I just read an interesting piece by Jeremy Siegel that explains Standard & Poor’s methodology for calculating the earnings for the S&P 500 Index. The S&P 500 Index is a market-weighted index, which means that larger companies (based on market value) are a larger percentage of the index. However, as Dr. Siegel points out in his article, S&P does not account for earnings on a weighted basis:

Unlike their calculation of returns, S&P adds together, dollar for dollar, the large losses of a few firms to the profits of healthy firms without any regard to the market weight of the firm in the S&P 500. If they instead weight each firm’s earnings by its relative market weight, identical to how they calculate returns on the S&P 500, the earnings picture becomes far brighter.

A simple example can illustrate S&P’s error. Suppose on a given day the only price changes in the S&P 500 are that the largest stock, Exxon-Mobil, rose 10% in price and the smallest stock, Jones Apparel Group, fell 10%. Would S&P report that the S&P 500 was unchanged that day? Of course not. Exxon-Mobil has a market weight of over 5% in the S&P 500, while the weight of Jones Apparel is less than .04%, so that the return on Exxon-Mobil is weighted 1,381 times the return on Jones Apparel. In fact, a 10% rise in Exxon-Mobil’s price would boost the S&P 500 by 4.64 index points, while the same fall in Jones Apparel would have no impact since the change is far less than the one-hundredth of one point to which the index is routinely rounded.

Yet when S&P calculates earnings, these market weights are ignored. If, for example, Exxon-Mobil earned $10 billion while Jones Apparel lost $10 billion, S&P would simply add these earnings together to compute the aggregate earnings of its index, ignoring the vast discrepancy in the relative weights on these firms. Although the average investor holds 1,381 times as much stock in Exxon-Mobil as in Jones Apparel, S&P would say that that portfolio has no earnings and hence an “infinite” P/E ratio. These incorrect calculations are producing an extraordinarily low reported level of earnings, high P/E ratios, and the reported fourth-quarter “loss.”

I never thought about this before but Dr. Siegel’s way does seem to make more sense. Maybe they should do both—a market-weighted earnings and P/E ratio and a standard earnings and P/E ratio.

Although stocks seem cheap right now on a P/E basis, they won’t be as cheap if earnings continue to fall. For example:

Say you have a company that is trading at $20 per share and earns $2 per share, giving the stock a P/E of 10. Then lets say this company’s earnings drop 25% to $1.50 per share. If the stock price remains at $20 per share (it most likely wouldn’t if its earning dropped 25% but this is an example), its P/E would now be 13.3 or roughly 33% higher. Remember, the way to think of P/E is the price you pay for each dollar of a company’s earnings. So, with earnings of $2 per share and a $20 stock, you are essentially paying $10 for each dollar of earnings. Now that the earnings are lower, you are paying $13.33 for each dollar of earnings.

There’s no doubt that stocks look a lot cheaper than they have in the past but there are still risks out there. That’s why I think the best thing to do in this market is to dollar-cost average.

Your thoughts on Jeremy Siegel’s thoughts?

Hum, interesting thought. I just have a few (possibly naive) questions:

Aren’t the earnings for a company divided by the number of outstanding shares to get the per-share earnings? And wouldn’t Jones, with far fewer shares outstanding, have a significantly larger portion of its profits/losses allocated to each share? In the above example, while Exxon represents 1381 times as much of the S&P 500 as Jones, if they had identical earnings, wouldn’t Exxon’s per share earnings be 1/1381th the size of Jones’? It seems like that would be the logic behind Standard & Poor’s decision for how they calculate earnings for the portfolio.

It seems like there have to be better ways to calculate the P/E ratio for a portfolio than this, though, as it seems to distort the meaning of the P/E ratio as it applies to individual companies.

I am in agreement with Roger. S&P us doing this correctly and you should understand Siegel’s motivation. He is trumpeting how cheap stocks are and he is trying to find a way to prove it (I don’t completely disagree that stocks are cheap). We can all agree with the daily movement of the index calculation, it makes sense to weight it. But earnings are earnings, if the sum of all S&P earnings is $100 then at the end of the day that is what it is. If you use Siegel’s example and you owned the Exxon and Jones outright you would have had earnings of $0. But using his logic because Exxon is the larger portion of you portfolio you actually made money. Can someone help me find the flaw in my logic.

Roger,

While a good thought, what you said is not correct. The number of shares outstanding really has nothing to do with the size of the company. The price of the shares multiplied by the number of shares outstanding is the “market capitalization” – the important metric here.

Think Berkshire Hathaway… they may have less shares outstanding than a given company, but their shares sell for $80,000 compared to say $4.50 for the other company.

Therefore I would say that Siegel has a good point. When you buy a share of an S&P Index Fund, you are getting the 1,400 times more ownership of Exxon than the other company. Therefore more of the gains (losses) of Exxon are attributable to your portion than the profits (losses) of Jones. So if Exxon makes $10B and jones loses $10B, you do not end up with zero attributable retained earnings in your name with those companies – it is somewhere in between.

Brandon (comment #3), you should take a look at your math again and reevalute some of the assumptions that you made.

With a market cap-weighted index fund, you essentially own the same percentage of each company in the index. To illustrate, if the total market cap is say $500billion for the S&P, and Exxon is $300B of that and Jones is only $100M, you still own the same percentage of both companies. For example, if the index fund share price is $500/share, you own 1 billionth of the S&P, and therefore 1 billionth of Exxon (or $300 worth of Exxon) and 1 billionth of Jones (10 cents). Since the percentage of ownership is the exact same, the earnings are distributed to you on the same percentage, namely a $10 loss for Exxon and a $10 loss for Jones resulting in a net zero. In essence, the large loss for the smaller company hits the smaller “number” of shareholders harder.

The fallacy in the logic of Siegel is mixing absolute numbers and percentages. If you are not careful, these numbers can lead to inaccurate results.

second fallacy: Also, Jeremy uses “new” P/E ratio with historically (empirically) formulated basis of P/E

i.e. P/E of 20 is high based on empirically studied data according to the current way of calculating the P/E. If you change the benchmark, historical analysis would yield different numbers for what P/E value means as far as undervalued or overvalued market is concerned