Impact of Hedging Strategy on Capital Charges for Variable Annuity Portfolios
Social Science Research Network, 2020
Efficient and robust techniques are crucial for hedging a book of variable annuities. For insurer... more Efficient and robust techniques are crucial for hedging a book of variable annuities. For insurers, the profitability of variable annuity contracts heavily depend on the hedging schemes used to mitigate their associated financial liabilities. Beyond financial performance, the inclusion of protection, in the form of protective put options, in hedging portfolios contributes to reduce the capital charges imposed on the insurer. Although this external source of profit affect the total performance of the hedge, it has not been quantified in the literature. This paper fills that gap by quantifying the contribution of capital charge reductions to hedging performance for a number of hedging methodologies. We provide statistics using price simulations following normal and student distributions with fatter tails.
Optimal equity protection of Solvency II regulated portfolios
The journal of risk, 2018
The Solvency II regulatory framework creates incentives for using derivatives to mitigate risk. H... more The Solvency II regulatory framework creates incentives for using derivatives to mitigate risk. However, for investors willing to reduce capital charges by protecting their portfolio against losses, very few practical solutions exist. In the context of equity investments, we examine the relationship between the cost of acquiring protection (in the form of a put option) and the reduction of capital charges that it entails. We develop the idea that Solvency II regulations introduce an external utility that modifies the economic value of options. Using these findings, we show that there is a way to choose protection levels that maximizes reductions in capital charges for every dollar spent on the put options. We provide results for both risk-based and drawdown-based capital requirements and argue that risk-based capital requirements offer even greater incentives for using derivatives in the context of risk mitigation.
Optimal Factor Investing: Good Portfolios Matter More than Bad Views
Social Science Research Network, Jan 30, 2015
ABSTRACT We focus on the selection of stocks in the context of factor investing. We show how to b... more ABSTRACT We focus on the selection of stocks in the context of factor investing. We show how to build an optimal stocks selection methodology based on factor exposures, factor correlations and also views, even ambiguous ones, on the factor returns. We examine the real-world behaviour of several portfolio whose components are selected using our methodology. Also, we explain why our selection methodology exhibits resilience to changing or even plain wrong views on the factor returns.
We present a stock selection methodology that maximizes the expected returns of equity portfolios... more We present a stock selection methodology that maximizes the expected returns of equity portfolios by efficiently managing their exposures to a given ensemble of risk premia, also known as factors. Our approach is mathematically grounded, robust in its design, and applicable in practice. It addresses several issues specific to factor investing, such as cross-sectional interactions between factors, the mismatch between the factors performance cycles and typical rebalancing periods, or the mitigation of interactions between the capital allocation schemes and factor exposures.
Impact of Hedging Strategy on Capital Charges for Variable Annuity Portfolios
ERN: Hedging (Topic), 2020
Efficient and robust techniques are crucial for hedging a book of variable annuities. For insurer... more Efficient and robust techniques are crucial for hedging a book of variable annuities. For insurers, the profitability of variable annuity contracts heavily depend on the hedging schemes used to mitigate their associated financial liabilities. Beyond financial performance, the inclusion of protection, in the form of protective put options, in hedging portfolios contributes to reduce the capital charges imposed on the insurer. Although this external source of profit affect the total performance of the hedge, it has not been quantified in the literature. This paper fills that gap by quantifying the contribution of capital charge reductions to hedging performance for a number of hedging methodologies. We provide statistics using price simulations following normal and student distributions with fatter tails.
Optical lattices make it possible to trap and coherently control large ensembles of ultracold a... more Optical lattices make it possible to trap and coherently control large ensembles of ultracold atoms. They provide the possibility to create lattice potentials that mimic the structure of solid-state systems, and to control these potentials dynamically. In this thesis, we study how dynamical manipulations of the lattice geometry can be used to perform different tasks, ranging from quantum information processing to the creation of diatomic molecules. We first examine the dynamical properties of ultracold atoms trapped in a lattice whose periodicity is dynamically doubled. We derive a model describing the dynamics of the atoms during this process, and compute the different interaction parameters of this model. We investigate different ways of using this lattice manipulation to optimise the initialisation time of a Mott-insulating state with one atom per site, and provide a scaling law related to the interaction parameters of the system. We go on to show that entangling operations bet...
