Unexpectedly Intriguing!
May 22, 2014

Now that we've discussed what "reverting to the mean" means for stock prices, let's peer into the future to see when that will likely happen for the S&P 500.

To do that, we're building upon our original observations of the relationship between changes in the growth rate of stock prices and changes in the growth rate of dividends per share.

Here, we discovered that by applying a simple amplification factor and by shifting the data for dividends backward in time, we could pretty closely match the change in the growth rate of stock prices at given points in time with the change in the growth rate of dividends per share at later date.

What that indicates is that investors are looking forward to specific points of time in the future as they set stock prices in the current day. And if you know what investors expect for the future for dividends, you can then forecast with a decent amount of accuracy how stock prices will change over time.

The challenge in doing that is determining which point of time in the future they have focused their attention upon in setting stock prices. Thanks to dividend futures data, we know what dividends are expected to be at specific points of time in the future, but can only identify which point in time that might be by observation.

Let's do that now. Starting with our power law statistical equilibrium chart, which shows the daily closing value of the S&P 500 against its underlying trailing year dividends per share (with the daily data interpolated between quarters):

Power Law Equilibrium Chart with Daily S&P 500 Prices vs Trailing Year Dividends Per Share, 2011-06-30 through 2014-05-16

Let's focus just on 2014 and superimpose what stock prices are projected to be for a given investor forward-looking focus on the dividends expected to be earned in each of the next four future quarters, from 2014-Q2 through 2015-Q1:

Alternate Futures Superimposed on Power Law Equilibrium Chart with Daily S&P 500 Prices vs Trailing Year Dividends Per Share, 2014-01-02 through 2014-05-16

In this chart, you can see how stock prices have closely paralleled the projected stock prices for the various points of time in the future that investors have focused upon since the beginning of the year. More importantly, you can also see how stock prices have shifted to follow the trajectory for the future focused upon by investors whenever they have shifted their attention from one point in the future to another.

Looking forward through the end of 2014-Q2, we see that regardless of which future investors choose to focus upon, stock prices should fall below the mean trajectory of their established long term trend in the very near future.

That's the when for mean reversion, at least according to the math that describes how stock prices work. We should also note that there are times when stock prices deviate from these defined trajectories, which we typically describe as noise events when they occur. Subsequent event studies of the data during these times suggests that these are periods in which investors are splitting their forward-looking focus between two or more points of time in the future as they set current day stock prices.

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