When do 10 and 50 not average to 30? When computing fund P/E ratios

msf

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.aspx

Well, 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-ratios

That'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

LewisBraham

Regarding the exclusion of negative earning companies in p-e calculations, that is correct and actually leads to major distortions in valuations of especially small-cap index funds. But I would think for large-cap funds, the calculation is closer to being accurate as most blue chip companies have some sort of earnings. But to include the negative earning companies in the calculation makes small-cap Russell 2000 index funds seems wildly expensive.

msf

In another Bogleheads thread, there is the observation that negative earnings may not be that big a factor in S&P index funds. That is because the S&P indexing methodology excludes nonprofitable companies. Though there would still be a lag before the losers were kicked out.

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.

LewisBraham

That is also correct. In some respects, S&P funds aren’t automated index funds in that the stocks in them are selected by members of the S&P index committee and one of the criteria for the committee’s inclusion of a stock in the S&P 500 historically has been profitability. I believe that is true for the S&P 600 for small stocks as well.

ProtonAnalyst33

I'ves seen an increase in the use of harmonic average, because it supposedly eliminates outliers, is that correct?

Observant1

LewisBraham said:

That is also correct. In some respects, S&P funds aren’t automated index funds in that the stocks in them are selected by members of the S&P index committee and one of the criteria for the committee’s inclusion of a stock in the S&P 500 historically has been profitability. I believe that is true for the S&P 600 for small stocks as well.

Companies must have positive earnings over the most recent quarter as well as over the most recent four quarters (in aggregate) to be considered for inclusion. Consequently, the S&P 600 has a bit of a quality tilt versus the Russell 2000.

msf

ProtonAnalyst33 said:

I'ves seen an increase in the use of harmonic average, because it supposedly eliminates outliers, is that correct?

Since no data points are excluded in calculating a harmonic average, outliers are not being eliminated. The formula doesn't even identify which points, if any, are outliers.

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.

ProtonAnalyst33

@msf thanks for the detailed description. Actually, I might of read that wiki when I first looked up the differences - glad to know i remembered the language correctly. Not glad to know it's misleading?