Optimal equity protection of Solvency II regulated portfolios
Journal of Risk, 2018
The Solvency II regulatory framework creates incentives for using derivatives to mitigate risk. H... more The Solvency II regulatory framework creates incentives for using derivatives to mitigate risk. However, for investors willing to reduce capital charges by protecting their portfolio against losses, very few practical solutions exist. In the context of equity investments, we examine the relationship between the cost of acquiring protection (in the form of a put option) and the reduction of capital charges that it entails. We develop the idea that Solvency II regulations introduce an external utility that modifies the economic value of options. Using these findings, we show that there is a way to choose protection levels that maximizes reductions in capital charges for every dollar spent on the put options. We provide results for both risk-based and drawdown-based capital requirements and argue that risk-based capital requirements offer even greater incentives for using derivatives in the context of risk mitigation.
We present a stock selection methodology that maximizes the expected returns of equity portfolios... more We present a stock selection methodology that maximizes the expected returns of equity portfolios by efficiently managing their exposures to a given ensemble of risk premia, also known as factors. Our approach is mathematically grounded, robust in its design, and applicable in practice. It addresses several issues specific to factor investing, such as cross-sectional interactions between factors, the mismatch between the factors performance cycles and typical rebalancing periods, or the mitigation of interactions between the capital allocation schemes and factor exposures.
For investors subject to Solvency II regulations, the capital charges for holding equities are hi... more For investors subject to Solvency II regulations, the capital charges for holding equities are high. This reduces the appeal of this asset class as an investment of choice for realizing long-term growth objectives. Here we propose a simple risk mitigation technique that reduces capital charges associated with equity investments by optimizing the selection of put option contracts. Key words and phrases. option, risk management, insurance, portfolio construction, portfolio allocation,risk parity, risk-based portfolio management, equities, mutual fund, risk mitigation. 1 See e.g. Ref. [4]. 2 These shocks can be re-calibrated in accordance with a Value-At-Risk measure on the MSCI World and hence may vary in amplitude by an adjustment factor of at most ±10%. This recalibration, called "equity dampener" reduces capital charge after a market downward move, while increasing it after a market upward move. That is, after a prolonged period of negative performance of the MSCI World, the capital charge for Global et Other equities may be reduced to 29% and 39% respectively.
Optimal Factor Investing: Good Portfolios Matter More than Bad Views
SSRN Electronic Journal
We focus on the selection of stocks in the context of factor investing. We show how to build an o... more We focus on the selection of stocks in the context of factor investing. We show how to build an optimal stocks selection methodology based on factor exposures, factor correlations and also views, even ambiguous ones, on the factor returns. We examine the real-world behaviour of several portfolio whose components are selected using our methodology. Also, we explain why our selection methodology exhibits resilience to changing or even plain wrong views on the factor returns.
Minimum Variance Portfolio Optimisation under Parameter Uncertainty: A Robust Control Approach
The global minimum variance portfolio computed using the sample covariance matrix is known to be ... more The global minimum variance portfolio computed using the sample covariance matrix is known to be negatively affected by parameter uncertainty. Using a robust control approach, we introduce a portfolio rule for investors who wish to invest in the global minimum variance portfolio due to its strong historical track record but seek a rule that is robust to parameter uncertainty. Our robust portfolio theoretically corresponds to the global minimum variance portfolio in the worst-case scenario, with respect to a set of plausible alternative estimators of the covariance matrix, in the neighbourhood of the sample covariance matrix. Hence, it provides protection against errors in the reference sample covariance matrix. Monte Carlo simulations illustrate the dominance of the robust portfolio over its non-robust counterpart, in terms of portfolio stability, variance and risk-adjusted returns. Empirically, we compare the out-of-sample performance of the robust portfolio to various competing minimum variance portfolio rules in the literature. We observe that the robust portfolio often has lower turnover and variance and higher Sharpe ratios than the competing minimum variance portfolios.
