Bullish analysts are claiming that U.S. stocks are "cheap" based on 12-month forward PEs.

Bearish analysts actually claim that stocks are expensive on a proper accounting of the historical average 12-month forward PE, and/or alternatively claim that valuing stocks on the basis of forward operating earnings is an incorrect procedure.

Analyzing the value of the S&P 500 index (Pending:GSPC) based on the 12-month forward estimated PE would seem to be a rather simple matter - almost trivial. Yet this subject has recently generated a great deal of heated debate amongst bullish and bearish analysts.

As it turns out, both bullish and bearish pundits have been displaying an embarrassing degree of confusion regarding the empirical data on projected earnings. Worse still, the vast majority of analysts are revealing a shocking degree of conceptual ignorance regarding proper analysis of PE ratios.

Unfortunately, to fully address the issue of PE analysis as applied to a large stock index would require about 30 pages. We cannot make that sort of exposition here. My main goal in this essay will be to help readers understand that, for the most part, the arguments that have been offered by bulls and bears on this issue are fundamentally mistaken and misleading.

In Part I we will focus exclusively on two problems. First, we point out certain incompatibilities and insufficiencies in the data used to calculate 12-month forward PE ratios. Second, we will point out the limitations of the data used to calculate a historical "average" 12-month PE.

**What Is The Proper Estimate of 12-Month Forward Earnings?**

To calculate the 12-month forward PE we need to start with a proper estimate of 12-month forward earnings. As it turns out, this task is complicated by the fact that analysts and the general public tend to carelessly throw around different and incompatible figures for projected EPS.

First of all, many analysts cite figures for a "consensus top-down" 12-month forward estimated EPS. These figures are derived from surveys of Wall Street strategists. Unfortunately, not all of the estimates of "consensus" coincide. This figure is currently either 104, 103 or 102, depending on the specific source consulted.

The differences amongst these figures arise from the various samples that the "consensus" figures are aggregated from and which are only partly overlapping. Depending on the source, a "consensus" estimate might be aggregated from 8, 14 or 20 different brokerage houses, and figures will differ accordingly. Furthermore, not all information providers update the various sources with the same regularity causing further inconsistency amongst the data.

Second, some analysts cite the consensus "bottom-up" 12-month forward estimated EPS. These figures are fundamentally different from the "top-down" EPS estimates. "Top-down" figures are generally estimated using macro-econometric methods. The "bottom-up" estimates are derived from large databases containing earnings estimates by individual stock analysts for individual companies. The most common source cited for the bottom-up figure is IBES. Factset and other data providers provide their own widely-cited estimates. Currently the IBES bottom-up 12-month forward EPS estimate is $106. The Factset estimate is $105. Again, these estimates differ based on the data that they aggregate and based on the frequency of updates.

Mixing top-down estimates with bottom-up estimates is a fundamental error because the methodologies used to calculate them are radically different. It's like comparing apples to steak.

Please note that bottom-up EPS estimates systematically tend to be significantly higher than top-down estimates - the difference can frequently exceed 10%. This means that bearish analysts like to cite PEs derived from top-down figures (to derive high PEs) and bullish analysts like to cite bottom-up figures (to derive low PEs). However, the two figures are not comparable.

The various data incompatibilities reviewed are currently producing PE differences that are significant but not as large as they frequently are. For example, Gary Shilling, a prominent bearish analyst, recently said that consensus 12-month forward earnings had dropped to 102. Such a figure would yield a 12-month forward PE of 13.5. However, using the same closing price, more bullish analysts can use the IBES bottom-up estimate of 106 to cite a 12-month forward PE of 13.0.

Unfortunately, many analysts, and the vast majority of individual investors, have no idea where various estimates of 12-month forward PE come from or what goes into them. This leads to frequent confusion and contradictions when discussing 12-month forward PEs.

