In this paper, we propose a complex return scenario generation process that can be incorporated i... more In this paper, we propose a complex return scenario generation process that can be incorporated into portfolio selection problems. In particular, we assume that returns follow the ARMA-GARCH model with stable-distributed and skewed t-copula dependent residuals. Since the portfolio selection problem is large-scale, we apply the multifactor model with a parametric regression and a nonparametric regression approaches to reduce the complexity of the problem. To do this, the recently proposed trend-dependent correlation matrix is used to obtain the main factors of the asset dependency structure by applying principal component analysis (PCA). However, when a few main factors are assumed, the obtained residuals of the returns still explain a non-negligible part of the portfolio variability. Therefore, we propose the application of a novel approach involving a second PCA to the Pearson correlation to obtain additional factors of residual components leading to the refinement of the final prediction. Future return scenarios are predicted using Monte Carlo simulations. Finally, the impact of the proposed approaches on the portfolio selection problem is evaluated in an empirical analysis of the application of a classical mean-variance model to a dynamic dataset of stock returns from the US market. The results show that the proposed scenario generation approach with nonparametric regression outperforms the traditional approach for out-of-sample portfolios.
The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the... more The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the performance of a selected target benchmark and it is sometimes referred to as to active portfolio management. It is well known that many professional investors achieve this benchmarking strategy: The aim of this work is to solve the benchmark tracking problem implementing active strategies to manage a portfolio with the aim to outperform the benchmark index. We develop linear formulation portfolio optimization problems which maximize some performance measures. Then, introducing first and second order stochastic dominance constraints, we evaluate their impact in the invested portfolio wealth path in a high dimensionality framework.
In this paper, we deal with portfolio selection decisions when the portfolio returns are approxim... more In this paper, we deal with portfolio selection decisions when the portfolio returns are approximated by stable Paretian distributions. Therefore, we examine some dominance rules to determine the optimal choices of non-satiable risk averse investors. In particular, we first preselect a subclass of assets which are not dominated by the point of view of non-satiable and risk-averse investors. Then, we optimize a multi-parametric portfolio optimization problem that takes into account the asymptotic stochastic dominance rule. Finally, we compare the ex-post wealth obtained by optimal portfolios with different levels of asymptotic skewness and stability index.
In this paper, we discuss how to approximate the conditional expectation of a random variable Y g... more In this paper, we discuss how to approximate the conditional expectation of a random variable Y given a random variable X, i.e. E(Y|X). We propose and compare two different non parametric methodologies to approximate E(Y|X). The first approach (namely the OLP method) is based on a suitable approximation of the-algebra generated by X. A second procedure is based on the well known kernel non-parametric regression method. We analyze the convergence properties of the OLP estimator and we compare the two approaches with a simulation study.
Summary In this paper we propose to use a Markov chain in order to price contingent claims. In pa... more Summary In this paper we propose to use a Markov chain in order to price contingent claims. In particular, we describe a non parametric markovian approach to price American and European options. First, we discuss the risk neutral valuation of the non parametric approach. Secondly, we examine the problems of the computational complexity and of the stability with respect to
The aim of this study is to verify whether the average value at risk (AVaR) can be a good alterna... more The aim of this study is to verify whether the average value at risk (AVaR) can be a good alternative to the value at risk (VaR) for estimating portfolio losses, especially regarding tail events. To achieve this aim, we use a copula framework to estimate the dependence between the stock returns of a portfolio composed of 94 components of the S&P100 index to compute the AVaR and VaR and compare the results with respect to the Gaussian exponentially weighted moving average (EWMA). To compute the simulated returns, we employ the algorithm used by Biglova et al. (2014) in portfolio selection problems and then back test the model with Kupiec’s and Christoffersen’s tests. The results are coherent with the literature, in particular, the VaR computed both via the copula and via the EWMA seems to fail to provide an accurate risk measurement while the AVaR with the copula and EWMA appears to be more reliable.