We wish to thank Lorenzo Peccati (the editor), and three anonymous referees for their constructiv... more We wish to thank Lorenzo Peccati (the editor), and three anonymous referees for their constructive comments and suggestions. The first two authors thank the Global Risk Institute in Financial Services for support; the first author also gratefully acknowledges the support of the Risk Foundation Chair Dauphine-ENSAE-Groupama "Behavioral and Household Finance, Individual and Collective Risk Attitudes" (Louis Bachelier Institute). The usual disclaimer applies. Decision Support
In contrast with existing literature that focuses on conditional Value-At-Risk (CVaR) as a portfo... more In contrast with existing literature that focuses on conditional Value-At-Risk (CVaR) as a portfolio risk measure, we examine here the properties of portfolios built to minimize CVaR. We look into the stability and performance potential of CVaR-optimal portfolios and compare our results with Minimum Variance portfolios. Finally, we run realistic simulations of risk-minimising strategies using CVaR as risk measure and compare their performances to otherwise identical variance minimising strategies.
We propose a method for the fast generation of a quantum register of addressable qubits consistin... more We propose a method for the fast generation of a quantum register of addressable qubits consisting of ultracold atoms stored in an optical lattice. Starting with a half filled lattice we remove every second lattice barrier by adiabatically switching on a superlattice potential which leads to a long wavelength lattice in the Mott insulator state with unit filling. The larger periodicity of the resulting lattice could make individual addressing of the atoms via an external laser feasible. We develop a Bose-Hubbard-like model for describing the dynamics of cold atoms in a lattice when doubling the lattice periodicity via the addition of a superlattice potential. The dynamics of the transition from a half filled to a commensurately filled lattice is analysed numerically with the help of the time evolving block decimation algorithm and analytically using the Kibble-Zurek theory. We show that the timescale for the whole process, i.e. creating the half filled lattice and subsequent doubling of the lattice periodicity, is significantly faster than adiabatic direct quantum-freezing of a superfluid into a Mott insulator for large lattice periods. Our method therefore provides a high-fidelity quantum register of addressable qubits on a fast timescale.
We investigate the dynamics of Rydberg electrons excited from the ground state of ultracold atoms... more We investigate the dynamics of Rydberg electrons excited from the ground state of ultracold atoms trapped in an optical lattice. We first consider a lattice comprising an array of double-well potentials, where each double well is occupied by two ultracold atoms. We demonstrate the existence of molecular states with equilibrium distances of the order of experimentally attainable inter-well spacings and binding energies of the order of 10 3 GHz. We also consider the situation whereby ground-state atoms trapped in an optical lattice are collectively excited to Rydberg levels, such that the charge-density distributions of neighboring atoms overlap. We compute the hopping rate and interaction matrix elements between highly-excited electrons separated by distances comparable to typical lattice spacings. Such systems have tunable interaction parameters and a temperature ∼ 10 4 times smaller than the Fermi temperature, making them potentially attractive for the study and simulation of strongly correlated electronic systems.
We investigate how to create entangled states of ultracold atoms trapped in optical lattices by d... more We investigate how to create entangled states of ultracold atoms trapped in optical lattices by dynamically manipulating the shape of the lattice potential. We consider an additional potential (the superlattice) that allows both the splitting of each site into a double well potential, and the control of the height of potential barrier between sites. We use superlattice manipulations to perform entangling operations between neighbouring qubits encoded on the Zeeman levels of the atoms without having to perform transfers between the different vibrational states of the atoms. We show how to use superlattices to engineer many-body entangled states resilient to collective dephasing noise. Also, we present a method to realize a 2D resource for measurement-based quantum computing via Bell-pair measurements. We analyze measurement networks that allow the execution of quantum algorithms while maintaining the resilience properties of the system throughout the computation.
Arbitrarily perfect quantum communication using unmodulated spin chains, a collaborative approach
Journal of Optics B: Quantum and Semiclassical Optics, 2005
ABSTRACT We shall consider a quantum communication channel constituted by two open spin chains wi... more ABSTRACT We shall consider a quantum communication channel constituted by two open spin chains with nearest neighbour interactions and fixed coupling strengths, connected to several users. Assuming that the users of this quantum data bus can apply simple gates on sites of the chain that they are connected to, we will see that it is possible to gain information on the position of the qubit during the transmission, and to use this information to accelerate the communication process. We will also see that performing frequent measurements on the system affects the dynamics of propagation of quantum information in an interesting way.
