RM-CVaR: Regularized Multiple β\beta-CVaR Portfolio

The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the most fundamental risk measure to be minimized, it has several drawbacks. Conditional Value-at-Risk (CVaR) is a relatively new risk measure that addresses some of the shortcomings of well-known variance-related risk measures, and because of its computational efficiencies, it has gained popularity. CVaR is defined as the expected value of the loss that occurs beyond a certain probability level ($\beta$). However, portfolio optimization problems that use CVaR as a risk measure are formulated with a single $\beta$ and may output significantly different portfolios depending on how the $\beta$ is selected. We confirm even small changes in $\beta$ can result in huge changes in the whole portfolio structure. In order to improve this problem, we propose RM-CVaR: Regularized Multiple $\beta$-CVaR Portfolio. We perform experiments on well-known benchmarks to evaluate the proposed portfolio. Compared with various portfolios, RM-CVaR demonstrates a superior performance of having both higher risk-adjusted returns and lower maximum drawdown.Comment: accepted by the IJCAI-PRICAI 2020 Special Track AI in FinTec

Estimación de expectativas del mercado para la selección de portafolios usando modelos estadísticos penalizados

The portfolio selection problem can be viewed as an optimization problem that maximizes the risk–return relationship. It consists of a number of elements, such as an objective function, decision variables and input parameters, which are used to predict expected returns and the covariance between the said returns. However, the real values of these parameters cannot be directly observed; thus, estimations based on historical data are required. Historical data, however, can often result in modelling errors when the parameters are replaced by their estimations. We propose to address this by using some regularization mechanisms in the optimization.  In addition, we explore the use of implicit information to improve the portfolio performance, such as options market prices, which are a rich source of investor expectations. Accordingly, we propose a new estimator for risk and return that combines historical and implicit information in the portfolio selection problem. We implement the new estimators for the mean-VAR and mean-VaR2 problems using an elastic-net model that reduces the risk of all estimations performed. The results suggest that the model has a good out-of-sample performance that is superior to models with pure historical estimations.El problema de selección de portafolios puede ser visto como un problema de optimización que maximiza una relación riesgo-retorno cuyos parámetros son los retornos esperados y las covarianzas entre ellos. Sin embargo, los valores reales de dichos parámetros no son observables, por lo cual es necesario realizar estimaciones que comúnmente están basadas en datos históricos. Estas estimaciones pueden introducir errores en el modelo, haciendo necesario usar diferentes mecanismos de regularización, como los propuestos en el presente estudio. Además, proponemos el uso de información adicional para mejorar el desempeño de los portafolios, como los son los precios de las opciones que contienen una rica fuente de información que muestra las expectativas de los inversionistas con base en sus conocimientos acerca de cada uno de los subyacentes. De esta manera, proponemos el uso de un nuevo estimador de riesgo-retorno que mezcla la información histórica con la implícita para el problema de selección de portafolios. Implementamos los nuevos estimadores para el problema de Media-Varianza y Media-VaR2 a través de un modelo de red-elástica que permite reducir el impacto del riesgo de las estimaciones realizadas. Los resultados sugieren rendimientos de portafolio superiores a los modelos con estimadores basados en datos históricos

A constrained swarm optimization algorithm for large-scale long-run investments using Sharpe ratio-based performance measures

We study large-scale portfolio optimization problems in which the aim is to maximize a multi-moment performance measure extending the Sharpe ratio. More specifically, we consider the adjusted for skewness Sharpe ratio, which incorporates the third moment of the returns distribution, and the adjusted for skewness and kurtosis Sharpe ratio, which exploits in addition the fourth moment. Further, we account for two types of real-world trading constraints. On the one hand, we impose stock market restrictions through cardinality, buy-in thresholds, and budget constraints. On the other hand, a turnover threshold restricts the total allowed amount of trades in the rebalancing phases. To deal with these asset allocation models, we embed a novel hybrid constraint-handling procedure into an improved dynamic level-based learning swarm optimizer. A repair operator maps candidate solutions onto the set characterized by the first type of constraints. Then, an adaptive l1-exact penalty function manages turnover violations. The focus of the paper is to highlight the importance of including higher-order moments in the performance measures for long-run investments, in particular when the market is turbulent. We carry out empirical tests on two worldwide sets of assets to illustrate the scalability and effectiveness of the proposed strategies, and to evaluate the performance of our investments compared to the strategy maximizing the Sharpe ratio

On the Directional Predictability of Equity Premium Using Machine Learning Techniques

This paper applies a plethora of machine learning techniques to forecast the direction of the U.S. equity premium. Our techniques include benchmark binary probit models, classification and regression trees (CART), along with penalized binary probit models. Our empirical analysis reveals that the sophisticated machine learning techniques significantly outperformed the benchmark binary probit forecasting models, both statistically and economically. Overall, the discriminant analysis classifiers are ranked first among all the models tested. Specifically, the high dimensional discriminant analysis (HDDA) classifier ranks first in terms of statistical performance, while the quadratic discriminant analysis (QDA) classifier ranks first in economic performance. The penalized likelihood binary probit models (Least Absolute Shrinkage and Selection Operator, Ridge, Elastic Net) also outperformed the benchmark binary probit models, providing significant alternatives to portfolio managers