TLDR: Prediction markets rely on efficiency, but efficiency is not guaranteed.

Prediction market structures can work. However, they rely on so many different components being in place that they do not consistently create accurate probability.

The systems rely on complete market efficiency, which is not realistic.

In my first piece on prediction markets, I broadly covered how prediction markets can act as a source of truth in a dark cloud. I also listed three fallacies that prevent specific markets from reaching true probability. This second article attempts to go in-depth on those three fallacies: skew from bias, hedging, and time.

Market efficiency

Market efficiency is integral to the accuracy of prediction markets because, without efficiency, probability skews exist.

This is an example of market efficiency in the purest form:

A market is set up on a coin flip, with the market maker selling flips at 55c. The market-maker effectively receives a 10% edge for each flip because he is selling .5 odds at .55. In this example, the buyer expects to lose 5c per coin flip.

Another market maker sees the market and wants to participate. He undercuts the other seller and sets the odds at 52.5c. His edge on each flip is 5%, and the buyer is expecting to lose 2.5c per coin flip.

A third market maker comes in and undercuts by setting odds at 51c. His edge on each flip is 2%, and the buyer is expecting to lose 1c per coin flip.

The point is that in an efficient market, profitable opportunities will be reduced until the risk premium is reached. For a coin flip, that risk premium is very low because of a highly predictable outcome, and thus, the market will be very efficient (+/- ~1 basis point). However, risk premiums are more significant for something like insurance because of higher outcome uncertainty (e.g., a forest fire destroying a neighborhood). This requires a more significant gap between the expected cost and the insurance price to ensure insurance providers remain profitable.

Skew from Bias

Without pure market efficiency, prediction markets' predictions' can be skewed (typically upwards).

When individuals look at a market, they are biased towards outcomes they benefit from. This leads to them indirectly pricing the probability of that event occurring higher than the real probability (e.g., a Chelsea fan is more likely to bid shares of Chelsea winning the Champions League than an Arsenal fan).

The issue is that in an inefficient market, no one is willing to bid shares of Chelsea NO back to the 'true' probability.

I also want to use a real-world example relating to everyone's favorite topic: the United States Presidential Election.

Currently, Polymarket is pricing Trump YES at ~57% and Kamala YES at ~39.5%.

How does this compare to other forecasting tools?

Silver Bulletin: Trump (56.9%) & Harris (42.5%).

Manifold Markets: Trump (54%) & Harris (43)%.

Metaculus: Trump (55%) & Harris (45%).

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

Polymarket's core user base consists of crypto users who lean right on the political spectrum. This is evident as Polymarket is pricing Trump's probability higher than any other primary forecasting tool/market.

Polymarket is the most liquid prediction market in the world, and this election has surpassed $460M in total volume. If there was any market that was going to be efficient, it would have been this one. Yet it's not efficient by any means.

If prediction markets rely on efficiency but cannot revert to true probability when bias skews the odds, should they be used as probability sources?

Skew from Time

Prediction market efficiency is not as simple as the coin flip scenario above. If someone wants to revert a market back to true probability, the edge they capture must be worthwhile.

If a market is skewed 1% upwards but resolves in six months, it will not be arbitraged back to true probability by someone interested in capturing the edge. This is because 1% in six months is 2% annually, which is lower than the risk-free rate.

The only way a market like this could be reverted back to true probability is if someone is interested in taking a directional position on the opposite side.

Therefore, the market will not reflect efficiency until the skew grows or the time until resolution decreases (where it is +EV to play market-maker and beat the risk-free rate).

Skew from Hedging

Hedging distorts actual probability by pushing odds above or below the true probability of an event occurring.

The following is a clear example of how hedging manipulates prediction market probability:

A trader purchases $1M of SPY EOD calls on the morning of the FOMC.

The trader believes a rate cut will increase the SPY, and no rate change will lower the SPY. The market is currently pricing odds at 50:50.

Shortly before the decision, the trader gets cold feet and wants to reduce his directional risk. He doesn't want to sell the SPY calls because the book is relatively illiquid (remember, the example is theoretical).

To solve this, the trader purchases $200k worth of NO on the rate change market, pushing the probability of a rate cut change to 48/52.

If the market consensus is 50:50, and the prediction market is at 48/52, market efficiency would call for traders to purchase YES shares until the market reverts to 50:50. That does not always happen.

There are numerous reasons why this market would not revert back to the real probability of 50/50.

The first is the most obvious: no trader might be willing to take on the directional risk of arbitraging the market to capture a slight edge.

Unlike a coin flip, which can be repeated infinitely, the FOMC only occurs 12 times a year. This infrequency results in a significantly higher risk premium because each event carries significant weight.

The EV formula below shows a 48c investment expects to return 2c, on average.

EV = (.5 * 1) + (.5 * 0) - .48 = 0.02

Given the infrequency of FOMC meetings, we likely won't find a trader willing to take on the directional risk of this position. Additionally, it is unlikely this specific market opportunity will present itself at the next FOMC meeting, as this market irregularity was due to a one-off hedge.

Disregarding external markets to hedge/use (these do not always exist), arbitraging this market is effectively the same as purchasing a singular coin flip at 48c.

