Essays on stochastic orderings in portfolio selection
Stochastic Ordering represents a relevant approach in portfolio selection for various reasons. Firstly, stochastic ordering is theoretically justified by expected utility theory. Typically, investors are classified according to their attitude towards risk. For each class of investors then, it is possible to define stochastic orderings coherent with their risk preference. Secondly, stochastic ordering is flexible enough to allow different definitions of efficiency suitable for each category of investors. This thesis proposes several applications of stochastic ordering to portfolio selection problems. In the first chapter, an analysis of the relationship between second order stochastic dominance efficient sets and the mean variance efficient frontier is proposed. Not only do the two sets differ under many aspects, but the global minimum variance portfolio and other mean variance efficient portfolios are dominated in the sense of second order stochastic dominance. Based on this fact, the chapter proposes some dominating strategies that are able to outperform the global minimum variance portfolio. In the second chapter, starting from recent findings in the literature, that address the behavior of investors as neither non-satiable, nor risk averse or risk seeking, an extension of the classic definition of stochastic dominance efficiency linked to behavioral finance is given. In particular, investors’ behavior changes according to market conditions. The last part of the chapter presents a methodology, based on estimation function theory, that allows to test for portfolio efficiency with respect to a general stochastic ordering. Both the analysis of efficiency for second order of stochastic dominance and behavioral finance, questions the validity of highly diversified choices. For this reason, this thesis continues the analysis by introducing risk diversification measures, a new class of functional quantifying the amount of idiosyncratic risk diversified among the assets in a portfolio. The mean risk diversification efficient frontier is introduced, along with the concept of mean risk diversification efficiency. The empirical analysis describes the relationship between risk aversion, risk diversification and classic diversification, and shows how risk diversification based strategies perform under periods of financial distress.