Essays in statistical methods for asset allocation

The present work, divided into three main chapters, discusses the development and the application of novel statistical techniques for portfolio selection problems. The first chapter is devoted to the estimation theory, and a new estimator for the precision matrix, called precision shrinkage, is developed to reduce the estimation error. The analysis provided in the chapter show that the use of precision shrinkage lead to the construction of more desirable portfolios in terms of return/risk trade-off with respect to well established alternatives. The second chapter studies the ability of forecasting techniques in constructing more attractive portfolios than strategies based on static estimation. Classical model-based econometric methods are compared with data-driven machine learning ones. We find that, for both low and large dimensions, the use of forecasts improves the out-of-sample portfolio performances if model-based approaches are employed. The last chapter discusses the usefulness of clustering in portfolio selection. Clustering can be used to reduce the asset allocation dimensionality. Several algorithms are compared in terms of out-of-sample profitability. As a main result, we show that clustering-based portfolios dominate the classical approaches.