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Quadratic programming for portfolio planning: Insights into algorithmic and computational issues

Part I — Solving a family of QP models

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Abstract

Convex quadratic programming (QP) as applied to portfolio planning is established and well understood. In this paper, presented in two parts, we highlight the importance of choosing an algorithm that processes a family of problems efficiently. In Part I in particular we describe an adaptation of the simplex method for QP. The method takes advantage of the sparse features of simplex and the use of the duality property makes it ideally suited for processing the discrete optimisation models. Part II (to be published in issue 8/4) of the paper considers a family of discrete QP formulations of the portfolio problem, which captures threshold constraints and cardinality restrictions. We describe the adaptation of a novel method ‘branch, fix and relax’ to process this class of models efficiently. Theory and computational results are presented.

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Authors and Affiliations

  1. CARISMA — The Centre for the Analysis of Risk and Optimisation Modelling Applications, Brunel University, London, UK

    Gautam Mitra

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  1. Gautam Mitra
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  2. Frank Ellison
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  3. Alan Scowcroft
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Correspondence to Gautam Mitra.

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2was educated at Clifton College Bristol and at The Queen's College Oxford, where he received a first class honours degree in mathematics. Subsequently, he worked for several computer software companies and did work on mathematical programming, database and survey research systems. He was closely associated with the development of the Ophelie LP system, designed and built the integer sub-system of APEX2 for CDC 6600 and 7600 mainframe computers, and prepared the design for much of LP2900 for ICL 2900 series computers. His recent work with Brunel and OptiRisk Systems includes development and maintenance of the FortMP system, assistance with various post-graduate studies, and he has recently been awarded a PhD for his thesis on quadratic programming.

3was educated at Ruskin College, Oxford and Wolfson College, Cambridge, where he was awarded the Jennings Prize for academic achievement. He taught econometrics at Clare College, Cambridge before joining Phillips & Drew as an econometrician in 1984. There he worked with the leading macro research group at UBS and since that time he has worked on every aspect of quantitative modelling from stock selection to asset allocation. He has been closely associated with pioneering work on equity style and portfolio analysis developed by UBS Warburg. His research interests include practical applications of Bayesian econometrics and portfolio optimisation. Until his recent retirement in June 2006 he was the global Head of the top ranked equities quantitative research team at UBS Warburg.

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Mitra, G., Ellison, F. & Scowcroft, A. Quadratic programming for portfolio planning: Insights into algorithmic and computational issues. J Asset Manag 8, 200–214 (2007). https://doi.org/10.1057/palgrave.jam.2250075

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  • DOI: https://doi.org/10.1057/palgrave.jam.2250075

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