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Article

A Revisit to Estimation of Beta Risk and an Analysis of Stock Market Through Copula Transformation and Winsorization with S&P 500 Index as Proxy

Ravindra Khattree and Manoj Bahuguna
The Journal of Index Investing Spring 2018, jii.2018.1.058; DOI: https://doi.org/10.3905/jii.2018.1.058
Ravindra Khattree
is a professor in the Department of Mathematics and Statistics at Oakland University in Rochester, MI
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Manoj Bahuguna
is a graduate student in the Department of Mathematics and Statistics at Oakland University in Rochester, MI
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Abstract

We consider the problem of reliable estimation of market betas. Estimation using least squares can be very sensitive to underlying assumptions of normality and the presence of outliers, whereas various robust estimation procedures have a certain degree of arbitrariness in their implementation. This is especially of concern because returns for various equities may have very different statistical distributions. Our approach is to bring all estimation problems to a common platform through bivariate Gaussian copula transformation where, in view of the linearity of regression, correlation is a meaningful measure of dependence. We then carry out the estimation of betas by combining it with the winsorized relative volatility of the asset. Extensive analysis of the U.S. market with the S&P 500 as proxy indicates that, when the data show departure from assumptions, our approach provides more stable estimates of betas than least squares, and estimates are essentially the same when assumptions are met. Improvement is realized in up to 53% of instances.

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The Journal of Index Investing: 11 (3)
The Journal of Index Investing
Vol. 11, Issue 3
Winter 2020
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A Revisit to Estimation of Beta Risk and an Analysis of Stock Market Through Copula Transformation and Winsorization with S&P 500 Index as Proxy
Ravindra Khattree, Manoj Bahuguna
The Journal of Index Investing Feb 2018, jii.2018.1.058; DOI: 10.3905/jii.2018.1.058

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A Revisit to Estimation of Beta Risk and an Analysis of Stock Market Through Copula Transformation and Winsorization with S&P 500 Index as Proxy
Ravindra Khattree, Manoj Bahuguna
The Journal of Index Investing Feb 2018, jii.2018.1.058; DOI: 10.3905/jii.2018.1.058
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  • Article
    • Abstract
    • BIVARIATE COPULA TRANSFORMATION
    • ESTIMATION OF β BASED ON COPULA TRANSFORMATION
    • AN APPLICATION IN THE ANALYSIS OF MARKET DATA WITH S&P 500 INDEX AS PROXY
    • MODIFIED ESTIMATORS FOR β THROUGH WINSORIZATION
    • AN APPLICATION IN THE ANALYSIS OF MARKET DATA WITH S&P 500 AS PROXY (CONTINUED)
    • COPULA TRANSFORMATION APPROACH VS. DUAL BETA METHOD
    • RISK BETA AND SELECTION OF STOCKS FOR PORTFOLIO
    • CONCLUDING REMARKS
    • APPENDIX A
    • APPENDIX B
    • ENDNOTES
    • REFERENCES
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