Galton's Error and the under-representation of systematic risk

Science progresses by improving its measurement apparatus. This holds true in finance too. The new methodology of “complete identification”, using simple algebraic geometry, throws new light on Galton's Error in finance and economics 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 the new methodology it is found that, out of a total of 3217 mutual funds, 2047 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 mispricing of mutual funds. Complete bivariate projections produce a correct representation of the epistemic uncertainty inherent in the bivariate measurement of relative market risk and provide a new CAPM taxonomy. Our conclusions have also serious consequences for the proper “bench-marking” and recent regulatory proposals for the mutual funds industry. Extension of the new methodology to multivariate systematic risk measurement by Asset Pricing Theory (APT) is suggested.