Delphi Researcher: Do prediction markets work?

Original article by Benjamin Sturisky, Researcher at Delphi Digital

Original translation: Shaofaye 123, Foresight News

Prediction market structures can work. However, they rely on many different components and therefore cannot consistently provide accurate probabilities.

It is unrealistic for these systems to rely on perfect market efficiency.

In my first article on prediction markets, I provided a general overview of how prediction markets can serve as a source of truth in cloudy markets. I also listed three fallacies that prevent specific markets from reaching true probabilities. This second article attempts to delve deeper into these three fallacies: bias bias, hedging bias, and timing bias.

Market efficiency

Market efficiency is critical to the accuracy of prediction markets because without efficiency, there will be probability biases.

Here’s an example of market efficiency in its purest form:

1. Establish a market on a coin toss, with the market maker selling the coin toss at 55c odds. The market maker actually gets a 10% edge on each coin toss because he sells the 0.5 odds at 0.55. In this example, the buyer expects to lose 5 cents on each coin toss.

2. Another market maker sees the market and wants to participate. He undercuts the other seller by setting the odds at 52.5 cents. His advantage per coin toss is 5%, while the buyers expected loss per coin toss is 2.5 cents.

3. A third market maker joins in and undercuts the market with odds of 51 cents. His edge on each coin flip is 2%, while buyers expect to lose 1 cent on each flip.

The key point is that in an efficient market, profit opportunities diminish until they reach the risk premium. For a coin toss, since the outcome is highly predictable, the risk premium is very low, so the market will be very efficient (+/- ~1 basis point). However, for something like insurance where the outcome is more uncertain, the risk premium is larger (e.g., a forest fire destroying a community). This requires a larger gap between expected costs and insurance prices to ensure that the insurance company is profitable.

Bias

Without pure market efficiency, prediction markets’ forecasts will be biased (usually upward).

When people observe the market, they are biased towards outcomes that they can benefit from. This causes them to indirectly price the probability of that event happening higher than it actually is (e.g. Chelsea fans are more likely to bid on Chelsea winning the Champions League than Arsenal fans).

The problem is that in an inefficient market, no one is willing to bid Chelseas share price back to its true probability.

I also want to use a real-world example related to everyone’s favorite topic: the U.S. presidential election.

Currently, Polymarkets forecast for Trumps YES is about 57%, and the forecast for Harriss YES is about 39.5%.

How does this compare to other forecasting tools?

• Silver Bulletin: Trump (56.9%) and Harris (42.5%).

• Manifold Markets: Trump (54%) and Harris (43%).

• Metaculus: Trump (55%) and Harris (45%).

• PredictIT: Harris (51%) % Trump (50%).

Polymarket’s core user base consists of cryptocurrency users who lean towards the political right. This is evident as Polymarket places Trump’s chances of winning higher than any other prediction tool/market.

Polymarket is the world’s most liquid prediction market, with total trading volume for this election exceeding $460 million. If any market is efficient, it’s this one. But it’s not efficient by any means.

If prediction markets rely on efficiency but cannot recover to true probabilities when bias distorts the odds, should they be used as a source of probabilities?

Time deviation

Predicting market efficiency is not as simple as the coin toss scenario above. If someone wants the market to return to true probability, the advantage they gain must be worthwhile.

If a market deviates 1% upward but resolves six months later, the hedger will not be able to restore the market to true probability through arbitrage. This is because 1% in six months is equivalent to 2% per year, which is less than the risk-free rate.

The only way for a market like this to return to true probability is if someone is interested in the opposite direction.

Therefore, the market will not reflect efficiency until the bias increases or the settlement time decreases (playing the market maker and beating the risk-free rate to +EV).

Hedging Bias

Hedging distorts actual probabilities by pushing the odds higher or lower.

Here is an example of how hedging can manipulate prediction market probabilities:

1. A trader buys $1 million worth of SPY EOD call options on the morning of the FOMC meeting.

2. Traders believe that a rate cut will increase SPY, while no rate change will decrease SPY. The market is currently pricing in a 50:50 split between these two scenarios.

3. Shortly before making the decision, the trader gets cold feet and wants to reduce directional risk. He does not want to sell the SPY call option because the option is relatively illiquid (remember, this example is theoretical).

4. To address this issue, the trader buys $200,000 worth of NO in the interest rate change market, pushing the probability of a rate cut to 48/52.

5. If the market consensus is 50:50, and the forecast market is 48/52, market efficiency would require traders to buy YES stock until the market returns to 50:50. But this does not always happen.

There are many reasons why this market will not return to true 50/50 odds.

The first is the most obvious: no trader wants to take the directional risk of arbitrage markets to gain a slight advantage.

Unlike a coin toss, which can be repeated indefinitely, FOMC meetings occur only 12 times a year. This infrequency leads to a significant increase in the risk premium because each event has a significant impact.

The EV formula below shows that an investment of 48 cents is expected to return an average of 2 cents.

EV = (.5 * 1) + (.5 * 0) – .48 = 0.02

Given the infrequency of FOMC meetings, we may not find traders willing to take the directional risk of this position. Furthermore, since this market irregularity is due to a one-time hedge, it is unlikely that this particular market opportunity will present itself at the next FOMC meeting. Ignoring external market hedges/uses (these do not always exist), arbitrage this market is effectively like buying a single coin toss for 48 cents.

The second reason is theoretical and highlights information asymmetry. If prediction markets are used as the only source of truth for event probabilities, traders will likely be reluctant to arbitrage the market because they don’t know if the bidder has access to information that they don’t. They can’t know if the bidder is simply looking to hedge their SPY call options. This changes the model significantly because now traders not only need to be willing to take directional risk, but also need to bet that the 5 2c bidder has no asymmetric information.

How do I see it?

I am a big believer in prediction markets. However, it would be a mistake to view them as the only truth about probability.

They are great for information discovery - I believe prediction markets will become the go-to place to view live odds on any event. At the same time, I disagree with the idea that they are always completely accurate.

For large events, I think it is helpful to add a margin of error to the forecast to account for bias, hedging, or time-induced deviations.