IDEAS home Printed from https://ideas.repec.org/a/tpr/restat/v102y2020i3p531-551.html
   My bibliography  Save this article

Characteristic-Sorted Portfolios: Estimation and Inference

Author

Listed:
  • Matias D. Cattaneo

    (Princeton University)

  • Richard K. Crump

    (Federal Reserve Bank of New York)

  • Max H. Farrell

    (University of Chicago)

  • Ernst Schaumburg

    (AQR Capital Management)

Abstract

Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We develop a general framework for portfolio sorting by casting it as a nonparametric estimator. We present valid asymptotic inference methods and a valid mean square error expansion of the estimator leading to an optimal choice for the number of portfolios. In practical settings, the optimal choice may be much larger than the standard choices of five or ten. To illustrate the relevance of our results, we revisit the size and momentum anomalies.

Suggested Citation

  • Matias D. Cattaneo & Richard K. Crump & Max H. Farrell & Ernst Schaumburg, 2020. "Characteristic-Sorted Portfolios: Estimation and Inference," The Review of Economics and Statistics, MIT Press, vol. 102(3), pages 531-551, July.
    • Handle: RePEc:tpr:restat:v:102:y:2020:i:3:p:531-551
    as

    Download full text from publisher

    File URL: http://www.mitpressjournals.org/doi/pdf/10.1162/rest_a_00883
    Download Restriction: Access to PDF is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Harrison Hong & Terence Lim & Jeremy C. Stein, 2000. "Bad News Travels Slowly: Size, Analyst Coverage, and the Profitability of Momentum Strategies," Journal of Finance, American Finance Association, vol. 55(1), pages 265-295, February.
    2. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2015. "Regression-based estimation of dynamic asset pricing models," Journal of Financial Economics, Elsevier, vol. 118(2), pages 211-244.
    3. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    4. Tobias J. Moskowitz & Mark Grinblatt, 1999. "Do Industries Explain Momentum?," Journal of Finance, American Finance Association, vol. 54(4), pages 1249-1290, August.
    5. Nagel, Stefan, 2005. "Short sales, institutional investors and the cross-section of stock returns," Journal of Financial Economics, Elsevier, vol. 78(2), pages 277-309, November.
    6. Banz, Rolf W., 1981. "The relationship between return and market value of common stocks," Journal of Financial Economics, Elsevier, vol. 9(1), pages 3-18, March.
    7. Jennifer Conrad & Michael Cooper & Gautam Kaul, 2003. "Value versus Glamour," Journal of Finance, American Finance Association, vol. 58(5), pages 1969-1996, October.
    8. Donald W. K. Andrews, 2005. "Cross-Section Regression with Common Shocks," Econometrica, Econometric Society, vol. 73(5), pages 1551-1585, September.
    9. Grundy, Bruce D & Martin, J Spencer, 2001. "Understanding the Nature of the Risks and the," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 29-78.
    10. Bruce N. Lehmann, 1990. "Fads, Martingales, and Market Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 1-28.
    11. Jennifer Conrad & Michael Cooper & Gautam Kaul, 2003. "Value versus Glamour," Journal of Finance, American Finance Association, vol. 58(5), pages 1969-1995, October.
    12. Stefan Nagel & Kenneth J. Singleton, 2011. "Estimation and Evaluation of Conditional Asset Pricing Models," Journal of Finance, American Finance Association, vol. 66(3), pages 873-909, June.
    13. Shanken, Jay & Zhou, Guofu, 2007. "Estimating and testing beta pricing models: Alternative methods and their performance in simulations," Journal of Financial Economics, Elsevier, vol. 84(1), pages 40-86, April.
    14. Basu, S, 1977. "Investment Performance of Common Stocks in Relation to Their Price-Earnings Ratios: A Test of the Efficient Market Hypothesis," Journal of Finance, American Finance Association, vol. 32(3), pages 663-682, June.
    15. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    16. Narasimhan Jegadeesh & Sheridan Titman, 2001. "Profitability of Momentum Strategies: An Evaluation of Alternative Explanations," Journal of Finance, American Finance Association, vol. 56(2), pages 699-720, April.
    17. Reinganum, Marc R., 1981. "Misspecification of capital asset pricing : Empirical anomalies based on earnings' yields and market values," Journal of Financial Economics, Elsevier, vol. 9(1), pages 19-46, March.
