An alternative nonparametric tail risk measure

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The proposition of tail risk as a new asset pricing factor has gained traction in recent years. Recent work by Almeida, Ardison, Garcia, and Vicente (Nonparametric tail risk, stock returns, and the macroeconomy. J. Financ. Economet., 2017, 15(3), 333–376) proxies the cross-sectional variation in returns by Fama-French portfolios, which are further summarized into a few basis assets via principal component analysis. The number of states of nature is set higher than that of the basis assets to estimate the stochastic discount factors, which in turn risk-neutralize the excess expected shortfall as a tail risk measure. As an alternative approach to this means of dimension reduction, we propose tackling the problem directly by forming portfolios that minimize the excess expected shortfall. Our direct measure exhibits greater explanatory power when applied to more liquid, nonlottery-style stock returns. More importantly, our proposed approach reveals direct exposure to downside systematic risk without the need for an additional risk-neutralization step. Copyright © 2020 Informa UK Limited, trading as Taylor & Francis Group.
Original languageEnglish
Pages (from-to)685-696
JournalQuantitative Finance
Issue number4
Early online dateAug 2020
Publication statusPublished - 2021


Law, K. K. F., Li, W. K., & Yu, P. L. H. (2021). An alternative nonparametric tail risk measure. Quantitative Finance, 21(4), 685-696. doi: 10.1080/14697688.2020.1787491


  • Asset pricing
  • Risk neutralization
  • Risk optimization
  • Stochastic discount factor


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