**What Is The Historical Average 12-Month Forward PE for The S&P 500?**

David Kostin from Goldman Sachs has presented the longest data series that I have seen illustrating the 12-forward PE for the S&P 500. The average forward PE is 12.8, going back to 1976. Unfortunately, there are several problems with using this historical average figure:

- Arguably, the data sample is insufficient to derive a reliable mean since the period covered is not representative of a more complete history of U.S. stock valuations.

- The limited data sample means that the start date for the calculation of the mean PE matters a great deal. In this case, the 1976 start date biases the number downward as forward PEs between 1976 and 1986 were historically very low. If a data series going back to 1960 were in existence the average PE would be significantly higher (we know this because actual PEs were higher).

- The Kostin estimate is derived from IBES "bottom-up" data, whereas most analysts prefer to utilize "top down" data that tends to estimate 12-month forward earnings more accurately. This makes Kostin's estimate of the average historical PE incompatible for purposes of comparison with current top-down estimates of the 12-month forward PE.

Notwithstanding these problems, other analysts are citing average 12-month forward PE figures that are much more problematic than the one Kostin posits. For example:

- Some bullish analysts cite an "average" historical PE figure of 15. Even more bullish analysts cite figures as high as 16 or 17. Such estimates make the current forward PE ratio of 13.4 seem "cheap." The problem is that, as a point of fact, the only way you can posit an average historical forward PE of 15 or above is to only consider data since 1995 - a period that encompasses not only the dotcom bubble but also the very high PEs produced by the collapse of earnings in 2008-2009. Such a procedure is obviously problematic. Analysts that cite average PE figures of 15-17 are usually confusing forward PE averages with backwards-looking PE averages such as 12-month trailing earnings and/or figures produced by using Robert Shiller's PE10 methodology. Backward looking PE calculations obviously produce higher average PEs.

- John Hussman, a prominently bearish analyst, has estimated that going back to 1948, the average 12-month forward PE is 11. Unfortunately this is speculation. As I pointed out earlier, estimates for forward earnings are only available since 1976. Hussmann derives his estimate using a "best-fit" linear regression model based on macroeconomic data between 1986 and 2007. The data from 1948 through 1986 is estimated based on this regression. For reasons I cannot go into here in any detail, the estimates derived from such a procedure are not reliable because there is little reason to believe that the relationship between macroeconomic data and earnings were the same between in the periods 1986-2007 and 1948-1986 - and in fact, there are good reasons to believe that the relationship was not constant.

- Other bearish analysts have attempted to calculate the average amount by which forward earnings estimates diverge from actual reported numbers and then apply this average error to the current forward EPS estimate. Again, the PE yielded is 11. This is an utterly fallacious procedure. You simply cannot reasonably subtract an "average error" from a forward estimate at any given point in time because the average error differs radically depending on where you are located in the earnings cycle.

In sum, there is no empirically robust and/or directly comparable average 12-month forward PE that can be used to compare the current top-down 12-month forward PE of around 13.4. The 12.8 PE figure cited by David Kostin is probably the best available and it suggests that the S&P is currently modestly "overvalued." However, the 12.8 figure is not directly comparable to the 13.4 figure since the former is based on bottom up data and the latter is based on top down estimates. Furthermore, the 12.8 average PE figure suffers from limitations related to sample size and the start date of the data series.

**Conclusion**

Contrary to popular belief, there is virtually no basis for claiming that U.S. stocks and index ETFs such as (NYSEARCA:SPY), (NYSEARCA:DIA), (NASDAQ:QQQ), (NYSEARCA:WFVK) or (NYSEARCA:IWM) are "undervalued" on a 12-month forward PE basis. The best data available suggest that S&P 500 stocks are slightly *overvalued* based on the current forward PE of 13.4 and the average historical 12-month forward PE of 12.8 since 1976.

On the other hand, it is also true that valuing stocks by comparing the current 12-month forward PE to a historical average is highly problematic. Issues related to data sample size and start date will plague any attempt to value stocks on this basis.

Most importantly, for reasons that will become clear in Part 2, it would be better if investors paid less attention to simplistic analysis of forward PEs and focused on more conceptually sound and robust methodologies for valuing stocks and stock indices.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.