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Since PE is the inverse of yield, the portfolio's PE is:

Portfolio PE = sum(p) / sum(e),

which is the same as DTM's method. For the simple example of 2 stocks of the same value with respective PE's 10 and 20. The cheaper stock has 2/3 of the portfolio's total earnings yield and hence contributes that much to the total portfolio PE (the inverse of the portfolio earnings yield).

ShadowDragon's reasoning is correct.

The average of two PE's of 10 and 20 is not 15, even if that would seem logical at first glance. This is sort of akin to the common mathematical problem of paddling downstream at 10 km/h and back upstream at 20 km/h, and not having an average speed of 15 km/h, despite the same (false) intuition you would have with your 2 P/E ratios.

In both cases, you have fractions, X/Y, with X/Y behaving properly and Y/X not behaving properly. So for instance it is true that the average of 2 and 4 is 3, but it is not true that the average of 1/2 and 1/4 is 1/3.

With your P/E's of 10 and 20, it is the same thing, except that the 'well-behaved' fraction is not P/E, it is E/P, aka earnings yield. It is better to think of your stocks trading at 10 and 20 times earnings as giving you yields of 10% and 5%, respectively, with an average yield of, yes, 7.5%. If you turn that earnings yield of 7.5% on its head, you get 13.3, the correct answer.

Maybe you are not quite convinced yet. "The average of 10 and 20 is 15, I'm not going to be persuaded to abandon the obviously correct answer and say that the average of 10 and 20 is 13.333!", you might reasonably say. In the same way, you might say that the canoeist's average speed is 15, calculations be damned. And in a way, you would be right: you had two speeds during your return trip, and the average of those two speeds was 15. It's just that you spent 2/3 of your time going at 10, and only 1/3 of the time going at 20, so it would make more sense for you to weight your speeds by time, NOT weight by distance. In the same way, you should weight your P/E's by earnings, not by price.

In the end, you can do it any way you want, but doing it my way will give you a more sensible answer, the same answer you would get by just adding all the earnings and all the prices and calculating the ratio of the sums, as in Dragon's calculation.

Regards, DTM
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