The consequences of any extreme event can deteriorate any system at all levels: socially, economi... more The consequences of any extreme event can deteriorate any system at all levels: socially, economically, and operationally. The COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), provides a good example of the tremendous impact that can be produced by such extreme events. To effectively measure and mitigate the impact of the COVID-19 pandemic and relaunch the Moroccan economy, policymakers need to determine which sectors have been most impacted. Due to the high level of uncertainty and complexity surrounding this health crisis, this study first develops a new technique for dealing with decision problems under uncertainty using exclusive-or (XOR) logic, called the XOR-analytic network process (XOR-ANP). Then, the proposed technique is adopted to assess the impact of COVID-19 on seven relevant sectors (tourism, transport, industrial, financial, agriculture, education, and healthcare) by considering social, operational, and economic dimensions. The key findings show that COVID-19 has a significant impact on Moroccan’s tourism, healthcare, and transport sectors, with respect to social-economic and operational dimensions by 30.99%, 21.81%, and 17.88%, respectively. These results indicate that most of the United Nations Sustainable Development Goals for 2030, such as “Healthy Lives”, “Decent Work” and “Economic Growth” have been severely impacted, thus, assistance and recovery are urgently needed.
In this paper, we propose a multivariate stochastic dominance comparison among different sectors ... more In this paper, we propose a multivariate stochastic dominance comparison among different sectors from the point of view of non-satiable risk-averse investors. In particular, we consider different distributional hypotheses for the multivariate distribution of financial sectors and we examine if there exist some dominance among them. In this framework we also discuss the asymptotic dominance between financial sectors. Finally, we empirically examine the choices of some non-satiable investors taking into account the proposed studies.
We propose semiparametric tests for portfolio efficiency, with respect to different Behavioral Fi... more We propose semiparametric tests for portfolio efficiency, with respect to different Behavioral Finance orderings. In particular, we focus on Markovitz order and Prospect order. We assume that return distributions belong to a scale invariant family, weakly determined by a finite number of parameters: a reward measure, a risk measure and other distributional parameters. We recall stochastic dominance rules for such family of distributions and provide efficiency conditions when the reward measure is isotonic with Markovitz or Prospect type of investors’ preference. Finally, we empirically test portfolio efficiency (in the sense of Markovitz and prospect orderings) when return distribution is uniquely determined by four parameters, using estimation function theory.
The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the... more The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the performance of a selected target benchmark and it is sometimes referred to as to active portfolio management. It is well known that many professional investors achieve this benchmarking strategy: The aim of this work is to solve the benchmark tracking problem implementing active strategies to manage a portfolio with the aim to outperform the benchmark index. We develop linear formulation portfolio optimization problems which maximize some performance measures. Then, introducing first and second order stochastic dominance constraints, we evaluate their impact in the invested portfolio wealth path in a high dimensionality framework.
In this paper, we present alternative methods to evaluate the presence of the arbitrage opportuni... more In this paper, we present alternative methods to evaluate the presence of the arbitrage opportunities in the market. In particular, we investigate empirically the well-known put-call parity no-arbitrage relation and the state price density. First, we measure the violation of the put call parity as the difference in implied volatilities between call and put options that have the same strike price, the same maturity and the same underlying asset. Then, we examine the nonnegativity of the state price density since its negative values immediately correspond to the possibility of free-lunch in the market. We evaluate the effectiveness of the proposed approaches by an empirical analysis on S&P 500 index options data. Moreover, we propose different approaches to estimate the state price density under the classical hypothesis of the Black and Scholes model. In this context, we use two different methodologies to evaluate the conditional expectation and its relationship with the state price density. Firstly, we examine the real mean return function using local polynomial smoothing technique. Then, we evaluate the conditional expectation using the real probability density. According to the hypothesis of the Black and Scholes model, we are able to derive a closed formula for approximating the conditional expectation with the risk neutral probability. Finally, we propose a comparison among two estimators of the state price density.
In this paper, we present alternative methods to evaluate the presence of the arbitrage opportuni... more In this paper, we present alternative methods to evaluate the presence of the arbitrage opportunities in the market. In particular, we investigate empirically the well-known put-call parity no-arbitrage relation and the state price density. First, we measure the violation of the put call parity as the difference in implied volatilities between call and put options that have the same strike price, the same maturity and the same underlying asset. Then, we examine the nonnegativity of the state price density since its negative values immediately correspond to the possibility of free-lunch in the market. We evaluate the effectiveness of the proposed approaches by an empirical analysis on S&P 500 index options data. Moreover, we propose different approaches to estimate the state price density under the classical hypothesis of the Black and Scholes model. In this context, we use two different methodologies to evaluate the conditional expectation and its relationship with the state price d...
