In the last 12 months, ending on September 30, 2008, the S&P 500 lost more than 20% of its value. Investors who are seeking opportunities in the current crisis are curious to know whether the U.S. stock market has become cheaper now. Surprisingly, a recent article in the New York Times (Why the bear is alive and well) claims that stocks have actually become more expensive. The reasoning is that the P/E ratio of the S&P 500 has gone up to almost 25—a very high value in historical perspective—according to Standard & Poor's calculations.

On the other hand, if you check any financial Web site that covers ETFs and you look for the P/E ratio of a fund that tracks the S&P 500, you will find a totally different story. In Table 1, I present some examples of P/E ratios that I collected from several financial data providers.

The difference between the Standard & Poor's figure and the rest is striking, it's almost double in value. So whose figure is the correct one?

Apparently, the answer to that is not straightforward. The disparity in the figures is the result of two different methods of calculating the aggregate P/E ratio. The first method, which I will call the Total P/E Ratio, divides the total market value of all the companies in the index by their total net earnings. This method is used by Standard & Poor's. The second method, which is called the Average P/E Ratio, calculates the aggregate ratio as the weighted average of the P/E ratios of all the companies in the index. This method is used by all the other financial data providers.

An illustration of the two methods is presented in Table 2. For illustrative purposes, I have constructed a synthetic index that comprises four companies: large-cap with high P/E ratio; small-cap with high P/E ratio; large-cap with low P/E ratio and small-cap with low P/E ratio. The calculation of the aggregate P/E ratio by each method is presented in the last (yellow) row.

The aggregate P/E ratios that are calculated by each method are not identical, but they are quite similar and do not provide an explanation to the disparity shown in Table 1. The difference between the methods arises when one (or more) of the companies is reporting a net loss. At the company level, the P/E ratio has no meaning when the bottom line is negative, and thus it is not calculated. At the index level, however, the treatment of losses makes all the difference between the two methods. The Total P/E Ratio approach is straightforward: The numerator of the ratio is the total market value and the denominator is the total net earnings; losses are counted as net earnings with a minus sign, and thus decrease the denominator and increase the P/E ratio.

How does the Average P/E Ratio approach address losses? None of the financial data providers gives any details about this issue. Nevertheless, the most plausible way is to exclude the companies with the losses and then to recalculate the weights of the index only for the companies that have a valid P/E ratio. Based on these new weights, the Average P/E can be calculated.

Each one of the methods has its pros and cons. The Total P/E Ratio looks at the index as one company with many profit centers. If this were the case, it is obviously the best method. However, an index is not equivalent to a large company. P/E ratios of loss-making companies are not calculated because they are not economically meaningful. If investors had thought that a company would continue to lose money in the long run, its market value would have become zero. Thus, it is more reasonable to assume that investors relate to its losses as a temporary phenomenon and use a hypothetical profit in order to determine its value. In that respect, it makes sense to exclude such company from the calculation of the average P/E.

Providing that the weight of the excluded companies is only a small fraction of the index, the Average P/E Ratio can be more informative. In order to illustrate this point, I have analyzed the behavior of the two aggregate P/E ratios using the synthetic index of Table 2. In the first stage, I calculated the aggregate P/E ratios using four scenarios. In each one of them, one of the companies is reporting a net loss. I kept the values of all the other variables unchanged in order to measure only the effect of the reported net loss. The calculation of the P/E ratios in the four scenarios is presented in Table 3.

Apparently, each one of the methods gives different results. Using the Total P/E Ratio method, we get a higher aggregate P/E ratio (compared with the original aggregate P/E ratio in Table 2) in all the four scenarios. On the other hand, the using the Average P/E Ratio method, we get mixed results, depending on the identity of the company that was excluded from the calculation. The P/E ratio is higher when a lower P/E company is excluded from the calculation, and higher in the opposite case.

Interpretation of these results is not straightforward. At first glance, the Total P/E Ratio results seem more reasonable, since the total net earnings is smaller, the index got more expensive. However, an index is not a large company with many profit centers, but rather, a list of many companies that are grouped together by a certain criteria. Given the fact that in each scenario, in three of the four companies there was no change, it seems a bit misleading to claim that the index got more expensive.

In any event, the example in Table 3 is too schematic, since it is more likely that changes in net earnings will be accompanied by changes in market values. For illustrative purposes, let's assume first that the market value of all the companies in the index went down by 20%, with no other changes. The results are presented in Table 4.

This is a very straightforward case: Since the only change is the decrease in the companies' market values, the two aggregate P/Es are also reduced by 20%, indicating that the index became cheaper. A more realistic case is a combination of the examples in Tables 3 and 4. In this case, one of the companies in the index reports a net loss, but at the same time, the market value of all the companies in the index goes down by 20% (similar to the situation that we see in the market nowadays). The aggregate P/E ratios in this case are presented in Table 5, using the same format as in Table 3.

Interestingly, the two methods point to opposite directions. Using the Total P/E Ratio, we get higher aggregate P/E ratios in all the scenarios, indicating that the index got more expensive. On the other hand, according to the Average P/E Ratio method, all the aggregate P/E ratios became lower, indicating that the index became cheaper. In this case, the Average P/E Ratio method seems to reflect the reality more accurately. Since three of the four companies in the index became cheaper, the fact that one company reported a net loss does not seem to justify a higher P/E ratio to the entire index.

Now let's go back to our initial question: Has the U.S. stock market become cheaper?

The Average P/E Ratio of the SPY (as reported by IndexUniverse.com) was 17 as of October 31, 2007. According to Standard & Poor's data, the Total P/E Ratio as of September 30, 2007 was 18. In spite of the month difference, it is evident that the aggregate P/E ratio based on the two methods was very close at the fourth quarter of 2007. The current ratios, as presented in Table 1, are pointing to opposite directions. Based on the analysis presented above, it seems to me that the Average P/E Ratio is a better indicator of the market's direction, and the S&P 500 is now cheaper than last year.

Elli Malki is an economic consultant and the editor of www.inbest.co.il/, an Israeli Web site that provides a decision support service for savers and investors. He can be reached at This e-mail address is being protected from spambots. You need JavaScript enabled to view it .