Minimizing Value-At-Risk In A Portfolio Optimization Problem Using A Multiobjective Genetic Algorithm

Abstract

In this paper we develop a general framework for market risk optimization. The model is valid for any given risk measure (e.g. deviation, Value-at-Risk, Conditional Value-at-Risk...). Our empirical procedure is focused on VaR. The reason for choosing this particular risk measure is the complexity of the risk-return optimization problems that it generates (non-convex and non-differential). We solve the problem using a multiobjective genetic algorithm (GA). The algorithm is very efficient and it can handle hundreds of assets in reasonable computer time. One of the advantages of this approach is that it is easily extendable. We could simultaneously introduce cardinality constrains, non-linear, non-differentiable transaction cost structures, buy-in thresholds or round lots, all of them constraints that lead to non-convex, non-differential models or consider another risk measure without needing to modify the GA.