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On certain geometric aspects of portfolio optimisation with higher moments

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  • Flôres Junior, Renato Galvão
  • Athayde, Gustavo M. de

Abstract

We discuss geometric properties related to the minimisation of a portfolio kurtosis given its first two odd moments, considering a risk-less asset and allowing for short sales. The findings are generalised for the minimisation of any given even portfolio moment with fixed excess return and skewness, and then for the case in which only excess return is constrained. An example with two risky assets provides a better insight on the problems related to the solutions. The importance of the geometric properties and their use in the higher moments portfolio choice context is highlighted.

Suggested Citation

  • Flôres Junior, Renato Galvão & Athayde, Gustavo M. de, 2002. "On certain geometric aspects of portfolio optimisation with higher moments," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 453, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
  • Handle: RePEc:fgv:epgewp:453
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    1. Bertrand Maillet & Emmanuel Jurczenko, 2002. "The 3-CAPM: Theoretical Foundations and a Comparison of Asset Pricing Models in an Unified Framework," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00308997, HAL.
    2. Barone-Adesi, Giovanni, 1985. "Arbitrage Equilibrium with Skewed Asset Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(3), pages 299-313, September.
    3. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    4. Hwang, Soosung & Satchell, Stephen E, 1999. "Modelling Emerging Market Risk Premia Using Higher Moments," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 4(4), pages 271-296, October.
    5. Athayde, Gustavo M. de & Flôres Junior, Renato Galvão, 1997. "A CAPM with higher moments: theory and econometrics," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 317, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    6. Pedersen, Christian S. & Satchell, Stephen E., 2000. "Small Sample Analysis of Performance Measures in the Asymmetric Response Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(3), pages 425-450, September.
    7. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
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