In this paper, we propose a multivariate stochastic dominance comparison among different sectors ... more In this paper, we propose a multivariate stochastic dominance comparison among different sectors from the point of view of non-satiable risk-averse investors. In particular, we consider different distributional hypotheses for the multivariate distribution of financial sectors and we examine if there exist some dominance among them. In this framework we also discuss the asymptotic dominance between financial sectors. Finally, we empirically examine the choices of some non-satiable investors taking into account the proposed studies.
In this paper, we discuss and examine the portfolio optimization problems in the Italian fixed in... more In this paper, we discuss and examine the portfolio optimization problems in the Italian fixed income market considering two main sources of risk: prices risk and market risk. To achieve this aim, we propose a two-step optimization problem for two types of bonds. In particular, we manage the price risk implementing the classical immunization method and then, using the ex-post results from the optimal immunization problem, we are able to deal with market risk maximizing the portfolio wealth in a reward-risk framework. Adopting this approach, the paper then explores empirical applications on the Italian fixed income market using data for the period 2005-2015. Empirical results shows that the two-step optimization build efficient portfolios that minimize the price risk and the market risk. This ex-post analysis indicates the usefulness of the proposed methodology, maximizing the investor’s wealth and understanding the dynamics of the bonds.
In this paper, we examine the use of conditional expectation, either to reduce the dimensionality... more In this paper, we examine the use of conditional expectation, either to reduce the dimensionality of large-scale portfolio problems or to propose alternative reward-risk performance measures. In particular, we focus on two financial problems. In the first part, we discuss and examine correlation measures (based on a conditional expectation) used to approximate the returns in large-scale portfolio problems. Then, we compare the impact of alternative return approximation methodologies on the ex-post wealth of a classic portfolio strategy. In this context, we show that correlation measures that use the conditional expectation perform better than the classic measures do. Moreover, the correlation measure typically used for returns in the domain of attraction of a stable law works better than the classic Pearson correlation does. In the second part, we propose new performance measures based on a conditional expectation that take into account the heavy tails of the return distributions. Then, we examine portfolio strategies based on optimizing the proposed performance measures. In particular, we compare the ex-post wealth obtained from applying the portfolio strategies, which use alternative performance measures based on a conditional expectation. In doing so, we propose an alternative use of conditional expectation in various portfolio problems.
In this paper, we propose a complex return scenario generation process that can be incorporated i... more In this paper, we propose a complex return scenario generation process that can be incorporated into portfolio selection problems. In particular, we assume that returns follow the ARMA-GARCH model with stable-distributed and skewed t-copula dependent residuals. Since the portfolio selection problem is large-scale, we apply the multifactor model with a parametric regression and a nonparametric regression approaches to reduce the complexity of the problem. To do this, the recently proposed trend-dependent correlation matrix is used to obtain the main factors of the asset dependency structure by applying principal component analysis (PCA). However, when a few main factors are assumed, the obtained residuals of the returns still explain a non-negligible part of the portfolio variability. Therefore, we propose the application of a novel approach involving a second PCA to the Pearson correlation to obtain additional factors of residual components leading to the refinement of the final prediction. Future return scenarios are predicted using Monte Carlo simulations. Finally, the impact of the proposed approaches on the portfolio selection problem is evaluated in an empirical analysis of the application of a classical mean-variance model to a dynamic dataset of stock returns from the US market. The results show that the proposed scenario generation approach with nonparametric regression outperforms the traditional approach for out-of-sample portfolios.
The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the... more The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the performance of a selected target benchmark and it is sometimes referred to as to active portfolio management. It is well known that many professional investors achieve this benchmarking strategy: The aim of this work is to solve the benchmark tracking problem implementing active strategies to manage a portfolio with the aim to outperform the benchmark index. We develop linear formulation portfolio optimization problems which maximize some performance measures. Then, introducing first and second order stochastic dominance constraints, we evaluate their impact in the invested portfolio wealth path in a high dimensionality framework.
In this paper, we deal with portfolio selection decisions when the portfolio returns are approxim... more In this paper, we deal with portfolio selection decisions when the portfolio returns are approximated by stable Paretian distributions. Therefore, we examine some dominance rules to determine the optimal choices of non-satiable risk averse investors. In particular, we first preselect a subclass of assets which are not dominated by the point of view of non-satiable and risk-averse investors. Then, we optimize a multi-parametric portfolio optimization problem that takes into account the asymptotic stochastic dominance rule. Finally, we compare the ex-post wealth obtained by optimal portfolios with different levels of asymptotic skewness and stability index.
