In 2008, Nate Silver accurately forecasted the outcome of the presidential election as well as which way 49 out of 50 states would vote. In 2012, he again correctly forecasted the winning presidential candidate and went a perfect 50 for 50 at the state level. That same year, he published the book The Signal and The Noise: Why So Many Predictions Fail-but Some Don’t. In his book, Silver lays out a framework for thinking about forecasting that should place the book on the required reading list for any serious investor.

Investors are challenged every day to make forecasts. Many value investors are fond of saying they don’t make forecasts, but since the value of a stock is the net present value of future cash flows, all investments are predicated on an implicit or explicit forecast of the future.

Silver’s book has two key messages for investors:

• Make probabilistic forecasts, not yes/no predictions. A smart forecaster will attempt to determine the odds that company sells at least X widgets over the next five years. The foolhardy predictor will attempt to guess the number of widgets the company will sell in a given year. Silver argues that the world is not predictable, but it is forecastable. You can place reasonable odds on various outcomes and make decisions accordingly.
• Ground your forecasting in Bayes Theorem, which essentially offers a framework for adjusting forecasts based on new information. One of the core insights of Bayes is that incremental information often only slightly changes the pre-existing odds, despite the fact that most investors react to each new data point as if it is all that matters while throwing out the collective weight of previously collected data.

The first point suggests that investors should not decide to own an oil stock depending on if they believe oil will trade above $50 in 2017, but rather should think about the probability of various oil prices and buy an oil stock when the valuation of the company embeds an excessively high probability of a persistently low oil price. While this sort of thinking is more complicated and won’t get you on financial news shows where high conviction predictions about the future are the currency of the realm, we believe it is likely to result in a more humble approach to investing that delivers stronger long-term returns.

The second point is more complicated due to the need for a working understanding of a statistical theorem. To better understand the logic behind Bayes Theorem so we can implement Silver’s forecasting framework when we approach investing, we turn to Sanjay Bakshi, an Indian business professor and investor whose essays on investing are some of the best contemporary writing in the field (you can learn more about Bakshi in this transcript from an interview he did with Shane Parrish’s Farnam Street blog).

In an essay titled Worldly Wisdom in an Equation, Bakshi explores the implication of Bayes Theorem for investors and adapts a story told by Riccardo Rebonato in his book Plight of the Fortune Tellers:

A Martian has just landed on earth, a planet he has never visited before. In particular, he has never seen a coin, let alone flipped one. The Martian has landed next to you.

Not knowing how to strike up polite conversation, you take a coin out of your pocket. This is any old regular coin. You toss the coin four times. Both you and your Martian friend record the outcomes of the four coin tosses. All four tosses happen to yield heads.

What do you conclude about the fairness of the coin? What is the Martian likely to conclude? Let’s start with you.

If you’re at all like me, you would view the occurrence of four consecutive heads as only very mildly odd. Would you draw any strong conclusions about the biasedness of the coin from this outcome? Personally, I would not. I may have a small niggling doubt that might prompt me to toss the coin a few more times just to check. But, if I were forced to bet on the next outcome on the basis of the available evidence, I would be likely to require odds of fifty-fifty for heads or tails.

Things look very different to our Martian friend. He has never seen a coin. He does not even know that coins are for buying goods. For all he knows, and judging from his four observations, they could just as well be devices that earthlings have invented to produce heads after a toss. He cannot be sure of this, of course, but in his mind the possibility that heads are much more likely than tails is very real. If forced to bet on the outcome of the fifth coin toss, he will not accept fifty-fifty odds. For him heads is much more likely than tails.

You and your Martian friend have observed the same experiment, yet you reach very different conclusions. How can that be?

The answer to that profound question lies in the fact that we almost never approach anything without having some prior beliefs.

New evidence should modify our prior beliefs and transforms them into our posterior beliefs. The stronger the prior belief, the more difficult it will be to change it. If we really and truly have no prior beliefs about the situation at hand, as was the case with the Martian, then and only then will we be totally guided by the new evidence.

Preconceived notions. That term normally has a negative connotation but for our purposes that shouldn’t be the case. Is having preconceived notions a bad idea? Clearly, the above example shows that having pre-conceived notions — the correct ones of course — gives you an advantage over the Martian.

Bakshi goes on to explain the mechanics behind using Bayes Theorem, a form of conditional probability, to update your forecasts based on new evidence. Too many investors mistakenly act like the martian when they seek to make investing forecasts. In 2009, while current economic conditions were horrendous, the new evidence being presented about the state of the economy should not have caused an investor to ignore the substantial historical evidence that the US economy had a high probability of eventually reversing any cyclical downturn. Likewise, in 1999, investors who expected earnings multiples that were far in excess of historical averages to persist forever were ignoring the past evidence that market level earnings multiples are highly mean-reverting and not prone to persisting at levels far in excess or below the long-term average for extended periods of time.

What Bayes Theorem shows, an insight that Silver has exploited to become the most well-regarded political forecaster of the day, is that new evidence should always cause us to revise our prior expectations, but when we have strong historical evidence that is contradicted by new evidence, we should allow the new evidence to only modestly change our expectations. In the political lingo of Silver’s industry, “game changers” are far rarer than most forecasters believe.

When we talk about investing in “moaty” businesses that exhibit significant competitive advantages, what we’re looking for are companies that are relatively resistant to new evidence that might derail their historical ability to generate strong results. Most companies on the other hand do not exhibit traits which suggest their historical results will be resilient and instead are effectively adrift on the competitive winds of change with each new development sharply impacting their outlook.

In our next post, we’ll explore strong historical evidence that can help guide investors in a very practical manner in making forecasts about future growth. We believe that investors systematically misprice stocks due to their tendency to overweight the newest information about a company’s growth characteristics while ignoring substantial historical evidence about the rate at which companies grow.

Note: Readers intrigued by Nate Silver’s political forecasting can follow his forecasts for the 2016 election here.

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