Dynamic risk management of multi asset portfolios
Even though the development of mean variance portfolio selection earned its inventor Harry Markowitz the Nobel Prize, the theory is usually perceived to be flawed in practical applications. Its main deficiency is that it builds on known asset return moments, although inputs have to be estimated in real life. Straightforward application hence tends to maximize errors: assets that appear to be better due to estimation errors will be overweight in portfolios, which leads to suboptimal portfolio choices. In other words, Markowitz portfolio selection is too powerful for the quality of its inputs (Scherer 2002) While increased precision of inputs obviously would lead to better portfolio choices, in this thesis we examine another way to improve results: increasing the resilience to faulty inputs. Therefore, we propose a diversification aware approach that allows to conduct mean variance portfolio selection under constraints on diversification. A minimum required level of diversification serves as single parameter to control sensitivity with regards to inputs, and limit cases are plain Markowitz efficient frontier portfolios on the one end, and the equal weights portfolio on the other. The single diversification parameter keeps the amount of manual decisions to a minimum, and the convex nature of the optimization problem allows fast and robust solving. In an empirical application we show that this diversification aware approach produces promising allocation decisions when used as part of a dynamic risk management strategy. In a backtest period of approximately 17 years, it achieves out of sample risk return profiles close to the true, in sample efficient frontier. Even more remarkable, results hold although asset return moments are obtained from an unreflected application of exponentially weighted sample moments to assets of multiple asset classes. This estimator is predestined to generate poor portfolio optimization inputs, as it is backward looking only and treats highly heterogeneous assets equally. Still, backtest results are promising and hence indicate that diversification aware portfolio choices have the potential to effectively deal with faulty inputs. In addition, dynamic risk management helps to considerably reduce drawdowns as compared to static portfolio weights, and hence results are promising even beyond a perspective on mean variance utility only. Dynamic strategies are set up with particular focus on real life feasibility, and hence should reflect some aspects that go beyond the usual academic requirements. In order to address a broad range of clients, the strategy is built to be scalable with regards to a spectrum of risk aversion levels. Furthermore, within each risk category clients are managed individually, in order to allow customization with regards to client specific tax situations in a subsequent layer. The dynamic strategy hence has an additional optimization step based on relative tracking errors, designed to keep both trading costs and dispersion of client performances within bounds. This particularly cost efficient implementation provides the dynamic risk management approach with enough scope for action. Again, tracking error optimization is formulated as convex optimization problem, such that it allows fast and robust solving.