In many ways, the recent political history of Donald Trump mirrors Alejandro G Inarritu’s 2015 film: The Revenant. In both, a man is left for dead in the wilderness, only to return with a bloody minded determination to wreak his vengeance. For the Republican frontrunner, his political savaging by Barack Obama at the 2011 White House Correspondents dinner was perhaps the metaphorical parallel of Hugh Glass’ grisly mauling by a bear in the opening act of The Revenant. It is not entirely fanciful to note that Trump the political phenomenon, like Glass in later acts, is largely the metastasis of that brief, brutal moment in time.

In another, more practical sense, The Revenant offers us an insight into the presumptive Republican nominee’s current situation. Heading into Oscar night, The Revenant had attained the air of inevitability for Best Picture that we now see in Donald Trump’s campaign for the Republican nomination. Prediction markets, driven by buyers and sellers placing money on possible outcomes, put both as strong favourites.

Indeed, as it currently stands, the distribution of probabilities for various candidates in the Republican race looks as follows ( Trump : 79%, Cruz: 13%, Kasich: 6%, Ryan: 2%). This is eerily similar to the distribution of probabilities observed for the best picture Oscar on the eve of the Academy Awards ( The Revenant : 75%, Spotlight : 14%, The Big Short : 8%, Mad Max : 1%)*

Yet, on Oscar night, The Revenant was bested in the final tally for the Oscar by Spotlight. T’he 25% probability of The Revenant losing came true.

The Predictive Power of The Market

In academic circles, the underpinnings of the power of prediction markets are best distilled into two factors. First is the concept of the “Wisdom of Crowds”. In its simplest form, this is the idea that some averaging of a large group of people’s estimates of reality is better than one person’s guess.

A reasonable example of this is that to best estimate the (unknown) number of candies in a jar, you are better off asking 100 people and averaging their guesses than just taking one random person’s guess. Without descending into technicalities, this follows from a well understood and accepted statistical result known as the central limit theorem.**

The second pillar of the power of prediction markets is the concept of ” Efficient Markets”. This is a hotly debated topic within the field of economics, but the foundation of the theory is that markets are reliable estimators of underlying fundamental probabilities.

The argument goes that if markets did not accurately represent the underlying fundamentals, then someone smart would take advantage of this inefficiency and put money to work betting against the ” mispriced” market. The very act of their doing so would then drive the market back to efficient equilibrium.

Think of an example where the market was pricing it 75% likely that I would beat Steph Curry in a 3 point shootout. Almost instantaneously you can imagine everyone with any money and any sense betting against me, until the market priced something more in line with reality ( a 1 % chance of me winning, say). In this way, any market mispricing cannot exist for long; markets will self correct towards efficiency.

It is a very elegant and important theory, but it is also misrepresentative of reality.

Price Becomes News

In my years on Wall Street, I have seen unending demonstrations of the inefficiencies of markets. As traders like to point out; if markets were truly efficient, George Soros and Warren Buffet would not be billionaires.

One of the frequent causes of inefficiency in markets comes from the phenomenon of herding. Herding arises when market participants observe price changes and rationalise that these changes tell them something they did not know about the underlying fundamentals. In the parlance of Wall Street, this is when “Price becomes News”.

A common example is when a company’s stock price falls and investors take it as a sign that something (they are unaware of) is wrong at that company. The price, sometimes incorrectly, is perceived to be transmitting some information to investors. Market participants observe the price falling and, thinking something is amiss, sell their shares. This drives the stock down further, whereupon investors become even more concerned and sell more shares.

Phenomena like this are very common in financial markets and can lead to violent price moves in either direction that persist for some time. The amazing thing is that, all the while, the fundamentals underlying the company may well have remained exactly the same.

Prediction Markets Are Human, All Too Human

In the 3 point shootout example from earlier, suppose some exogenous shock drives the market priced probability of my beating Steph Curry from the “rational” equilibrium of 1% to an “irrational” 25%. Perhaps a large early bettor on Steph Curry unwinds that bet, driving his odds of winning down in the market. Nothing has changed in the underlying fundamentals, but the priced odds are now wildly different.

The Efficient Markets Hypothesis says that the price should quickly return to a 1% probability of me winning, as other bettors take advantage of the mispricing and bet on Steph Curry. But instead, what if market participants see the price change as reflecting some change in the fundamentals they are unaware of?

Perhaps people start to think Steph Curry has broken his arm, or that I’m secretly Kyle Korver. This ” sentiment change” could then drive the market probability of me winning higher still, even though Steph Curry’s arm is fine and I’m not Kyle Korver. All it has taken is a change in price to make bettors re-evaluate their understanding of the fundamentals. Fundamentals which, importantly, have not changed.

The market has thus herded, as price became news and bettors followed NOT the fundamentals but what they believed the price was telling them about the fundamentals. The predictive power of the market has been broken by the human, all too human, nature of its participants.

