As an investor, you probably know a lot about the price-to-earnings ratio. You might not always pay attention to it (who cares about valuation when your favorite company is doubling its earnings every year?), but you recognize its use in valuing many stocks on the market. You might even follow the valuation of the entire market, just to make sure that everyone else's exuberance isn't getting a bit irrational. It's pretty easy to do so if you stick to the S&P 500 (^GSPC -0.69%), which has been analyzed vigorously enough (in various forms) to show a historical P/E going back to 1871:


Source: Robert Shiller.

Unfortunately, ridiculous extremes caused by the last major crash have skewed the ratio, which makes it somewhat less than ideal for analyzing the potential direction of the market. Does it matter that the median P/E is 14.5 and the mean P/E is 15.5, dating all the way back to 1871, if valuations can soar into the triple digits in less than a year? Probably not. There's a lot of noise in this number. That's why we have the cyclically adjusted P/E, or CAPE -- a 10-year historical valuation that goes a long way toward smoothing out the bumpiness of a short-term P/E:


Source: Robert Shiller.

This looks more like what we'd expect out of extreme bull and bear markets: The CAPE peaks around the same time as the market and tends to bottom out at the same time as well. You can see more of this correlation in my secular market cycle overview. Smoothing things out in this way actually has the effect of increasing both median and mean values, as the CAPE's historical median is 15.9, and its historical mean is 16.5. But there's another problem: What seems unusually high for the 1930s or the 1970s may simply be a "new normal" for today's investors. With the brief exception of the 2008 crash, the market hasn't been below a CAPE of 20 since the early '90s, but such a high level was always a warning sign before.

Further smoothing out an already smoothed-out (i.e., cyclically adjusted) P/E produces something like a historical moving average, which we can match to a long-term trend line:


Source: Robert Shiller; author's calculations.

As you can see, the CAPE has been gradually increasing over time from about 12.5 just prior to the start of the 20th century to about 20 today. That doesn't make today's market look particularly cheaper, given that the smoothed-out CAPE would still have to fall by about 15% just to return to the trend line.

On the other hand, if higher valuations really are a new normal, perhaps we should be looking at a shorter time frame for the CAPE, rather than trying to lengthen it through averaging. Let's see how the 10-year CAPE looks when stacked up against a three-year CAPE:


Source: Robert Shiller and author's calculations.

At the moment, the S&P 500's 10-year CAPE is 23.8, which is about 22% higher than the three-year CAPE of 19.5. That's not particularly surprising, as the three-year CAPE has a historic median of 14.9 and a historic average of 15.5 -- both below the 10-year CAPE's median and mean figures.

Can we use these two numbers to assess future returns? Not exactly, but they can serve as a guide. In this graph, positive results in blue show that the 10-year CAPE is higher than the three-year CAPE, and negative results are evidence that it's lower:


Source: Robert Shiller; author's calculations.

Let's look at that on a shorter timeline for a bit more clarity:


Source: Robert Shiller and author's calculations.

We can't calculate three-year annualized returns for the S&P past 2010 yet, but if history is any guide, the recent reversal in 10-year and three-year CAPEs could point to a more difficult investing climate ahead.

With the exception of the early postwar period (both on the longer and the shorter timeline), the market has historically performed better when the 10-year CAPE is lower than the three-year CAPE. That could be because the three-year CAPE is more likely to be affected by the negative earnings trends typically seen during bear markets, which would push valuations higher when measured on shorter intervals. It could also be the result of short-term profit peaks producing greater swings in the three-year CAPE than in the 10-year CAPE, pushing the shorter-term valuation down before the longer-term measurement can catch up.

Ultimately, historical results can only tell you so much. Every market cycle is similar to previous markets, but it comes with its own unique set of economic and corporate conditions. If you're interested in learning more about market cycles, click here for a complete guide to more than 100 years of bull and bear markets.