Chapter 16: Key Takeaways

1. Arbitrage Is the Exploitation of Price Inconsistency

Arbitrage in prediction markets exploits situations where prices violate mathematical constraints that must hold. The fundamental no-arbitrage condition for a binary market is $P(\text{YES}) + P(\text{NO}) = 1.00$. For a multi-outcome market with $n$ mutually exclusive and exhaustive outcomes: $\sum_{i=1}^{n} P_i = 1.00$. Any deviation from these conditions, after accounting for fees, represents a potential profit opportunity.

2. True Arbitrage vs. Quasi-Arbitrage Is a Critical Distinction

True arbitrage guarantees profit in every possible outcome with zero risk. Quasi-arbitrage is statistically likely to profit but has scenarios where losses occur. Most prediction market "arbitrage" falls in the quasi-arbitrage category, because of resolution risk (platforms may resolve differently), execution risk (legs may not fill simultaneously), and settlement risk. Always classify an opportunity honestly before sizing your position.

3. Fees Determine Whether an Opportunity Is Real

The raw price discrepancy is meaningless without fee adjustment. The formula for fee-adjusted cross-platform arbitrage profit is:

$$\pi_{\text{guaranteed}} = \min\bigl(\pi_{\text{YES wins}},\; \pi_{\text{NO wins}}\bigr)$$

where each scenario accounts for trading fees, per-contract fees, settlement fees, and withdrawal fees on the relevant platforms. A 5-cent gross discrepancy can become a 1-cent loss after a 10% settlement fee. Always compute the worst-case net profit across all outcomes.

4. Four Types of Arbitrage Exist in Prediction Markets

• Within-platform: Prices on a single platform violate no-arbitrage conditions (YES + NO < \$1.00, or multi-outcome sum deviates from 1.00). Simplest to detect and execute but rarest, because platforms actively prevent it.
• Cross-platform: The same event is priced differently on different platforms. Most common and profitable, but carries resolution risk and execution complexity.
• Related-market: Logical relationships between different markets are violated (subset/superset, sequential dependency, conditional probability, complement constraint). Requires domain knowledge to identify.
• Temporal: Prices on one platform lag behind another after news. Quasi-arbitrage that depends on speed and information quality.

5. Annualized Return Is the Right Comparison Metric

A 2% profit settling in 7 days (annualized ~332%) is vastly more attractive than a 5% profit settling in 180 days (annualized ~10%). The annualized return formula is:

$$R_{\text{annual}} = \left(1 + \frac{\pi_{\text{net}}}{C_{\text{total}}}\right)^{365/T} - 1$$

where $T$ is the number of days until settlement. Always prefer short-dated opportunities when the per-trade return is comparable.

6. Execution Is Harder Than Detection

The mathematics of arbitrage is elegant; the execution is treacherous. Key execution challenges:

• Leg risk: If one leg fills but the other does not, you have an unhedged directional bet.
• Slippage: The displayed price is not the fill price, especially on AMMs or thin order books.
• Partial fills: Order books may not have sufficient depth at the quoted price.
• Latency: Prices can move between the time you detect an opportunity and the time you execute.

Best practice: execute the less liquid leg first, pre-fund both platforms, use APIs for speed, and accept that some trades will fail.

7. "Risk-Free" Trades Carry Real Risks

Even true arbitrage involves:

8. Position Sizing Is Constrained by Multiple Factors

The optimal position size is:

$$Q^* = \min(Q_{\text{capital}},\; Q_{\text{depth}},\; Q_{\text{limit}},\; Q_{\text{risk}})$$

where $Q_{\text{capital}}$ is what your funds can support, $Q_{\text{depth}}$ is the order book depth, $Q_{\text{limit}}$ is the platform-imposed limit, and $Q_{\text{risk}}$ is your maximum acceptable operational risk exposure. Never size based on capital alone.

9. Statistical Arbitrage Is Not Arbitrage

Statistical arbitrage (pairs trading on correlated markets) generates expected profit over many trades but can lose on any single trade. It requires: - Strong historical correlation between markets. - Mean-reverting spread with a finite half-life. - Sufficient trade frequency to realize the statistical edge. - Proper risk management (stop losses, position limits).

It is a trading strategy, not arbitrage, and should be sized accordingly (fractional Kelly or smaller).

10. Automation Is Essential for Systematic Arbitrage

The median arbitrage opportunity in prediction markets lasts 10--20 minutes and yields less than 1 cent per pair. Capturing these opportunities requires: - Continuous price monitoring across platforms (5--60 second intervals). - Automated fee-adjusted profit calculation. - Pre-funded accounts on multiple platforms. - API-based order execution. - Risk checks and position tracking.

Manual arbitrage is possible for large, persistent mispricings (election nights, major events), but systematic profit requires automation.

Key Formulas

Key Vocabulary