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

Ángel León () and Manuel Moreno
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Ángel León: Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica, Postal: University of Alicante, San Vicente del Raspeig, 03080, A licante, Spain.

No 15-3, QM&ET Working Papers from University of Alicante, D. Quantitative Methods and Economic Theory

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.

Keywords: Downside risk; peformance measure; rank correlation; efficient frontier; co-lower partial moment matrix; copula; SNP distribution (search for similar items in EconPapers)
JEL-codes: C10 C61 G11 G17 (search for similar items in EconPapers)
Pages: 44 pages
Date: 2015-03-02
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Persistent link: https://EconPapers.repec.org/RePEc:ris:qmetal:2015_003

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