1932

Abstract

We survey recent methodological contributions in asset pricing using factor models and machine learning. We organize these results based on their primary objectives: estimating expected returns, factors, risk exposures, risk premia, and the stochastic discount factor as well as model comparison and alpha testing. We also discuss a variety of asymptotic schemes for inference. Our survey is a guide for financial economists interested in harnessing modern tools with rigor, robustness, and power to make new asset pricing discoveries, and it highlights directions for future research and methodological advances.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-financial-101521-104735
2022-11-01
2024-06-16
Loading full text...

Full text loading...

/deliver/fulltext/financial/14/1/annurev-financial-101521-104735.html?itemId=/content/journals/10.1146/annurev-financial-101521-104735&mimeType=html&fmt=ahah

Literature Cited

  1. Ahn DH, Conrad J, Dittmar RF 2009. Basis assets. Rev. Financ. Stud. 22:125133–74
    [Google Scholar]
  2. Aït-Sahalia Y, Jacod J, Xiu D. 2021. Inference on risk premia in continuous-time asset pricing models. Work. Pap. Univ. Chicago Chicago, IL: https://dachxiu.chicagobooth.edu/download/RPContTime.pdf
    [Google Scholar]
  3. Anatolyev S, Mikusheva A. 2022. Factor models with many assets: strong factors, weak factors, and the two-pass procedure. J. Econom. 229:1103–26
    [Google Scholar]
  4. Ang A, Hodrick R, Xing Y, Zhang X. 2006. The cross-section of volatility and expected returns. J. Finance 61:259–99
    [Google Scholar]
  5. Ang A, Liu J, Schwarz K. 2020. Using individual stocks or portfolios in tests of factor models. J. Financ. Quant. Anal. 55:709–50
    [Google Scholar]
  6. Bai J. 2003. Inferential theory for factor models of large dimensions. Econometrica 71:1135–71
    [Google Scholar]
  7. Bai J, Ng S. 2002. Determining the number of factors in approximate factor models. Econometrica 70:191–221
    [Google Scholar]
  8. Bai J, Ng S. 2008. Forecasting economic time series using targeted predictors. J. Econom. 146:2304–17
    [Google Scholar]
  9. Bailey N, Kapetanios G, Pesaran MH. 2021. Measurement of factor strength: theory and practice. J. Appl. Econom. 36:5587–613
    [Google Scholar]
  10. Bajgrowicz P, Scaillet O. 2012. Technical trading revisited: false discoveries, persistence tests, and transaction costs. J. Financ. Econ. 106:3473–91
    [Google Scholar]
  11. Baldi P, Hornik K. 1989. Neural networks and principal component analysis: learning from examples without local minima. Neural Netw. 2:153–58
    [Google Scholar]
  12. Bansal R, Yaron A. 2004. Risks for the long run: a potential resolution of asset pricing puzzles. J. Finance 59:41481–509
    [Google Scholar]
  13. Barillas F, Kan R, Robotti C, Shanken J. 2020. Model comparison with Sharpe ratios. J. Financ. Quant. Anal. 55:61840–74
    [Google Scholar]
  14. Barillas F, Shanken J. 2017. Which alpha?. Rev. Financ. Stud. 30:41316–38
    [Google Scholar]
  15. Barillas F, Shanken J. 2018. Comparing asset pricing models. J. Finance 73:2715–54
    [Google Scholar]
  16. Barras L, Scaillet O, Wermers R. 2010. False discoveries in mutual fund performance: measuring luck in estimated alphas. J. Finance 65:1179–216
    [Google Scholar]
  17. Benjamini Y, Hochberg Y. 1995. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. Ser. B Methodol. 57:1289–300
    [Google Scholar]
  18. Benjamini Y, Yekutieli D. 2001. The control of the false discovery rate in multiple testing under dependency. Ann. Stat. 28:41165–88
    [Google Scholar]
  19. Brandt MW, Santa-Clara P, Valkanov R. 2009. Parametric portfolio policies: exploiting characteristics in the cross-section of equity returns. Rev. Financ. Stud. 22:93411–47
    [Google Scholar]
