Here is a logarithmic chart of the S&P 500 since 1950:

It appears to consistently grow at an exponential rate. Remember this is a logarithmic graph, so exponential growth is represented as a straight line. This is growth of about 6% per year over 68 years. If you invested $1000 in 1950, that would be worth about $50,000 today. If you kept on adding $1000 per year, you would have nearly $1 million. That’s simply the magic of compounding interest.

Complex dynamic systems, like the stock market, can often be described by fractals. One attribute of fractals is that they are self-similar, that is if you zoom in on one part of a fractal, it often appears similar to the whole image. The same phenomenon happens with coastlines and plants for example, but more about that in other post.

Anyway, when a non-trivial period of time does not follow this basic growth rate, people begin to ask why. Take, for example, this chart of the S&P 500 of the past 12 months:

Some features of this chart appear to resemble the 68 year chart above, except for one glaring exception: it appears upside down! A long investor sees this chart and they cry themselves to sleep :0 . In this chart the growth rate is a dismal -40%.

When this happens, investors look for people who predicted such a huge divergence from the trend. One predictor, getting such attention right now, is the famous economist Robert Shiller. In 2000, he wrote the book *Irrational Exuberance*, where he explained why he believed the stock market was overvalued. One of his main statistical weapon of choice, is called the P/E 10 (or Shiller P/E). It is a chart of price-to-earnings ratios, but earnings are averaged over the previous 10 years instead of the usual 1 year. Here is a chart from James Hamilton’s economics blog:

On average, when the market has a P/E of greater than 20, it means generally that prices will fall and/or earnings will rise. Conversely, when the P/E 10 is less than 10, it means generally that prices will rise and/or earnings will fall. The historical P/E 10 average is 16.3 (the red line in the chart), while the current P/E 10 is 14. This measure demonstrates that the market is reasonably valued.

Hindsight is 20/20, so is this chart actually predictive? Well, we’ll have to wait and see, but the idea behind it is there are times when the market is over-valued and times when it is under-valued. This seems logical, but according to the Efficient-Market Hypothesis, this will never happen because the market *defines *the value. Shiller is an economic behaviorist, and believes the market is not efficient but rather based largely on psychological factors which are not entirely logical. To me, both positions seem to make sense, and I intuitively feel (I’m sure naively) that there is common ground with these two perspectives. (My basic idea has to do with the relativity of value by individual investors and specifically their time-frame in which they must sell the equity.)

One last interesting fact about the P/E 10: it is difficult to find! You cannot go to any financial site and pull up the P/E 10 for a given index or equity. In fact the chart above was built from Shiller’s own data in Excel format which he thankfully distributes on his site!

**UPDATE**: Today, Gregory Mankiw posted this remarkable graph on his blog:

It’s hard to look at this and deny the inverse relationship between the P/E 10 and future earnings. Currently we’re smack-in-the-middle of the x-axis, and you can see how future returns along the vertical appears random. Just a few years ago we would have been on the right-side of the chart, leading to the conclusion that returns would likely decline.

Tags: Economics, Efficient-Market Hypothesis, fractals, P/E 10, Robert Shiller, S&P 500