There is ongoing controversy in the business valuation literature regarding the preferability of the arithmetic mean or the harmonic mean when estimating ratios for use in business valuation. This research conducts a simulation using data reported from actual market transactions. Successive random samples were taken from data on valuation multiples and alternative measures of central tendency were calculated, accumulating more than 3.7 million data points. The measures (arithmetic mean, median, harmonic mean, geometric mean) were compared using hold-out sampling to identify which measure provided the closest approximation to actual results, evaluated in terms of least squares differences. Results indicated the harmonic mean delivered superior predictions to the other measures of central tendency, with less overstatement. Further, differences in sample size from 5 to 50 observations were evaluated to assess their impact on predictive performance. Results showed substantial improvements up to sample sizes of 20 or 25, with diminished improvements thereafter.
Research Article| June 24 2020
Empirical Investigation of Alternative Measures of Central Tendency
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William H Black, Lari B Masten; Empirical Investigation of Alternative Measures of Central Tendency. Journal of Financial Reporting doi: https://doi.org/10.2308/JFAR-19-030
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