  20. Bryzgalova S. 2015. Spurious factors in linear asset pricing models Work. Pap. Stanford Univ. Stanford, CA:
    [Google Scholar]
  21. Bryzgalova S, Huang J, Julliard C. 2022. Bayesian solutions for the factor zoo: We just ran two quadrillion models. Work. Pap. Lond. Sch. Econ. Political Sci. London, UK: https://personal.lse.ac.uk/julliard/papers/BSftFT.pdf
    [Google Scholar]
  22. Bryzgalova S, Pelger M, Zhu J. 2020. Forest through the trees: building cross-sections of asset returns. SSRN Work. Pap. https://dx.doi.org/10.2139/ssrn.3493458
    [Crossref] [Google Scholar]
  23. Bchner M, Kelly BT. 2022. A factor model for option returns. J. Financ. Econ. 143:31140–61
    [Google Scholar]
  24. Campbell JY, Cochrane JH. 1999. By force of habit: a consumption-based explanation of aggregate stock market behavior. J. Political Econ. 107:2205–51
    [Google Scholar]
  25. Chamberlain G, Rothschild M. 1983. Arbitrage, factor structure, and mean-variance analysis on large asset markets. Econometrica 51:1281–304
    [Google Scholar]
  26. Chen AY. 2021. The limits of p-hacking: some thought experiments. J. Finance 76:52447–80
    [Google Scholar]
  27. Chen AY, Zimmermann T. 2022. Open source cross-sectional asset pricing. Crit. Finance Rev. 11:220764
    [Google Scholar]
  28. Chen L, Pelger M, Zhu J. 2019. Deep learning in asset pricing. Work. Pap. Stanford Univ. Stanford, CA:
    [Google Scholar]
  29. Chen NF, Roll R, Ross SA. 1986. Economic forces and the stock market. J. Bus. 59:3383–403
    [Google Scholar]
  30. Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C et al. 2018. Double/debiased machine learning for treatment and structure parameters. Econom. J. 21:1C1–68
    [Google Scholar]
  31. Chib S, Zeng X, Zhao L. 2020. On comparing asset pricing models. J. Finance 75:1551–77
    [Google Scholar]
  32. Chinco A, Clark-Joseph AD, Ye M 2019. Sparse signals in the cross-section of returns. J. Finance 74:449–92
    [Google Scholar]
  33. Cong LW, Tang K, Wang J, Zhang Y 2021. Alphaportfolio: direct construction through deep reinforcement learning and interpretable AI. Work. Pap. Cornell Univ. Ithaca, NY:
    [Google Scholar]
  34. Connor G, Hagmann M, Linton O. 2012. Efficient semiparametric estimation of the Fama–French model and extensions. Econometrica 80:2713–54
    [Google Scholar]
  35. Connor G, Korajczyk RA. 1986. Performance measurement with the arbitrage pricing theory: a new framework for analysis. J. Financ. Econ. 15:3373–94
    [Google Scholar]
  36. Daniel K, Hirshleifer D, Sun L. 2020. Short- and long-horizon behavioral factors. Rev. Financ. Stud. 33:41673–736
    [Google Scholar]
  37. DeMiguel V, Martin-Utrera A, Nogales FJ, Uppal R. 2020. A transaction-cost perspective on the multitude of firm characteristics. Rev. Financ. Stud. 33:52180–222
    [Google Scholar]
  38. Fama EF, French KR. 1993. Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 33:13–56
    [Google Scholar]
  39. Fama EF, French KR. 2008. Dissecting anomalies. J. Finance 63:41653–78
    [Google Scholar]
  40. Fama EF, French KR. 2010. Luck versus skill in the cross-section of mutual fund returns. J. Finance 65:51915–47
    [Google Scholar]
  41. Fama EF, French KR. 2015. A five-factor asset pricing model. J. Financ. Econ. 116:11–22
    [Google Scholar]
  42. Fama EF, MacBeth JD. 1973. Risk, return, and equilibrium: empirical tests. J. Political Econ. 81:3607–36
    [Google Scholar]
  43. Fan J, Liao Y, Mincheva M. 2011. High-dimensional covariance matrix estimation in approximate factor models. Ann. Stat. 39:63320–56
    [Google Scholar]
  44. Fan J, Liao Y, Wang W. 2016. Projected principal component analysis in factor models. Ann. Stat. 44:1219–54
    [Google Scholar]
  45. Fan J, Liao Y, Yao J. 2015. Power enhancement in high-dimensional cross-sectional tests. Econometrica 83:41497–541