    18. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    19. Patton, Andrew J. & Timmermann, Allan, 2010. "Monotonicity in asset returns: New tests with applications to the term structure, the CAPM, and portfolio sorts," Journal of Financial Economics, Elsevier, vol. 98(3), pages 605-625, December.
    20. Kleibergen, Frank & Zhan, Zhaoguo, 2015. "Unexplained factors and their effects on second pass R-squared’s," Journal of Econometrics, Elsevier, vol. 189(1), pages 101-116.
    21. Lo, Andrew W & MacKinlay, A Craig, 1990. "Data-Snooping Biases in Tests of Financial Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 431-467.
    22. Sebastian Calonico & Matias D. Cattaneo & Rocío Titiunik, 2015. "Optimal Data-Driven Regression Discontinuity Plots," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1753-1769, December.
    23. Cattaneo, Matias D. & Farrell, Max H., 2013. "Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators," Journal of Econometrics, Elsevier, vol. 174(2), pages 127-143.
    24. Jegadeesh, Narasimhan, 1990. "Evidence of Predictable Behavior of Security Returns," Journal of Finance, American Finance Association, vol. 45(3), pages 881-898, July.
    25. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2010. "Robust Data-Driven Inference for Density-Weighted Average Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1070-1083.
    26. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2017. "Spurious Inference in Reduced‐Rank Asset‐Pricing Models," Econometrica, Econometric Society, vol. 85, pages 1613-1628, September.
    27. Romano, Joseph P. & Wolf, Michael, 2013. "Testing for monotonicity in expected asset returns," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 93-116.
    28. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    29. Jonathan B. Berk, 2000. "Sorting Out Sorts," Journal of Finance, American Finance Association, vol. 55(1), pages 407-427, February.
    30. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2014. "Spurious Inference in Unidentified Asset-Pricing Models," FRB Atlanta Working Paper 2014-12, Federal Reserve Bank of Atlanta.
    31. 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.
    32. Joseph P. Romano & Michael Wolf, 2011. "Testing for monotonicity in expected asset returns," ECON - Working Papers 017, Department of Economics - University of Zurich, revised Jan 2013.
    33. Ibragimov, Rustam & Müller, Ulrich K., 2010. "t-Statistic Based Correlation and Heterogeneity Robust Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 453-468.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Matias D. Cattaneo & Richard K. Crump & Max H. Farrell & Yingjie Feng, 2019. "On binscatter," Staff Reports 881, Federal Reserve Bank of New York.
      • Matias D. Cattaneo & Richard K. Crump & Max H. Farrell & Yingjie Feng, 2019. "On Binscatter," Papers 1902.09608, arXiv.org, revised Nov 2023.
    2. Ni, Xuanming & Zheng, Tiantian & Zhao, Huimin & Zhu, Shushang, 2023. "High-dimensional portfolio optimization based on tree-structured factor model," Pacific-Basin Finance Journal, Elsevier, vol. 81(C).
    3. Joachim Freyberger & Andreas Neuhierl & Michael Weber, 2020. "Dissecting Characteristics Nonparametrically," Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2326-2377.
    4. Chaieb, Ines & Langlois, Hugues & Scaillet, Olivier, 2021. "Factors and risk premia in individual international stock returns," Journal of Financial Economics, Elsevier, vol. 141(2), pages 669-692.
    5. Christophe J. GODLEWSKI & Katarzyna BYRKA-KITA & Renata GOLA & Jacek CYPRYJANSKI, 2022. "Silence is not golden anymore? Social media activity and stock market valuation in Europe," Working Papers of LaRGE Research Center 2022-04, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    6. Matias D. Cattaneo & Richard K. Crump & Weining Wang, 2022. "Beta-Sorted Portfolios," Papers 2208.10974, arXiv.org, revised Jul 2023.
    7. Guillaume Coqueret, 2022. "Characteristics-driven returns in equilibrium," Papers 2203.07865, arXiv.org.
    8. Matias D. Cattaneo & Max H. Farrell & Yingjie Feng, 2018. "Large Sample Properties of Partitioning-Based Series Estimators," Papers 1804.04916, arXiv.org, revised Jun 2019.

