The performance of trend following strategies can be ascribed to the difference between long-term... more The performance of trend following strategies can be ascribed to the difference between long-term and short-term realized variance. We revisit this general result and show that it holds for various definitions of trend strategies. This explains the positive convexity of the aggregate performance of Commodity Trading Advisors (CTAs) which-when adequately measured-turns out to be much stronger than anticipated. We also highlight interesting connections with so-called Risk Parity portfolios. Finally, we propose a new portfolio of strangle options that provides a pure exposure to the longterm variance of the underlying, offering yet another viewpoint on the link between trend and volatility.
In this article, we discuss various implementation of L1 filtering in order to detect some proper... more In this article, we discuss various implementation of L1 filtering in order to detect some properties of noisy signals. This filter consists of using a L1 penalty condition in order to obtain the filtered signal composed by a set of straight trends or steps. This penalty condition, which determines the number of breaks, is implemented in a constrained least square problem and is represented by a regularization parameter λ which is estimated by a cross-validation procedure. Financial time series are usually characterized by a long-term trend (called the global trend) and some short-term trends (which are named local trends). A combination of these two time scales can form a simple model describing the process of a global trend process with some mean-reverting properties. Explicit applications to momentum strategies are also discussed in detail with appropriate uses of the trend configurations.
In this article, we discuss various implementation of L1 filtering in order to detect some proper... more In this article, we discuss various implementation of L1 filtering in order to detect some properties of noisy signals. This filter consists of using a L1 penalty condition in order to obtain the filtered signal composed by a set of straight trends or steps. This penalty condition, which determines the number of breaks, is implemented in a constrained least square problem and is represented by a regularization parameter λ which is estimated by a cross-validation procedure. Financial time series are usually characterized by a long-term trend (called the global trend) and some short-term trends (which are named local trends). A combination of these two time scales can form a simple model describing the process of a global trend process with some mean-reverting properties. Explicit applications to momentum strategies are also discussed in detail with appropriate uses of the trend configurations.
The objectives of this report are two-fold. We first studied some novel techniques in statistics ... more The objectives of this report are two-fold. We first studied some novel techniques in statistics and signal processing fields such as trend filtering, daily and high frequency volatility estimator or support vector machine. We employed these techniques to extract interesting financial signals. These signals are used to implement the momentum strategies which will be described in detail in every chapter of this report. The second objective concerns the study of the performance of momentum strategies based on the risk-return analysis framework (see B. Bruder and N. Gaussel 7th White Paper, Lyxor).
We study a two-component Fermi system with attractive interactions and different populations of t... more We study a two-component Fermi system with attractive interactions and different populations of the two species in a cubic lattice. For an intermediate coupling we find a uniformly polarized superfluid which is stable down to very low temperatures. The momentum distribution of this phase closely resembles that of the Sarma phase, characterized by two Fermi surfaces. This phase is shown to be stabilized by a potential energy gain, as in a BCS superfluid, in contrast to the unpolarized BEC which is stabilized by kinetic energy. We present general arguments suggesting that preformed pairs in the unpolarized superfluid favor the stabilization of a polarized superfluid phase.
We propose a Raman spectroscopy technique which is able to probe the one-particle Green's functio... more We propose a Raman spectroscopy technique which is able to probe the one-particle Green's function, the Fermi surface, and the quasiparticles of a gas of strongly interacting ultracold atoms. We give quantitative examples of experimentally accessible spectra. The efficiency of the method is validated by means of simulated images for the case of a usual Fermi liquid as well as for more exotic states: specific signatures of e.g. a d-wave pseudo-gap are clearly visible.
We investigate a momentum-resolved Raman spectroscopy technique which is able to probe the one-bo... more We investigate a momentum-resolved Raman spectroscopy technique which is able to probe the one-body spectral function and the quasi-particle states of a gas of strongly interacting ultracold atoms. This technique is inspired by Angle-Resolved Photo-Emission Spectroscopy, a powerful experimental probe of electronic states in solid-state systems. Quantitative examples of experimentally accessible spectra are given for the most significant regimes along the BEC-BCS crossover. When the theory is specialized to RF spectroscopy, agreement is found with recent experimental data. The main advantages of this Raman spectroscopy over existing techniques are pointed out.
