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A review of portfolio planning: Models and systems

By G Mitra, T Kyriakis, CA Lucas and M Pirbhai


In this chapter, we first provide an overview of a number of portfolio planning models\ud which have been proposed and investigated over the last forty years. We revisit the\ud mean-variance (M-V) model of Markowitz and the construction of the risk-return\ud efficient frontier. A piecewise linear approximation of the problem through a\ud reformulation involving diagonalisation of the quadratic form into a variable\ud separable function is also considered. A few other models, such as, the Mean\ud Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the\ud Minimax (MM) model which use alternative metrics for risk are also introduced,\ud compared and contrasted. Recently asymmetric measures of risk have gained in\ud importance; we consider a generic representation and a number of alternative\ud symmetric and asymmetric measures of risk which find use in the evaluation of\ud portfolios. There are a number of modelling and computational considerations which\ud have been introduced into practical portfolio planning problems. These include: (a)\ud buy-in thresholds for assets, (b) restriction on the number of assets (cardinality\ud constraints), (c) transaction roundlot restrictions. Practical portfolio models may also\ud include (d) dedication of cashflow streams, and, (e) immunization which involves\ud duration matching and convexity constraints. The modelling issues in respect of these\ud features are discussed. Many of these features lead to discrete restrictions involving\ud zero-one and general integer variables which make the resulting model a quadratic\ud mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the\ud algorithms and solution methods for this class of problems are also discussed. The\ud issues of preparing the analytic data (financial datamarts) for this family of portfolio\ud planning problems are examined. We finally present computational results which\ud provide some indication of the state-of-the-art in the solution of portfolio optimisation\ud problems

Publisher: The Centre for the Analysis of Risk and Optimisation Modelling Applications (CARISMA), Brunel University
Year: 2003
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