    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. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    2. Stephen A. Gorman & Frank J. Fabozzi, 2021. "The ABC’s of the alternative risk premium: academic roots," Journal of Asset Management, Palgrave Macmillan, vol. 22(6), pages 405-436, October.
    3. Adam Zaremba & Jacob Koby Shemer, 2018. "Price-Based Investment Strategies," Springer Books, Springer, number 978-3-319-91530-2, June.
    4. Cakici, Nusret & Zaremba, Adam & Bianchi, Robert J. & Pham, Nga, 2021. "False discoveries in the anomaly research: New insights from the Stock Exchange of Melbourne (1927–1987)," Pacific-Basin Finance Journal, Elsevier, vol. 70(C).
    5. Jiri NOVAK, 2014. "Does Stock Liquidity Explain the Premium for Stock Price Momentum?," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 64(1), pages 79-95, February.
    6. Eero Pätäri & Timo Leivo, 2017. "A Closer Look At Value Premium: Literature Review And Synthesis," Journal of Economic Surveys, Wiley Blackwell, vol. 31(1), pages 79-168, February.
    7. repec:gnv:wpaper:unige:76321 is not listed on IDEAS
    8. Patrick Gagliardini & Elisa Ossola & Olivier Scaillet, 2016. "Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets," Econometrica, Econometric Society, vol. 84, pages 985-1046, May.
    9. Kewei Hou & Chen Xue & Lu Zhang, 2017. "Replicating Anomalies," NBER Working Papers 23394, National Bureau of Economic Research, Inc.
    10. Martin H. Schmidt, 2017. "Trading strategies based on past returns: evidence from Germany," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 31(2), pages 201-256, May.
    11. Waszczuk, Antonina, 2013. "A risk-based explanation of return patterns—Evidence from the Polish stock market," Emerging Markets Review, Elsevier, vol. 15(C), pages 186-210.
    12. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
    13. Hannah Lea Hühn & Hendrik Scholz, 2019. "Reversal and momentum patterns in weekly stock returns: European evidence," Review of Financial Economics, John Wiley & Sons, vol. 37(2), pages 272-296, April.
    14. Heston, Steven L. & Sadka, Ronnie, 2008. "Seasonality in the cross-section of stock returns," Journal of Financial Economics, Elsevier, vol. 87(2), pages 418-445, February.
    15. Gabriel Hawawini & Donald B. Keim, "undated". "The Cross Section of Common Stock Returns: A Review of the Evidence and Some New Findings," Rodney L. White Center for Financial Research Working Papers 08-99, Wharton School Rodney L. White Center for Financial Research.
    16. Anton Astakhov & Tomas Havranek & Jiri Novak, 2019. "Firm Size And Stock Returns: A Quantitative Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 33(5), pages 1463-1492, December.
    17. Han, Yufeng & Zhou, Guofu & Zhu, Yingzi, 2016. "A trend factor: Any economic gains from using information over investment horizons?," Journal of Financial Economics, Elsevier, vol. 122(2), pages 352-375.
    18. Ivelina Pavlova & A. M. Parhizgari, 2011. "In search of momentum profits: are they illusory?," Applied Financial Economics, Taylor & Francis Journals, vol. 21(21), pages 1617-1639.
    19. Adam Zaremba, 2019. "The Cross Section of Country Equity Returns: A Review of Empirical Literature," JRFM, MDPI, vol. 12(4), pages 1-26, October.
    20. Hurst, Gareth & Docherty, Paul, 2015. "Trend salience, investor behaviours and momentum profitability," Pacific-Basin Finance Journal, Elsevier, vol. 35(PB), pages 471-484.
    21. Fernando Rubio, 2005. "Eficiencia De Mercado, Administracion De Carteras De Fondos Y Behavioural Finance," Finance 0503028, University Library of Munich, Germany, revised 23 Jul 2005.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    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:tpr:restat:v:102:y:2020:i:3:p:531-551. 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: Kelly McDougall (email available below). General contact details of provider: https://direct.mit.edu/journals .

    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.