Leveraging DAGs for Asset Allocation

The aim of this thesis is to develop optimization techniques for financial portfolios, in order to exploit information regarding causal relationships between considered financial variables, described through directed acyclic graphs (DAGs) encoding the causal structure underlying the data. More precisely we consider: (i) a budget B; (ii) a set of N_A investible financial assets; (iii) a set of N_F non-investible financial factors, causally determining the evolution of the returns for the considered financial assets. The objective of this thesis is to investigate the utility of causal information in asset allocation tasks by theorizing and testing different models for portfolio optimization. These models should be more resistant to sudden shocks to the market structure and should loose less in terms of performance when the system is subjected to an unpredictable shock. This work is divided into three main chapters: In chapter 2 some theoretical background material about portfolio optimization, DAGs and causality is introduced; in chapter 3 are introduced portfolio optimization models based on Markovitz's framework and afterwards are theorized and explained a series of different methods for asset allocation based on graph clustering techniques; In chapter 4 all the models presented in the previous chapter are tested against a randomly sampled dataset based on the causal structure of the system, both in the static and intervened cases (where a sudden event changed the causal structure), in order to assess their performances before and after a shock occurred and the results obtained are discussed. Results showed the utility of causal information and causal graph structure in asset allocation tasks and causal models proposed proved to be more stable than benchmark ones in case of soft and hard interventions on the system. Future research can be conducted to improve further the methods proposed and to better exploit causal information and graph clustering techniques.