Heuristic portfolio optimization: Bayesian updating with the Johnson family of distributions 271
11.8 Conclusion
The obvious appeal of the mean – variance paradigm is that it captures the
two fundamental aspects of portfolio choice — diversification and the trade-
off between risk and reward — in an analytically tractable and easily extend-
able framework. Mean – variance portfolios are, however, optimal only when
asset returns are elliptically distributed or when investors have quadratic utility
functions. In all other cases, there is no guarantee that the optimal portfolio
will be chosen. Yet, this approach still continues to underlie the overwhelm-
ing majority of the asset allocation decisions made within the finance industry.
It seems that practitioners believe, rightly or wrongly, that the benefits gained
from considering alternative approaches with more realistic assumptions do
not outweigh their associated costs.
The purpose of this chapter has been to challenge this long-held belief and in
doing so, to illustrate how solutions to otherwise intractable large-dimension
optimization problems can be obtained with modest amounts of computa-
tional power via the combination of threshold acceptance search algorithm and
Johnson distribution specification. Together they allow us to adopt a brute-
force approach to expected utility maximization, which does not rely upon
Taylor approximation methods or restrictive functional forms. Most impor-
tantly, the framework is sufficiently flexible to allow for a wide range of distri-
butional shapes, covering the entire skewness – kurtosis plane no less, a plethora
of potential objective functions, all of which may exhibit discontinuity, nonlin-
earity, etc., and all manner of portfolio constraints.
Since performance measurements are often based on out-of-sample metrics,
we also introduced the ideas of data reweighting and Bayesian updating via
alpha information as two simple and, most importantly, computationally effi-
cient extensions of the baseline algorithm for improving the robustness. We
then applied these techniques to a real-world dataset based on the FTSE 100
list of companies where we found evidence pertaining to superior performance
of the TA algorithm against its MV counterpart. Moreover, we also showed
how the results of estimation could be used to derive simple rules for the deter-
mination of the various “ tuning ” parameters that are a critical input into the
optimization process.
In summary, we have sought to contribute to the ongoing discussion between
practitioners and academics in order to advance the methodological basis for
the use of non-Gaussian alternatives to traditional mean – variance analysis for
large-dimension portfolio optimization problems. Especially if technological
progress continues at the same pace witnessed in recent decades, the compu-
tational convenience of mean – variance analysis will become less important as
practitioners shift their preferences toward algorithms that are based on more
realistic, albeit computationally more burdensome, assumptions. To this end,
we hope that our exposition has illustrated the complexity of the problems that
can now be solved and will stimulate future developments in this area.