Morningstar writes that "The (P/E) ratio of a fund is the weighted average of the price/earnings ratios of the stocks in a fund's portfolio."
https://www.morningstar.com/invglossary/price_earnings_ratio.aspxWell, not exactly. Or at least I hope not. According to its 2005 methodology paper, "Morningstar now exclusively uses a harmonic weighted average method for calculating the average price ratio for an investment portfolio."
https://studylib.net/doc/7944379/average-price-ratiosThat's just a fancy way of saying that it takes the weighted average of E/P ratios and then inverts the average E/P to get the P/E for a fund. Which is really what one wants if one thinks about what P/E (or E/P) represents.
A P/E ratio tells you how many dollars you have to pay for one dollar of annual earnings. Suppose you have invested $2, half in a stock earning 10¢ per dollar invested (P/E of 10), and half in a stock earning 2¢ per dollar invested (P/E of 50). Then for your $2, you're getting 12¢ of earnings, for a P/E ratio of $2/$0.12 = 16⅔. Not 30 (the average of 10 and 50).
Of course there are still all sorts of variants: current P/Es, projected P/Es, excluding negative earnings, etc. This is just looking at the formula for fund average P/E, not what P/E values you plug into that formula.
Some pages explaining this::
Mean well - Why the average of 10 and 50 is not necessarily 30 (Schroeders)
- where it writes 162/3x it means 16⅔x
P/E for a fund or an index (Bogleheads Wiki)
- the index calculation it gives is equivalent to the fund calculation (left as an exercise for the reader)
Your Mutual Fund's P/E is Likely Very Wrong (Seeking Alpha)
- focuses more on the variants (whether negative earnings should be excluded) than the basic calculation
Comments
I haven't checked lately on the methodology details, but in broad strokes that rings true. It's why for small caps I'm more interested in funds that use the S&P companies as their universe rather than in funds that select companies out of the R2K.
Arguably one could claim that taking the harmonic average of a data set has a natural tendency to underweight extreme points. But even that is a myth.
Consider the data set {9, 10, 11, 20}. 20 is supposedly an "obvious" outlier. Without it, the average is 10. With it, the average is 12.5. The harmonic average is 11.36, which seems somehow "better".
Now consider the data set {1, 9, 10, 11}. Here 1 is the "obvious" outlier. Without it, the average is 10. With it, the average is 7.75. The harmonic average is 3.07. That seems somehow "worse".
The difference between these two examples is that inverting numbers gives proportionately less weight to larger numbers (desirable when 20 is the outlier) but more weight to smaller numbers (undesirable when 1 is the outlier).
I did cringe when I read in the Bogleheads wiki page I cited that " Using a harmonic average presents the advantage of reducing [not eliminating] the effect of outliers". I gave the page anyway because I felt the rest was useful as a terse summary.