NegRisk

#Definition

NegRisk (Negative Risk) markets are multi-outcome prediction markets on Polymarket where a set of mutually exclusive conditions share a common market ID. Each condition represents a possible outcome of a single event, and exactly one condition must resolve to "True."

#Formal Definition

A NegRisk market M = {C₁, C₂, ..., Cₙ} models an event E with n conditions. The market is:

• Exhaustive: The conditions collectively cover all possible outcomes
• Mutually exclusive: Only one condition can resolve to "True"

The set of valid resolutions V has exactly n possible outcomes, where each outcome assigns "True" to exactly one condition and "False" to all others.

NegRisk is a specialized prediction market. An Oscars Best Picture market with nine nominees enables film industry insiders to efficiently express views. A Hollywood producer confident that blockbuster films won't win could buy NO shares on commercial hits like "Barbie" and "Oppenheimer," then convert those to YES shares on art-house favorites plus cash. The conversion mechanism proves especially valuable when liquidity concentrates in the most famous nominees; buying NO shares on high-profile films often offers better execution than directly buying YES shares on lesser-known contenders, yet the conversion ensures mathematical equivalence. This conversion mechanism solves capital efficiency problems in categorical markets by recognizing mathematical equivalencies between positions.

#Why It Matters in Prediction Markets

NegRisk transforms how traders express complex views in multi-outcome events on platforms like Polymarket and potentially Kalshi. In traditional categorical markets, betting against multiple outcomes requires locking up capital for each NO share separately, which is capital inefficient. NegRisk allows these positions to be netted out, freeing up capital. If an election market lists three candidates but a fourth could enter, conversions made before that addition create positions that no longer match their theoretical equivalents. A trader converting 1 NO A + 1 NO B to 1 YES C + 1 USDC assumes only A, B, or C can win. If candidate D enters, the conversion equivalence breaks; the original NO positions would have paid out if D won, but the converted position (YES C + cash) loses entirely. A concrete scenario: with Trump at 55¢, Harris at 43¢, and Kennedy at 2¢, a trader believing "anyone but Kennedy" could buy NO Kennedy at 98¢. If they also bought NO on another low-probability candidate at 99¢, the two NO shares (197¢ total) convert to 1 YES on a major candidate + 100¢, effectively providing major candidate exposure for 97¢, cheaper than direct purchase if liquidity on NO shares of unlikely candidates offered better execution. The 2024 US Presidential Election market processed over $250 million in open interest using NegRisk structure, demonstrating the architecture's value for high-stakes political prediction.

Beyond capital efficiency, NegRisk strengthens price discovery. The conversion mechanism creates arbitrage opportunities that enforce mathematical constraints; if candidate probabilities drift apart incorrectly, traders can exploit the discrepancy by buying underpriced NO shares, converting to YES shares plus cash, and selling the overpriced outcome. This arbitrage mechanism keeps related market prices aligned, improving information aggregation accuracy.

#How It Works

The conversion mechanism implements a precise mathematical relationship: 1 NO share in any outcome = 1 YES share in all other outcomes + 1 USDC. This transformation happens atomically through the NegRiskAdapter smart contract deployed on Polygon, which simultaneously burns NO shares, mints equivalent YES shares across complementary markets, and releases the mathematically guaranteed USDC.

#Step-by-Step Mechanics

1. Identify equivalent positions: In a three-candidate election (Alice, Bob, Carol), a trader holds 1 NO Alice + 1 NO Bob
2. Calculate conversion: Those two NO shares convert to 1 YES Carol + 1 USDC
3. Execute atomic swap: The smart contract burns the NO shares, mints YES Carol, and transfers USDC; all in one transaction
4. Result: Trader holds the mathematically equivalent position with identical payoffs across all outcomes

#Visualizing NegRisk Conversion

The conversion mechanism allows you to swap between "Negative Risk" (betting against multiple outcomes) and "Positive Risk" (betting on the remaining outcome).

