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One-sided performance measures under Gram-Charlier distributions

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  • León, Angel
  • Moreno, Manuel

Abstract

We derive closed-form expressions for risk measures based on partial moments by assuming the Gram-Charlier (GC) density for stock returns. As a result, the lower partial moment (LPM) measures can be expressed as linear functions on both skewness and excess kurtosis. Under this framework, we study the behavior of portfolio rankings with performance measures based on partial moments, that is, both Farinelli-Tibiletti (FT) and Kappa ratios. Contrary to previous results, significant differences are found in ranking portfolios between the Sharpe ratio and the FT family. We also obtain closed-form expressions for LPMs under the semi non-parametric (SNP) distribution which allows higher flexibility than the GC distribution.

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  • León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    • Handle: RePEc:eee:jbfina:v:74:y:2017:i:c:p:38-50
    DOI: 10.1016/j.jbankfin.2016.10.005
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    7. Ñíguez, Trino-Manuel & Perote, Javier, 2017. "Moments expansion densities for quantifying financial risk," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 53-69.
    8. Inés Jiménez & Andrés Mora-Valencia & Javier Perote, 2022. "Dynamic selection of Gram–Charlier expansions with risk targets: an application to cryptocurrencies," Risk Management, Palgrave Macmillan, vol. 24(1), pages 81-99, March.
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    More about this item

    Keywords

    Lower/upper partial moment; Certainty equivalent; Rank correlation; Semi non-parametric distribution;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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