Prediction Market Arbitrage: Real Edges, Fake Edges and the Cost of Capital

Arbitrage in prediction markets is buying a set of claims that pays $1 for less than $1, or selling a set that pays $1 for more than $1, with no residual view on the event. On Polymarket the clean cases are binary complete sets, negative-risk conversions in multi-outcome events, and logical relationships across markets. The hard part is not finding a screen that shows a gap. It is proving the gap survives fees, depth, resolution rules and the time your capital is locked.

The academic record says real money has been extracted. A 2025 study of Polymarket order-book data estimated about $40 million of realized arbitrage profit across two families of trades. That is also the warning. A visible gap is usually being competed away by someone with faster data and cheaper capital.

Binary complete sets

Every binary market has Yes and No tokens. A complete set is backed by $1: 100 Yes plus 100 No can be merged into 100 pUSD. If you can buy both sides for less than $1, you can merge and lock the difference. If Yes asks $0.96 and No asks $0.03, 100 of each costs $99, merges into $100, and the gross profit is $1.

Gross is not net. The politics taker rate is 0.04. The Yes fee is 100 × 0.04 × 0.96 × 0.04 = $0.1536. The No fee is 100 × 0.04 × 0.03 × 0.97 = $0.1164. Total fees are $0.27, so the net profit is $0.73 on $99.27, or 0.735%. If the market resolves in 30 days, that is about 9.3% annualized. At 90 days it is about 3.0%. The trade is a money-market substitute with resolution risk attached, not a free lunch.

Quoted prices are midpoints. Polymarket's documentation says the displayed price is the midpoint of the bid-ask spread unless the spread is wider than $0.10, in which case the last traded price is shown. You pay the ask and receive the bid. An apparent gap between midpoints can disappear at the touch.

Negative risk and the event-level set

In a negative-risk event only one outcome can win, and 1 No share in one market converts atomically into 1 Yes share in every other market. The complete set still costs $1, but the relationship now spans the event. If the Yes prices for three mutually exclusive outcomes sum to $0.97, buying all three for $0.97 returns $1 at resolution: 3.09% gross before fees. If they sum to $1.06, the mirror trade is to buy all three No sides for $1.94, which pays $2 because exactly two No positions win. That is also 3.09% gross, on more capital.

Fees hit both versions. Take a three-way sports event at the 0.05 rate, with Yes prices of 0.62, 0.26 and 0.09. The fee per set is 0.05 × (0.62×0.38 + 0.26×0.74 + 0.09×0.91) = 0.0255, or 2.55 cents. The 3.09% gross becomes about 0.45% net. That is less than half a cent per set. Slippage of one tick can erase it.

Augmented negative risk adds a trap. New outcomes can appear after trading starts, with named outcomes, placeholders and an explicit Other. Polymarket's documentation warns traders to trade only named outcomes and says the definition of Other can change as placeholders are clarified. An arbitrage model that treats an unnamed placeholder as a fixed contract can be exactly wrong.

Cross-market and logical relationships

Cross-venue arbitrage is the same complete-set idea with two rulebooks. Suppose Polymarket Yes asks $0.58 and Kalshi No asks $0.39 on what is genuinely the same question and deadline. Buying 1,000 of each costs $970. Polymarket's politics fee is 1,000 × 0.04 × 0.58 × 0.42 = $9.74. Kalshi's general taker fee is 0.07 × contracts × price × (1 − price), so 1,000 × 0.07 × 0.39 × 0.61 = $16.65. All-in cost is $996.39. The pair pays $1,000. Net profit is $3.61, or 0.36%.

If the question resolves in 45 days, that is about 3.0% annualized. At 10 days it is about 14%. The resolution date is part of the price. So is the possibility that one venue pays early and the other pays late, leaving half the capital idle.

Logical relationships are the third family. If winning the championship implies winning the conference, the championship contract cannot rationally trade above the conference contract. The trade is to buy the conference Yes and buy the championship No. If the implication holds exactly, the pair pays at least $1 in every state. The catch is the word exactly. A rule that treats a vacated title, a mid-season trade or a postponed final differently can break the implication.

Why apparent arbitrage is often fake

Fees change the sign. Polymarket's fee is C × rate × p × (1 − p), and Kalshi's is 0.07 × C × p × (1 − p). Both peak in dollar terms at 50 cents. A three-cent gap at 50 cents is not a three-percent edge after two taker fees.

Depth is not the same as price. The top of the book may hold 100 shares. A 10,000-share order walks the book and turns a profit into a loss. The size that clears at the advertised price is the only size that matters.

Leg risk is real. One leg fills and the other does not. You are left with a naked position, possibly after the price has moved. On a cross-venue trade, the second venue may reject the order, move the quote or halt the market.

Similar titles hide different rules. Two markets can share a headline and disagree on the source, the deadline or the edge cases. "Win the election" and "be inaugurated" are not complements. A market that resolves on the official league result and one that resolves on a broadcaster's box score are not complements either.

Capital has a cost. A 0.4% return over 60 days is about 2.4% annualized, before transfer costs. If the capital could earn more in cash or in a simpler trade, the arbitrage is negative in opportunity-cost terms even when the arithmetic is positive.

Platform and transfer risk are costs. Moving funds between venues, chain settlement, withdrawal limits and counterparty risk all belong in the calculation. A cross-venue trade is a bet on two operators, two rulebooks and two payment rails, not just on the event.

What the research shows

The 2025 paper by Saguillo, Ghafouri, Kiffer and Suarez-Tangil used on-chain historical order-book data and found two forms: market rebalancing arbitrage within a market or condition, and combinatorial arbitrage across markets. Their realized estimate was about $40 million of profit extracted. That is a retrospective estimate, not a claim that $40 million is sitting on the screen today. It is evidence that arbitrage exists and that it gets taken.

The practical implication is uncomfortable. Arbitrage is a service business: you supply liquidity, hold basis risk and get paid a spread. Returns compress as more capital arrives. The traders who persist usually have an execution advantage, a cheaper cost of capital, or a better model of the resolution rules. A retail trader with a browser and a spreadsheet is in the third category at best.

A final checklist:

1. Read both rulebooks, including the edge cases.
2. Compute the all-in cost at the size you can actually fill, not the top-of-book size.
3. Annualize the return over the expected lockup.
4. Check leg risk: can you hold one leg if the other fails?
5. Use executable asks and bids, never midpoints.
6. Stress the resolution: what if one market voids or resolves 50/50?
7. Treat platform and transfer risk as real costs.

Arbitrage is not a secret price. It is a set of claims that survives costs. If the edge is still positive after all seven checks, it is a trade. If it is positive only before fees, it is a screenshot.