The second reason is theoretical and highlights information asymmetry. If prediction markets are used as the sole source of truth for event probability, it is likely traders would be unwilling to arbitrage the market because they are unaware if the bidder has access to information that they do not. They have no way of knowing that the bidder just wishes to hedge their SPY calls. That changes the model significantly because now a trader needs to be willing to take on the directional risk while simultaneously betting that the bidder at 52c has no asymmetric information.

What do I think?

I am a fairly big believer in prediction markets. However, relying on them as the sole truth of probability is a mistake.

They are fantastic at information discovery—I am confident prediction markets will be the “go-to” place to view real-time odds on any event. At the same time, I disagree with the notion that their predictions are always completely accurate.

On large-scale events, I think adding a margin of error to their predictions is beneficial to account for skew from bias, hedging, or time until resolution.

TLDR: Prediction markets rely on efficiency, but efficiency is not guaranteed.Prediction market structures

canwork. However, they rely on so many different components being in place that theydo notconsistently create accurate probability.The systems rely on complete market efficiency, which is not realistic.

In my first piece on prediction markets, I broadly covered how prediction markets can act as a source of truth in a dark cloud. I also listed three fallacies that prevent specific markets from reaching true probability. This second article attempts to go in-depth on those three fallacies:

skew from bias, hedging, and time.## Market efficiency

Market efficiency is integral to the accuracy of prediction markets because, without efficiency, probability skews exist.

This is an example of market efficiency in the purest form:

The point is that in an efficient market, profitable opportunities will be reduced until the risk premium is reached. For a coin flip, that risk premium is very low because of a highly predictable outcome, and thus, the market will be very efficient (+/- ~1 basis point). However, risk premiums are more significant for something like insurance because of higher outcome uncertainty (e.g., a forest fire destroying a neighborhood). This requires a more significant gap between the expected cost and the insurance price to ensure insurance providers remain profitable.

## Skew from Bias

Without pure market efficiency, prediction markets' predictions' can be skewed (typically upwards).

When individuals look at a market, they are biased towards outcomes they benefit from. This leads to them indirectly pricing the probability of that event occurring higher than the real probability (e.g., a Chelsea fan is more likely to bid shares of Chelsea winning the Champions League than an Arsenal fan).

The issue is that in an inefficient market, no one is willing to bid shares of Chelsea NO back to the 'true' probability.

I also want to use a real-world example relating to everyone's favorite topic: the United States Presidential Election.

Currently, Polymarket is pricing Trump YES at ~57% and Kamala YES at ~39.5%.

How does this compare to other forecasting tools?

Polymarket's core user base consists of crypto users who lean right on the political spectrum. This is evident as Polymarket is pricing Trump's probability higher than any other primary forecasting tool/market.

Polymarket is the most liquid prediction market in the world, and this election has surpassed $460M in total volume. If there was any market that was going to be efficient, it would have been this one. Yet it's not efficient by any means.

If prediction markets rely on efficiency but cannot revert to true probability when bias skews the odds, should they be used as probability sources?

## Skew from Time

Prediction market efficiency is not as simple as the coin flip scenario above. If someone wants to revert a market back to true probability, the edge they capture must be worthwhile.

If a market is skewed 1% upwards but resolves in six months, it will not be arbitraged back to true probability by someone interested in capturing the edge. This is because 1% in six months is 2% annually, which is lower than the risk-free rate.

The only way a market like this could be reverted back to true probability is if someone is interested in taking a directional position on the opposite side.

Therefore, the market will not reflect efficiency until the skew grows or the time until resolution decreases (where it is +EV to play market-maker and beat the risk-free rate).

## Skew from Hedging

Hedging distorts actual probability by pushing odds above or below the true probability of an event occurring.

The following is a clear example of how hedging manipulates prediction market probability:

There are numerous reasons why this market would not revert back to the real probability of 50/50.

The first is the most obvious: no trader might be willing to take on the directional risk of arbitraging the market to capture a slight edge.

Unlike a coin flip, which can be repeated infinitely, the FOMC only occurs 12 times a year. This infrequency results in a significantly higher risk premium because each event carries significant weight.

The EV formula below shows a 48c investment expects to return 2c, on average.

EV = (.5 * 1) + (.5 * 0) - .48 = 0.02Given the infrequency of FOMC meetings, we likely won't find a trader willing to take on the directional risk of this position. Additionally, it is unlikely this specific market opportunity will present itself at the next FOMC meeting, as this market irregularity was due to a one-off hedge.

Disregarding external markets to hedge/use (these do not always exist), arbitraging this market is effectively the same as purchasing a singular coin flip at 48c.

The second reason is theoretical and highlights information asymmetry. If prediction markets are used as the sole source of truth for event probability, it is likely traders would be unwilling to arbitrage the market because they are unaware if the bidder has access to information that they do not. They have no way of knowing that the bidder just wishes to hedge their SPY calls. That changes the model significantly because now a trader needs to be willing to take on the directional risk while simultaneously betting that the bidder at 52c has no asymmetric information.

## What do I think?

I am a fairly big believer in prediction markets. However, relying on them as the sole truth of probability is a mistake.

They are fantastic at information discovery—I am confident prediction markets will be the “go-to” place to view real-time odds on any event. At the same time, I disagree with the notion that their predictions are always completely accurate.

On large-scale events, I think adding a margin of error to their predictions is beneficial to account for skew from bias, hedging, or time until resolution.