"For bubbles, I want a systematic way of identifying them. In my view It is a simple proposition. You have to be able to predict that there is some ending to it. All the test people have done trying to do that they can't do it. So statistically people have not come up with ways of identifying bubbles. I think that there is a lot of identification of bubbles based on 20/20 hindsight and it very easy to do with that situation".
The following charts are based on Professor Robert J. Shiller's online data base. While Professor Shiller uses a 10-year moving average of inflation adjusted S&P 500 composite earnings to calculate the S&P 500 price earnings ratio, I recommend using the exponential regression of inflation adjusted S&P 500 composite earnings and the inflation adjusted earnings from Cowles and Associates (Common Stock Indexes) for the last 138 years to calculate the S&P 500 P/E (i.e. an exponential P/E).
A 10-year moving average of earnings was used by Benjamin Graham when calculating the P/E ratio for individual companies. While a 10-year moving average can do a good job smoothing out a company's short-term earnings fluctuations it may not be up to the task when dealing with abnormally elevated or depressed S&P 500 profit margins over extended periods of time.
While the vast majority of investors find the scenario of a S&P 500 P/E of 10 extremely unlikely (no matter what earnings measurement one uses), I believe that if a given outcome is possible, even if highly improbable, it must be taken into account. Please keep in mind that given high inflation, the S&P 500 does not need to fall to 499 to hit an exponential P/E of 10 (based on July 3, 2009 exponential earnings of $49.99). A rise in the inflation adjusted exponential earnings trend line could push an S&P 500 exponential P/E low of 10 to an S&P 500 value of 600, 700 or more.
Since it is rather hard to see the current S&P 500 value and exponential P/E values on the 1871 - 2015 charts I am including charts for 1982 - 2015.