In this paper, we discuss how to approximate the conditional expectation of a random variable Y g... more In this paper, we discuss how to approximate the conditional expectation of a random variable Y given a random variable X, i.e. E(Y|X). We propose and compare two different non parametric methodologies to approximate E(Y|X). The first approach (namely the OLP method) is based on a suitable approximation of the-algebra generated by X. A second procedure is based on the well known kernel non-parametric regression method. We analyze the convergence properties of the OLP estimator and we compare the two approaches with a simulation study.
Summary In this paper we propose to use a Markov chain in order to price contingent claims. In pa... more Summary In this paper we propose to use a Markov chain in order to price contingent claims. In particular, we describe a non parametric markovian approach to price American and European options. First, we discuss the risk neutral valuation of the non parametric approach. Secondly, we examine the problems of the computational complexity and of the stability with respect to
The aim of this study is to verify whether the average value at risk (AVaR) can be a good alterna... more The aim of this study is to verify whether the average value at risk (AVaR) can be a good alternative to the value at risk (VaR) for estimating portfolio losses, especially regarding tail events. To achieve this aim, we use a copula framework to estimate the dependence between the stock returns of a portfolio composed of 94 components of the S&P100 index to compute the AVaR and VaR and compare the results with respect to the Gaussian exponentially weighted moving average (EWMA). To compute the simulated returns, we employ the algorithm used by Biglova et al. (2014) in portfolio selection problems and then back test the model with Kupiec’s and Christoffersen’s tests. The results are coherent with the literature, in particular, the VaR computed both via the copula and via the EWMA seems to fail to provide an accurate risk measurement while the AVaR with the copula and EWMA appears to be more reliable.
The consequences of any extreme event can deteriorate any system at all levels: socially, economi... more The consequences of any extreme event can deteriorate any system at all levels: socially, economically, and operationally. The COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), provides a good example of the tremendous impact that can be produced by such extreme events. To effectively measure and mitigate the impact of the COVID-19 pandemic and relaunch the Moroccan economy, policymakers need to determine which sectors have been most impacted. Due to the high level of uncertainty and complexity surrounding this health crisis, this study first develops a new technique for dealing with decision problems under uncertainty using exclusive-or (XOR) logic, called the XOR-analytic network process (XOR-ANP). Then, the proposed technique is adopted to assess the impact of COVID-19 on seven relevant sectors (tourism, transport, industrial, financial, agriculture, education, and healthcare) by considering social, operational, and economic dimensions. The key findings show that COVID-19 has a significant impact on Moroccan’s tourism, healthcare, and transport sectors, with respect to social-economic and operational dimensions by 30.99%, 21.81%, and 17.88%, respectively. These results indicate that most of the United Nations Sustainable Development Goals for 2030, such as “Healthy Lives”, “Decent Work” and “Economic Growth” have been severely impacted, thus, assistance and recovery are urgently needed.
In this paper, we propose a multivariate stochastic dominance comparison among different sectors ... more In this paper, we propose a multivariate stochastic dominance comparison among different sectors from the point of view of non-satiable risk-averse investors. In particular, we consider different distributional hypotheses for the multivariate distribution of financial sectors and we examine if there exist some dominance among them. In this framework we also discuss the asymptotic dominance between financial sectors. Finally, we empirically examine the choices of some non-satiable investors taking into account the proposed studies.
We propose semiparametric tests for portfolio efficiency, with respect to different Behavioral Fi... more We propose semiparametric tests for portfolio efficiency, with respect to different Behavioral Finance orderings. In particular, we focus on Markovitz order and Prospect order. We assume that return distributions belong to a scale invariant family, weakly determined by a finite number of parameters: a reward measure, a risk measure and other distributional parameters. We recall stochastic dominance rules for such family of distributions and provide efficiency conditions when the reward measure is isotonic with Markovitz or Prospect type of investors’ preference. Finally, we empirically test portfolio efficiency (in the sense of Markovitz and prospect orderings) when return distribution is uniquely determined by four parameters, using estimation function theory.
The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the... more The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the performance of a selected target benchmark and it is sometimes referred to as to active portfolio management. It is well known that many professional investors achieve this benchmarking strategy: The aim of this work is to solve the benchmark tracking problem implementing active strategies to manage a portfolio with the aim to outperform the benchmark index. We develop linear formulation portfolio optimization problems which maximize some performance measures. Then, introducing first and second order stochastic dominance constraints, we evaluate their impact in the invested portfolio wealth path in a high dimensionality framework.
