Dissertation writing help: Coherent Asset Allocation and Diversi cation in the Presence of Stress Events

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The backward looking approach of Markowitz theory and even of some of its improved versions does not reflect the necessity to consider information present in the current world about events that might create market dislocations. Information about such events might be absent from any historical dataset but not taking it into consideration could seriously understate the risk for many asset classes. This necessity is underlined in numerous publications by scholars, practitioners and regulators, especially after the subprime debacle 2007-2009. Such mood is already incorporated in investors' strategies who protect their portfolios with insurance trades in case an extreme event or series of such events materializes. However, this strategy is realized ex post i.e. after running mathematical models to calculate optimal asset allocations, as an afterthought. Having a mathematical tool to satisfy both the need for diversification and forward looking information about stress events in an integrated fashion is still missing. This thesis tries to fill this gap by introducing a new framework for asset allocation in the presence of stress events carried out in a coherent way and not ad hoc, as an afterthought. We propose a procedure that blends standard statistical techniques such as correlations, copulae etc. with a subjective Bayesian approach based on causality assumptions to model stress events. The approach is highly transparent, auditable and easy to be understood by non-specialists.

Because the practical application of the procedure is of extreme importance we introduce also some original tools that ease its implementation, its robustness and its calculation speed. More specifically, we present

 i) a maximum entropy approach for the degree of condense in the model

ii) a fast numerical technique which avoids continuous repetitions of Monte Carlo simulations

iii) a linear programming technique which helps the estimation of probabilities

iv) the concept of stressed efficient frontier.

Finally, we suggest a link with the Black-Litterman model which becomes in this context a particular case of our approach.