    [Google Scholar]
  46. Feng G, Giglio S, Xiu D. 2020. Taming the factor zoo: a test of new factors. J. Finance 75:31327–70
    [Google Scholar]
  47. Freyaldenhoven S. 2019. A generalized factor model with local factors Work. Pap. 19-23, Fed Reserve Bank Phila. Philadelphia, PA:
    [Google Scholar]
  48. Freyberger J, Neuhierl A, Weber M. 2020. Dissecting characteristics nonparametrically. Rev. Financ. Stud. 33:52326–77
    [Google Scholar]
  49. Gagliardini P, Ossola E, Scaillet O. 2016. Time-varying risk premium in large cross-sectional equity datasets. Econometrica 84:3985–1046
    [Google Scholar]
  50. Gagliardini P, Ossola E, Scaillet O. 2019. A diagnostic criterion for approximate factor structure. J. Econom. 212:2503–21
    [Google Scholar]
  51. Gibbons M, Ross SA, Shanken J. 1989. A test of the efficiency of a given portfolio. Econometrica 57:51121–52
    [Google Scholar]
  52. Giglio S, Liao Y, Xiu D. 2021. Thousands of alpha tests. Rev. Financ. Stud. 34:73456–96
    [Google Scholar]
  53. Giglio S, Xiu D. 2021. Asset pricing with omitted factors. J. Political Econ. 129:71947–90
    [Google Scholar]
  54. Giglio S, Xiu D, Zhang D. 2021. Test assets and weak factors NBER Work. Pap. 29002
    [Google Scholar]
  55. Gospodinov N, Kan R, Robotti C. 2013. Chi-squared tests for evaluation and comparison of asset pricing models. J. Econom. 173:1108–25
    [Google Scholar]
  56. Gospodinov N, Kan R, Robotti C. 2014. Misspecification-robust inference in linear asset-pricing models with irrelevant risk factors. Rev. Financ. Stud. 27:72139–70
    [Google Scholar]
  57. Gu S, Kelly B, Xiu D. 2020. Empirical asset pricing via machine learning. Rev. Financ. Stud. 33:52223–73
    [Google Scholar]
  58. Gu S, Kelly BT, Xiu D. 2021. Autoencoder asset pricing models. J. Econom. 222:429–50
    [Google Scholar]
  59. Hansen LP. 1982. Large sample properties of generalized method of moments estimators. Econometrica 50:1029–54
    [Google Scholar]
  60. Hansen LP, Jagannathan R. 1997. Assessing specification errors in stochastic discount factor models. J. Finance 52:557–90
    [Google Scholar]
  61. Harvey CR, Ferson WE. 1999. Conditioning variables and the cross-section of stock returns. J. Finance 54:1325–60
    [Google Scholar]
  62. Harvey CR, Liu Y. 2020. False (and missed) discoveries in financial economics. J. Finance 75:52503–53
    [Google Scholar]
  63. Harvey CR, Liu Y, Zhu H. 2016. ... and the cross-section of expected returns. Rev. Financ. Stud. 29:15–68
    [Google Scholar]
  64. Harvey CR, Zhou G. 1990. Bayesian inference in asset pricing tests. J. Financ. Econ. 26:2221–54
    [Google Scholar]
  65. He Z, Kelly B, Manela A. 2017. Intermediary asset pricing: new evidence from many asset classes. J. Financ. Econ. 126:11–35
    [Google Scholar]
  66. He Z, Krishnamurthy A. 2013. Intermediary asset pricing. Am. Econ. Rev. 103:2732–70
    [Google Scholar]
  67. Hou K, Xue C, Zhang L. 2015. Digesting anomalies: an investment approach. Rev. Financ. Stud. 28:3650–705
    [Google Scholar]
  68. Huang D, Jiang F, Li K, Tong G, Zhou G. 2021. Scaled PCA: a new approach to dimension reduction. Manag. Sci. 68:31678–95
    [Google Scholar]
  69. Huberman G. 1982. A simple approach to arbitrage pricing theory. J. Econ. Theory 28:1183–91
    [Google Scholar]
  70. Huberman G, Kandel S, Stambaugh RF. 1987. Mimicking portfolios and exact arbitrage pricing. J. Finance 42:11–9
    [Google Scholar]
  71. Ingersoll JE. 1984. Some results in the theory of arbitrage pricing. J. Finance 39:41021–39
    [Google Scholar]
  72. Ioffe S, Szegedy C. 2015. Batch normalization: accelerating deep network training by reducing internal covariate shift. Proceedings of the 32nd International Conference on Machine Learning F Bach, D Blei 448–56 New York: Assoc. Comput. Mach.
