248 Optimizing Optimization
The purpose of this chapter is to introduce one such alternative and to
illustrate more generally how solutions to otherwise intractable optimization
problems can be obtained with modest amounts of computational power via
an appropriate choice of local search algorithm and parametric density speci-
fication. With regards to the former, a deterministic threshold acceptance
algorithm is used to generate transitions between portfolio weights while simul-
taneously avoiding local solutions ( Dueck & Winker, 1992 ). For the latter, one
of the Johnson family of distributions is fitted to the time series of portfolio
returns ( Johnson, 1949 ). Johnson distributions are uniquely determined by the
first four moments, which can be chosen mutually independently and so they
are well suited to modeling the complex nature of asset returns.
The combination of search algorithm and density estimation procedure is
then used to maximize a hitherto impractical disappointment-averse expected
utility function for portfolios comprising large numbers of assets. The results
of extensive simulation and out-of-sample testing reveal that the algorithm per-
forms well under a variety of circumstances and constitutes a viable alternative
to the traditional mean – variance approach to asset allocation. Since out-of-
sample performance is a critical aspect of this success, we also describe two
simple and most importantly, computationally efficient extensions to the base-
line algorithm that further improve the robustness of the final allocation.
The first of these extensions describes how data reweighting techniques
can be used to give more weight to the observations that we believe are most
informative about the current state of the underlying data-generating process,
whereas the second illustrates in a more direct manner how asset return fore-
casts can be used to guide the search process. In the case of the latter, the pos-
terior density of portfolio returns is derived from the meta-Gaussian model of
Kelly and Krzysztofowicz (1995).
The rest of this chapter is structured as follows. Section 11.2 surveys the lit-
erature pertaining to portfolio optimization in large dimensions, with partic-
ular emphasis on heuristic algorithms. The theoretical properties of Johnson
family of distributions are reviewed in Section 11.3 along with an explanation
of the estimation procedure. Section 11.4 describes the utility maximization
problem and illustrates how the density estimation and threshold accept-
ance algorithms are combined to obtain the optimal portfolio allocation. The
related ideas of data reweighting and Bayesian updating are then introduced in
Sections 11.5 and 11.6 as two possible extensions to the baseline framework.
Finally, the techniques are applied to a portfolio of equities from the FTSE 100
list of companies in Section 11.7. Section 11.8 concludes.
11.2 A brief history of portfolio optimization
In his seminal work, Markowitz (1952) described how an investor should allo-
cate his or her wealth when asset returns are normally distributed. Within this
framework, he showed that the complex problem of portfolio optimization