamic Covariance Matrices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 363-375, April.
    13. Admati, Anat R. & Pfleiderer, Paul, 1985. "Interpreting the factor risk premia in the arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 35(1), pages 191-195, February.
    14. Eugene F Fama & Kenneth R French, 2020. "Comparing Cross-Section and Time-Series Factor Models," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 1891-1926.
    15. Eugene F Fama & Kenneth R French & Andrew KarolyiEditor, 2020. "Comparing Cross-Section and Time-Series Factor Models," Review of Finance, European Finance Association, vol. 33(5), pages 1891-1926.
    16. Lu, Cuicui & Schmidt, Peter, 2012. "Conditions for the numerical equality of the OLS, GLS and Amemiya–Cragg estimators," Economics Letters, Elsevier, vol. 116(3), pages 538-540.
    17. Reisman, Haim, 1988. "A General Approach to the Arbitrage Pricing Theory (APT)," Econometrica, Econometric Society, vol. 56(2), pages 473-476, March.
    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. Guillaume Coqueret, 2022. "Characteristics-driven returns in equilibrium," Papers 2203.07865, arXiv.org.
    2. Ma, Tian & Leong, Wen Jun & Jiang, Fuwei, 2023. "A latent factor model for the Chinese stock market," International Review of Financial Analysis, Elsevier, vol. 87(C).
    3. Francisco Peñaranda & Enrique Sentana, 2024. "Portfolio management with big data," Working Papers wp2024_2411, CEMFI.
    4. Lioui, Abraham & Tarelli, Andrea, 2022. "Chasing the ESG factor," Journal of Banking & Finance, Elsevier, vol. 139(C).
    5. Thomas Conlon & John Cotter & Iason Kynigakis, 2021. "Machine Learning and Factor-Based Portfolio Optimization," Papers 2107.13866, arXiv.org.
    6. De Nard, Gianluca & Zhao, Zhao, 2023. "Using, taming or avoiding the factor zoo? A double-shrinkage estimator for covariance matrices," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 23-35.
    7. Söhnke M. Bartram & Harald Lohre & Peter F. Pope & Ananthalakshmi Ranganathan, 2021. "Navigating the factor zoo around the world: an institutional investor perspective," Journal of Business Economics, Springer, vol. 91(5), pages 655-703, July.
    8. Wolfgang Drobetz & Tizian Otto, 2021. "Empirical asset pricing via machine learning: evidence from the European stock market," Journal of Asset Management, Palgrave Macmillan, vol. 22(7), pages 507-538, December.
    9. Smith, Simon C., 2022. "Time-variation, multiple testing, and the factor zoo," International Review of Financial Analysis, Elsevier, vol. 84(C).
    10. Bakalli, Gaetan & Guerrier, Stéphane & Scaillet, Olivier, 2023. "A penalized two-pass regression to predict stock returns with time-varying risk premia," Journal of Econometrics, Elsevier, vol. 237(2).
    11. Clarke, Charles, 2022. "The level, slope, and curve factor model for stocks," Journal of Financial Economics, Elsevier, vol. 143(1), pages 159-187.
    12. Baba-Yara, Fahiz & Boons, Martijn & Tamoni, Andrea, 2024. "Persistent and transitory components of firm characteristics: Implications for asset pricing," Journal of Financial Economics, Elsevier, vol. 154(C).
    13. Svetlana Bryzgalova & Jiantao Huang & Christian Julliard, 2023. "Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models," Journal of Finance, American Finance Association, vol. 78(1), pages 487-557, February.
    14. Ai He & Guofu Zhou, 2023. "Diagnostics for asset pricing models," Financial Management, Financial Management Association International, vol. 52(4), pages 617-642, December.
    15. Smith, Simon C. & Timmermann, Allan, 2022. "Have risk premia vanished?," Journal of Financial Economics, Elsevier, vol. 145(2), pages 553-576.
    16. Simon Hediger & Jeffrey Näf & Marc S. Paolella & Paweł Polak, 2023. "Heterogeneous tail generalized common factor modeling," Digital Finance, Springer, vol. 5(2), pages 389-420, June.
    17. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    18. Khan, M. Ali & Sun, Yeneng, 2003. "Exact arbitrage, well-diversified portfolios and asset pricing in large markets," Journal of Economic Theory, Elsevier, vol. 110(2), pages 337-373, June.
    19. Yan, Jingda & Yu, Jialin, 2023. "Cross-stock momentum and factor momentum," Journal of Financial Economics, Elsevier, vol. 150(2).
    20. Doron Avramov & Si Cheng & Lior Metzker, 2023. "Machine Learning vs. Economic Restrictions: Evidence from Stock Return Predictability," Management Science, INFORMS, vol. 69(5), pages 2587-2619, May.

    More about this item

    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:arx:papers:2409.02521. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.