    [Google Scholar]
  73. Jegadeesh N, Noh J, Pukthuanthong K, Roll R, Wang J. 2019. Empirical tests of asset pricing models with individual assets: resolving the errors-in-variable bias in risk premium estimation. J. Financ. Econ. 133:2273–98
    [Google Scholar]
  74. Jensen TI, Kelly B, Pedersen LH. 2021. Is there a replication crisis in finance?. J. Finance. In press
    [Google Scholar]
  75. Jiang J, Kelly B, Xiu D. 2021. (Re-)Imag(in)ing price trends. SSRN Work. Pap. https://dx.doi.org/10.2139/ssrn.3756587
    [Crossref] [Google Scholar]
  76. Kan R, Robotti C. 2009. Model comparison using the Hansen-Jagannathan distance. Rev. Financ. Stud. 22:93449–90
    [Google Scholar]
  77. Kan R, Robotti C, Shanken J. 2013. Pricing model performance and the two-pass cross-sectional regression methodology. J. Finance 68:62617–49
    [Google Scholar]
  78. Kan R, Zhang C. 1999. Two-pass tests of asset pricing models with useless factors. J. Finance 54:1203–35
    [Google Scholar]
  79. Kass RE, Raftery AE. 1995. Bayes factors. J. Am. Stat. Assoc. 90:430773–95
    [Google Scholar]
  80. Ke T, Kelly B, Xiu D. 2019. Predicting returns with text data. Work. Pap. 2019-69 Univ. Chicago Chicago, IL: https://bfi.uchicago.edu/wp-content/uploads/BFI_WP_201969.pdf
    [Google Scholar]
  81. Kelly B, Moskowitz T, Pruitt S. 2021. Understanding momentum and reversal. J. Financ. Econ. 140:3726–43
    [Google Scholar]
  82. Kelly B, Palhares D, Pruitt S. 2021. Modeling corporate bond returns. J. Finance. In press
    [Google Scholar]
  83. Kelly B, Pruitt S. 2013. Market expectations in the cross-section of present values. J. Finance 68:51721–56
    [Google Scholar]
  84. Kelly B, Pruitt S, Su Y. 2019. Characteristics are covariances: a unified model of risk and return. J. Financ. Econ. 134:3501–24
    [Google Scholar]
  85. Kelly B, Pruitt S, Su Y. 2020. Instrumented principal component analysis. SSRN Work. Pap. https://dx.doi.org/10.2139/ssrn.2983919
    [Crossref] [Google Scholar]
  86. Kim S, Korajczyk RA, Neuhierl A. 2021. Arbitrage portfolios. Rev. Financ. Stud. 34:62813–56
    [Google Scholar]
  87. Kingma D, Ba J. 2014. Adam: a method for stochastic optimization. arXiv:1412.6980 [cs.LG]
  88. Kleibergen F. 2009. Tests of risk premia in linear factor models. J. Econom. 149:2149–73
    [Google Scholar]
  89. Koijen R, Nieuwerburgh SV. 2011. Predictability of returns and cash flows. Annu. Rev. Financ. Econ. 3:467–91
    [Google Scholar]
