Abstract
We compare several approaches to portfolio efficiency based either on Data Envelopment Analysis (DEA) or stochastic dominance relations. In the DEA methodology, the efficiency score is defined as a weighted sum of outputs compared to a weighted sum of inputs when optimal weights are used.
In our DEA-risk efficiency models, several risk measures and functionals which quantify risk of the portfolios are used as the inputs. Mean return is considered as the only DEA output.
Moreover, we consider models with constant return to scale (CRS), variable return to scale (VRS) as well as diversification consistent (DC) DEA models. Using stochastic dominance criteria, we test three different efficiency classifications: pair-wise stochastic dominance efficiency, convex stochastic dominance efficiency and stochastic dominance portfolio efficiency.
Since we consider only risk averse decision makers, we focus on second-order stochastic dominance (SSD). In the empirical application, we test the efficiency of 48 US representative industry portfolios using all considered DEA-risk models and SSD tests.