Enhanced index tracking in portfolio optimization with two-stage mixed integer programming model

Enhanced index tracking is a portfolio management which aims to construct the optimal portfolio to generate higher return than the benchmark index return at minimum tracking error without purchasing all the stocks that make up the index. The objective of this paper is to propose a two-stage mixed integer programming model to improve the existing single-stage mixed integer programming model for tracking FBMKLCI Index in Malaysia. The optimal portfolio performance of both models are determined and compared in terms of portfolio mean return, tracking error, excess return and information ratio. The results of this study indicate that the optimal portfolio of the proposed model generates weekly excess return over the benchmark FBMKLCI index return at minimum tracking error. Besides that, the proposed model is able to outperform the existing model in tracking the benchmark index.Keywords: mean return; tracking error; optimal portfolio; portfolio performanc

Evaluating the performance of global emerging markets equity exchange-traded funds

We examine the performance of passively managed exchange-traded funds (ETFs) that provide exposure to global emerging markets equities. We find that the tracking errors of these funds are substantially higher than previously reported levels for developed markets ETFs. ETFs that use statistical index replication techniques turn out to be especially prone to high tracking errors, and particularly so during periods of high cross-sectional dispersion in stock returns. At the same time, we find no convincing evidence that these funds earn higher returns than ETFs that rely on full-replication techniques

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 similarity measure for the cardinality constrained frontier in the mean-variance optimization model

[EN] This paper proposes a new measure to find the cardinality constrained frontier in the meanvariance portfolio optimization problem. In previous research, assets belonging to the cardinality constrained portfolio change according to the desired level of expected return, so that the cardinality constraint can actually be violated if the fund manager wants to satisfy clients with different return requirements. We introduce a perceptual approach in the meanvariance cardinality constrained portfolio optimization problem by considering a novel similarity measure, which compares the cardinality constrained frontier with the unconstrained mean-variance frontier. We assume that the closer the cardinality constrained frontier to the mean-variance frontier, the more appealing it is for the decision maker. This makes the assets included in the portfolio invariant to any specific level of return, through focusing not on the optimal portfolio but on the optimal frontier.Guijarro, F. (2018). A similarity measure for the cardinality constrained frontier in the mean-variance optimization model. Journal of the Operational Research Society. 69(6):928-945. doi:10.1057/s41274-017-0276-6S92894569

A Heuristic Approach To The Index Tracking Problem: A Case Study Of The Tehran Exchange Price Index

Index tracking, the most popular form of passive fund management, is a portfolio selection problem in which the return of one of the stock market indexes is reproduced by creating a tracking portfolio consisting of a subset of the stocks included in the index. Index tracking has been known as an NP-Hard problem, and sophisticated approaches have been proposed in the literature to solve this problem. This paper presents an easyto-implement heuristic solution to this complex problem. The proposed approach was implemented to develop a tracking portfolio of 438 stocks listed in the Tehran Exchange Price Index. The numerical results indicate that the approach is able to identify quality solutions within reasonable model runtime