Ordered Mean Difference Benchmarking, Utility Generators, and Capital Market Equilibrium
Designed as a fund performance measure, the ordered mean difference is extended to characterize zero-surplus situations, such as a capital market equilibrium generated by arbitrary risk preferences. This enables nonparametric testing for whether CAPM applies and the detection of pricing inefficiencies or anomalies from historical data, including international capital market segmentation. Any risk-averse utility function can be decomposed into a weighted average of elementary put option profiles ("gnomic" utility functions), which collectively generate the OMD areas. The investor's risk profile can be summarized as a representative gnome, so can the market risk premium. Pricing efficiency turns on whether such a representative gnome exists.
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