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 quot;complete identification,quot; using simple algebraic geometry, throws new light on Galton's Error in finance and economics and the resulting mis-information of investors. Mutual funds conventionally advertise their relative systematic market risk, or quot;betas,quot; 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 quot;defensive quot;and too few as quot;aggressive.quot; Using the new methodology it is 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. 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 quot;bench-marking quot; and recent regulatory proposals for the mutual funds industry. Extension of the new methodology to multivariate systematic risk measurement by Asset Pricing Theory is suggested