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Betas are possibly the most frequently applied tool to analyze how securitiesrelate to the market. While in very widespread use, betas only express dynamicsderived from second moment statistics. Financial returns data often deviatefrom normal assumptions in the sense that they have significant third andfourth order moments and contain outliers. This paper targets to introduce away to calculate generalized betas that also account for higher order momenteffects, while maintaining the conceptual simplicity and interpretability ofbetas. Thereunto, the co-moment analysis projection index (CAPI) is introduced.When applied as a projection index in the projection pursuit (PP) framework,generalized betas are obtained as the directions optimizing the CAPI objective.A version of CAPI based on trimmed means is introduced as well, which is morestable in the presence of outliers. Simulation results underpin the statisticalproperties of all projections and a small, yet highly illustrative example ispresented.

Projection pursuit based generalized betas accounting for higher order co-moment effects in financial market analysis