Optimizing Omega

Kane, S. J.; Bartholomew‐Biggs, M. C.; Cross, Megan; Dewar, Mike

doi:10.1007/s10898-008-9396-5

Cited by 39 publications

(24 citation statements)

References 7 publications

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“…The main reason is that maximizing the Omega ratio has been thought, until recently, to be computationally intractable and, as a consequence, most of the limited research has been focused on the design of heuristic algorithms. To the best of our knowledge, the first authors to investigate the use of the Omega ratio as a basis for portfolio selection are Kane et al [14]. The authors observe that the maximization of the Omega ratio leads to a non-convex and non-smooth optimization problem which has many local optima.…”

Section: The Omega Ratiomentioning

confidence: 99%

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Guastaroba

Mansini

Ogryczak

et al. 2016

European Journal of Operational Research

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Modern performance measures differ from the classical ones since they assess the performance against a benchmark and usually account for asymmetry in return distributions. The Omega ratio is one of these measures. Until recently, limited research has addressed the optimization of the Omega ratio since it has been thought to be computationally intractable. The Enhanced Index Tracking Problem (EITP) is the problem of selecting a portfolio of securities able to outperform a market index while bearing a limited additional risk. In this paper, we propose two novel mathematical formulations for the EITP based on the Omega ratio. The first formulation applies a standard definition of the Omega ratio where it is computed with respect to a given value, whereas the second formulation considers the Omega ratio with respect to a random target. We show how each formulation, nonlinear in nature, can be transformed into a Linear Programming model. We further extend the models to include real features, such as a cardinality constraint and buy-in thresholds on the investments, obtaining Mixed Integer Linear Programming problems. Computational results conducted on a large set of benchmark instances show that the portfolios selected by the model assuming a standard definition of the Omega ratio are consistently outperformed, in terms of out-of-sample performance, by those obtained solving the model that considers a random target. Furthermore, in most of the instances the portfolios optimized with the latter model mimic very closely the behavior of the benchmark over the out-of-sample period, while yielding, sometimes, significantly larger returns.

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Section: The Omega Ratiomentioning

confidence: 99%

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Guastaroba

Mansini

Ogryczak

et al. 2016

European Journal of Operational Research

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“…In particular, Omega separately considers gains and losses without reference to a specific distribution for asset returns. For its implementation in portfolio construction see, for example, Avouyi-Dovi et al (2004), Passow (2005), Gilli et al (2006), Mausser et al (2006) and Kane et al (2009). Omega is defined for any portfolio return level as the probability weighted ratio of gains to losses relative to a threshold return defined by the investor, b r .…”

Section: Omega Optimization Modelmentioning

confidence: 99%

Dynamic hedge fund portfolio construction: A semi-parametric approach

Harris

Mazibas

2013

Journal of Banking & Finance

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In this paper, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. Using monthly hedge fund index returns for the period 1990 to 2011, we compare the standard mean-variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semiparametric methodology, in which we first model the marginal density of each hedge fund index using extreme value theory and construct the joint density of hedge fund index returns using a copula-based approach. We then simulate hedge fund returns from this joint density in order to compute CVaR, CDaR and Omega, which are used in the optimization process. We compare the semi-parametric approach with the standard, non-parametric approach, in which the quantiles of the marginal density of portfolio returns are estimated empirically and used to compute CVaR, CDaR and Omega. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the mean-variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.

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“…One example is the Omega function [8] which measures the performance of an asset, or of a portfolio of assets, by the ratio of the weighted gains (above a given threshold) over the weighted losses (below the threshold). Such function exhibits numerous discontinuities and recent studies involving its derivative-free optimization are reported in [15,18]. Another example arises in the tuning of algorithmic parameters for a given method/code (see [6] for instances where DSM have been applied to solve such problems) -the resulting objective functions are likely to exhibit all sorts of discontinuities given the way that typically a method/code responds to changes in its parameters.…”

Section: Introductionmentioning

confidence: 99%

Analysis of direct searches for discontinuous functions

Vicente

Custódio²

2010

Math. Program.

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It is known that the Clarke generalized directional derivative is nonnegative along the limit directions generated by directional directsearch methods at a limit point of certain subsequences of unsuccessful iterates, if the function being minimized is Lipschitz continuous near the limit point.In this paper we generalize this result for discontinuous functions using Rockafellar generalized directional derivatives (upper subderivatives). We show that Rockafellar derivatives are also nonnegative along the limit directions of those subsequences of unsuccessful iterates when the function values converge to the function value at the limit point. This result is obtained assuming that the function is directionally Lipschitz with respect to the limit direction.It is also possible under appropriate conditions to establish more insightful results by showing that the sequence of points generated by these methods eventually approaches the limit point along the locally best branch or step function (when the number of steps is equal to two).The results of this paper are presented for constrained optimization and illustrated numerically.

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Optimizing Omega

Cited by 39 publications

References 7 publications

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Dynamic hedge fund portfolio construction: A semi-parametric approach

Analysis of direct searches for discontinuous functions

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