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A Simple Skewed Distribution with Asset Pricing Applications

Author

Listed:
  • Frans de Roon
  • Paul Karehnke

Abstract

Recent research has identified skewness and downside risk as one of the most important features of risk. We present a new distribution which makes modeling skewed risks no more difficult than normally distributed (symmetric) risks. Our distribution is a combination of the “downside” and “upside” half of two normal distributions, and its parameters can be calculated in closed form to match a given mean, variance, and skewness. Value at risk, expected shortfall, portfolio weights, and risk premia have simple expressions for our distribution and show economically meaningful deviations from the normal case already for very modest levels of skewness. An empirical application suggests that our distribution fits the data well.

Suggested Citation

  • Frans de Roon & Paul Karehnke, 2017. "A Simple Skewed Distribution with Asset Pricing Applications," Review of Finance, European Finance Association, vol. 21(6), pages 2169-2197.
    • Handle: RePEc:oup:revfin:v:21:y:2017:i:6:p:2169-2197.
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    File URL: http://hdl.handle.net/10.1093/rof/rfw040
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    References listed on IDEAS

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    Cited by:

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    2. Choi, Ahjin & Kang, Kyu Ho, 2023. "Modeling the time-varying dynamic term structure of interest rates," Journal of Banking & Finance, Elsevier, vol. 153(C).
    3. Panayiotis Theodossiou & Polina Ellina & Christos S. Savva, 2022. "Stochastic properties and pricing of bitcoin using a GJR-GARCH model with conditional skewness and kurtosis components," Review of Quantitative Finance and Accounting, Springer, vol. 59(2), pages 695-716, August.
    4. Panayiotis Theodossiou & Dimitris Tsouknidis & Christos Savva, 2020. "Freight rates in downside and upside markets: pricing of own and spillover risks from other shipping segments," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1097-1119, June.
    5. Delis, Manthos D. & Savva, Christos S. & Theodossiou, Panayiotis, 2021. "The impact of the coronavirus crisis on the market price of risk," Journal of Financial Stability, Elsevier, vol. 53(C).
    6. Gaygysyz Guljanov & Willi Mutschler & Mark Trede, 2022. "Pruned Skewed Kalman Filter and Smoother: With Application to the Yield Curve," CQE Working Papers 10122, Center for Quantitative Economics (CQE), University of Muenster.
    7. Bottasso, Anna & Duchêne, Sébastien & Guerci, Eric & Hanaki, Nobuyuki & Noussair, Charles N., 2022. "Higher order risk attitudes of financial experts," Journal of Behavioral and Experimental Finance, Elsevier, vol. 34(C).
    8. Stephen Thiele, 2020. "Modeling the conditional distribution of financial returns with asymmetric tails," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 46-60, January.
    9. Lee, Cheol Woo & Kang, Kyu Ho, 2023. "Estimating and testing skewness in a stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 445-467.
    10. Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2020. "Risk Analysis through the Half-Normal Distribution," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    11. Carnero, M. Angeles & León, Angel & Ñíguez, Trino-Manuel, 2023. "Skewness in energy returns: estimation, testing and retain-->implications for tail risk," The Quarterly Review of Economics and Finance, Elsevier, vol. 90(C), pages 178-189.

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    More about this item

    Keywords

    Skewness; Value-at-risk; Expected shortfall; Portfolio choice; Asset pricing;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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