One-sided performance measures under Gram-Charlier distributions |
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| Institution: | 1. Department of Quantitative Methods and Economic Theory, University of Alicante, San Vicente del Raspeig, Alicante 03080, Spain;2. Department of Economics and Finance, Manuel Moreno is from University of Castilla La-Mancha,Toledo 45071, Spain;1. Universidad Pública de Navarra, Spain;2. Universidad CEU Cardenal Herrera, Spain;1. Antai College of Economics and Management, Shanghai Jiaotong University, Shanghai, PR China;2. Glorious Sun School of Business and Management, Donghua University, Shanghai, PR China;3. Carl H. Lindner College of Business, University of Cincinnati, Cincinnati, OH, USA;4. The University of Sydney Business School, The University of Sydney, Sydney, NSW, Australia |
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| 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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