Impact of Hedging Strategy on Capital Charges for Variable Annuity Portfolios
Social Science Research Network, 2020
Efficient and robust techniques are crucial for hedging a book of variable annuities. For insurer... more Efficient and robust techniques are crucial for hedging a book of variable annuities. For insurers, the profitability of variable annuity contracts heavily depend on the hedging schemes used to mitigate their associated financial liabilities. Beyond financial performance, the inclusion of protection, in the form of protective put options, in hedging portfolios contributes to reduce the capital charges imposed on the insurer. Although this external source of profit affect the total performance of the hedge, it has not been quantified in the literature. This paper fills that gap by quantifying the contribution of capital charge reductions to hedging performance for a number of hedging methodologies. We provide statistics using price simulations following normal and student distributions with fatter tails.
Optimal equity protection of Solvency II regulated portfolios
The journal of risk, 2018
The Solvency II regulatory framework creates incentives for using derivatives to mitigate risk. H... more The Solvency II regulatory framework creates incentives for using derivatives to mitigate risk. However, for investors willing to reduce capital charges by protecting their portfolio against losses, very few practical solutions exist. In the context of equity investments, we examine the relationship between the cost of acquiring protection (in the form of a put option) and the reduction of capital charges that it entails. We develop the idea that Solvency II regulations introduce an external utility that modifies the economic value of options. Using these findings, we show that there is a way to choose protection levels that maximizes reductions in capital charges for every dollar spent on the put options. We provide results for both risk-based and drawdown-based capital requirements and argue that risk-based capital requirements offer even greater incentives for using derivatives in the context of risk mitigation.
Optimal Factor Investing: Good Portfolios Matter More than Bad Views
Social Science Research Network, Jan 30, 2015
ABSTRACT We focus on the selection of stocks in the context of factor investing. We show how to b... more ABSTRACT We focus on the selection of stocks in the context of factor investing. We show how to build an optimal stocks selection methodology based on factor exposures, factor correlations and also views, even ambiguous ones, on the factor returns. We examine the real-world behaviour of several portfolio whose components are selected using our methodology. Also, we explain why our selection methodology exhibits resilience to changing or even plain wrong views on the factor returns.
We present a stock selection methodology that maximizes the expected returns of equity portfolios... more We present a stock selection methodology that maximizes the expected returns of equity portfolios by efficiently managing their exposures to a given ensemble of risk premia, also known as factors. Our approach is mathematically grounded, robust in its design, and applicable in practice. It addresses several issues specific to factor investing, such as cross-sectional interactions between factors, the mismatch between the factors performance cycles and typical rebalancing periods, or the mitigation of interactions between the capital allocation schemes and factor exposures.
Impact of Hedging Strategy on Capital Charges for Variable Annuity Portfolios
ERN: Hedging (Topic), 2020
Efficient and robust techniques are crucial for hedging a book of variable annuities. For insurer... more Efficient and robust techniques are crucial for hedging a book of variable annuities. For insurers, the profitability of variable annuity contracts heavily depend on the hedging schemes used to mitigate their associated financial liabilities. Beyond financial performance, the inclusion of protection, in the form of protective put options, in hedging portfolios contributes to reduce the capital charges imposed on the insurer. Although this external source of profit affect the total performance of the hedge, it has not been quantified in the literature. This paper fills that gap by quantifying the contribution of capital charge reductions to hedging performance for a number of hedging methodologies. We provide statistics using price simulations following normal and student distributions with fatter tails.
Optical lattices make it possible to trap and coherently control large ensembles of ultracold a... more Optical lattices make it possible to trap and coherently control large ensembles of ultracold atoms. They provide the possibility to create lattice potentials that mimic the structure of solid-state systems, and to control these potentials dynamically. In this thesis, we study how dynamical manipulations of the lattice geometry can be used to perform different tasks, ranging from quantum information processing to the creation of diatomic molecules. We first examine the dynamical properties of ultracold atoms trapped in a lattice whose periodicity is dynamically doubled. We derive a model describing the dynamics of the atoms during this process, and compute the different interaction parameters of this model. We investigate different ways of using this lattice manipulation to optimise the initialisation time of a Mott-insulating state with one atom per site, and provide a scaling law related to the interaction parameters of the system. We go on to show that entangling operations bet...
