Black-Litterman and Hidden Markov Model forecasts for Multi-Period Portfolio Optimization

The thesis deals with the implementation of a multi-period optimization model for portfolio choices. After examining the advantages of a multi-period optimization, the analysis focuses on the way the inputs of the model are provided, namely the returns and risks forecasts and the estimated transaction costs. Multi-period convex optimization, Black-Litterman and Hidden-Markov Model (HMM) are the three cornerstones of the dissertation, which are appropriately combined to provide with a real-word practical investment tool for portfolio choices. The Black-Litterman model is exploited in order to get the estimates of risks and returns, the main input of the multi-period optimization model, being one of the most used tools in portfolio choices among investors. Investor’s views, the main input of the Black-Litterman model needed for the computation of the posterior returns and risks estimates, are instead provided through the use of HMM as a regime switching predictive tool. Once the HMM provides with forecasted market regime for each asset chosen to build the portfolio, it also provides with the mean return forecasted by the HMM according to the most likely regime predicted for that asset. Combining the latter estimated asset return with the initial view return given by the investor, the model outputs dynamic confidence level for investor views needed for the final step of Black-Litterman, i.e., the computation of the posterior risks and returns. The first part of the dissertation is dedicated to a deep analysis on the functioning, the motivation, and the mathematical and statistical framework behind all the models implemented. The second part, instead, aim at empirical implementing the model by replicating the results of the “Multi-Period Portfolio Optimization with Investor Views under Regime Switching paper” written by Razvan Oprisor and Roy Kwon, which is the ground of the thesis.