We investigate the effect of mass imbalance in binary Fermi mixtures loaded in optical lattices. ... more We investigate the effect of mass imbalance in binary Fermi mixtures loaded in optical lattices. Using dynamical mean-field theory, we study the transition from a fluid to a Mott insulator driven by the repulsive interactions. For almost every value of the parameters we find that the light species with smaller bare mass is more affected by correlations than the heavy one, so that their effective masses become closer than their bare masses before a Mott transition occurs. The strength of the critical repulsion decreases monotonically as the mass imbalance grows so that the minimum is realized when one of the species is localized. The evolution of the spectral functions testifies that a continuous loss of coherence and a destruction of the Fermi liquid occur as the imbalance grows. The two species display distinct properties and experimentally-observable deviations from the behavior of a balanced Fermi mixture.
We propose a method to directly measure the temperature of a gas of weakly interacting fermionic ... more We propose a method to directly measure the temperature of a gas of weakly interacting fermionic atoms loaded into an optical lattice. This technique relies on Raman spectroscopy and is applicable to experimentally relevant temperature regimes. Additionally, we show that a similar spectroscopy scheme can be used to obtain information on the quasiparticle properties and Hubbard bands of the metallic and Mott-insulating states of interacting fermionic spin mixtures. These two methods provide experimentalists with novel probes to accurately characterize fermionic quantum gases confined to optical lattices.
We propose an all-optical scheme to probe the dynamical correlations of a strongly-interacting ga... more We propose an all-optical scheme to probe the dynamical correlations of a strongly-interacting gas of ultracold atoms in an optical lattice potential. The proposed technique is based on a pump-and-probe scheme: a coherent light pulse is initially converted into an atomic coherence and later retrieved after a variable storage time. The efficiency of the proposed method to measure the two-time one-particle Green function of the gas is validated by numerical and analytical calculations of the expected signal for the two cases of a normal Fermi gas and a BCS superfluid state. Protocols to extract the superfluid gap and the full quasi-particle dispersions are discussed.
We study the competition between one-body and two-body couplings in weakly-interacting twocompone... more We study the competition between one-body and two-body couplings in weakly-interacting twocomponent Bose gases, in particular as regards field correlations. We derive the meanfield theory for both ground state and low-energy pair excitations in the general case where both one-body and two-body couplings are position-dependent and the fluid is subjected to a state-dependent trapping potential. General formulas for phase and density correlations are also derived. Focusing on the case of homogeneous systems, we discuss the pair-excitation spectrum and the corresponding excitation modes, and use them to calculate correlation functions, including both quantum and thermal fluctuation terms. We show that the relative phase of the two components is imposed by that of the one-body coupling, while its fluctuations are determined by the modulus of the one-body coupling and by the two-body coupling. One-body coupling and repulsive two-body coupling cooperate to suppress relative-phase fluctuations, while attractive two-body coupling tends to enhance them. Further applications of the formalism presented here and extensions of our work are also discussed.
We study the effect of mass imbalance on the phase diagram of a two-component fermionic mixture w... more We study the effect of mass imbalance on the phase diagram of a two-component fermionic mixture with attractive interactions in optical lattices. Using static and dynamical mean-field theories, we show that the pure superfluid phase is stable for all couplings when the mass imbalance is smaller than a limiting value. For larger imbalance, phase separation between a superfluid and a charge-density wave takes place when the coupling exceeds a critical strength. The harmonic trap induces a spatial segregation of the two phases, with a rapid variation of the density at the boundary.
This paper studies trend filtering methods. These methods are widely used in momentum strategies,... more This paper studies trend filtering methods. These methods are widely used in momentum strategies, which correspond to an investment style based only on the history of past prices. For example, the CTA strategy used by hedge funds is one of the best-known momentum strategies. In this paper, we review the different econometric estimators to extract a trend of a time series. We distinguish between linear and nonlinear models as well as univariate and multivariate filtering. For each approach, we provide a comprehensive presentation, an overview of its advantages and disadvantages and an application to the S&P 500 index. We also consider the calibration problem of these filters. We illustrate the two main solutions, the first based on prediction error, and the second using a benchmark estimator. We conclude the paper by listing some issues to consider when implementing a momentum strategy.
