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Measurement of factor strength: Theory and practice

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  • Natalia Bailey
  • George Kapetanios
  • M. Hashem Pesaran

Abstract

This paper proposes an estimator of factor strength and establishes its consistency and asymptotic distribution. The estimator is based on the number of statistically significant factor loadings, taking multiple testing into account. Both cases of observed and unobserved factors are considered. The small sample properties of the proposed estimator are investigated using Monte Carlo experiments. It is shown that the proposed estimation and inference procedures perform well and have excellent power properties, especially when the factor strength is sufficiently high. Empirical applications to factor models for asset returns show that out of 146 factors recently considered in the finance literature, only the market factor is truly strong, while all other factors are at best semi‐strong, with their strength varying considerably over time. Similarly, we only find evidence of semi‐strong factors using a large number of US macroeconomic indicators.

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  • Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2021. "Measurement of factor strength: Theory and practice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 587-613, August.
    • Handle: RePEc:wly:japmet:v:36:y:2021:i:5:p:587-613
    DOI: 10.1002/jae.2830
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    1. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2021. "Economic Predictions With Big Data: The Illusion of Sparsity," Econometrica, Econometric Society, vol. 89(5), pages 2409-2437, September.
    2. Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2016. "Exponent of Cross‐Sectional Dependence: Estimation and Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(6), pages 929-960, September.
    3. A. Chudik & G. Kapetanios & M. Hashem Pesaran, 2018. "A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High‐Dimensional Linear Regression Models," Econometrica, Econometric Society, vol. 86(4), pages 1479-1512, July.
    4. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    5. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    6. Guanhao Feng & Stefano Giglio & Dacheng Xiu, 2020. "Taming the Factor Zoo: A Test of New Factors," Journal of Finance, American Finance Association, vol. 75(3), pages 1327-1370, June.
    7. Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2019. "Exponent of Cross-sectional Dependence for Residuals," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 46-102, September.
    8. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    9. 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..
    10. Daron Acemoglu & Vasco M. Carvalho & Asuman Ozdaglar & Alireza Tahbaz‐Salehi, 2012. "The Network Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 80(5), pages 1977-2016, September.
    11. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    12. M Hashem Pesaran & Takashi Yamagata, 2024. "Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities," Journal of Financial Econometrics, Oxford University Press, vol. 22(2), pages 407-460.
    13. Lettau, Martin & Pelger, Markus, 2020. "Estimating latent asset-pricing factors," Journal of Econometrics, Elsevier, vol. 218(1), pages 1-31.
    14. Roll, Richard, 1977. "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory," Journal of Financial Economics, Elsevier, vol. 4(2), pages 129-176, March.
    15. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    16. M. Hashem Pesaran & Ron P. Smith, 2021. "Factor Strengths, Pricing Errors, and Estimation of Risk Premia," CESifo Working Paper Series 8947, CESifo.
    17. Simon Freyaldenhoven, 2017. "A Generalized Factor Model with Local Factors," 2017 Papers pfr361, Job Market Papers.
    18. Veronika Ročková & Edward I. George, 2016. "Fast Bayesian Factor Analysis via Automatic Rotations to Sparsity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1608-1622, October.
    19. Yoshimasa Uematsu & Takashi Yamagata, 2019. "Estimation of Weak Factor Models," ISER Discussion Paper 1053, Institute of Social and Economic Research, Osaka University.
    20. Anatolyev, Stanislav & Mikusheva, Anna, 2022. "Factor models with many assets: Strong factors, weak factors, and the two-pass procedure," Journal of Econometrics, Elsevier, vol. 229(1), pages 103-126.
    21. Pesaran, M. Hashem & Yang, Cynthia Fan, 2020. "Econometric analysis of production networks with dominant units," Journal of Econometrics, Elsevier, vol. 219(2), pages 507-541.
    22. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference for high-dimensional sparse econometric models," CeMMAP working papers CWP41/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    23. Kleibergen, Frank, 2009. "Tests of risk premia in linear factor models," Journal of Econometrics, Elsevier, vol. 149(2), pages 149-173, April.
    24. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    25. Pesaran, M. Hashem, 2015. "Time Series and Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780198759980.
    26. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    27. Freyaldenhoven, Simon, 2022. "Factor models with local factors — Determining the number of relevant factors," Journal of Econometrics, Elsevier, vol. 229(1), pages 80-102.
    28. 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.
    29. 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.
    30. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    31. Yoshimasa Uematsu & Takashi Yamagata, 2019. "Estimation of Weak Factor Models," ISER Discussion Paper 1053r, Institute of Social and Economic Research, Osaka University, revised Mar 2020.
    32. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    33. 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.
    34. M. Hashem Pesaran & Ron P. Smith, 2019. "The Role of Factor Strength and Pricing Errors for Estimation and Inference in Asset Pricing Models," CESifo Working Paper Series 7919, CESifo.
    35. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
    36. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    37. James H. Stock & Mark W. Watson, 2012. "Disentangling the Channels of the 2007-2009 Recession," NBER Working Papers 18094, National Bureau of Economic Research, Inc.
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    Cited by:

    1. M. Hashem Pesaran & Ron P. Smith, 2023. "The Role of Pricing Errors in Linear Asset Pricing Models with Strong, Semi-Strong, and Latent Factors," CESifo Working Paper Series 10282, CESifo.
    2. Ge, S., 2020. "Text-Based Linkages and Local Risk Spillovers in the Equity Market," Cambridge Working Papers in Economics 20115, Faculty of Economics, University of Cambridge.
    3. Freyaldenhoven, Simon, 2022. "Factor models with local factors — Determining the number of relevant factors," Journal of Econometrics, Elsevier, vol. 229(1), pages 80-102.
    4. Jie Wei & Yonghui Zhang, 2023. "Does Principal Component Analysis Preserve the Sparsity in Sparse Weak Factor Models?," Papers 2305.05934, arXiv.org, revised Nov 2024.
    5. Jianqing Fan & Yuling Yan & Yuheng Zheng, 2024. "When can weak latent factors be statistically inferred?," Papers 2407.03616, arXiv.org, revised Sep 2024.
    6. M Hashem Pesaran & Takashi Yamagata, 2024. "Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities," Journal of Financial Econometrics, Oxford University Press, vol. 22(2), pages 407-460.
    7. Choi, In & Lin, Rui & Shin, Yongcheol, 2023. "Canonical correlation-based model selection for the multilevel factors," Journal of Econometrics, Elsevier, vol. 233(1), pages 22-44.
    8. Pesaran, M. Hashem & Smith, Ron P., 2023. "Arbitrage pricing theory, the stochastic discount factor and estimation of risk premia from portfolios," Econometrics and Statistics, Elsevier, vol. 26(C), pages 17-30.
    9. Ge, Shuyi & Li, Shaoran & Linton, Oliver, 2023. "News-implied linkages and local dependency in the equity market," Journal of Econometrics, Elsevier, vol. 235(2), pages 779-815.
    10. M. Hashem Pesaran & Run Smith, 2021. "Arbitrage pricing theory, the stochastic discount factor and estimation of risk premia in portfolios," BCAM Working Papers 2108, Birkbeck Centre for Applied Macroeconomics.

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    More about this item

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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