In an Op-Ed in this morning's *Wall Street Journal*, Jeremy Siegel argued that the earnings for the S&P 500 are understating actual earnings. While his entire argument can be read here, his basic premise is that Standard and Poor's calculates earnings based on each company's total earnings without taking into account their weight in the index. Siegal goes on to say that earnings should instead be calculated using each company's earnings *times* its weight.

While the argument may sound convincing, it doesn't really make sense. The S&P 500 is meant to represent the total value of the 500 largest companies in the US based on market cap. While a $10 million increase in a company's market cap will have a bigger impact on the stock price of Jones Apparel, which is the smallest company in the index, than it will on ExxonMobil, which is the largest company in the index, the impact on the index is the same. *If the prices of all other 499 stocks remain the same, a $10 million increase in market cap for any one company has the same impact on the index regardless of the company's size. *

Now let's apply this logic to earnings. Imagine you have two investments. The first is worth $1,000, and over the last year it generated $100 in income. The second investment is only worth $100, but over the last year, it had a loss of $100. Most people would probably think of their investments in the way S&P calculates the earnings for the S&P 500. You would have total investments of $1,100 ($1,000+$100) and earnings of zero ($100 profit on $1,000 investment plus $100 loss on $100 investment). Using Siegel's logic, however, your total earnings would be much better (although you would be living in la la land). Since your $100 investment is only worth one tenth of the value of the $1,000 investment, the loss from that investment would only be a tenth as much. In this case, your total earnings would be $90, as the $100 loss would only be worth $10 ($100 + $10 loss = $90).

We'll let readers decide for themselves which approach makes more sense, but before making your decision, think about the result if the returns on the two investment were reversed and the $1,000 investment had a $100 loss while the $100 investment earned $100. According to S&P methodology, your total earnings would still be $0, but under Siegel's method, you would have a total loss of $90.

If anyone wants to test out Siegel's XOM / JNY calculation, please see this spreadsheet

http://spreadsheets.google.com/ccc?key=p01aGY6hUKEfttcDkrRHuRg

(any corrections/challanges/better data greatfully received

Posted by: peter xyz | February 25, 2009 at 04:49 PM

Siegel's argument is incorrect because all S&P500 calcs (index price; earnings; dividends) are market weighted, and thus comparable.

Here is the calc: Sum [price*shares*float], then divided by the index divisor (which is each company's index weight) to get the price.

He claims that the S&P 'ignores' market weights when it calculates index earnings per share. He is simply, and embarrassingly, incorrect.

Posted by: TBob | February 25, 2009 at 05:41 PM

I don't know. I found the argument pretty interesting. He could be wrong but I think he's on to something: the financials taking these huge writedowns are distorting the P/E of the overall index. Outside of financials, stocks are much cheaper than the overall P/E would have them appear.

Posted by: Greg Feirman | February 25, 2009 at 11:29 PM

Rationalizations like Siegel''s always come up when you are getting your head handed to you.

Posted by: Norman | February 26, 2009 at 01:24 AM

Siegel is right, you guys are missing something. I dunked your 2 investment argument here

http://macrospeculations.blogspot.com

Posted by: fernando | February 26, 2009 at 07:30 AM

Both sides are missing the problem with using a combined P/E ratio for a group stocks that includes negative earnings. Because stocks cannot be worth less than zero it does not make sense to use negative earnings to cancel positive earnings. As an example let's suppose that all of the firms with negative earnings in Q4 went bankrupt. Their stock would therefore be worth zero. But the S&P Index would not go to zero, because the stock of companies with positive earnings would still have value. In other words the negative earnings of one company do not cancel the positive earnings of another because stocks are like calls cannot be worth less than zero. A combined P/E ratio makes sense when all companies in the index are profitable. When they are not, it probably makes more sense to zero out the negative earnings, rather than to add them as a negative number. Even this assumes that stocks of companies with short term losses are worthless, which is untrue, but it's better than assuming they pull down the value of other, profitable, companies.

Posted by: Robert Jacks | February 26, 2009 at 11:58 AM

We certainly simplified the argument in the post, and realize there are weaknesses to the S&P 500 approach. However, the method suggested by Siegel is an inferior approach.

Posted by: Paul Hickey | February 26, 2009 at 12:06 PM

"We certainly simplified the argument in the post, and realize there are weaknesses to the S&P 500 approach. However, the method suggested by Siegel is an inferior approach."

His method is actually VERY close to the SP MOST of the TIME. That is because companies that have big earnings/dividends have big market caps. So his method will yield very similar PEs to the S&P a lot of the time as any time an outlier occurs(massive earnings), investors will bid up the price of the stock and 'adjust' that earnings to a higher market cap.

The difference is that his method IS MORE ROBUST as it adapts to situations where LARGE LEVERED firms are losing huge and distorting the PE ratio of the SP500

But most of the time his method will yield very similar PEs and DYs to the SP method

Posted by: fernando | February 26, 2009 at 02:39 PM

1$ invested in S&P = SumOf( w_i dollars invested in each security i in s&p). w_i is calculated by market cap of the security i.

Lets assume that security i has a price/share of P_i and earnings/share of E_i. So, 1$ invested in security i gives you an earnings of E_i/P_i

So, if w_i dollars is invested in the security i, the earnings yield will be w_i*(E_i/P_i)

Therefore 1$ invested in S&P has an earnings yield of SumOf( w_i*(E_i/P_i))

Therefore, adding earnings without the weighted multiplier gives you a number for a equal weighted index not cap weighted index.

Posted by: Harry | February 28, 2009 at 11:02 PM

For Harry,

Please expand w_i further. w_i = P_i*Num of Shares_i. So P_i is cancelled off by by P_i in E_i/P_i. And

SumOf(Num of share_i*eps_i) = the sum of constituents' earnings (in total $, not per share $)

Posted by: Jamie | March 05, 2009 at 11:53 AM

Peter XYZ claims:

"Siegel's argument is incorrect because all S&P500 calcs (index price; earnings; dividends) are market weighted, and thus comparable.

Here is the calc: Sum [price*shares*float], then divided by the index divisor (which is each company's index weight) to get the price.

He claims that the S&P 'ignores' market weights when it calculates index earnings per share. He is simply, and embarrassingly, incorrect."

The only embarrassment if for Peter. The S&P data is available at the link below, and it not, in any way, market weighted.

When you don't know what you are talking about, you should keep your mouth shut. Otherwise, you end up looking like an idiot.

http://www2.standardandpoors.com/spf/xls/index/SP500_EPS_DIV_20090326.XLS

Posted by: Ivan Terrier | April 06, 2009 at 04:42 PM