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Heuristics for Portfolio Selection

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Optimal Financial Decision Making under Uncertainty

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 245))

Abstract

Portfolio selection is about combining assets such that investors’ financial goals and needs are best satisfied. When operators and academics translate this actual problem into optimisation models, they face two restrictions: the models need to be empirically meaningful, and the models need to be soluble. This chapter will focus on the second restriction. Many optimisation models are difficult to solve because they have multiple local optima or are ‘badly-behaved’ in other ways. But on modern computers such models can still be handled, through so-called heuristics. To motivate the use of heuristic techniques in finance, we present examples from portfolio selection in which standard optimisation methods fail. We then outline the principles by which heuristics work. To make that discussion more concrete, we describe a simple but effective optimisation technique called Threshold Accepting and how it can be used for constructing portfolios. We also summarise the results of an empirical study on hedge-fund replication.

Thus computing is, or at least should be, intimately bound up with both the source of the problem and the use that is going to be made of the answers—it is not a step to be taken in isolation from reality. Richard W. Hamming, An Essay on Numerical Methods

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Notes

  1. 1.

    Such a merging of roles did not only happen in computational finance; it also took place in publishing and data analysis in general.

  2. 2.

    In an empirically sound way, which essentially means careful data analysis and replication. See, for example, Cohen [7].

  3. 3.

    Mathematically a function is nothing but a mapping, so there is no contradiction here. But when people see ϕ(x) they intuitively often think of something like \(\phi (x) = \sqrt{x} + x^{2}\) . We would prefer they thought of a programme, not a formula.

  4. 4.

    In principle, because of such mechanisms a heuristic could drift farther and farther off a good solution. But practically, that is very unlikely because every heuristic has a bias towards good solutions. In Threshold Accepting, the method that we describe in Sect. 10.4, that bias comes into effect because a better solution is always accepted, a worse one only if it is not too bad. Since we repeat this creating of new candidate solutions thousands of times, we can be very certain that the scenario of drifting-off a good solution does practically not occur.

  5. 5.

    The number of iterations depends on the problem. Here, again, Principle (ii) tells us how to proceed: small-scale experiments will quickly provide us with a reasonable idea of how many iterations are needed. See Gilli et al. [27]; in particular Chaps. 11 and 12.

  6. 6.

    Similar techniques are used to obtain settings for Simulated Annealing; see for instance Johnson et al. [33].

  7. 7.

    The example builds on Gilli et al. [26].

  8. 8.

    In this case we computed 100 trajectories for each specification of the objective function.

  9. 9.

    The median path is defined with respect to the final wealth of the portfolios generated with the jackknifing.

  10. 10.

    Such an approach has been explored in Gilli and Këllezi [19] using artificial data.

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Author information

Authors and Affiliations

  1. University of Geneva and Swiss Finance Institute, Geneva, Switzerland

    Manfred Gilli

  2. AQ Investment AG, Zurich, Switzerland

    Enrico Schumann

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  1. Manfred Gilli
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  2. Enrico Schumann
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Correspondence to Manfred Gilli .

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Editors and Affiliations

  1. University of Bergamo, Bergamo, Italy

    Giorgio Consigli

  2. EPFL, Lausanne, Cham, United Kingdom

    Daniel Kuhn

  3. Politecnico di Torino, Torino, Italy

    Paolo Brandimarte

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Gilli, M., Schumann, E. (2017). Heuristics for Portfolio Selection. In: Consigli, G., Kuhn, D., Brandimarte, P. (eds) Optimal Financial Decision Making under Uncertainty. International Series in Operations Research & Management Science, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-41613-7_10

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