Testing Asset Pricing Models With Coskewness

In this article we investigate portfolio coskewness using a quadratic market model as a return-generating process. We show that the portfolios of small (large) firms have negative (positive) coskewness with the market. We test an asset pricing model including coskewness by checking the validity of the restrictions that it imposes on the return-generating process. We find evidence of an additional component in expected excess returns, which is not explained by either covariance or coskewness with the market. However, this unexplained component is homogeneous across portfolios in our sample and modest in magnitude. Finally, we investigate the implications of erroneously neglecting coskewness for testing asset pricing models, with particular attention to the empirically detected explanatory power of firm size.

[1]  Marno Verbeek,et al.  Evaluating portfolio Value-at-Risk using semi-parametric GARCH models , 2009 .

[2]  Massimo Guidolin,et al.  Small caps in international equity portfolios: the effects of variance risk , 2005 .

[3]  Marie-Claude Beaulieu,et al.  Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions , 2005 .

[4]  Robert F. Dittmar.  Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns , 2002 .

[5]  R. Jagannathan,et al.  Empirical Evaluation of Asset Pricing Models: A Comparison of the Sdf and Beta Methods , 2001 .

[6]  Raymond Kan,et al.  GMM tests of stochastic discount factor models with useless factors , 1999 .

[7]  Guofu Zhou,et al.  Testing multi-beta asset pricing models , 1999 .

[8]  Guofu Zhou,et al.  A critique of the stochastic discount factor methodology , 1999 .

[9]  Raymond Kan,et al.  Two‐Pass Tests of Asset Pricing Models with Useless Factors , 1999 .

[10]  A. Lo,et al.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1996, Macroeconomic Dynamics.

[11]  R. Jagannathan,et al.  The Conditional CAPM and the Cross-Section of Expected Returns , 1996 .

[12]  E. Fama,et al.  Size and Book-to-Market Factors in Earnings and Returns , 1995 .

[13]  Guofu Zhou,et al.  Small sample rank tests with applications to asset pricing , 1995 .

[14]  Ravi Jagannathan,et al.  Assessing Specification Errors in Stochastic Discount Factor Models , 1994 .

[15]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[16]  Giovanni Barone-Adesi,et al.  Arbitrage Equilibrium with Skewed Asset Returns , 1985, Journal of Financial and Quantitative Analysis.

[17]  Jay Shanken,et al.  Multi‐Beta CAPM or Equilibrium‐APT?: A Reply , 1985 .

[18]  C. Gouriéroux,et al.  PSEUDO MAXIMUM LIKELIHOOD METHODS: THEORY , 1984 .

[19]  G. Barone-Adesi,et al.  Market Models and Heteroscedasticity of Residual Security Returns , 1983 .

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

[21]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[22]  R. Banz,et al.  The relationship between return and market value of common stocks , 1981 .

[23]  Douglas T. Breeden.  An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities , 1979 .

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

[25]  R. Litzenberger,et al.  SKEWNESS PREFERENCE AND THE VALUATION OF RISK ASSETS , 1976 .

[26]  R. C. Merton,et al.  AN INTERTEMPORAL CAPITAL ASSET PRICING MODEL , 1973 .

[27]  J. B. Ramsey,et al.  Tests for Specification Errors in Classical Linear Least‐Squares Regression Analysis , 1969 .

[28]  J. Lintner.  THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[29]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[30]  A. Zellner.  An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[31]  G. Furlan,et al.  On the e++e−→π0+γ process , 1961 .

[32]  René Garcia,et al.  The Stochastic Discount Factor: Extending the Volatility Bound and a New Approach to Portfolio Selection with Higher-Order Moments , 2005 .

[33]  J. Wooldridge,et al.  Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances , 1992 .

[34]  Jay Shanken.  On the Estimation of Beta-Pricing Models , 1992 .

[35]  Monfort,et al.  Moindres carrés asymptotiques , 1985 .

[36]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[37]  Mark Rubinstein,et al.  A Comparative Statics Analysis of Risk Premiums , 1973 .

[38]  F. Black.  Capital Market Equilibrium with Restricted Borrowing , 1972 .