Robust Prediction of Beta

The estimation of β plays a basic role in the evaluation of expected return and market risk. Typically this is performed by ordinary least squares (OLS). To cope with the high sensitivity of OLS to outlying observations and to deviations from the normality assumptions, several methods suggest to use robust estimators. It is argued that, from a predictive point of view, the simple use of either OLS or robust estimators is not sufficient but that some shrinking of the robust estimators toward OLS is necessary to reduce the mean squared error. The performance of the proposed shrinkage robust estimator is shown by means of a small simulation study and on a real data set.

[1]  W. Sharpe.  Mean-Absolute-Deviation Characteristic Lines for Securities and Portfolios , 1971 .

[2]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[3]  P. Rousseeuw.  Least Median of Squares Regression , 1984 .

[4]  R. Welsch,et al.  Resistant estimation for simultaneous-equations models using weighted instrumental variables , 1985 .

[5]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[6]  R. Chambers.  Outlier Robust Finite Population Estimation , 1986 .

[7]  V. Yohai.  HIGH BREAKDOWN-POINT AND HIGH EFFICIENCY ROBUST ESTIMATES FOR REGRESSION , 1987 .

[8]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[9]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[10]  F. Peracchi,et al.  Robust m-estimators , 1990 .

[11]  Gordon Leitch,et al.  Economic Forecast Evaluation: Profits versus the Conventional Error Measures , 1991 .

[12]  Louis K.C. Chan,et al.  Robust Measurement of Beta Risk , 1992, Journal of Financial and Quantitative Analysis.

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

[14]  K. West,et al.  A Utility Based Comparison of Some Models of Exchange Rate Volatility , 1992 .

[15]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[16]  E. Ronchetti,et al.  Robust Estimators for Simultaneous Equations Models , 1997 .

[17]  John H. Earl.  On the Robustness of Size and Book-to-Market in Cross-Sectional Regressions , 1998 .

[18]  E. Ronchetti,et al.  Bias‐calibrated estimation from sample surveys containing outliers , 1998 .

[19]  Anthony Y. C. Kuk,et al.  Robust estimation for finite populations based on a working model , 2001 .

[20]  E. Ronchetti,et al.  Robust inference with GMM estimators , 2001 .

[21]  Halbert White,et al.  Tests of Conditional Predictive Ability , 2003 .

[22]  R. Martin,et al.  Outlier-Resistant Estimates of Beta , 2003 .

[23]  V. Yohai,et al.  Robust Statistics: Theory and Methods , 2006 .