Explain how the median, arithmetic mean, harmonic mean and weighted harmonic mean summarise the typical level of a set of multiples
The idea
Summarising a group of multiples requires a choice of average. The arithmetic mean is pulled up by outliers, especially very high multiples. The harmonic mean, the number of observations divided by the sum of the reciprocals, gives less weight to large values and more to small ones, and is below the arithmetic mean unless every value is equal. The weighted harmonic mean, with weights equal to portfolio holdings, gives the correct multiple for a portfolio or an index. The median is robust to outliers at both ends. The trap is averaging P/E ratios arithmetically when one or two very high multiples, often caused by temporarily depressed earnings, inflate the benchmark and make every other share look cheap.
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