We review in this note the well-known machine learning technique so-called support vector machine... more We review in this note the well-known machine learning technique so-called support vector machine (SVM). This technique can be employed in different contexts such as classification, regression or density estimation according to Vapnik [1998]. Within this paper, we would like first to give an overview on this method and its numerical variation implementation, then bridge it to financial applications such as the stock selection or the prediction of market trend.
Cette these est consacree a l'etude theorique des etats quantiques fortement correles de ultr... more Cette these est consacree a l'etude theorique des etats quantiques fortement correles de ultra-froids pieges atomes fermioniques dans les reseaux optiques. Ce champ a considerablement augmente Ces dernieres annees, suite aux progres experimentaux realises dans le refroidissement et le controle des gaz atomiques, qui a conduit a l'observation de la premiere condensation de Bose-Einstein (en 1995 [4]). Le le piegeage de ces gaz dans les reseaux optiques a ouvert un nouveau champ de recherche a l'interface entre la physique atomique et physique de la matiere condensee. L'observation de la transition a partir d'un superfluide a un isolant de Mott d'atomes bosoniques [46] a ouvert la voie pour l'etude de fortement correlee phases et transitions de phase quantique dans ces systemes. Tres recemment, le enquete sur l'etat isolant de Mott d'atomes fermioniques [63] fournit une motivation supplementaire de proceder a ces etudes theoriques. Cette these peut ...
We propose a set of novel experimental tools to cool and measure the temperature of fermionic ato... more We propose a set of novel experimental tools to cool and measure the temperature of fermionic atoms loaded into an optical lattice. The proposed cooling method is based on spatial entropy modulation while the temperature detection scheme relies on Raman spectroscopy.
Recently, our group has published two papers that have received some attention in the finance com... more Recently, our group has published two papers that have received some attention in the finance community. One is about the profitability of trend following strategies over 200 years, the second is about the correlation between the profitability of "Risk Premia" and their skewness. In this short note, we present two additional plots that fully corroborate our findings on new data.
The performance of trend following strategies can be ascribed to the difference between long-term... more The performance of trend following strategies can be ascribed to the difference between long-term and short-term realized variance. We revisit this general result and show that it holds for various definitions of trend strategies. This explains the positive convexity of the aggregate performance of Commodity Trading Advisors (CTAs) which-when adequately measured-turns out to be much stronger than anticipated. We also highlight interesting connections with so-called Risk Parity portfolios. Finally, we propose a new portfolio of strangle options that provides a pure exposure to the longterm variance of the underlying, offering yet another viewpoint on the link between trend and volatility.
In this article, we discuss various implementation of L1 filtering in order to detect some proper... more In this article, we discuss various implementation of L1 filtering in order to detect some properties of noisy signals. This filter consists of using a L1 penalty condition in order to obtain the filtered signal composed by a set of straight trends or steps. This penalty condition, which determines the number of breaks, is implemented in a constrained least square problem and is represented by a regularization parameter λ which is estimated by a cross-validation procedure. Financial time series are usually characterized by a long-term trend (called the global trend) and some short-term trends (which are named local trends). A combination of these two time scales can form a simple model describing the process of a global trend process with some mean-reverting properties. Explicit applications to momentum strategies are also discussed in detail with appropriate uses of the trend configurations.
In this article, we discuss various implementation of L1 filtering in order to detect some proper... more In this article, we discuss various implementation of L1 filtering in order to detect some properties of noisy signals. This filter consists of using a L1 penalty condition in order to obtain the filtered signal composed by a set of straight trends or steps. This penalty condition, which determines the number of breaks, is implemented in a constrained least square problem and is represented by a regularization parameter λ which is estimated by a cross-validation procedure. Financial time series are usually characterized by a long-term trend (called the global trend) and some short-term trends (which are named local trends). A combination of these two time scales can form a simple model describing the process of a global trend process with some mean-reverting properties. Explicit applications to momentum strategies are also discussed in detail with appropriate uses of the trend configurations.