  90. Korsaye SA, Quaini A, Trojani F. 2019. Smart SDFs. Work. Pap. Univ. Geneva Geneva, Switz:.
    [Google Scholar]
  91. Kosowski R, Timmermann A, Wermers R, White H. 2006. Can mutual fund “stars” really pick stocks? New evidence from a bootstrap analysis. J. Finance 61:62551–95
    [Google Scholar]
  92. Kozak S, Nagel S, Santosh S. 2018. Interpreting factor models. J. Finance 73:31183–223
    [Google Scholar]
  93. Kozak S, Nagel S, Santosh S. 2020. Shrinking the cross section. J. Financ. Econ. 135:2271–92
    [Google Scholar]
  94. Lamont OA. 2001. Economic tracking portfolios. J. Econom. 105:1161–84
    [Google Scholar]
  95. Lettau M, Pelger M. 2020a. Estimating latent asset-pricing factors. J. Econom. 218:11–31
    [Google Scholar]
  96. Lettau M, Pelger M. 2020b. Factors that fit the time series and cross-section of stock returns. Rev. Financ. Stud. 33:52274–325
    [Google Scholar]
  97. Lewellen J. 2015. The cross-section of expected stock returns. Crit. Finance Rev. 4:11–44
    [Google Scholar]
  98. Lewellen J, Nagel S, Shanken J. 2010. A skeptical appraisal of asset pricing tests. J. Financ. Econ. 96:2175–94
    [Google Scholar]
  99. Lo AW, MacKinlay AC. 1990. Data-snooping biases in tests of financial asset pricing models. Rev. Financ. Stud. 3:3431–67
    [Google Scholar]
  100. Merton RC. 1973. An intertemporal capital asset pricing model. Econometrica 41:5867–87
    [Google Scholar]
  101. Mitchell TJ, Beauchamp JJ. 1988. Bayesian variable selection in linear regression. J. Am. Stat. Assoc. 83:4041023–32
    [Google Scholar]
  102. Obaid K, Pukthuanthong K. 2022. A picture is worth a thousand words: measuring investor sentiment by combining machine learning and photos from news. J. Financ. Econ. 144:1273–97
    [Google Scholar]
  103. Onatski A. 2009. Testing hypotheses about the number of factors in large factor models. Econometrica 77:51447–79
    [Google Scholar]
  104. Onatski A. 2012. Asymptotics of the principal components estimator of large factor models with weakly influential factors. J. Econom. 168:2244–58
    [Google Scholar]
  105. Pesaran MH, Smith R. 2019. The role of factor strength and pricing errors for estimation and inference in asset pricing models. SSRN Work. Pap. http://dx.doi.org/10.2139/ssrn.3480925
    [Crossref] [Google Scholar]
  106. Pesaran MH, Yamagata T. 2017. Testing for alpha in linear factor pricing models with a large number of securities. SSRN Work. Pap. http://dx.doi.org/10.2139/ssrn.2973079
    [Crossref] [Google Scholar]
  107. Pukthuanthong K, Roll R, Subrahmanyam A. 2019. A protocol for factor identification. Rev. Financ. Stud. 32:41573–607
    [Google Scholar]
  108. Rapach D, Strauss JK, Zhou G. 2013. International stock return predictability: What is the role of the United States?. J. Finance 68:41633–62
    [Google Scholar]
  109. Rapach D, Zhou G 2013. Forecasting stock returns. Handbook of Economic Forecasting, Vol. 2 G Elliott, A Timmermann 328–83 Amsterdam: Elsevier
    [Google Scholar]
  110. Raponi V, Robotti C, Zaffaroni P. 2020. Testing beta-pricing models using large cross-sections. Rev. Financ. Stud. 33:2796–842
    [Google Scholar]
  111. Rosenberg B. 1974. Extra-market components of covariance in security returns. J. Financ. Quant. Anal. 9:2263–74
    [Google Scholar]
  112. Ross SA. 1976. The arbitrage theory of capital asset pricing. J. Econ. Theory 13:3341–60
    [Google Scholar]
  113. Santos T, Veronesi P. 2004. Conditional betas NBER Work. Pap. 10413
    [Google Scholar]
  114. Shanken J. 1992. On the estimation of beta pricing models. Rev. Financ. Stud. 5:11–33
    [Google Scholar]
  115. Sharpe WF. 1964. Capital asset prices: a theory of market equilibrium under conditions of risk. J. Finance 19:3425–42
    [Google Scholar]
  116. Stambaugh RF, Yuan Y. 2017. Mispricing factors. Rev. Financ. Stud. 30:41270–315
    [Google Scholar]
  117. Sullivan R, Timmermann A, White H. 1999. Data-snooping, technical trading rule performance, and the bootstrap. J. Finance 54:51647–91
    [Google Scholar]
  118. Welch I, Goyal A. 2007. A comprehensive look at the empirical performance of equity premium prediction. Rev. Financ. Stud. 21:41455–508
    [Google Scholar]
  119. White H. 2000. A reality check for data snooping. Econometrica 68:51097–126
    [Google Scholar]
  120. Zaffaroni P. 2019. Factor models for asset pricing. Work. Pap. Imp. Coll. Lond. London, UK:
    [Google Scholar]
/content/journals/10.1146/annurev-financial-101521-104735
Loading
/content/journals/10.1146/annurev-financial-101521-104735
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error