Data-generating process uncertainty: What difference does it make in portfolio decisions?

Abstract As the usual normality assumption is firmly rejected by the data, investors encounter a data-generating process (DGP) uncertainty in making investment decisions. In this paper, we propose a novel way to incorporate uncertainty about the DGP into portfolio analysis. We find that accounting for fat tails leads to nontrivial changes in both parameter estimates and optimal portfolio weights, but the certainty–equivalent losses associated with ignoring fat tails are small. This suggests that the normality assumption works well in evaluating portfolio performance for a mean-variance investor.

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

[2]  K. Mardia.  Measures of multivariate skewness and kurtosis with applications , 1970 .

[3]  D. Dey,et al.  A General Class of Multivariate Skew-Elliptical Distributions , 2001 .

[4]  G. Chamberlain.  A characterization of the distributions that imply mean—Variance utility functions☆ , 1983 .

[5]  A. Zellner.  Bayesian and Non-Bayesian Analysis of the Regression Model with Multivariate Student- t Error Terms , 1976 .

[6]  Guofu Zhou,et al.  Temporary Components of Stock Returns: What Do the Data Tell Us? , 1996 .

[7]  Tom Smith,et al.  A Test for Multivariate Normality in Stock Returns , 1993 .

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

[9]  Ľuboš Pástor,et al.  Costs of Equity Capital and Model Mispricing , 1998 .

[10]  Mark Grinblatt,et al.  Do Industries Explain Momentum , 1999 .

[11]  Eric Ghysels,et al.  On Stable Factor Structures in the Pricing of Risk: Do Time-Varying Betas Help or Hurt? , 1998 .

[12]  S. Kotz,et al.  Symmetric Multivariate and Related Distributions , 1989 .

[13]  Yihong Xia,et al.  Assessing Asset Pricing Anomalies , 2001 .

[14]  K. J. Martijn Cremers,et al.  Stock Return Predictability: A Bayesian Model Selection Perspective , 2000 .

[15]  Zhenyu Wang.  A Shrinkage Theory of Asset Allocation Using Asset-Pricing Models , 2000 .

[16]  Arnold Zellner,et al.  Prediction and Decision Problems in Regression Models from the Bayesian Point of View , 1965 .

[17]  A. Craig MacKinlay,et al.  Using Generalized Method of Moments to Test Mean‐Variance Efficiency , 1991 .

[18]  N. Barberis.  Investing for the Long Run When Returns are Predictable , 2000 .

[19]  Bill McDonald,et al.  Nonnormalities and Tests of Asset Pricing Theories , 1989 .

[20]  B. King.  Market and Industry Factors in Stock Price Behavior , 1966 .

[21]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[22]  Chris Kirby,et al.  The Economic Value of Volatility Timing , 2000 .

[23]  Nicholas G. Polson,et al.  The Impact of Jumps in Volatility and Returns , 2000 .

[24]  P. Bossaerts,et al.  Implementing Statistical Criteria to Select Return Forecasting Models: What Do We Learn? , 1999 .

[25]  Joel Owen,et al.  On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice , 1983 .

[26]  Phhilippe Jorion.  Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[27]  R. Stambaugh,et al.  On the Predictability of Stock Returns: An Asset-Allocation Perspective , 1995 .

[28]  Eric Ghysels.  On Stable Factor Structurs in the Pricing of Risk. , 1995 .

[29]  Ľuboš Pástor.  Portfolio Selection and Asset Pricing Models , 1999 .

[30]  Guofu Zhou,et al.  Asset‐pricing Tests under Alternative Distributions , 1993 .

[31]  J. Lewellen,et al.  Learning, Asset-Pricing Tests, and Market Efficiency , 2002 .

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

[33]  Kent D. Daniel,et al.  NBER WORKING PAPER SERIES EVIDENCE ON THE CHARACTERISTICS OF CROSS SECTIONAL VARIATION IN STOCK RETURNS , 1996 .

[34]  Martijn Cremers,et al.  Multifactor Efficiency and Bayesian Inference , 2005 .

[35]  John C. Chao,et al.  An Exact Bayes Test of Asset Pricing Models with Application to International Markets , 2003 .

[36]  Doron Avramov,et al.  Stock Return Predictability and Model Uncertainty , 2001 .

[37]  J. Geweke,et al.  Measuring the pricing error of the arbitrage pricing theory , 1996 .

[38]  Guofu Zhou,et al.  Bayesian Inference in Asset Pricing Tests , 1990 .