Long-term asset allocation based on stochastic multistage multi-objective portfolio optimization - Chagas, Guido Marcelo Borma (2016)
Multi-Period Stochastic Programming (MSP) offers an appealing approach to identity optimal portfolios, particularly over longer investment horizons, because it is inherently suited to handle uncertainty. Moreover, it provides flexibility to accommodate coherent risk measures, market frictions, and most importantly, major stylized facts as volatility clustering, heavy tails, leverage effects and tail co-dependence. However, to achieve satisfactory results a MSP model relies on representative and arbitrage-free scenarios of the pertaining multivariate financial series. Only after we have constructed such scenarios, we can exploit it using suitable risk measures to achieve robust portfolio allocations. In this thesis, we discuss a comprehensive framework to accomplish that. First, we construct joint scenarios based on a combined GJR-GARCH + EVT-GPD + t-Copula approach. Then, we reduce the original scenario tree and remove arbitrage opportunities using a method based on Optimal Discretization and Process Distances. Lastly, using the approximated scenario tree we perform a multi-period Mean-Variance-CVaR optimization taking into account market frictions such as transaction costs and regulatory restrictions. The proposed framework is particularly valuable to real applications because it handles various key features of real markets that are often dismissed by more common optimization approaches.