## Summary

- Simple mathematical model predicted over 50 years of index returns with R^2 of 0.91.
- Simple models with excellent fits make a compelling argument that they are meaningful.
- Applying the model to current data allows extrapolations of future movements in the Dow.

Predicting the ups and downs of the stock market is considered by some to be the holy grail of trading. Many think that it is impossible to time to market to any extent on a consistent basis. However, others still try to predict future market movements by various means.

Thanks to a recent SA article by Jeff Miller, I was recently exposed to a simple mathematical model, which predicts the 10-year total return on equities to a very high degree of accuracy. As Jeff alluded to in his article, exceptionally good fits from a *simple* mathematical model are incredibly compelling, as compared to a *complex* model. Why are simple models more interesting?

It turns out that when you have a very complex model with lots and lots of parameters, with the appropriate parameter values, it can fit ANY data set. So, for example, someone might construct a model to predict the 10-year return of stock prices that had 5 adjustable parameters in it, and 5 fixed parameters (reported economic numbers of some kind, perhaps) and build a search algorithm to choose the parameter values that would make the best fit. This is the sort of approach that Ivan Kitov takes in his Seeking Alpha articles - he uses the reported values of a variety of economic indices, plus plenty of adjustable parameters, to create models to predict the future direction of stock prices. Unfortunately, these models often fail to predict what will happen with any degree of accuracy. The fundamental reason for this is that any mathematical model with lots and lots of parameters is very flexible, and can fit any data set. But this fitting does not mean that the fit is meaningful, or that it will continue to hold - and this is why this sort of approach to prediction very often fails.

In contrast, if one discovers a very simple model that is able to fit a complicated data set very well, there is a very good chance that the fits it creates are meaningful and predictive. This is because it is very hard to randomly make a good fit to a complicated data set with not very many parameters. If a simple model is able to fit a complicated data set without many parameters, that in and of itself is a very convincing argument that it is highly meaningful - and it is more likely to be meaningful and hold true into the future the fewer parameters that are used.

That was why I was absolutely blown out of the water when I read Jeff's recent article. He presented the work of The Philosophical Economist, which showed that the 10-year total return of the stock market could be described over a 50-year period by a TWO parameter model - with an R^2 correlation coefficient of an astoundingly high 0.913! The meaningful parameters in question are 1) The price of a market index at time *t*, and 2) the total % of capital invested in equities out of a total at any given time *t*.

## FIG 1.

I immediately realized that, since this model predicted the 10-year return, I could easily use it to extrapolate the price action of the DIA 10 years into the future. All I have done to generate the chart of projected DJIA price below is to take the price index at a given time point, back out a dividend yield (I assumed 1.8%), and multiply by the compounded 10-year return that is projected by the above model for every given time point. So for example, the market level and investor equity allocation in summer 2005 predicts the market level in summer 2015, and so on. Shockingly, this simple model predicts in essence that we are just now entering a very long ascending triangle chart pattern, which will finally break out to the upside in 2018. I find this sort of long-term chart pattern quite interesting, since the Dow also broke out of a multi-year rising wedge pattern that I identified in 2012 in early 2013 to the upside. Of course, I was quite wrong about the direction it would break, but that is because I did not understand the predictive power of simple models back then. Nor was I aware of this model then. We live and learn.

## FIG 2.

The 2-parameter model thus can be used to make very specific price level predictions for the future. The very high correlation coefficient of 0.913 over the past 50 years for this model with market returns, combined with the exceeding simplicity of the model, argues strongly that it will continue to be valid in the future. The model argues that the markets have essentially topped out for now, and will not exceed these levels for any length of time by any appreciable amount until 2018. However, the model argues that the corrections that come will be relatively shallow, with the lowest point on the Dow over the next 10 years coming later this year, and probably not reaching below Dow 10,000 at any time.

You can download the data used to build this model and make future price projections from the St. Louis Fed yourself, and play with it. I expect you will come to similar conclusions as I have. However, while the model in question is simple and the fit is excellent, it strains credulity that it has to necessarily hold true no matter what. For example, a widespread nuclear war would surely completely destroy the market value of equities (in an extreme example, if there are no people left, then no equity has any bid and there is no return). I suppose you have to believe that "this time isn't different" to accept the predictive power of this simple model for the broad value of equities. And the model says there is some near-term hope for the bears, but that the markets will frustrate bear and bull alike for the next 4 years before finally making bulls happy by breaking out hard to the upside. Only time will tell if this comes to pass, but the simplicity and fit quality of this model makes as compelling an argument as any to augur the course of future price swings in the market.

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