An Empirical Bayes Estimate of Market Risk

Starting with a market model of security returns, we describe how the parameters of a distribution for security characteristics can be estimated in a manner correcting for a subtle but significant source of error. When this error is removed, strong negative correlations between "alpha" and...

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Bibliographic Details
Published in:Management science 1982-07, Vol.28 (7), p.728-737
Main Authors: Maier, Steven F, Peterson, David W, Vander Weide, James H
Format: Article
Language:English
Subjects:
Bayes estimators
Beta
beta estimation
Consistent estimators
Covariance matrices
Data security
Estimates
Estimating techniques
Estimation methods
Estimators
market model
market risk
Markets
Parametric models
Rates of return
Risk
Securities
Statistical analysis
Statistical variance
Systematic risk
Time series
Unbiased estimators
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Description
Summary:Starting with a market model of security returns, we describe how the parameters of a distribution for security characteristics can be estimated in a manner correcting for a subtle but significant source of error. When this error is removed, strong negative correlations between "alpha" and "beta" and between "alpha" and "sigma squared," and a strong positive correlation between "beta" and "sigma squared" are observed. With this feature in the prior distribution, and with the results of a regression for a particular security, we develop an empirical Bayes estimate of the security's three parameters (alpha, beta and sigma squared) which makes use of more information than other estimates described in the literature.
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.28.7.728