Estimating Flexible, Fat-Tailed Asset Return Distributions

39 Pages Posted: 20 Jun 2010 Last revised: 10 Apr 2012

See all articles by Craig A. Friedman

Craig A. Friedman

TIAA-CREF

Yangyong Zhang

Standard & Poor's - Quantitative Analytics

Jinggang Huang

Standard & Poor's - Quantitative Analytics

Date Written: April 9, 2012

Abstract

We introduce new robust numerical methods, based on the minimum relative U−entropy (MRUE) principle, to estimate univariate probability density functions for power-law (fat-tailed) random variables. The semi-parametric models that we estimate via convex programming are flexible enough to conform well to potentially plentiful data for not-too-extreme values, while allowing for power-law tails (which need not be symmetric). We observe that a number of well-known power-law models, including the exponential, Pareto, Student-t, and skewed generalized-t (SGT) distributions, are special cases of the family of power-law probability densities that we consider. We benchmark our method against state-of-the-art asset return models on S&P500 index returns, individual stock returns, and power price returns and find that our models outperform the benchmarks out-of-sample. We attribute this out-performance to simultaneously conforming to data where it is plentiful, while building in reasonably conservative tails.

Keywords: Minimum Relative U−Entropy, Probability Distribution, Fattailed, Power-Law Distribution, Financial Data, Asset Returns

Suggested Citation

Friedman, Craig A. and Zhang, Yangyong and Huang, Jinggang, Estimating Flexible, Fat-Tailed Asset Return Distributions (April 9, 2012). Available at SSRN: https://ssrn.com/abstract=1626342 or http://dx.doi.org/10.2139/ssrn.1626342

Craig A. Friedman (Contact Author)

TIAA-CREF ( email )

730 3rd Ave
New York, NY 10017
United States

Yangyong Zhang

Standard & Poor's - Quantitative Analytics ( email )

55 Water Street
New York, NY 10041
United States

Jinggang Huang

Standard & Poor's - Quantitative Analytics ( email )

55 Water Street
New York, NY 10041
United States

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