Mean reversion adjusted betas used in business valuation practice: a research note

A major concern in business valuation is how to derive a beta value that adequately represents the assessment of long-term risk for a company. Against this background Morningstar (Ibbotson SBBI valuation yearbook 2012: market results for stocks, bonds, bills, and inflation 1926–2011. Ibbotson Associates, 2013 ), Bloomberg and Thomson Reuters recommend adjusting betas estimated for company valuation purposes (using β i a d j . = . 371 + . 635 β i r a w commonly named as the “ 1 3 + 2 3 -adjustment”) to take into account research findings from Blume (J Finance 26(1):1–10, 1971 ) demonstrating that betas revert towards the mean value of one over time. Using theoretical analysis as well as a simulated data set reflecting real market patterns, we analyse the eligibility of this beta adjustment formula for company valuation practice. We show that derived adjustment formula coefficients are influenced by the variation of market returns, the length of the analysis period chosen, the measurement error for beta, as well as the distribution of true betas, quantifying the impact of all four elements, and confirm the regression to the mean fallacy interpretation as discussed by Friedman (J Econ Lit 30(4):2129–2132, 1992 ), Quah (Scand J Econ 95(4):427–443, 1993 ), Stigler (Stat Sci 11(3):244–252, 1996 , Stat Methods Med Res 6(2):103–114, 1997 ), and Barnett et al. (Int J Epidemiol 34(1):215–220, 2004 ). We further demonstrate the biasing effect on company values when using the 1 3 + 2 3 -adjustment which is particularly intensified for small betas measured. Based on our analysis we conclude that the recommended 1 3 + 2 3 -adjustment as a justification for converging risk profiles lacks fundamental substance and, accordingly, its potential use in business valuation should be subject to critical consideration.