Probability, Mean Reversion and Forecasting

We’re down to the Final Four in this year’s iteration of March Madness, also known as the national collegiate basketball tournament. Our earlier discussion of “The March Madness Theory of Investing didn’t sit well with some readers. The lessons we sussed out from the bracket-destroying results included home-country bias, how expert forecasts are about as good as those of nonexperts, and the impact of noise and distraction.

One issue I want to delve into further is why predicting the future seems to be so hard, if not impossible. That particular “lesson” caused quite a bit of pushback.

There were many good responses, but Cullen Roche of Pragmatic Capitalism made perhaps the most interesting observation. In a blog post he wrote:

(P)redicting the future is actually pretty easy in a macro sense. For instance, anyone with a sound understanding of macroeconomics and the capital structure knows, with a very high probability, that stocks will tend to become more valuable over long periods of time because stocks reflect the value of some portion of our overall output.

 I don’t see this so much as a factual disagreement as simply defining epistemological elements differently.

At the risk of repeating myself, let’s define just what a prediction is:

At the risk of repeating myself, let’s define just what a prediction is: It contains three key elements — a forecast of a future event, specific in time and numerical value. A few examples include: The Dow Jones Industrial Average will reach 21,500 by March 2017; the University of Kansas will make the Final Four this year; the yield on the 10-year bond will be 1 percent by the end of next year; and the Apple Watch will sell 10 million units in its first two quarters.

All of the above are actual forecasts made by various people. I like this simple-to-remember template for determining whether something fits the definition of a prediction: What, when and how much. In investing terms, that takes the form of asset class, price and date. Perhaps most important of all, this definition means that every forecast can be proven at some point to be either right or wrong.

Indeed, being disprovable is a key component of a prediction. Merely stating an observation which can’t be either proven or disproven isn’t forecasting; rather, it is a form of rhetoric.

A sentence such as “Wait until next year” isn’t a forecast so much as it is an expression of hope. Even though that statement eventuallyproved to be of cheer to Boston Red Sox fans, Chicago Cubs fans have been futilely waiting until next year to win a World Series for more than a century. At this point, saying the Cubs won’t win looks less like a prediction and more like a restatement of historical facts. But it is indeed a prediction — because it will be either right or wrong by the end of next season.

There are two related variations on this theme that require a few words: Mean Reversion and Probability. These are decidedly not predictions, and it is more accurate to declare them members of the mathematical family of simple statistics.

Let’s take a close look at both, and see why they don’t fall into the prediction camp.

Mean reversion is simply the expectation that longstanding historical relationships between different quantifiable elements will eventually reassert themselves. It helps if there is an established causal interrelationship. For example, the ratio of median home prices to median incomes has moved historically within a fairly narrow band. When that ratio shifted several standard deviations away from the norm in the mid-2000s, it was reasonable to assume that somethingwas going to drive them back toward the historic average. After all, home buyers who use a mortgage need to earn enough to make payments on that mortgage. This meant that home prices were going to fall, incomes were going to rise, or there would be some combination of the two.

Similarly, there has been a longstanding relationship between future returns and equity valuations. Mean reversion suggests that when price-to-earnings ratios for stocks are high, either expected returns will be below average or corporate earnings will accelerate.

Note that probability is often an assessment of mean reversions. How likely is it that home prices were going to drop in 2006? How likely is it that U.S. stock returns will be above average? (Note: Don’t confusepossible with probable).

It is a challenge to make observations about probability, but many people seemingly do it with some degree of both accuracy and consistency. Now compare that with the random outcomes we see in the sphere of predictions. They are worlds apart!



Originally published as: March Madness and the Perils of Predicting




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  1. faulkner commented on Mar 30

    In addition to defining differences in forecasting elements, your description suggests different families. Predictions belong to narrative ‘why’, while mean reversion and probability belong to descriptive ‘how’.

    Narrative ‘whys’ have endings with what, when, and how much. (Winning the girl, game, prediction by the end of the movie, season, fiscal year = happy ending. Losing the girl, game, prediction = tragedy.)

    Descriptive ‘hows’ have prescribed relationships among the elements: i.e. an equation or formula. Giving up narrative ‘whys’ in favor of descriptive ‘hows’ is the beginning of scientific thinking. It is also a higher developmental level of thinking than narrative ‘whys’ and so much harder to do with few doing so.

  2. wally commented on Mar 30

    Past performance is no guarantee of future results.

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