Several risk measures in portfolio selection: Is it worthwhile?

espanolEste articulo aborda el problema de seleccion de activos utilizando tres medidas del riesgo ampliamente utilizadas: varianza o desviacion tipica, Valor en Riesgo y Valor en Riesgo condicional. Nuestro objetivo es evaluar si resolver el problema de seleccion de activos con varias medidas del riesgo es relevante o no, dada la complejidad computacional que supone. La principal contribucion de este articulo es la solucion de dos modelos que consideran varias medidas del riesgo: el modelo de media-varianza-VaR y el modelo media-VaR-CVaR. La inclusion del VaR como uno de los objetivos a minimizar convierte el problema en no convexo, por tanto el metodo de resolucion propuesto esta basado en una heuristica: algoritmo genetico multiobjetivo. Nuestros resultados muestran la adecuacion de el enfoque multiobjetivo para resolver el problema de optimizacion de carteras y enfatiza la importancia de abordar los modelos de media-varianza-VaR o media-VaR-CVaR en lugar del modelo media-varianza-CVaR. EnglishThis paper is concerned with asset allocation using a set of three widely used risk measures, which are the variance or deviation, Value at Risk and the Conditional Value at Risk. Our purpose is to evaluate whether solving the asset allocation problem under several risk measures is worthwhile or not, given the added computational complexity. The main contribution of the paper is the solution of two models that consider several risk measures: the mean-VaR-CVaR model and the mean-o-VaR model. The inclusion of VaR as one of the objectives to minimize leads to nonconvex problems, therefore the approach we propose is based on a heuristic: multi-objective genetic algorithms. Our results show the adequacy of the multi-objective approach for the portfolio optimization problem and emphasize the importance of dealing with mean-o-VaR or mean-VaR-CVaR models as opposed to mean-o-CVaR.