Enhanced indexation based on second-order stochastic dominance

Second order Stochastic Dominance (SSD) has a well recognised importance in portfolio selection, since it provides a natural interpretation of the theory of risk-Averse investor behaviour. Recently, SSD-based models of portfolio choice have been proposed; these assume that a reference distribution is available and a portfolio is constructed, whose return distribution dominates the reference distribution with respect to SSD. We present an empirical study which analyses the effectiveness of such strategies in the context of enhanced indexation. Several datasets, drawn from FTSE 100, SP 500 and Nikkei 225 are investigated through portfolio rebalancing and backtesting. Three main conclusions are drawn. First, the portfolios chosen by the SSD based models consistently outperformed the indices and the traditional index trackers. Secondly, the SSD based models do not require imposition of cardinality constraints since naturally a small number of stocks are selected. Thus, they do not present the computational difficulty normally associated with index tracking models. Finally, the SSD based models are robust with respect to small changes in the scenario set and little or no rebalancing is necessary. In this paper we present a unified framework which incorporates (a) SSD, (b) downside risk (Conditional Value-At-Risk) minimisation and (c) enhanced indexation. © 2013 Elsevier B.V. All rights reserved

Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

A two-stage stochastic mixed-integer program modelling and hybrid solution approach to portfolio selection problems

In this paper, we investigate a multi-period portfolio selection problem with a comprehensive set of real-world trading constraints as well as market random uncertainty in terms of asset prices. We formulate the problem into a two-stage stochastic mixed-integer program (SMIP) with recourse. The set of constraints is modelled as mixed-integer program, while a set of decision variables to rebalance the portfolio in multiple periods is explicitly introduced as the recourse variables in the second stage of stochastic program. Although the combination of stochastic program and mixed-integer program leads to computational challenges in finding solutions to the problem, the proposed SMIP model provides an insightful and flexible description of the problem. The model also enables the investors to make decisions subject to real-world trading constraints and market uncertainty. To deal with the computational difficulty of the proposed model, a simplification and hybrid solution method is applied in the paper. The simplification method aims to eliminate the difficult constraints in the model, resulting into easier sub-problems compared to the original one. The hybrid method is developed to integrate local search with Branch-and-Bound (B&B) to solve the problem heuristically. We present computational results of the hybrid approach to analyse the performance of the proposed method. The results illustrate that the hybrid method can generate good solutions in a reasonable amount of computational time. We also compare the obtained portfolio values against an index value to illustrate the performance and strengths of the proposed SMIP model. Implications of the model and future work are also discussed

Portfolio optimization and index tracking for the shipping stock and freight markets using evolutionary algorithms

This paper reproduces the performance of an international market capitalization shipping stock index and two physical shipping indexes by investing only in US stock portfolios. The index-tracking problem is addressed using the differential evolution algorithm and the genetic algorithm. Portfolios are constructed by a subset of stocks picked from the shipping or the Dow Jones Composite Average indexes. To test the performance of the heuristics, three different trading scenarios are examined: annually, quarterly and monthly rebalancing, accounting for transaction costs where necessary. Competing portfolios are also assessed through predictive ability tests. Overall, the proposed investment strategies carry less risk compared to the tracked benchmark indexes while providing investors the opportunity to efficiently replic ate the performance of both the stock and physical shipping indexes in the most cost-effective way

A multiobjective model for passive portfolio management: an application on the S&P 100 index

This is an author's accepted manuscript of an article published in: “Journal of Business Economics and Management"; Volume 14, Issue 4, 2013; copyright Taylor & Francis; available online at: http://dx.doi.org/10.3846/16111699.2012.668859Index tracking seeks to minimize the unsystematic risk component by imitating the movements of a reference index. Partial index tracking only considers a subset of the stocks in the index, enabling a substantial cost reduction in comparison with full tracking. Nevertheless, when heterogeneous investment profiles are to be satisfied, traditional index tracking techniques may need different stocks to build the different portfolios. The aim of this paper is to propose a methodology that enables a fund s manager to satisfy different clients investment profiles but using in all cases the same subset of stocks, and considering not only one particular criterion but a compromise between several criteria. For this purpose we use a mathematical programming model that considers the tracking error variance, the excess return and the variance of the portfolio plus the curvature of the tracking frontier. The curvature is not defined for a particular portfolio, but for all the portfolios in the tracking frontier. This way funds managers can offer their clients a wide range of risk-return combinations just picking the appropriate portfolio in the frontier, all of these portfolios sharing the same shares but with different weights. An example of our proposal is applied on the S&P 100.García García, F.; Guijarro Martínez, F.; Moya Clemente, I. (2013). A multiobjective model for passive portfolio management: an application on the S&P 100 index. Journal of Business Economics and Management. 14(4):758-775. doi:10.3846/16111699.2012.668859S758775144Aktan, B., Korsakienė, R., & Smaliukienė, R. (2010). TIME‐VARYING VOLATILITY MODELLING OF BALTIC STOCK MARKETS. 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Mixed-integer programming approaches for index tracking and enhanced indexation

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