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Using truncated Lévy flight to estimate downside risk

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  • Xiong, James X.

Abstract

It is well known that the normal distribution model fails to describe the fat tails of markets. The Lévy stable distribution model, meanwhile, has fat tails but leads to an infinite variance, thus complicating risk estimation. This study introduces truncated Lévy flight (TLF) — a better distribution model that has fat tails, finite variance, and more importantly, scaling properties. The paper uses TLF to estimate the downside risk of a variety of asset classes. The downside risk measure used is the conditional value-at-risk (CVaR). The study shows that the lognormal model can underestimate the monthly CVaR by 2.27 per cent for the S&P 500 Index, 0.48 per cent for the US Long-Term Government Bond Index, and 1.16 per cent for the MSCI UK Equity Index. Moreover, the paper extends a univariate TLF model to a multivariate TLF model to study the impact of fat tails on portfolios' downside risk and wealth accumulation.

Suggested Citation

  • Xiong, James X., 2010. "Using truncated Lévy flight to estimate downside risk," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 3(3), pages 231-242, June.
    • Handle: RePEc:aza:rmfi00:y:2010:v:3:i:3:p:231-242
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    More about this item

    Keywords

    truncated Lévy flight; downside risk; conditional value-at-risk; fat tail;
    All these keywords.

    JEL classification:

    • G2 - Financial Economics - - Financial Institutions and Services
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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