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The Cross-Section of Risk and Returns

Author

Listed:
  • Kent Daniel
  • Lira Mota
  • Simon Rottke
  • Tano Santos

Abstract

A common practice in the finance literature is to create characteristic portfolios by sorting on characteristics associated with average returns. We show that the resultant portfolios are likely to capture not only the priced risk associated with the characteristic but also unpriced risk. We develop a procedure to remove this unpriced risk using covariance information estimated from past returns. We apply our methodology to the five Fama-French characteristic portfolios. The squared Sharpe ratio of the optimal combination of the resultant characteristic-efficient portfolios is 2.13, compared with 1.17 for the original characteristic portfolios.

Suggested Citation

  • Kent Daniel & Lira Mota & Simon Rottke & Tano Santos, 2020. "The Cross-Section of Risk and Returns," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 1927-1979.
    • Handle: RePEc:oup:rfinst:v:33:y:2020:i:5:p:1927-1979.
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    File URL: http://hdl.handle.net/10.1093/rfs/hhaa021
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    Cited by:

    1. Cong, Lin William & Feng, Guanhao & He, Jingyu & He, Xin, 2025. "Growing the efficient frontier on panel trees," Journal of Financial Economics, Elsevier, vol. 167(C).
    2. Armin Varmaz & Christian Fieberg & Thorsten Poddig, 2024. "Portfolio optimization for sustainable investments," Annals of Operations Research, Springer, vol. 341(2), pages 1151-1176, October.
    3. Tengfei Zhang, 2020. "Manager Uncertainty and Cross-Sectional Stock Returns," 2020 Papers pzh934, Job Market Papers.
    4. Mikhail Chernov & Lars A Lochstoer & Stig R H Lundeby, 2022. "Conditional Dynamics and the Multihorizon Risk-Return Trade-Off," The Review of Financial Studies, Society for Financial Studies, vol. 35(3), pages 1310-1347.
    5. G Andrew Karolyi & Stijn Van Nieuwerburgh, 2020. "New Methods for the Cross-Section of Returns," Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 1879-1890.
    6. Lin William Cong & Guanhao Feng & Jingyu He & Xin He, 2022. "Growing the Efficient Frontier on Panel Trees," NBER Working Papers 30805, National Bureau of Economic Research, Inc.
    7. Clarke, Charles, 2022. "The level, slope, and curve factor model for stocks," Journal of Financial Economics, Elsevier, vol. 143(1), pages 159-187.
    8. 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).
    9. Guillaume Coqueret, 2022. "Characteristics-driven returns in equilibrium," Papers 2203.07865, arXiv.org.
    10. Breitung, Christian & Müller, Sebastian, 2025. "Global Business Networks," Journal of Financial Economics, Elsevier, vol. 166(C).
    11. Cujean, Julien & Andrei, Daniel & Fournier, Mathieu, 2019. "The Low-Minus-High Portfolio and the Factor Zoo," CEPR Discussion Papers 14153, C.E.P.R. Discussion Papers.
    12. Langlois, Hugues, 2023. "What matters in a characteristic?," Journal of Financial Economics, Elsevier, vol. 149(1), pages 52-72.
    13. I-Cheng Yeh & Yi-Cheng Liu, 2020. "Discovering optimal weights in weighted-scoring stock-picking models: a mixture design approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-28, December.
    14. Soebhag, Amar & Van Vliet, Bart & Verwijmeren, Patrick, 2024. "Non-standard errors in asset pricing: Mind your sorts," Journal of Empirical Finance, Elsevier, vol. 78(C).
    15. Yukun Liu & Aleh Tsyvinski & Xi Wu, 2019. "Common Risk Factors in Cryptocurrency," NBER Working Papers 25882, National Bureau of Economic Research, Inc.
    16. Bertelli, Beatrice & Torricelli, Costanza, 2025. "Sustainable optimal stock portfolios: What relationship between sustainability and performance?," European Journal of Operational Research, Elsevier, vol. 323(1), pages 323-340.
    17. Yuxiao Jiao & Guofu Zhou & Wu Zhu & Yingzi Zhu, 2025. "Interpretable Factors of Firm Characteristics," Papers 2508.02253, arXiv.org.
    18. Favero, Carlo A. & Melone, Alessandro, 2020. "Asset Pricing vs Asset Expected Returning in Factor-Portfolio Models," CEPR Discussion Papers 14417, C.E.P.R. Discussion Papers.
    19. Lambert, Marie & Fays, Boris & Hübner, Georges, 2020. "Factoring characteristics into returns: A clinical study on the SMB and HML portfolio construction methods," Journal of Banking & Finance, Elsevier, vol. 114(C).

    More about this item

    JEL classification:

    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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