Publication: Cartera réplica de mínima varianza relativa
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2014
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Abstract
En la gestión de activos muy frecuentemente se requiere replicar el perfil de rendimiento de un índice bursátil sin tener la posibilidad de invertir en todos los componentes del mismo ni en las mismas proporciones. El producto financiero más frecuentemente utilizado en estos casos es una cartera réplica formada por un subconjunto de componentes del índice de referencia. La bondad de réplica se suele medir a posteriori a través del indicador de Tracking Error. A priori, o sea en fase de construcción de la cartera réplica, ese mismo indicador es frecuentemente usado como función objetivo de modelos de optimización. En este trabajo en primer lugar se ilustran los modelos de optimización más comúnmente utilizados para la construcción de carteras réplica (modelos de media-varianzas clásicos) para luego tratar los más interesantes desde el punto de vista práctico que incluyen limitaciones sobre el número de componentes (K) y sobre los porcentajes máximos y mínimos de inversión por título. Analizamos con detalle un modelo con restricción sobre el número de componentes de la cartera y límites de inversión ya que este representa el caso más interesante y complejo desde el punto de vista operativo. Este modelo ha sido estudiado por Chang, Meade, Beasley y Sharaiha (Chang et al. (2000)) que han propuesto una solución del mismo con algoritmos heurísticos. Por lo contrario en este trabajo la resolución del modelo se realiza a través de GAMS (General Algebraic Modelling System) que proporciona una solución óptima.Este trabajo pretende validar los modelos de optimización más usados comúnmente en la práctica utilizando como criterio la desviación entre Tracking Error ex ante (calculado en fase de optimización de cartera) respecto al valor a posteriori (calculado sobre la ventana de test).Con este fin se construye una cartera que replique el Ibex 35 compuesta por un subconjunto de los 35 componentes y se analizan los resultados validando el modelo propuesto sobre ventanas temporales históricas.
Tracking an index performance is a common issue within the asset management industry. It often requires replicating the performance profile of a stock index while not investing in all index members nor in the same proportions. The financial product most frequently used in these cases is a tracking portfolio composed by a subset of benchmark constituents. The best-fit performance is usually measured on an historical basis via the Tracking Error indicator. While constructing a tracking portfolio the same indicator (Tracking Error) is often used as the objective function for model optimization. In this paper we illustrate the most widely used optimization models for tracking portfolio purposes. They range from the standard mean-variance model to some most interesting and complex models that include constraints on the number of assets (K) in portfolio and restrictions on the maximum and minimum investment. We analyze in detail a model with restrictions on the number of portfolio components since this represents the most interesting case from an operational point of view. This model has been studied by Chang, Meade, Beasley and Sharaiha (Chang et al. (2000)) who proposed a solution using heuristic methods. On the contrary in this paper the solution is attained using GAMS (General Algebraic Modelling System) which provides optimal portfolio weights.This work aims to validate the most common tracking portfolio optimization models using the difference between ex ante tracking error (output of the portfolio optimization process) and the realized value calculated in the historical test window. In order to do this we have set up a tracking portfolio benchmarking the Ibex 35, composed by a subset of the index constituents, and finally we have presented the test results calculated on a historical dataset.
Tracking an index performance is a common issue within the asset management industry. It often requires replicating the performance profile of a stock index while not investing in all index members nor in the same proportions. The financial product most frequently used in these cases is a tracking portfolio composed by a subset of benchmark constituents. The best-fit performance is usually measured on an historical basis via the Tracking Error indicator. While constructing a tracking portfolio the same indicator (Tracking Error) is often used as the objective function for model optimization. In this paper we illustrate the most widely used optimization models for tracking portfolio purposes. They range from the standard mean-variance model to some most interesting and complex models that include constraints on the number of assets (K) in portfolio and restrictions on the maximum and minimum investment. We analyze in detail a model with restrictions on the number of portfolio components since this represents the most interesting case from an operational point of view. This model has been studied by Chang, Meade, Beasley and Sharaiha (Chang et al. (2000)) who proposed a solution using heuristic methods. On the contrary in this paper the solution is attained using GAMS (General Algebraic Modelling System) which provides optimal portfolio weights.This work aims to validate the most common tracking portfolio optimization models using the difference between ex ante tracking error (output of the portfolio optimization process) and the realized value calculated in the historical test window. In order to do this we have set up a tracking portfolio benchmarking the Ibex 35, composed by a subset of the index constituents, and finally we have presented the test results calculated on a historical dataset.