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Lower Partial Moments under Gram Charlier Distribution: Performance Measures and Efficient Frontiers

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  • León, Ángel

    () (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

  • Moreno, Manuel

    (University of Castilla La-Mancha. Department of Economic Analysis and Finance,)

Abstract

We derive closed-form expressions for the performance measures(PMs)based on the lower partial moments (LPMs), such as the Farinelli-Tibiletti and Kappa measures, with Gram-Charlier (GC) density for returns. It is verified that the LPMs can be obtained as a linear function on both higher moments, skewness and excess kurtosis. We also show that these PMs influence differently to the Sharpe ratio in ranking portfolios due to the effects of the higher moments. We also obtain the efficient frontiers (EFs) based on the mean-LPM framework. We find important differences between portfolios from different EFs regarding their stock compositions, portfolio skewness and excess kurtosis levels. Finally, we also obtain closed-form expressions for PMs under a more flexible density like the SNP density which nests the GC density.

Suggested Citation

  • León, Ángel & Moreno, Manuel, 2015. "Lower Partial Moments under Gram Charlier Distribution: Performance Measures and Efficient Frontiers," QM&ET Working Papers 15-3, University of Alicante, D. Quantitative Methods and Economic Theory.
  • Handle: RePEc:ris:qmetal:2015_003
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    References listed on IDEAS

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    More about this item

    Keywords

    Downside risk; peformance measure; rank correlation; efficient frontier; co-lower partial moment matrix; copula; SNP distribution;

    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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