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Multi-Period Risk Measures and Optimal Investment Policies Read chapter Read first chapter

2017 | OriginalPaper | Chapter

10. Heuristics for Portfolio Selection

Authors : Manfred Gilli, Enrico Schumann

Published in: Optimal Financial Decision Making under Uncertainty

Publisher: Springer International Publishing

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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.

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Footnotes
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
In an empirically sound way, which essentially means careful data analysis and replication. See, for example, Cohen [7].
 
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
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
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
Similar techniques are used to obtain settings for Simulated Annealing; see for instance Johnson et al. [33].
 
7
The example builds on Gilli et al. [26].
 
8
In this case we computed 100 trajectories for each specification of the objective function.
 
9
The median path is defined with respect to the final wealth of the portfolios generated with the jackknifing.
 
10
Such an approach has been explored in Gilli and Këllezi [19] using artificial data.
 
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Metadata
Title
Heuristics for Portfolio Selection
Authors
Manfred Gilli
Enrico Schumann
Copyright Year
2017
Book
Optimal Financial Decision Making under Uncertainty

Print ISBN: 978-3-319-41611-3

Electronic ISBN: 978-3-319-41613-7

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-41613-7_10