Optimal equity protection of Solvency II regulated portfolios
Journal of Risk, 2018
The Solvency II regulatory framework creates incentives for using derivatives to mitigate risk. H... more The Solvency II regulatory framework creates incentives for using derivatives to mitigate risk. However, for investors willing to reduce capital charges by protecting their portfolio against losses, very few practical solutions exist. In the context of equity investments, we examine the relationship between the cost of acquiring protection (in the form of a put option) and the reduction of capital charges that it entails. We develop the idea that Solvency II regulations introduce an external utility that modifies the economic value of options. Using these findings, we show that there is a way to choose protection levels that maximizes reductions in capital charges for every dollar spent on the put options. We provide results for both risk-based and drawdown-based capital requirements and argue that risk-based capital requirements offer even greater incentives for using derivatives in the context of risk mitigation.
We present a stock selection methodology that maximizes the expected returns of equity portfolios... more We present a stock selection methodology that maximizes the expected returns of equity portfolios by efficiently managing their exposures to a given ensemble of risk premia, also known as factors. Our approach is mathematically grounded, robust in its design, and applicable in practice. It addresses several issues specific to factor investing, such as cross-sectional interactions between factors, the mismatch between the factors performance cycles and typical rebalancing periods, or the mitigation of interactions between the capital allocation schemes and factor exposures.
For investors subject to Solvency II regulations, the capital charges for holding equities are hi... more For investors subject to Solvency II regulations, the capital charges for holding equities are high. This reduces the appeal of this asset class as an investment of choice for realizing long-term growth objectives. Here we propose a simple risk mitigation technique that reduces capital charges associated with equity investments by optimizing the selection of put option contracts. Key words and phrases. option, risk management, insurance, portfolio construction, portfolio allocation,risk parity, risk-based portfolio management, equities, mutual fund, risk mitigation. 1 See e.g. Ref. [4]. 2 These shocks can be re-calibrated in accordance with a Value-At-Risk measure on the MSCI World and hence may vary in amplitude by an adjustment factor of at most ±10%. This recalibration, called "equity dampener" reduces capital charge after a market downward move, while increasing it after a market upward move. That is, after a prolonged period of negative performance of the MSCI World, the capital charge for Global et Other equities may be reduced to 29% and 39% respectively.
Optimal Factor Investing: Good Portfolios Matter More than Bad Views
SSRN Electronic Journal
We focus on the selection of stocks in the context of factor investing. We show how to build an o... more We focus on the selection of stocks in the context of factor investing. We show how to build an optimal stocks selection methodology based on factor exposures, factor correlations and also views, even ambiguous ones, on the factor returns. We examine the real-world behaviour of several portfolio whose components are selected using our methodology. Also, we explain why our selection methodology exhibits resilience to changing or even plain wrong views on the factor returns.
Minimum Variance Portfolio Optimisation under Parameter Uncertainty: A Robust Control Approach
The global minimum variance portfolio computed using the sample covariance matrix is known to be ... more The global minimum variance portfolio computed using the sample covariance matrix is known to be negatively affected by parameter uncertainty. Using a robust control approach, we introduce a portfolio rule for investors who wish to invest in the global minimum variance portfolio due to its strong historical track record but seek a rule that is robust to parameter uncertainty. Our robust portfolio theoretically corresponds to the global minimum variance portfolio in the worst-case scenario, with respect to a set of plausible alternative estimators of the covariance matrix, in the neighbourhood of the sample covariance matrix. Hence, it provides protection against errors in the reference sample covariance matrix. Monte Carlo simulations illustrate the dominance of the robust portfolio over its non-robust counterpart, in terms of portfolio stability, variance and risk-adjusted returns. Empirically, we compare the out-of-sample performance of the robust portfolio to various competing minimum variance portfolio rules in the literature. We observe that the robust portfolio often has lower turnover and variance and higher Sharpe ratios than the competing minimum variance portfolios.
