The main point of this post is to present some models of how to calculate the "fair value" or "central mean" of an index like the S&P 500. Note that all 4 models to some degree rely on mean reversion and a stationary mean (but the world of finance is conflicted between theories of a "random walk" move in stock prices versus an actual intrinsic value and central mean). See this paper on mean reversion for stocks.
1) Shiller/Yale 10-Year Normalized Earnings P/E Test: To avoid short-term profit distortions, use an average of profits (net earnings) over the previous 10 years. Over the long run, stocks trade at an average of about 16 times annual corporate profits—that is, their price-to-earnings ratio, or P/E ratio, is about 16.
Shiller's Research: When this ratio has gotten above 20, as it is today, it has signaled that the market was expensive and sooner or later would hit a stretch of subpar returns. Adjusted for inflation, stocks have declined on average about 2% a year in the decade after they hit a P/E of 20. When dividends are factored in, they had a small positive return. Eventually, stock investors capitulate and stop buying, so the P/E ratio has always fallen back below the average level (mean reversion in action), after which the market becomes cheap, paving the way for above-average performance.
The problem with the S&P 500 today isn't just that the current P/E is above 20. It is that since 1991 it has spent only seven months, in late 2008 and early 2009, below the average level of 16. At the start of 2000, it was above 40. No one can say how much longer the P/E can keep rising or when the past year's bull market might end, especially with the government providing heavy stimulus. But past trends, and the law of averages, suggest that at some point the P/E is likely to fall below 16, pulling stocks with it.
The biggest flaw with Shiller's research is that the future needn't repeat the past. Siegel criticizes it saying the abnormal losses of financial companies (AIG and Citi) in 2007-2009 shouldn't weigh down earnings. But one can calculate this for the S&P excluding financials, since financials are essentially a twilight zone.
2) Siegel/Wharton Single-Year Historical P/Es Applied to Next Year's Earnings Forecasts: Use analysts' projections of future earnings, adjusted to exclude special write-offs and charges that are unlikely to recur (operating earnings).
Siegel's Research: The common P/E is 18.5 when the economy is coming out of a recession. Because the market now is trading at about 14.5 times forecast 2010 profits, making it cheap compared with the typical P/E of 18.5. If stocks rise to 18.5 times profits, the S&P 500 could rise to 1400 this year, a 23% gain from today's level, he notes. "We could easily see 10% to 12% stock returns with low inflation" in future years, he says.
Most market participants prefer this measure, but I see it as deeply flawed for these reasons: i) Operating earnings don't come close to approximating free cash flows, which is what investors can take out. A better measure is neat earnings, or even CFO minus capex; ii) One year's operating earnings shouldn't determine a central value, as any point of the business cycle could be misleading, so it's better to use 10-years and have data over a market cycle; iii) Forecasts about future earnings tend not to be very good.
3) Ben Graham's Risk Premium of Stocks over Bonds Approach: Graham's calculations of a "central value" of the DJIA for the 1924-55 period showed that "the simple formula of dividing the ten-year average earnings by twice the current high-grade bond interest rate produced values which did correspond fairly well with the actual midpoints of successive market swings." This partly takes the Shiller 10-year earnings (net earnings, not the operating earnings that Siegel uses), but discounts it with a rate twice that of the investment grade (IG) bonds rate. See Security Analysis, 4th edition, p. 510 and 744. NOTE: This is different than the so-called "Fed Model" which compares S&P 500 earnings yields to US Treasury yields. Graham compares IG yields to the S&P 500, while making an empirical observation that the central mean happens to be around a 2x yield (for his 1924-55 time period).
4) Buffett's after-tax corporate profits as % of GDP Sanity Check: Uses historical after-tax corporate profits as a % of GDP, which settled in a 4% to 6.5% range after 1951. Use a generous historical 6% margin and applying it to current GDP under different growth scenarios. Then compare this to the sum value of equities traded in the US. Alternatively, look at the current corporate profits margin and compare it as a percentile to the historical band. The only way for stocks in aggregate to rise faster than GDP growth are for the share of corporate profits to grow, or for interest rates to stay very low (the known unknown: How long will the the 10-year USG stay between 3.5% to 4.0%, and where will it go from here?).