Abstract
Investment portfolios should be rebalanced to take account of changing market conditions and changes in funding. Standard mean-variance (MV) portfolio selection methods are not appropriate for portfolio rebalancing, as the initial portfolio, change in funding and transaction costs are not considered. A quadratic mixed integer programming portfolio rebalancing model, which takes account of these factors is developed in this paper. The transaction costs in this portfolio rebalancing model are composed of fixed charges and variable costs, including the market impact costs associated with large market trades of individual securities, where these variable transaction costs are assumed to be non-linear functions of traded value. The use of this model is demonstrated and it is shown that when initial portfolio, funding changes and transaction costs are taken into account in portfolio construction and rebalancing, MV efficient portfolios that include risk-free lending do not have the structure expected from portfolio theory.
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References
Almgren RF (2003). Optimal execution with nonlinear impact functions and trading-enhanced risk . Appl Math Financ 10: 1–18.
Bertsimas D, Darnell C and Soucy R (1999). Portfolio selection through mixed-integer programming at Grantham, Mayo, Van Otterloo and Company . Interfaces 20(1): 49–66.
Best MJ and Hlouskova J (2005). An algorithm for portfolio optimisation with transaction costs . Mngt Sci 51: 1676–1688.
Chang TJ, Meade N, Beasley JE and Sharaiha YM (2000). Heuristics for cardinality constrained portfolio optimisation . Comput Opns Res 27: 1271–1302.
Collins BM and Fabozzi FJ (1991). A methodology for measuring transaction costs . Financ Anal J 27: 27–36.
Dash Optimization (2007). Xpress-MP, Release 2007. Dash Optimization Ltd: Leamington Spa.
Elton EJ, Gruber MJ, Brown SJ and Goetzmann WN (2007). Modern Portfolio Theory and Investment Analysis, 7th edn. Wiley: New York.
Ferraris A (2008). Equity Market Impact Models. Mathematics at the Interface between Business and Research. Stifterverband für die Deutsche Wissenschaft: Berlin, http://www.dbquant.com/Presentations/Berlin200812.pdf, accessed 16 October 2009.
Grinold RC and Kahn RN (1999). Active Portfolio Management, 2nd edn. McGraw-Hill: New York.
Jacobs BI, Levy KN and Markowitz HM (2005). Portfolio optimization with factors, scenarios, and realistic short positions . Opns Res 53: 586–599.
Jobst NJ, Horniman MD, Lucas CA and Mitra G (2001). Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints . Quant Financ 1: 489–501.
Li D and Ng W-L (2000). Optimal dynamic portfolio selection: Multiperiod mean-variance formulation . Math Financ 10: 387–406.
Markowitz HM (1952). Portfolio selection . J Financ 7: 77–91.
Markowitz HM (1959). Portfolio Selection: Efficient Diversification of Investments . Wiley: New York.
Merton RC (1969). Lifetime portfolio selection under uncertainty: The continuous-time case . Rev Econ Stat 51: 247–257.
Mossin J (1968). Optimal multiperiod portfolio policies . J Bus 41: 215–229.
Mulvey JM (1993). Incorporating transaction costs in models for asset allocation . In: Zenios SA (ed). Financial Optimization. Cambridge University Press: Cambridge, pp. 243–259.
Muthuraman K and Zha H (2008). Simulation-based portfolio optimization for large portfolios with transaction costs . Math Financ 18: 115–134.
Perold AF (1984). Large-scale portfolio optimization . Mngt Sci 30: 1143–1160.
Pogue GA (1970). An extension of the Markowitz portfolio selection model to include variable transactions' costs, short sales, leverage policies and taxes . J Financ 25: 1005–1027.
Williams HP (1993). Model Building in Mathematical Programming . Wiley: Chichester.
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Glen, J. Mean-variance portfolio rebalancing with transaction costs and funding changes. J Oper Res Soc 62, 667–676 (2011). https://doi.org/10.1057/jors.2009.148
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DOI: https://doi.org/10.1057/jors.2009.148