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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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=\(\frac{{{\mu _p} - \tau }}{{\sqrt {LP{M_2}(\tau )} }}.\)
References
Athayde, G., Flores, R.G.: The portfolio frontier with higher moments: The undiscovered country. Computing in Economics and Finance 2002 209, Society for Computational Economics (2002)
Bernardo, A., Ledoit, O., Brennan, M., Grinblatt, M., Roll, R., Santa-clara, P., Vila, J.: Gain, loss and asset pricing (1996)
Davies, R., Harry, M.K., Sa, L.: Fund of hedge funds portfolio selection: A multiple-objective approach. Journal of derivatives & Hadge Funds 15, 91–115 (2009)
Dowd, K.: Adjusting for risk: An improved sharpe ratio. International Review of Economics & Finance 9(3), 209–222 (2000)
Farinelli, S., Tibiletti, L.: Sharpe thinking in asset ranking with one-sided measures. European Journal of Operational Research 185(3), 1542–1547 (2008)
Gilli, M., Schumann, E., Tollo, G., Cabej, G.: Constructing long/short portfolios with the omega ratio. Swiss Finance Institute Research Paper Series 08–34, Swiss Finance Institute
Hitaj, A., Mercuri, L.: Portfolio allocation using multivariate variance gamma. Financial Markets and Portfolio Management 27(1), 65–99 (2013)
Jensen, M.C.: The performance of mutual funds in the period 1945–1964. Journal of Finance 23, 389–416 (1968)
Jondeau, E., Poon, S., Rockinger, M.: Financial modeling under non-gaussian distributions. Springer Finance. Springer (2007)
Kane, S.J., Bartholomew, M.C., Cross, M., Dewar, M.: Optimizing omega. Journal of Global Optimization, 153-167 (2009)
Kaplan, P.D, Knowles, J.A.: Kappa: A generalized downside risk-adjusted performance measure. January (2004)
Keating, C, Shadwick, W.F.: A universal performance measure. Technical report, The Finance development center, London, May (2002)
Kendall, M.G., Hill, A., Bradford: The analysis of economic Time-Series part i: Prices. Journal of the Royal Statistical Society A 116(1), 11–34 (1953)
Martellini, L., Ziemann, V.: Improved estimates of higher-order comoments and implications for portfolio selection. Review of Financial Studies 23(4), 1467–1502 (2010)
Rachev, S.T., Stoyanov, S., Fabozzi, F.J.: Advanced Stochastic Models, Risk Assessment, and Portfolio. John Wiley (2007)
Sharpe, W.: Mutual fund performance. The Journal of Business 39, 119 (1965)
Sortino, F.A., Price, L.N.: Performance measurement in a downside risk framework. Journal of Investing 3(3), 59–64 (1994)
Tibiletti, L., Farinelli, S.: Upside and downside risk with a benchmark. Atlantic Economic Journal 31(4), 387–387 (2003)
Zakamouline, V., Koekebakker, S.: Portfolio performance evaluation with generalized sharpe ratios: Beyond the mean and variance. Journal of Banking & Finance 33(7), 1242–1254 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-02499-8_17
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02498-1
Online ISBN: 978-3-319-02499-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)