Chapter 9 - Portfolio optimization with “Threshold Accepting”: a practical guide

Abstract

Recent years have seen a proliferation of new risk and performance measures in investment management. These measures take into account stylized facts of financial time series like fat tails or asymmetric return distributions. In practice, these measures are mostly used for ex post performance evaluation, only rarely for explicit portfolio optimization. One reason is that, other than in the case of classical mean–variance portfolio selection, the optimization under these new risk measures is more difficult since the resulting problems are often not convex and can thus not be solved with standard methods. This chapter describes a simple but effective optimization technique called “Threshold Accepting (TA),” which is versatile enough to be applied to different objective functions and constraints, essentially without restrictions on their functional form. This technique is capable of optimizing portfolios under various recently proposed performance or (downside) risk measures, like value at risk, drawdown, Expected Shortfall, the Sortino ratio, or Omega, while not requiring any parametric assumptions for the data, i.e., the technique works directly on the empirical distribution function of portfolio returns. This chapter gives an introduction to TA and details how to move from a general description of the algorithm to a practical implementation for portfolio selection problems.