The objectives of this report are two-fold. We first studied some novel techniques in statistics ... more The objectives of this report are two-fold. We first studied some novel techniques in statistics and signal processing fields such as trend filtering, daily and high frequency volatility estimator or support vector machine. We employed these techniques to extract interesting financial signals. These signals are used to implement the momentum strategies which will be described in detail in every chapter of this report. The second objective concerns the study of the performance of momentum strategies based on the risk-return analysis framework (see B. Bruder and N. Gaussel 7th White Paper, Lyxor).
We study a two-component Fermi system with attractive interactions and different populations of t... more We study a two-component Fermi system with attractive interactions and different populations of the two species in a cubic lattice. For an intermediate coupling we find a uniformly polarized superfluid which is stable down to very low temperatures. The momentum distribution of this phase closely resembles that of the Sarma phase, characterized by two Fermi surfaces. This phase is shown to be stabilized by a potential energy gain, as in a BCS superfluid, in contrast to the unpolarized BEC which is stabilized by kinetic energy. We present general arguments suggesting that preformed pairs in the unpolarized superfluid favor the stabilization of a polarized superfluid phase.
We propose a Raman spectroscopy technique which is able to probe the one-particle Green's functio... more We propose a Raman spectroscopy technique which is able to probe the one-particle Green's function, the Fermi surface, and the quasiparticles of a gas of strongly interacting ultracold atoms. We give quantitative examples of experimentally accessible spectra. The efficiency of the method is validated by means of simulated images for the case of a usual Fermi liquid as well as for more exotic states: specific signatures of e.g. a d-wave pseudo-gap are clearly visible.
We investigate a momentum-resolved Raman spectroscopy technique which is able to probe the one-bo... more We investigate a momentum-resolved Raman spectroscopy technique which is able to probe the one-body spectral function and the quasi-particle states of a gas of strongly interacting ultracold atoms. This technique is inspired by Angle-Resolved Photo-Emission Spectroscopy, a powerful experimental probe of electronic states in solid-state systems. Quantitative examples of experimentally accessible spectra are given for the most significant regimes along the BEC-BCS crossover. When the theory is specialized to RF spectroscopy, agreement is found with recent experimental data. The main advantages of this Raman spectroscopy over existing techniques are pointed out.
We investigate the effect of mass imbalance in binary Fermi mixtures loaded in optical lattices. ... more We investigate the effect of mass imbalance in binary Fermi mixtures loaded in optical lattices. Using dynamical mean-field theory, we study the transition from a fluid to a Mott insulator driven by the repulsive interactions. For almost every value of the parameters we find that the light species with smaller bare mass is more affected by correlations than the heavy one, so that their effective masses become closer than their bare masses before a Mott transition occurs. The strength of the critical repulsion decreases monotonically as the mass imbalance grows so that the minimum is realized when one of the species is localized. The evolution of the spectral functions testifies that a continuous loss of coherence and a destruction of the Fermi liquid occur as the imbalance grows. The two species display distinct properties and experimentally-observable deviations from the behavior of a balanced Fermi mixture.
We propose a method to directly measure the temperature of a gas of weakly interacting fermionic ... more We propose a method to directly measure the temperature of a gas of weakly interacting fermionic atoms loaded into an optical lattice. This technique relies on Raman spectroscopy and is applicable to experimentally relevant temperature regimes. Additionally, we show that a similar spectroscopy scheme can be used to obtain information on the quasiparticle properties and Hubbard bands of the metallic and Mott-insulating states of interacting fermionic spin mixtures. These two methods provide experimentalists with novel probes to accurately characterize fermionic quantum gases confined to optical lattices.
We propose an all-optical scheme to probe the dynamical correlations of a strongly-interacting ga... more We propose an all-optical scheme to probe the dynamical correlations of a strongly-interacting gas of ultracold atoms in an optical lattice potential. The proposed technique is based on a pump-and-probe scheme: a coherent light pulse is initially converted into an atomic coherence and later retrieved after a variable storage time. The efficiency of the proposed method to measure the two-time one-particle Green function of the gas is validated by numerical and analytical calculations of the expected signal for the two cases of a normal Fermi gas and a BCS superfluid state. Protocols to extract the superfluid gap and the full quasi-particle dispersions are discussed.
