Efficient Estimation of a Semiparametric Characteristic-Based Factor Model of Security Returns

This paper develops a new estimation procedure for characteristic-based factor models of security returns. We treat the factor model as a weighted additive nonparametric regression model, with the factor returns serving as time-varying weights, and a set of univariate non-parametric functions relating security characteristic to the associated factor betas. We use a time-series and cross-sectional pooled weighted additive nonparametric regression methodology to simultaneously estimate the factor returns and characteristic-beta functions. By avoiding the curse of dimensionality our methodology allows for a larger number of factors than existing semiparametric methods. We apply the technique to the three-factor Fama-French model, Carhart's four-factor extension of it adding a momentum factor, and a five-factor extension adding an own-volatility factor. We found that momentum and own-volatility factors are at least as important if not more important than size and value in explaining equity return comovements. We test the multifactor beta pricing theory against the Capital Asset Pricing model using a standard test, and against a general alternative using a new nonparametric test.

[1]  C. J. Stone,et al.  Optimal Rates of Convergence for Nonparametric Estimators , 1980 .

[2]  Joel L. Horowitz,et al.  Optimal estimation in additive regression models , 2006 .

[3]  Dag Tjøstheim,et al.  NONPARAMETRIC ADDITIVE MODELS FOR PANELS OF TIME SERIES , 2009, Econometric Theory.

[4]  Christopher S. Jones,et al.  Extracting factors from heteroskedastic asset returns , 2001 .

[5]  Oliver Linton,et al.  Miscellanea Efficient estimation of additive nonparametric regression models , 1997 .

[6]  Narasimhan Jegadeesh,et al.  Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency , 1993 .

[7]  Jushan Bai,et al.  Estimating cross-section common stochastic trends in nonstationary panel data , 2004 .

[8]  Sheridan Titman,et al.  On Persistence in Mutual Fund Performance , 1997 .

[9]  Stephen A. Ross,et al.  A Test of the Efficiency of a Given Portfolio , 1989 .

[10]  E. Mammen,et al.  Nonparametric Transformation to White Noise , 2006 .

[11]  Sara van de Geer,et al.  Estimating Multiplicative and Additive Hazard Functions by Kernel Methods , 2001 .

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

[13]  Enno Mammen,et al.  Bandwidth selection for smooth backfitting in additive models , 2005, math/0507425.

[14]  M. Pesaran.  Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure , 2004, SSRN Electronic Journal.

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

[16]  Oliver Linton,et al.  The Common and Specific Components of Dynamic Volatility , 2003 .

[17]  M. Lettau,et al.  Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk , 2000 .

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

[19]  E. Mammen,et al.  Time Series Modelling With Semiparametric Factor Dynamics , 2007 .

[20]  Thomas M. Stoker,et al.  Semiparametric Estimation of Index Coefficients , 1989 .

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

[22]  Oliver Linton,et al.  Testing additivity in generalized nonparametric regression models with estimated parameters , 2001 .

[23]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[24]  Two sided analysis of variance with a latent time series , 2004 .

[25]  D. Andrews.  CONSISTENCY IN NONLINEAR ECONOMETRIC MODELS: A GENERIC UNIFORM LAW OF LARGE NUMBERS , 1987 .

[26]  J. Florens,et al.  Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization , 2003 .

[27]  Enno Mammen,et al.  Estimating Semiparametric Arch (∞) Models by Kernel Smoothing Methods , 2003 .

[28]  O. Linton,et al.  A kernel method of estimating structured nonparametric regression based on marginal integration , 1995 .

[29]  Qi Li,et al.  A nonparametric test for poolability using panel data , 1996 .

[30]  E. Mammen,et al.  Comparing Nonparametric Versus Parametric Regression Fits , 1993 .

[31]  E. Fama,et al.  Common risk factors in the returns on stocks and bonds , 1993 .

[32]  A. Lo,et al.  When are Contrarian Profits Due to Stock Market Overreaction? , 1989 .

[33]  Enno Mammen,et al.  The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions , 1999 .

[34]  M. Rosenblatt.  A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION. , 1956, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Jianqing Fan,et al.  Efficient Estimation of Conditional Variance Functions in Stochastic Regression , 1998 .

[36]  E. Fama,et al.  Value Versus Growth: The International Evidence , 1997 .

[37]  Joel L. Horowitz,et al.  Nonparametric estimation of an additive model with a link function , 2002, math/0508595.

[38]  Identification of Marginal Effects in a Nonparametric Correlated Random Effects Model , 2009 .

[39]  Cheng Hsiao,et al.  Analysis of Panel Data , 1987 .

[40]  R. Hodrick,et al.  The Cross-Section of Volatility and Expected Returns , 2006 .

[41]  P. Phillips,et al.  Linear Regression Limit Theory for Nonstationary Panel Data , 1999 .

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

[43]  Gregory Connor,et al.  Semiparametric Estimation of a Characteristic-Based Factor Model of Stock Returns , 2000 .

[44]  L. Bauwens,et al.  Multivariate GARCH Models: A Survey , 2003 .

[45]  P. Santa-clara,et al.  Idiosyncratic Risk Matters! , 2002 .