In this paper, we present alternative methods to evaluate the presence of the arbitrage opportuni... more In this paper, we present alternative methods to evaluate the presence of the arbitrage opportunities in the market. In particular, we investigate empirically the well-known put-call parity no-arbitrage relation and the state price density. First, we measure the violation of the put call parity as the difference in implied volatilities between call and put options that have the same strike price, the same maturity and the same underlying asset. Then, we examine the nonnegativity of the state price density since its negative values immediately correspond to the possibility of free-lunch in the market. We evaluate the effectiveness of the proposed approaches by an empirical analysis on S&P 500 index options data. Moreover, we propose different approaches to estimate the state price density under the classical hypothesis of the Black and Scholes model. In this context, we use two different methodologies to evaluate the conditional expectation and its relationship with the state price density. Firstly, we examine the real mean return function using local polynomial smoothing technique. Then, we evaluate the conditional expectation using the real probability density. According to the hypothesis of the Black and Scholes model, we are able to derive a closed formula for approximating the conditional expectation with the risk neutral probability. Finally, we propose a comparison among two estimators of the state price density.
In this paper, we present alternative methods to evaluate the presence of the arbitrage opportuni... more In this paper, we present alternative methods to evaluate the presence of the arbitrage opportunities in the market. In particular, we investigate empirically the well-known put-call parity no-arbitrage relation and the state price density. First, we measure the violation of the put call parity as the difference in implied volatilities between call and put options that have the same strike price, the same maturity and the same underlying asset. Then, we examine the nonnegativity of the state price density since its negative values immediately correspond to the possibility of free-lunch in the market. We evaluate the effectiveness of the proposed approaches by an empirical analysis on S&P 500 index options data. Moreover, we propose different approaches to estimate the state price density under the classical hypothesis of the Black and Scholes model. In this context, we use two different methodologies to evaluate the conditional expectation and its relationship with the state price d...
In this paper, we propose a multivariate stochastic dominance comparison among different sectors ... more In this paper, we propose a multivariate stochastic dominance comparison among different sectors from the point of view of non-satiable risk-averse investors. In particular, we consider different distributional hypotheses for the multivariate distribution of financial sectors and we examine if there exist some dominance among them. In this framework we also discuss the asymptotic dominance between financial sectors. Finally, we empirically examine the choices of some non-satiable investors taking into account the proposed studies.
In this paper, we discuss and examine the portfolio optimization problems in the Italian fixed in... more In this paper, we discuss and examine the portfolio optimization problems in the Italian fixed income market considering two main sources of risk: prices risk and market risk. To achieve this aim, we propose a two-step optimization problem for two types of bonds. In particular, we manage the price risk implementing the classical immunization method and then, using the ex-post results from the optimal immunization problem, we are able to deal with market risk maximizing the portfolio wealth in a reward-risk framework. Adopting this approach, the paper then explores empirical applications on the Italian fixed income market using data for the period 2005-2015. Empirical results shows that the two-step optimization build efficient portfolios that minimize the price risk and the market risk. This ex-post analysis indicates the usefulness of the proposed methodology, maximizing the investor’s wealth and understanding the dynamics of the bonds.
In this paper, we examine the use of conditional expectation, either to reduce the dimensionality... more In this paper, we examine the use of conditional expectation, either to reduce the dimensionality of large-scale portfolio problems or to propose alternative reward-risk performance measures. In particular, we focus on two financial problems. In the first part, we discuss and examine correlation measures (based on a conditional expectation) used to approximate the returns in large-scale portfolio problems. Then, we compare the impact of alternative return approximation methodologies on the ex-post wealth of a classic portfolio strategy. In this context, we show that correlation measures that use the conditional expectation perform better than the classic measures do. Moreover, the correlation measure typically used for returns in the domain of attraction of a stable law works better than the classic Pearson correlation does. In the second part, we propose new performance measures based on a conditional expectation that take into account the heavy tails of the return distributions. Then, we examine portfolio strategies based on optimizing the proposed performance measures. In particular, we compare the ex-post wealth obtained from applying the portfolio strategies, which use alternative performance measures based on a conditional expectation. In doing so, we propose an alternative use of conditional expectation in various portfolio problems.
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Papers by Sergio Ortobelli Lozza