Estimating Latent Asset-Pricing Factors

We develop an estimator for latent factors in a large-dimensional panel of financial data that can explain expected excess returns. Statistical factor analysis based on Principal Component Analysis (PCA) has problems identifying factors with a small variance that are important for asset pricing. We generalize PCA with a penalty term accounting for the pricing error in expected returns. Our estimator searches for factors that can explain both the expected return and covariance structure. We derive the statistical properties of the new estimator and show that our estimator can find asset-pricing factors, which cannot be detected with PCA, even if a large amount of data is available. Applying the approach to portfolio data we find factors with Sharpe-ratios more than twice as large as those based on conventional PCA and with significantly smaller pricing errors.

[1]  J. Bai,et al.  Large Dimensional Factor Analysis , 2008 .

[2]  Jianqing Fan,et al.  Large covariance estimation by thresholding principal orthogonal complements , 2011, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[3]  Seung C. Ahn,et al.  Eigenvalue Ratio Test for the Number of Factors , 2013 .

[4]  Daniel Ferreira,et al.  Spurious Factors in Linear Asset Pricing Models , 2015 .

[5]  A. Onatski.  Determining the Number of Factors from Empirical Distribution of Eigenvalues , 2010, The Review of Economics and Statistics.

[6]  J. Bai,et al.  Inferential Theory for Factor Models of Large Dimensions , 2003 .

[7]  Alexei Onatski,et al.  Asymptotics of the principal components estimator of large factor models with weakly influential factors , 2012 .

[8]  Serena Ng,et al.  Principal Components and Regularized Estimation of Factor Models , 2017, 1708.08137.

[9]  Matthew Harding,et al.  Estimating the Number of Factors in Large Dimensional Factor Models 1 , 2013 .

[10]  Jianqing Fan,et al.  PROJECTED PRINCIPAL COMPONENT ANALYSIS IN FACTOR MODELS. , 2014, Annals of statistics.

[11]  Raj Rao Nadakuditi,et al.  The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices , 2009, 0910.2120.

[12]  Yacine Aït-Sahalia,et al.  Principal Component Estimation of a Large Covariance Matrix with High-Frequency Data ∗ , 2015 .

[13]  H. Luetkepohl.  The Handbook of Matrices , 1996 .

[14]  B. Kelly,et al.  Instrumented Principal Component Analysis , 2017 .

[15]  J. Bai,et al.  Determining the Number of Factors in Approximate Factor Models , 2000 .

[16]  M. Lettau,et al.  Factors That Fit the Time Series and Cross-Section of Stock Returns , 2018, The Review of Financial Studies.

[17]  Yiqiao Zhong,et al.  Optimal Subspace Estimation Using Overidentifying Vectors via Generalized Method of Moments , 2018, 1805.02826.

[18]  Gregory Connor,et al.  Risk and Return in an Equilibrium Apt: Application of a New Test Methodology , 1988 .

[19]  M. Rothschild,et al.  Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets , 1983 .

[20]  M. Rothschild,et al.  Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets , 1982 .

[21]  M. Hallin,et al.  The Generalized Dynamic-Factor Model: Identification and Estimation , 2000, Review of Economics and Statistics.

[22]  D. Paul.  ASYMPTOTICS OF SAMPLE EIGENSTRUCTURE FOR A LARGE DIMENSIONAL SPIKED COVARIANCE MODEL , 2007 .

[23]  Serhiy Kozak,et al.  Shrinking the Cross Section , 2017, Journal of Financial Economics.

[24]  Raj Rao Nadakuditi,et al.  OptShrink: An Algorithm for Improved Low-Rank Signal Matrix Denoising by Optimal, Data-Driven Singular Value Shrinkage , 2013, IEEE Transactions on Information Theory.

[25]  Serena Ng,et al.  A Factor Analysis of Bond Risk Premia , 2009 .

[26]  Markus Pelger.  Large-Dimensional Factor Modeling Based on High-Frequency Observations , 2018 .

[27]  Gregory Connor,et al.  A Test for the Number of Factors in an Approximate Factor Model , 1993 .

[28]  S. Ross.  The arbitrage theory of capital asset pricing , 1976 .

[29]  J. W. Silverstein,et al.  Spectral Analysis of Large Dimensional Random Matrices , 2009 .

[30]  Z. Bai,et al.  Large Sample Covariance Matrices and High-Dimensional Data Analysis , 2015 .