Galton's Error and the Under-Representation of Systematic Risk

Our methodology of 'complete identification,' using simple algebraic geometry, throws new light on the continued commitment of Galton's Error in finance and the resulting misinformation of investors. Mutual funds conventionally advertise their relative systematic market risk, or 'betas,' to potential investors based on incomplete measurement by unidirectional bivariate projections: they commit Galton's Error by under-representing their systematic risk. Consequently, far too many mutual funds are marketed as 'defensive' and too few as 'aggressive.' Using our new methodology we found that, out of a total of 3,217 mutual funds, 2,047 funds (63.7%) claimed to be defensive based on the current industry standard methodology, but only 608 (18.9%) actually are. This under-representation of systematic risk leads to inefficiencies in the capital allocation process, since biased betas lead to mis-pricing of mutual funds. Our complete bivariate projection produces a correct representation of the epistemic uncertainty inherent in the bivariate measurement of relative market risk. Our conclusions have also serious consequences for the proper 'bench-marking' and recent regulatory proposals for the mutual funds industry.