We study the competition between one-body and two-body couplings in weakly-interacting twocompone... more We study the competition between one-body and two-body couplings in weakly-interacting twocomponent Bose gases, in particular as regards field correlations. We derive the meanfield theory for both ground state and low-energy pair excitations in the general case where both one-body and two-body couplings are position-dependent and the fluid is subjected to a state-dependent trapping potential. General formulas for phase and density correlations are also derived. Focusing on the case of homogeneous systems, we discuss the pair-excitation spectrum and the corresponding excitation modes, and use them to calculate correlation functions, including both quantum and thermal fluctuation terms. We show that the relative phase of the two components is imposed by that of the one-body coupling, while its fluctuations are determined by the modulus of the one-body coupling and by the two-body coupling. One-body coupling and repulsive two-body coupling cooperate to suppress relative-phase fluctuations, while attractive two-body coupling tends to enhance them. Further applications of the formalism presented here and extensions of our work are also discussed.
We study the effect of mass imbalance on the phase diagram of a two-component fermionic mixture w... more We study the effect of mass imbalance on the phase diagram of a two-component fermionic mixture with attractive interactions in optical lattices. Using static and dynamical mean-field theories, we show that the pure superfluid phase is stable for all couplings when the mass imbalance is smaller than a limiting value. For larger imbalance, phase separation between a superfluid and a charge-density wave takes place when the coupling exceeds a critical strength. The harmonic trap induces a spatial segregation of the two phases, with a rapid variation of the density at the boundary.
This paper studies trend filtering methods. These methods are widely used in momentum strategies,... more This paper studies trend filtering methods. These methods are widely used in momentum strategies, which correspond to an investment style based only on the history of past prices. For example, the CTA strategy used by hedge funds is one of the best-known momentum strategies. In this paper, we review the different econometric estimators to extract a trend of a time series. We distinguish between linear and nonlinear models as well as univariate and multivariate filtering. For each approach, we provide a comprehensive presentation, an overview of its advantages and disadvantages and an application to the S&P 500 index. We also consider the calibration problem of these filters. We illustrate the two main solutions, the first based on prediction error, and the second using a benchmark estimator. We conclude the paper by listing some issues to consider when implementing a momentum strategy.
We review in this note the well-known machine learning technique so-called support vector machine... more We review in this note the well-known machine learning technique so-called support vector machine (SVM). This technique can be employed in different contexts such as classification, regression or density estimation according to Vapnik [1998]. Within this paper, we would like first to give an overview on this method and its numerical variation implementation, then bridge it to financial applications such as the stock selection or the prediction of market trend.
Cette these est consacree a l'etude theorique des etats quantiques fortement correles de ultr... more Cette these est consacree a l'etude theorique des etats quantiques fortement correles de ultra-froids pieges atomes fermioniques dans les reseaux optiques. Ce champ a considerablement augmente Ces dernieres annees, suite aux progres experimentaux realises dans le refroidissement et le controle des gaz atomiques, qui a conduit a l'observation de la premiere condensation de Bose-Einstein (en 1995 [4]). Le le piegeage de ces gaz dans les reseaux optiques a ouvert un nouveau champ de recherche a l'interface entre la physique atomique et physique de la matiere condensee. L'observation de la transition a partir d'un superfluide a un isolant de Mott d'atomes bosoniques [46] a ouvert la voie pour l'etude de fortement correlee phases et transitions de phase quantique dans ces systemes. Tres recemment, le enquete sur l'etat isolant de Mott d'atomes fermioniques [63] fournit une motivation supplementaire de proceder a ces etudes theoriques. Cette these peut ...
We propose a set of novel experimental tools to cool and measure the temperature of fermionic ato... more We propose a set of novel experimental tools to cool and measure the temperature of fermionic atoms loaded into an optical lattice. The proposed cooling method is based on spatial entropy modulation while the temperature detection scheme relies on Raman spectroscopy.
Recently, our group has published two papers that have received some attention in the finance com... more Recently, our group has published two papers that have received some attention in the finance community. One is about the profitability of trend following strategies over 200 years, the second is about the correlation between the profitability of "Risk Premia" and their skewness. In this short note, we present two additional plots that fully corroborate our findings on new data.
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