Abstract
It is widely recognized that expected returns and covariances are not sufficient to characterize the statistical properties of securities in the context of portfolio selection. Therefore different models have been proposed. On one side the Markowitz model has been extended to higher moments and on the other side, starting from Sharpe ratio, a great attention has been addressed to the correct choice of the risk (or joint risk-performance) indicator. One such indicator has been proposed recently in the financial literature: the so-called Omega Function, that considers all the moments of the return distribution and whose properties are being investigated thoroughly. The main purpose of this paper is to investigate empirically, in an out-of-sample perspective, the portfolios obtained using higher moments and the Omega ratio. Moreover we analyze the impact of the target threshold (when the Omega Ratio is used) and the impact of different preferences for moments and comoments (when a higher-moments approach is used) on portfolio allocation. Our empirical analysis is based on a portfolio composed of 12 Hedge fund indexes.
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Notes
- 1.
We chose the rolling window strategy 48-3 as this is commonly used in real hedge fund world where the data are scarce.
- 2.
Actually, the term “polynomial” refers to the formulation whereby the aspiration levels are determined, not to the objective function of the main program.
- 3.
The data have been collected through the Dow Jones Credit Suisse Hedge Fund Index.
- 4.
The complete results are available upon request.
- 5.
For the Omega ratio we have reported only the out-of-sample performances for τ = 3%,7%,8% on annual basis.
- 6.
Sharpe=\(\frac{{{\mu _p} - \tau }}{{{\sigma _p}}}.\)
- 7.
Sortino=\(\frac{{{\mu _p} - \tau }}{{\sqrt {LP{M_2}(\tau )} }}.\)
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Hitaj, A., Martinelli, F., Zambruno, G. (2014). Portfolio Allocation Using Omega Function: An Empirical Analysis. In: Corazza, M., Pizzi, C. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-02499-8_17
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DOI: https://doi.org/10.1007/978-3-319-02499-8_17
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