The harmonic mean averages reciprocals and can aggregate positive valuation multiples when weights match the underlying investment amounts.
The harmonic mean is an average found by taking the reciprocal of the arithmetic average of reciprocals. In finance, it can combine positive valuation multiples, such as price-to-earnings ratios, when the weights match the amounts invested.
It is not automatically the best average for every rate or ratio. The right method depends on what is being combined and which quantities are held constant.
For n strictly positive values x_i, the unweighted harmonic mean is:
For nonnegative weights w_i that sum to one:
Equal weights of 1/n recover the unweighted formula. For a simple spreadsheet calculation, Excel’s HARMEAN function uses the unweighted form and rejects inputs at or below zero. Microsoft: HARMEAN Function.
Suppose a hypothetical portfolio has $1,000 invested in each of two stocks. Both companies have positive earnings, and both P/E ratios use the same price date and earnings basis.
| Holding | Market value held | P/E ratio | Earnings attributable to the shares held |
|---|---|---|---|
| Stock A | $1,000 | 10x | $100 |
| Stock B | $1,000 | 20x | $50 |
| Total | $2,000 | 13.33x aggregate | $150 |
The last column equals holding value divided by its P/E. These are the companies’ earnings attributable to the held shares, not cash distributions promised to the investor.
The aggregate multiple is total holding value divided by those earnings:
The arithmetic mean of 10x and 20x is 15x. That describes an equal-weighted average of the two quoted multiples, but it does not reproduce this portfolio’s aggregate price-to-earnings relationship.
Let V_i be the value of holding i and M_i its positive P/E multiple. Earnings attributable to that holding equal V_i/M_i. Therefore:
If Stock A instead represents 25% of the portfolio and Stock B represents 75%, the aggregate multiple becomes:
For a $2,000 portfolio, those weights imply holdings of $500 and $1,500, with attributable earnings of $50 and $75. Total value divided by $125 of earnings gives 16x.
This aggregation principle also appears in index methodologies. For example, MSCI’s June 2024 methodology calculates index valuation ratios from aggregated adjusted market values and fundamental amounts, with specified inclusion and missing-data rules. A provider’s published figure should be read with its own methodology, not assumed to be a simple mean. MSCI: Fundamental Data Methodology, section 3.1.
| Question | Suitable calculation | Important condition |
|---|---|---|
| What is the aggregate P/E of these holdings? | Value-weighted harmonic mean of positive P/Es | Consistent earnings definitions and portfolio weights |
| What is the average quoted multiple in a peer list? | Arithmetic mean or another stated summary, such as the median | Peer comparability and outlier treatment |
| What is the portfolio’s return for one period? | Beginning-value-weighted arithmetic average of holding returns | Consistent return measurement; no intra-period trading or external cash flows |
| What constant rate reproduces growth over successive periods? | Geometric mean of growth factors, minus one | Link comparable periods and account for external flows |
CFA Institute treats the arithmetic mean, harmonic mean, weighted harmonic mean, and median as distinct ways to summarize valuation multiples. No averaging method makes an unsuitable peer group comparable. CFA Institute: Market-Based Valuation.
Using equal company weights for unequal holdings. The unweighted harmonic mean works in the example because the investment values are equal, not because there are two companies.
Averaging incompatible P/Es. Do not mix trailing and forward earnings, or reported and adjusted earnings, without reconciling the inputs.
Silently dropping loss-making companies. A positive-only subset can give a different picture from total portfolio earnings. State what is excluded and whether the remaining weights are renormalized. When losses are included, calculating total value divided by total earnings directly is clearer than forcing signed P/Es into a positive-data average; a nonpositive aggregate denominator is not a conventional meaningful P/E.
Replacing zero earnings with a zero P/E. Zero earnings make P/E undefined, not zero. Conversely, a very small positive P/E has a large reciprocal and can pull the harmonic mean down sharply. It still requires an earnings-quality check.
Confusing earnings yield with an investment return. The reciprocal of P/E is earnings yield, not a guaranteed dividend, cash flow, or future return.
The examples explain valuation arithmetic and are not investment recommendations or personalized financial advice.