Measuring Central Tendency Involving Ratios - An Intuitive Approach
Common methods for estimating the central tendency of dataset values involving ratios include the median, mean, harmonic mean, and weighted harmonic mean. It is well-established that the harmonic mean and/or weighted harmonic mean are better indicators of central tendency than the mean when the data-set measured is comprised of ratios. This is because “___________”. As such, “the mean overestimates central tendency because it gives disproportionately greater weight to higher multiple values.”
For some professionals, such a definition does not assist their intuition for understanding the reasoning behind using a harmonic mean (or weighted harmonic mean) as opposed to a mean when estimating central tendency of a dataset involving ratios. As such, abandoning mathematical terminology or equations, at least initially, may assist professionals in forming an intuition behind the measures of central tendency when applied to ratios.
To do so, I view these measures as a sum of capital investment or earnings available in the dataset being measured.
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The ratio’s being measured are purchase price (MVIC) and free cash flow (FCF). The weighted harmonic mean provides the most basic and arguably the most intuitive method for finding the central tendency of the ratios. This is followed closely the harmonic mean. The mean, however, appears far-removed from how most investors would go about optimizing their investment strategy.
Here is the bottom-line:
Weighted Harmonic Mean - An investor would purchase each of the sample companies at their respective purchase prices and the earnings ratios observed are weighted according to the percentage of the corresponding company’s MVIC relative the the entire samples MVIC. In other words, it does not manipulate the data-set at all. Thus applying greater weight to the higher MVIC companies (and their multiples) and lessor weight to the lessor MVIC companies (and their multiples).
Harmonic Mean: An investor would purchase an equal amount of each company listed in the sample, and the earnings ratios observed are thus weighted equally according to the number of companies provided in the sample. Thus, equal weight is applied to all ratios regardless of the cost required to obtain such earnings. This is why the harmonic mean is typically the best method for measuring central tendency involving ratios.
Mean: An investor would purchase an equal amount of EARNINGS of each company listed in the sample. In other words, the investor purchases the pro-rata amount of each sample company in order to obtain exact same number of earnings provided by each company. In other words, harmonic mean = “equal purchasing” and mean = “equal earnings”. It would be like saying, you would purchase $10,000 of a high P/E company for every $1,000 you spend of a low P/E company merely because you would like for your earnings to be equal among all of your investments.
When viewed this way, it is the well-known mean that lacks any intuitional appeal. Rather it is the lessor-known harmonic mean and weighted harmonic mean that more accurately capture how an investor would consider making these purchases.
