Models and methods for portfolio selection

This work contributes to portfolio theory, the research field pioneered by Harry Markowitz in his seminal work “Portfolio selection” trough the presentation of the mean-variance optimization concept proposing to adopt a double perspective in looking at assets: wealth and risk. According to Markowitz's, a portfolio is said to be efficient if, given a desired return level, it presents the lowest value of variance. The emerging objective is the trade-off optimization between risk and reward. Since then, several authors are engaged in the attempt of developing new theories and improving Markowitz's ideas and portfolio theory. In the present work two models are presented. Within the first one a Markov bi-variate process is adopted to characterize the evolution of wealth and volatility generated by the portfolios, then the introduction of stochastic volatility has been examined through Sharpe ratio optimization. Then, the performance indicators have been optimized with respect to a dynamic Sharpe Ratio and conditional to extreme values combination of wealth and volatility. The second model presents a new deviation measure based on quantile regression and it is used to develop a tracking error portfolio subject to enhancement with second order stochastic constraints. The idea behind the proposed framework is to detect a new asymmetrical indicator based on the τ parameter of the quantile regression. Second Order Stochastic dominance and enhancement are other constraints introduced to complete the model and to create a portfolio strategy suitable to over-perform the benchmark. This thesis contributes to portfolio theory research field through the definition of two new performance indicators: the first based on Sharpe ratio and the second one on quantile regression. Both the models out-perform the benchmark with respect to the proposed indicators. These findings make the work a promising starting point for new research developments.