Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

The role of dispersion into assets allocation

Dispersion of returns has gained a lot of attention as a measure to distinguish good and bad investment opportunities time. In the following dissertation, the cross-sectional returns volatility is analyzed over a fifteen year period across the S&P100 Index composition. The main inference drawn from the data sample is that the canonical measure of dispersion is highly macro-risk driven and therefore more biased towards returns volatility rather than its correlation component.