Portfolio Selection Problems Consistent with a Given Preference Ordering

International Journal of Theoretical and Applied Finance, Volume 16, Issue 5, August 2013

This paper theoretically and empirically investigates the connection between portfolio theory and ordering theory. In particular, we examine three different portfolio problems and the respective orderings used to rank investors' choices: (1) risk orderings, (2) variability orderings, and (3) tracking-error orderings. For each problem, we discuss the properties of the risk measures, variability measures, and tracking-error measures, as well as their consistency with investor choices. Finally, for each problem, we propose an empirical application of several admissible portfolio optimization problems using the US stock market. The proposed empirical analysis permits us to evaluate the ex-post impact of the optimal choices, thereby deriving completely different investors' preference orderings during the recent financial crisis.

Keywords: Probability metrics, tracking-error measures, stochastic orderings, coherent measures, linearizable optimization problems, behavioral finance ordering