Portfolio optimisation: models and solution approaches, in Tutorials in Operations Research, vol.10, H. Topaloglu (ed), 2013, Chapter 11, pp201-221. Published by INFORMS.

In this tutorial we review portfolio optimisation, with a focus on financial applications. Here, the problem is to decide the assets (a portfolio) to hold that have desired characteristics. Markowitz mean-variance portfolio optimisation is relatively well known but has been extended in recent years to encompass cardinality constraints. Less considered in the scientific literature are problems such as (1) index tracking, where the objective is to match the return achieved on a benchmark index such as the S&P 500; (2) enhanced indexation, where the objective is to exceed the return achieved on a benchmark index; here we may have a desired specified excess return, or we may simply wish to do better than the benchmark; and (3) absolute return/market neutral, where the objective is to achieve return irrespective of how the market, as represented by the benchmark index, performs. We will outline the mathematical optimisation models that can be adopted for portfolio problems such as these and the solution approaches that can be adopted.

Keywords: enhanced indexation; index tracking; Markowitz mean-variance; portfolio optimisation

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