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 sim ple algebraic geometry, throws new light on Galton's Error in finance and e conomics and the resulting misinformation of investors. Mutual funds conven tionally advertise their relative systematic market risk, or "betas", to po tential investors based on incomplete measurement by unidirectional bivaria te projections: they commit Galton's Error by underrepresenting their syste matic risk. Consequently, far too many mutual funds are marketed as "defens ive" and too few as "aggressive". Using the new methodology it is found tha t, out of a total of 3217 mutual funds, 2047 funds (63.7%) claimed to be de fensive based on the current industry standard methodology, but only 608 (1 8.9%) actually are. This under-representation of systematic risk leads to i nefficiencies in the capital allocation process, since biased betas lead to mispricing of mutual funds. Complete bivariate projections produce a corre ct representation of the epistemic uncertainty inherent in the bivariate me asurement of relative market risk and provide a new CAPM taxonomy. Our conc lusions have also serious consequences for the proper "bench-marking" and r ecent regulatory proposals for the mutual funds industry. Extension of the new methodology to multivariate systematic risk measurement by Asset Pricin g Theory (APT) is suggested. (C) 1999 Elsevier Science B.V. All rights rese rved.