Economists have recently started to model this sort of behaviour using a concept known as an “information cascade”. It has found traction in explaining everything from currency crises to the emergence of fads that defy purely logical explanation.*** Any trader on Wall Street will tell you that these phenomena are as real and as old as markets themselves.

Herding in Prediction Markets

Looking for inefficiencies in prediction markets (while acknowledging how powerful they can be at throwing light on the underlying probability of outcomes) means accepting the notion that they can, at times, become distorted by the human biases and foibles of their participants. Having accepted this premise, these distortions can begin to be understood and explained with nuanced analysis of how markets really work.

As history has repeatedly demonstrated; bubbles, crashes, manias and panics are inextricably part of the fabric of financial markets. It would be unreasonable to suppose the same cannot take place in prediction markets. The implication is clear and profound; conflating the market’s estimate of reality with reality itself can be a dangerous mistake.

One of the most heavily traded and popularly observed prediction markets at the moment is the market for the Republican nominee for President. Currently, it is discounting a probability of 79% that Donald Trump will win the nomination. Is this a reasonable estimate, or is something akin to what happened with the market for Best Picture going on?

As a trader, it strikes me as far too high given the multiple possible paths this process could take in coming weeks. Perhaps most importantly, as a reaction to Trump’s perceived probability of nomination going so high, the focus of a Republican Party (that clearly would rather someone else be the nominee) will only increase in intensity. That is to say, expect a lot more time, money and political capital to be expended in taking on Trump (note Mitt Romney’s appeal to Mormon voters in Utah today). Secondly, there is the possibility of a second round of voting at the GOP convention (a brokered convention), which Donald Trump is arguably likely to lose. There is also the possible path where Donald Trump leaves the Republican Party to run a Third Party candidacy, particularly if he feels that the Party’s efforts to stop him are “unfair”. ****

The hypothesis then is that something, potentially herding, may driving the price of a Trump nomination too high in prediction markets. And perhaps a similar mechanism had been at work with The Revenant in the Best Picture race.

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Market Symmetries and Rhyming Histories

The price distribution across possible outcomes is, as I mentioned, eerily similar across the two markets. Mark Twain famously opined that history does not repeat, but it often rhymes. Markets likewise sometimes display symmetry over different time periods. At root, this is because both history and markets are driven by humans, with their (all too human) capacity for repeating the past. Paul Tudor Jones famously made billions by noticing the symmetry of the stock market ahead of the 1987 crash with the market prior to the crash of 1929.

Evidence for herding is hard to isolate, given the difficulty inherent in distinguishing between changes in price based on fundamentals and those driven by price itself. However, in my years on Wall Street I have seen herding happen time and time again. Absent a deep statistical analysis (which is, for the moment, beyond the scope of this blog) the best evidence observable for the phenomenon is to, like Paul Tudor Jones, look at what is known on Wall Street as the “price action” in each market, to see if it fits the narrative of herding.

Price action is, in its simplest sense, the evolution of market prices over time. The contention would be that herding markets would exhibit a certain specific symmetry in price action.

In the case of The Revenant I believe that market participants, observing the market implied probability jump above 50% around the 15th of February in a “gap” type move, then inferred that “someone somewhere knew something”, that is to say they believed that someone with insider knowledge had placed a large bet on The Revenant. As a consequence, people piled into bets on The Revenant. This resulted in the trending market we see from the 15th of February to the start of March, where the market steadily priced it more likely that The Revenant would win. In a very real sense, people took the signal from the market, and herded, driving the price away from the underlying reality.

This parallels with the price action exhibited in the market for Republican Nominee. Again, around the 15th of February there was a clear repricing of Donald Trump’s likelihood of victory from around 50% to 70%, thereafter trending higher to 85% as market participants digested the signal that Trump had become the odds-on favourite for the nomination, and herded into bets on him. Since then we have hovered between 65% and 80%.

While it cannot be expected that prediction markets get everything right (by their very nature this is impossible), fundamental inefficiencies arising from behaviours (including herding) are likely. For Wall Street traders, spotting these types of mispricings is a fundamental part of what they do on a day to day basis.

As a trader myself, the symmetry of price action in these two seemingly unrelated markets gives me pause. I believe there is a case to be made that herding behaviour in the market for the Republican nominee is leading to a mispricing of the probability of a Trump nomination.

Those betting on The Donald at current odds would do well to heed the lesson of The Revenant.

James Bayes, in the longstanding American tradition, has chosen to blog under a pseudonym. He works on Wall Street.

* Lower probability events such as The Bridge of Spies winning Best Picture or Mitt Romney becoming the nominee coupled with rounding account for the fact that the probabilities do not sum to 100%.

**There are a lot of problems with the “Wisdom of Crowds” as applied to prediction markets, which I will touch upon in a later post, but for now let us accept that there is some broad truth to the idea.

*** Third Generation currency crisis models using Bayesian learning and sunspots are my inspiration here.

**** I will do a detailed analysis of the multiple possible paths in a coming post