We wish to thank Lorenzo Peccati (the editor), and three anonymous referees for their constructiv... more We wish to thank Lorenzo Peccati (the editor), and three anonymous referees for their constructive comments and suggestions. The first two authors thank the Global Risk Institute in Financial Services for support; the first author also gratefully acknowledges the support of the Risk Foundation Chair Dauphine-ENSAE-Groupama "Behavioral and Household Finance, Individual and Collective Risk Attitudes" (Louis Bachelier Institute). The usual disclaimer applies. Decision Support
In contrast with existing literature that focuses on conditional Value-At-Risk (CVaR) as a portfo... more In contrast with existing literature that focuses on conditional Value-At-Risk (CVaR) as a portfolio risk measure, we examine here the properties of portfolios built to minimize CVaR. We look into the stability and performance potential of CVaR-optimal portfolios and compare our results with Minimum Variance portfolios. Finally, we run realistic simulations of risk-minimising strategies using CVaR as risk measure and compare their performances to otherwise identical variance minimising strategies.
We propose a method for the fast generation of a quantum register of addressable qubits consistin... more We propose a method for the fast generation of a quantum register of addressable qubits consisting of ultracold atoms stored in an optical lattice. Starting with a half filled lattice we remove every second lattice barrier by adiabatically switching on a superlattice potential which leads to a long wavelength lattice in the Mott insulator state with unit filling. The larger periodicity of the resulting lattice could make individual addressing of the atoms via an external laser feasible. We develop a Bose-Hubbard-like model for describing the dynamics of cold atoms in a lattice when doubling the lattice periodicity via the addition of a superlattice potential. The dynamics of the transition from a half filled to a commensurately filled lattice is analysed numerically with the help of the time evolving block decimation algorithm and analytically using the Kibble-Zurek theory. We show that the timescale for the whole process, i.e. creating the half filled lattice and subsequent doubling of the lattice periodicity, is significantly faster than adiabatic direct quantum-freezing of a superfluid into a Mott insulator for large lattice periods. Our method therefore provides a high-fidelity quantum register of addressable qubits on a fast timescale.
We investigate the dynamics of Rydberg electrons excited from the ground state of ultracold atoms... more We investigate the dynamics of Rydberg electrons excited from the ground state of ultracold atoms trapped in an optical lattice. We first consider a lattice comprising an array of double-well potentials, where each double well is occupied by two ultracold atoms. We demonstrate the existence of molecular states with equilibrium distances of the order of experimentally attainable inter-well spacings and binding energies of the order of 10 3 GHz. We also consider the situation whereby ground-state atoms trapped in an optical lattice are collectively excited to Rydberg levels, such that the charge-density distributions of neighboring atoms overlap. We compute the hopping rate and interaction matrix elements between highly-excited electrons separated by distances comparable to typical lattice spacings. Such systems have tunable interaction parameters and a temperature ∼ 10 4 times smaller than the Fermi temperature, making them potentially attractive for the study and simulation of strongly correlated electronic systems.
We investigate how to create entangled states of ultracold atoms trapped in optical lattices by d... more We investigate how to create entangled states of ultracold atoms trapped in optical lattices by dynamically manipulating the shape of the lattice potential. We consider an additional potential (the superlattice) that allows both the splitting of each site into a double well potential, and the control of the height of potential barrier between sites. We use superlattice manipulations to perform entangling operations between neighbouring qubits encoded on the Zeeman levels of the atoms without having to perform transfers between the different vibrational states of the atoms. We show how to use superlattices to engineer many-body entangled states resilient to collective dephasing noise. Also, we present a method to realize a 2D resource for measurement-based quantum computing via Bell-pair measurements. We analyze measurement networks that allow the execution of quantum algorithms while maintaining the resilience properties of the system throughout the computation.
Arbitrarily perfect quantum communication using unmodulated spin chains, a collaborative approach
Journal of Optics B: Quantum and Semiclassical Optics, 2005
ABSTRACT We shall consider a quantum communication channel constituted by two open spin chains wi... more ABSTRACT We shall consider a quantum communication channel constituted by two open spin chains with nearest neighbour interactions and fixed coupling strengths, connected to several users. Assuming that the users of this quantum data bus can apply simple gates on sites of the chain that they are connected to, we will see that it is possible to gain information on the position of the qubit during the transmission, and to use this information to accelerate the communication process. We will also see that performing frequent measurements on the system affects the dynamics of propagation of quantum information in an interesting way.
Uploads
Papers by Benoit Vaucher