Valuation Biases, Error Measures, and the Conglomerate Discount

We document the importance of the choice of error measure (percentage vs. logarithmic errors) for the comparison of alternative valuation procedures. We demonstrate for several multiple valuation methods (averaging with the arithmetic mean, harmonic mean, median, geometric mean) that the ranking of valuation methods is largely a function of the error measure chosen. Percentage errors give a higher weight to relative overestimates than to underestimates, and all established multiple valuation methods exhibit a positive bias according to this measure. Percentage errors lead to consequences that are not intuitive: E.g. setting company values equal to their book values often becomes the best valuation method. Logarithmic errors give equal weight to relative overestimates and underestimates and avoid unwanted consequences. With logarithmic errors, median and geometric mean are unbiased while the arithmetic mean is biased upward as much as the harmonic mean is biased downward. Measuring the diversification discount with the arithmetic mean generates a discount about twice as large as with the geometric mean or the median, whereas the harmonic mean leads to a diversification premium.