Abstract
An alleged weakness of heuristic optimisation methods is the stochastic character of their solutions: instead of finding the truly optimal solution, they only provide a stochastic approximation of this optimum. In this paper we look into a particular application, portfolio optimisation. We demonstrate that the randomness of the ‘optimal’ solution obtained from the algorithm can be made so small that for all practical purposes it can be neglected. More importantly, we look at the relevance of the remaining uncertainty in the out-of-sample period. The relationship between in-sample fit and out-of-sample performance is not monotonous, but still, we observe that up to a point better solutions in-sample lead to better solutions out-of-sample. Beyond this point there is no more cause for improving the solution any further: any in-sample improvement leads out-of-sample only to financially meaningless improvements and unpredictable changes (noise) in performance.
References
Barr, R.S., Golden, B.L., Kelly, J.P., Resende, M.G.C., Stewart, W.R.: Designing and reporting on computational experiments with heuristic methods. J. Heuristics 1(1), 9–32 (1995)
Blitz, D.C., van Vliet, P.: The volatility effect. J. Portf. Manag. 34(1), 120–113 (2007)
Board, J.L.G., Sutcliffe, C.M.S.: Estimation methods in portfolio selection and the effectiveness of short sales restrictions: UK evidence. Manag. Sci. 40(4), 516–534 (1994)
Brandt, M.W.: Portfolio choice problems. In: Aït-Sahalia, Y., Hansen, L.P. (eds.) Handbook of Financial Econometrics. Elsevier, Amsterdam (2009)
Chan, L.K.C., Karceski, J., Lakonishok, J.: On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model. Rev. Financ. Stud. 12(5), 937–974 (1999)
Clarke, R., de Silva, H., Thorley S.: Minimum-variance portfolios in the U.S. equity market. J. Portf. Manag. 33(1), 10–24 (2006)
Dueck, G., Scheuer, T.: Threshold accepting. A general purpose optimization algorithm superior to simulated annealing. J. Comput. Phys. 90(1), 161–175 (1990)
Dueck, G., Winker, P.: New concepts and algorithms for portfolio choice. Appl. Stoch. Models Data Anal. 8(3), 159–178 (1992)
Fishburn, P.C.: Mean-risk analysis with risk associated with below-target returns. Am. Econ. Rev. 67(2), 116–126 (1977)
Gigerenzer, G.: Fast and frugal heuristics: the tools of bounded rationality. In: Koehler, D.J., Harvey, N. (eds.) Blackwell Handbook of Judgment and Decision Making, Chap. 4, pp. 62–88. Blackwell, Oxford (2004)
Gigerenzer, G.: Why heuristics work. Perspect. Psychol. Sci. 3(1), 20–29 (2008)
Gilli, M., Schumann, E.: Portfolio optimization with “threshold accepting”: a practical guide. In: Satchell, S.E. (ed.) Optimizing Optimization: The Next Generation of Optimization Applications and Theory. Elsevier, Amsterdam (2010)
Gilli, M., Schumann, E.: Risk-reward optimisation for long-run investors: an empirical analysis. Eur. Actuar. J. (forthcoming). URL http://www.actuaries.org/Munich2009/Programme_EN.cfm
Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence. MIT Press, Cambridge (1992)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Leshno, M., Levy, H.: Preferred by “All” and preferred by “Most” decision makers: almost stochastic dominance. Manag. Sci. 48(8), 1074–1085 (2002)
Maringer, D.: Portfolio Management with Heuristic Optimization. Springer, Berlin (2005)
Markowitz, H.M.: Portfolio selection. J. Finance 7(1), 77–91 (1952)
Michalewicz, Z., Fogel, D.B.: How to Solve It: Modern Heuristics. Springer, Berlin (2004)
Moscato, P., Fontanari, J.F.: Stochastic versus deterministic update in simulated annealing. Phys. Lett. A 146(4), 204–208 (1990)
Pearl, J.: Heuristics. Addison-Wesley, Reading (1984)
Rockafellar, R.T., Uryasev, S.: Optimization of conditional value-at-risk. J. Risk 2(3), 21–41 (2000)
Winker, P.: Optimization Heuristics in Econometrics: Applications of Threshold Accepting. Wiley, New York (2001)
Winker, P., Maringer, D.: The threshold accepting optimisation algorithm in economics and statistics. In: Kontoghiorghes, E.J., Gatu, C. (eds.) Optimisation, Econometric and Financial Analysis. Advances in Computational Manag. Sci., vol. 9, pp. 107–125. Springer, Berlin (2007)
Winker, P., Maringer, D.: The convergence of estimators based on heuristics: theory and application to a GARCH model. Comput. Stat. 24(3), 533–550 (2009)
Zanakis, S.H., Evans, J.R.: Heuristic “Optimization”: why, when, and how to use it. Interfaces 11(5), 84–91 (1981)
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Both authors gratefully acknowledge financial support from the eu Commission through mrtn-ct-2006-034270 comisef; the data set was provided by DynaGest S.A., Geneva.
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Gilli, M., Schumann, E. Optimal enough?. J Heuristics 17, 373–387 (2011). https://doi.org/10.1007/s10732-010-9138-y
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DOI: https://doi.org/10.1007/s10732-010-9138-y
Keywords
- Optimisation heuristics
- Portfolio optimisation
- Threshold accepting