#Mathematical Verification: Payoff Matrix

This table proves that the two positions are mathematically identical across all possible outcomes.

Scenario: 3 Candidates (Alice, Bob, Carol). Position A: 1 NO Alice + 1 NO Bob Position B: 1 YES Carol + 1 USDC

#Arbitrage Enforcement

Price discrepancies create immediate arbitrage opportunities.

Example Scenario:

• YES Carol trades at 15¢ (Direct Buy)
• NO Alice trades at 40¢
• NO Bob trades at 75¢

The Arbitrage Opportunity:

1. Direct Cost: Buying YES Carol costs 15¢.
2. Conversion Cost: Buying NO Alice (40¢) + NO Bob (75¢) costs 115¢.
   • You convert these to 1 YES Carol + 100¢ Cash.
   • Net Cost = 115¢ - 100¢ = 15¢.

If prices diverge:

• Suppose NO Alice drops to 35¢ and NO Bob to 70¢.
• Conversion Cost = 35¢ + 70¢ = 105¢.
• Net Cost for YES Carol = 105¢ - 100¢ = 5¢.
• Arbitrage: Buy the "synthetic" YES Carol for 5¢ via conversion, sell the real YES Carol for 15¢. Profit: 10¢ per share.

#Developer Note: The Conversion Logic

Conceptually, the NegRisk adapter performs this logic atomically:

function convertNoToYes(uint256 amount) external {
    // 1. Burn the NO shares from the user
    burn(msg.sender, NO_ALICE, amount);
    burn(msg.sender, NO_BOB, amount);

    // 2. Mint the equivalent YES share
    mint(msg.sender, YES_CAROL, amount);

    // 3. Return the collateral (1 USDC per share)
    token.transfer(msg.sender, amount * 1e6);
}

#On-Chain Conversion Events

When conversions occur, the NegRiskAdapter contract emits specific events that can be tracked:

Researchers analyzing Polymarket data have used these events to identify sophisticated traders exploiting conversion-based arbitrage opportunities.

#Empirical Data: NegRisk Markets in Practice

Research analyzing Polymarket from April 2024 to April 2025 provides insights into NegRisk market behavior.

#Market Distribution

#Arbitrage in NegRisk Markets

NegRisk markets exhibited significant arbitrage opportunities:

#Liquidity Concentration

Over 90% of all liquidity in NegRisk markets concentrates in the top 4 conditions. This means:

• Most trading activity focuses on leading outcomes
• Long-tail conditions (low-probability candidates) have thin liquidity
• Arbitrageurs often ignore conditions priced below 2% probability

#Market Dependency

When NegRisk markets relate to the same underlying event differently, dependency creates additional arbitrage:

• Example: A market on "Who wins the election?" and another on "GOP wins by what margin?"
• The 2024 election had 11 pairs of dependent NegRisk markets identified through semantic analysis
• Combinatorial arbitrage across these pairs yielded profits ranging from $629 to$60,237 per pair

#Related Terms

• Polymarket
• Categorical Market
• Yes/No Shares
• Liquidity
• Arbitrage
• Combinatorial Markets

#FAQ

#What is the difference between NegRisk and single-condition markets?

Single-condition markets have one binary question with YES/NO outcomes. NegRisk markets have multiple mutually exclusive conditions where exactly one must be true. Single-condition markets are simpler, while NegRisk markets enable betting on categorical events like "Who will win?" with many possible winners.

#Why is over 90% of liquidity in the top 4 conditions?

Traders naturally focus on outcomes they consider plausible. Long-tail conditions (e.g., a fringe candidate winning) attract minimal attention because few believe they'll occur. This concentration creates inefficiencies that arbitrageurs can sometimes exploit.

#How do arbitrageurs handle low-probability conditions?

When analyzing NegRisk arbitrage, sophisticated traders often ignore conditions priced below 2% probability. The risk of a surprise outcome (like a dark horse winning) is deemed low enough to accept when executing Market Rebalancing Arbitrage strategies.