So, for example, let's say I formulate the hypothesis that when the stock market is above a Shiller P/E of 23x and counter-cyclical stocks are making new one year highs, the stock market is highly sensitive to a correction. The first thing I would do is formulate a null hypothesis--that the relationship laid out in my original hypothesis is not true. And then I would test whether I could prove the null hypothesis, which if I could, would be grounds to reject my original hypothesis. I have to be careful though because accepting a null hypothesis that turns out to be false is classic statistical error--a Type 2 error.
In the chart below is a plot of the MSCI World Index with blue bars representing periods where the Shiller P/E was over 23x and counter-cyclical stocks were at one year new highs. Over the last seven years, there are five clusters (some bigger than others) where these conditions have prevailed. In each period, stocks were lower 1-3 months after the condition ended. There were no periods where the null hypothesis was validated, meaning there were no Type 2 errors committed using this methodology over the last seven years.
The current cluster ended on June 5, 2014, so we are still within the window where the hypothesis is being tested. Based on the history of this valuation/leadership indicator, we are very skeptical that we are making a Type 2 error by rejecting a null hypothesis that turns out to be true. In other words, recent history would suggest that we accept the basic hypothesis that when the stock market is over 23x using a Shiller P/E and counter-cyclicals have recently made a new one year high, a correction is possible.
