CAPORIN Massimiliano

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Several recent finance articles use the Omega measure (Keating and Shadwick, 2002), defined as a ratio of potential gains out of possible losses, for gauging the performance of funds or active strategies, in substitution of the traditional Sharpe ratio, with the arguments that return distributions are not Gaussian and volatility is not always the relevant risk metric. Other authors also use Omega for optimizing (non-linear) portfolios with important downside risk. However, we question in this article the relevance of such approaches. First, we show through a basic illustration that the Omega ratio is inconsistent with the Second-order Stochastic Dominance criterion. Furthermore, we observe that the trade-off between return and risk corresponding to the Omega measure, may be essentially influenced by the mean return. Next, we illustrate in static and dynamic frameworks that Omega-based optimal portfolios can be closely associated with classical optimization paradigms depending on the chosen threshold used in Omega. Finally, we present robustness checks on long-only asset and hedge fund databases, that confirm our results.

Several recent finance articles employ the Omega measure, proposed by Keating and Shadwick (2002) - defined as a ratio of potential gains out of possible losses - for gauging the performance of funds or active strategies (e.g. Eling and Schuhmacher, 2007. Farinelli and Tibiletti, 2008. Annaert et al., 2009. Bertrand and Prigent, 2011. Zieling et al., 2014. Kapsos et al., 2014. Hamidi et al., 2014), in substitution of the traditional Sharpe ratio (1966), with the arguments that return distributions are not Gaussian and volatility is not, always, the relevant risk metric. Other authors also use the same criterion for optimizing (non-linear) portfolios with important downside risk. However, we wonder in this article about the relevance of such approaches. First, we show through a basic illustration that the Omega ratio is inconsistent with the Strict Inferior Second-order Stochastic Dominance criterion. Furthermore, we observe that the trade-off between return and risk, corresponding to the Omega measure, may be essentially influenced by the mean return. Next, we illustrate in static and dynamic frameworks that Omega-based optimal portfolios can be associated with traditional optimization paradigms depending on the chosen threshold used in the computation of Omega. Finally, we present some robustness checks on long-only asset and hedge fund databases that all confirm our general results.

Performance measurement is one of the most studied subjects in financial literature. Since the introduction of the Sharpe ratio in 1966, a large variety of new measures has appeared constantly in scientific journals as well as in practitioners' publications. The most complete and significant studies of performance measures, so far, have been written by Aftalion and Poncet, Le Sourd, Bacon, and Cogneau and H übner. A review of the most recent literature led us to collect several dozen measures that we classify into four families. We first present the class of relative measures, starting with the Sharpe ratio. Secondly, we analyse absolute measures, beginning with the most famous one ‐ the Jensen alpha. Thirdly, we study general measures based on specific features of the return distribution, where the pioneering contributions are those of Bernardo and Ledoit, and Keating and Shadwick. Finally, the fourth set concerns a few measures that explicitly take into account the investor's utility functions.

The main focus of the thesis is on modern nonlinear approaches to the analysis of economic and financial data, with a particular emphasis on business cycles and financial crises. A consensus in the statistical and financial literature has developed around the fact that economic variables behave non-linearly during different phases of the business cycle. As such, nonlinear approaches/models are required to capture the characteristics of the inherently asymmetric data generation mechanism, which linear models are unable to reproduce.In this regard, the thesis proposes a new interdisciplinary and open approach to the analysis of economic and financial systems. The thesis presents approaches robust to extreme values and non-stationarity, applicable to both small and large samples, for both economic and financial time series. The thesis provides step-by-step procedures in the analysis of economic and financial indicators by integrating concepts based on the data substitution method, wavelets, phase embedding space, delay vector variance (DVV) method and plot recurrences. The thesis also highlights transparent methods for identifying and dating turning points and assessing the impacts of economic and financial crises. In particular, the thesis also provides a procedure for anticipating future crises and its consequences.The study shows that the integration of these techniques in learning the structure and interactions within and between economic and financial variables will be very useful in the development of crisis policies, as it facilitates the choice of appropriate treatment methods suggested by the data.In addition, a new procedure for testing linearity and unit root in a nonlinear framework is proposed by introducing a new model - the MT-STAR model - which has similar properties to the ESTAR model but reduces the effects of identification problems and can also represent asymmetry in the adjustment mechanism towards equilibrium. The proposed asymptotic distributions of the unit root test are non-standard and are calculated. The power of the test is evaluated by simulation and some empirical illustrations on real exchange rates show its effectiveness. Finally, the thesis develops multi-variate Self-Exciting Threshold Autoregressive models with exogenous variables (MSETARX) and presents a parametric estimation method. The modeling of MSETARX models and the problems generated by its estimation are briefly discussed.

Performance measurement is one of the most studied subjects in financial literature. Since the introduction of the Sharpe ratio in 1966, a large variety of new measures has appeared constantly in scientific journals as well as in practitioners' publications. The most complete and significant studies of performance measures, so far, have been written by Aftalion and Poncet, Le Sourd, Bacon, and Cogneau and H übner. A review of the most recent literature led us to collect several dozen measures that we classify into four families. We first present the class of relative measures, starting with the Sharpe ratio. Secondly, we analyse absolute measures, beginning with the most famous one - the Jensen alpha. Thirdly, we study general measures based on specific features of the return distribution, where the pioneering contributions are those of Bernardo and Ledoit, and Keating and Shadwick. Finally, the fourth set concerns a few measures that explicitly take into account the investor's utility functions.