Enhanced index tracking with CVaR-based ratio measures

n/

Portfolio Optimization: Scenario Generation, Models and Algorithms

Finally, we study the index tracking and the enhanced index tracking problems. We present two mixed-integer linear programming formulations. We introduce a heuristic framework, called Enhanced Kernel Search, to solve the index tracking problem. We show its effectiveness comparing the performances of several heuristics with those of a general-purpose solver using benchmark instances.Thirdly, we study portfolio optimization in a rebalancing framework, considering transaction costs and evaluating how much they affect a re-investment strategy. Specifically, we modify the single-period portfolio optimization model with transaction costs, based on the CVaR as performance measure, to introduce portfolio rebalancing. We suggest a procedure to use the proposed optimization model in a rebalancing framework. Extensive computational results are presented.Secondly, we analyze portfolio optimization when data uncertainty is taken into consideration. In deterministic mathematical optimization, it is assumed that all the input data are equal to some nominal values. Nevertheless, the solution can be sub-optimal or even infeasible when some of the data take values different from the nominal ones. Several techniques that are immune to data uncertainty, called robust, are known. We investigate the effectiveness of two robust techniques when applied to a portfolio selection problem. The reference model assumes the CVaR as performance measure. We carried out extensive computational experiments under different market behaviors.Firstly, we consider the problem of generating scenarios. We survey different techniques to generate scenarios for the rates of return. We also compare these techniques by providing in-sample and out-of-sample analysis of the portfolios. As reference model we use the Conditional Value-at-Risk (CVaR) model with transaction costs. Extensive computational results are presented.In single-period portfolio optimization several facets of the problem may influence the goodness of the portfolios. In this thesis, we aim at investigating the impact of some of these facets on the performances of the portfolios

Models and Simulations for Portfolio Rebalancing

Risk management, Conditional value at risk, Portfolio rebalancing, Multi-period portfolio analysis, Mixed integer linear programming,

Integrated Vehicle Routing Problems: A Survey

The progress in algorithmic design, combined with the technological advances, has encouraged researchers to study integrated problems, that is problems that jointly optimize two or more previously studied sub-problems. The solutions of integrated problems, that are computationally harder to solve, offer substantial advantages with respect to the sequential solutions of the sub-problems. This chapter has the goal to discuss the main classes of integrated problems that include a routing component, namely, the inventory routing problems, the location routing problems, routing problems with loading constraints, and two-echelon routing problems

Approximating Multivariate Markov Chains for Bootstrapping Through Contiguous Partitions

This paper extends Markov chain bootstrapping to the case of multivariate continuous-valued stochastic processes. To this purpose, we follow the approach of searching an optimal partition of the state space of an observed (multivariate) time series. The optimization problem is based on a distance indicator calculated on the transition probabilities of the Markov chain. Such criterion aims at grouping those states exhibiting similar transition probabilities. A second methodological contribution is represented by the addition of a contiguity constraint, which is introduced to force the states to group only if they have “near” values (in the state space). This requirement meets two important aspects: first, it allows a more intuitive interpretation of the results; second, it contributes to control the complexity of the problem, which explodes with the cardinality of the states. The computational complexity of the optimization problem is also addressed through the introduction of a novel Tabu Search algorithm, which improves both the quality of the solution found and the computing times with respect to a similar heuristic previously advanced in the literature. The bootstrap method is applied to two empirical cases: the bivariate process of prices and volumes of electricity in the Spanish market; the trivariate process composed of prices and volumes of a US company stock (McDonald’s) and prices of the Dow Jones Industrial Average index. In addition, the method is compared with two other well-established bootstrap methods. The results show the good distributional properties of the present proposal, as well as a clear superiority in reproducing the dependence among the data

Approximating Markov Chains for Bootstrapping and Simulation

In this work we develop a bootstrap method based on the theory of Markov chains. The method moves from the two competing objectives that a researcher pursues when performing a bootstrap procedure: (i) to preserve the structural similarity – in statistical sense – between the original and the bootstrapped sample; (ii) to assure a diversification of the latter with respect to the former. The original sample is assumed to be driven by a Markov chain. The approach we follow is to implement an optimization problem to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. The basic ingredients of the model are the transition probabilities, whose distance is measured through a suitably defined functional. We apply the method to the series of electricity prices in Spain. A comparison with the Variable Length Markov Chain bootstrap, which is a well established bootstrap method, shows the superiority of our proposal in reproducing the dependence among data

Multivariate Markov Chain Bootstrapping and Contiguity Constraint, Working Paper no. 15 of the Department of Economics and Management of the University of Brescia, p. 1-53

This paper extends Markov chain bootstrapping to the case of multivariate continuous-valued processes. To this purpose we follow the approach of searching an optimal partition of the state space of an observed (multivariate) time series. The optimization problem is based on a distance indicator calculated on the transition probabilities of the Markov chain. Such criterion searches to group those states showing similar transition probabilities. A second methodological contribution is represented by the addition of a contiguity constraint, which is introduced to force the states to group only if they have “near” values (in the state space). This requirement meets two important aspects: firstly, it allows a more intuitive interpretation of the results; secondly, it contributes to control the complexity of the problem, which explodes with the cardinality of the states. The computational complexity of the optimization problem is also addressed through the introduction of a Tabu Search algorithm. The bootstrap method is applied to two empirical cases: the bivariate process of prices and traded volumes of electricity in the Spanish market; the trivariate process composed by prices and traded volumes of a US company stock (McDonald’s) and prices of the Dow Jones Industrial Average index. A comparison between our proposal and another Tabu Search procedure previously advanced in the literature is also performed. The analysis of the empirical studies and of the outcomes of the comparisons confirms good consistency properties for the bootstrap method here proposed

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Modern performance measures differ from the classical ones since they assess the performance against a benchmark and usually account for asymmetry in return distributions. The Omega ratio is one of these measures. Until recently, limited research has addressed the optimization of the Omega ratio since it has been thought to be computationally intractable. The Enhanced Index Tracking Problem (EITP) is the problem of selecting a portfolio of securities able to outperform a market index while bearing a limited additional risk. In this paper, we propose two novel mathematical formulations for the EITP based on the Omega ratio. The first formulation applies a standard definition of the Omega ratio where it is computed with respect to a given value, whereas the second formulation considers the Omega ratio with respect to a random target. We show how each formulation, nonlinear in nature, can be transformed into a Linear Programming model. We further extend the models to include real features, such as a cardinality constraint and buy-in thresholds on the investments, obtaining Mixed Integer Linear Programming problems. Computational results conducted on a large set of benchmark instances show that the portfolios selected by the model assuming a standard definition of the Omega ratio are consistently outperformed, in terms of out-of-sample performance, by those obtained solving the model that considers a random target. Furthermore, in most of the instances the portfolios optimized with the latter model mimic very closely the behavior of the benchmark over the out-of-sample period, while yielding, sometimes, significantly larger returns