On Feb 25, I originally posted the following (I subsequently withdrew the post to think about it more):
"The Wall Street Journal has an Op-ed piece by Jeremy Siegel who argues that earnings reported for the S&P 500 are understated because of the goofy way that S&P computes the index's aggregate earnings.
Whereas the returns on the S&P 500 are estimated on a value weighted basis, S&P estimates aggregate earnings by merely adding up the earnings of all the stocks in the index. Of course stocks that are loosing lots of money tend to have low values. So the earnings number for the index is artificially reduced by this approach. This means that a) S&P 500 earnings aren't as bad as they look, and b) the P/E ratio for the S&P 500 is actually much lower than reported."
Since posting this a commenter noted that I had it wrong. Also several blogs [here, here and here] had come to the same conclusion that indeed Siegel had messed up.
Their logic is simple - the S&P 500 is a value weighted index. The value of the index is basically all the market values added up (and adjusted for float - although that's not important here) and then divided by a fixed divisor.
Therefore a PE ratio of the index = [Sum of market values/divisor] / [Sum of earnings/divisor]
Obviously the divisor cancels and you are left with the sum of market values divided by the sum of earnings, which is what S&P does and what Siegel argued was wrong.
After thinking about it more, I think that Siegel is correct, although his point is perhaps not very well made.
Consider a simple value weighted index with two stocks:
A has 1000 shares and a price of 20, and a market value of 20,000.
B has 1000 shares and a price of 0.05, and market value of 50.
A is 99.751% of the index, B is 0.249% of the index.
B used to be a big company, but now isn't! (Think Citigroup).
A has net income of 2000, B has net income of -1000.
Using S&P's method the PE of the index is (20,000+50)/(2000-1000) = 20.05
Using Siegel's method the PE of the index is (20,000*.99751+50*.249)/(2000*.99751-1000*.249) = 10.013
OK, so what's going on here? It is quite unusual to have very low market cap firms loosing huge amounts of money, but with the financials in the S&P 500, that is what we are seeing now. If you bought the S&P 500 today, you are basically buying stock A, and a tiny stock called B which has a very bad history. But the bulk of your holdings come from stock A. Sure B has lost money, but if the losses exceed the market value, these aren't losses that you as a stock holder will bear. In fact the most you can loose now on your investment in B is 50. The losses are what got the stock down to this point. B has become trivial to your portfolio, you basically own A, and any decision to buy more of this portfolio should be based on whether you think A is fairly valued. I'd argue that assigning a PE of around 10 is far more realistic than A PE of 20. If the PE is a forward looking measure, then forward looking, your future contains mostly stock A, and hardly any B.
Another way of looking at this is that when a stock is close to zero, it is an option. You don't suffer the downside, you only get the upside. Therefore creating a PE that incorporates this huge downside is going to result in a PE that is too high.
This other blogger also thinks Siegel is correct