Hierarchical bayes methods for multifactor model estimation and portfolio selection

The factor model is an important construct for both portfolio managers and researchers in modern finance. For practitioners, factor model coefficients are used to guide the construction of optimal portfolios. For academicians, factor model parameters play a fundamental role in explaining equilibrium asset prices and other market phenomena. This paper presents a hierarchical modeling procedure that can substantially improve the accuracy of factor model parameter estimates through incorporation of cross-sectional information. It is shown that this improvement in parameter estimation accuracy translates into substantial improvement in portfolio performance. Expressions are derived that characterize the sensitivity of portfolio performance to parameter estimation error. Evidence with NYSE data suggests that the hierarchical estimation technique leads to superior out-of-sample portfolio performance when compared to alternative estimation approaches.

[1]  Adrian F. M. Smith,et al.  Bayesian Analysis of Linear and Non‐Linear Population Models by Using the Gibbs Sampler , 1994 .

[2]  Peter A. Frost,et al.  An Empirical Bayes Approach to Efficient Portfolio Selection , 1986, Journal of Financial and Quantitative Analysis.

[3]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[4]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[5]  E. Fama,et al.  The Cross‐Section of Expected Stock Returns , 1992 .

[6]  R. Kohn,et al.  Bayesian estimation of an autoregressive model using Markov chain Monte Carlo , 1996 .

[7]  Philippe Jorion.  Bayes-Stein Estimation for Portfolio Analysis , 1986, Journal of Financial and Quantitative Analysis.

[8]  Kalok Chan,et al.  An Unconditional Asset-Pricing Test and the Role of Firm Size as an Instrumental Variable for Risk , 1988 .

[9]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[10]  C. B. Barry.  PORTFOLIO ANALYSIS UNDER UNCERTAIN MEANS, VARIANCES, AND COVARIANCES , 1974 .

[11]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[12]  G. Andrew Karolyi,et al.  Predicting risk: some new generalizations , 1992 .

[13]  Barr Rosenberg,et al.  Prediction of Beta from Investment Fundamentals , 1995 .

[14]  Campbell R. Harvey,et al.  The Variation of Economic Risk Premiums , 1990, Journal of Political Economy.

[15]  Barr Rosenberg,et al.  The Prediction of Systematic and Specific Risk in Common Stocks , 1973, Journal of Financial and Quantitative Analysis.

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

[17]  Burton G. Malkiel,et al.  Risk and Return Revisited , 1997 .

[18]  A. Zellner.  An Introduction to Bayesian Inference in Econometrics , 1971 .

[19]  S. J. Press,et al.  Applied Multivariate Analysis. , 1973 .

[20]  A. Zellner,et al.  Gibbs Sampler Convergence Criteria , 1995 .

[21]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[22]  S. Chib,et al.  Bayes inference in regression models with ARMA (p, q) errors , 1994 .

[23]  W. Ziemba,et al.  The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice , 1993 .

[24]  E. Fama,et al.  Risk, Return, and Equilibrium: Empirical Tests , 1973, Journal of Political Economy.

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

[26]  Oldrich A Vasicek,et al.  A NOTE ON USING CROSS‐SECTIONAL INFORMATION IN BAYESIAN ESTIMATION OF SECURITY BETAS , 1973 .

[27]  Charles Sutcliffe,et al.  Estimation methods in portfolio selection and the effectiveness of short sales restrictions: UK evidence , 1994 .

[28]  Barr Rosenberg,et al.  Prediction of Beta from Investment Fundamentals: Part One , 1976 .

[29]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[30]  E. George.  A formal bayes multiple shrinkage estimator , 1986 .

[31]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[32]  Greg M. Allenby,et al.  Reassessing Brand Loyalty, Price Sensitivity, and Merchandising Effects on Consumer Brand Choice , 1995 .

[33]  M. Best,et al.  On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results , 1991 .

[34]  Greg M. Allenby,et al.  Reassessing Brand Loyalty, Price , 1995 .