Prospect Theory

#Definition

Prospect theory is a behavioral economics framework developed by Daniel Kahneman and Amos Tversky that describes how people actually make decisions under uncertainty—often deviating from rational expected value calculations. The theory explains that people feel losses more intensely than equivalent gains, overweight small probabilities, and evaluate outcomes relative to reference points rather than absolute values.

In prediction markets, prospect theory explains many common mispricings and trader behaviors that deviate from pure probability reasoning.

#Why It Matters in Prediction Markets

Prospect theory explains systematic biases that create both risks and opportunities:

Loss aversion effects: Traders often hold losing positions too long (hoping to avoid realizing losses) and sell winning positions too early (locking in gains). This creates predictable trading patterns.

Probability weighting mispricings: The tendency to overweight small probabilities may cause long-shot outcomes to be overpriced and near-certainties to be underpriced in prediction markets.

Reference point manipulation: How traders frame their positions (relative to purchase price, initial bankroll, or other anchors) affects their trading decisions regardless of current probabilities.

Exploiting behavioral patterns: Understanding prospect theory helps identify when markets misprice due to collective behavioral biases rather than information.

Personal trading improvement: Recognizing these biases in yourself helps make more rational trading decisions aligned with expected value.

#How It Works

#Core Components

Loss Aversion

Losses hurt roughly twice as much as equivalent gains feel good. A $100 loss feels worse than a$100 gain feels good.

Mathematical expression: The value function is steeper for losses than gains:

Value of +$100 ≈ +100 utility units
Value of -$100 ≈ -200 utility units

Prediction market implication: Traders irrationally hold losing positions (to avoid the pain of realized loss) and exit winners early (to secure the pleasure of realized gain).

Reference Dependence

Outcomes are evaluated as gains or losses relative to a reference point, not in absolute terms.

Example: You bought at $0.40, price is now$0.50.

• If reference is purchase price: You feel like you're +$0.10 (gain)
• If reference is yesterday's price of $0.55: You feel like you're -$0.05 (loss)

Same position, different feeling—and different trading behavior.

Probability Weighting

People don't treat probabilities linearly:

• Small probabilities are overweighted: 5% feels like more than 5%
• Large probabilities are underweighted: 95% feels like less than 95%

Subjective weighting:
Objective 5% → Subjective ~10%
Objective 50% → Subjective ~40%
Objective 95% → Subjective ~80%

Prediction market implication: Long shots may be overpriced (people love unlikely payoffs) and near-certainties may be underpriced (people discount "sure things").

#The Fourfold Pattern

Prospect theory predicts different risk attitudes depending on probability and outcome type:

Prediction market applications:

• Low-probability wins: People overpay for long shots (risk-seeking for small-probability gains)
• High-probability wins: People may sell too early (risk-averse, want to lock in gain)
• Low-probability losses: People buy insurance/hedges even at bad prices (risk-averse)
• High-probability losses: People hold losing positions hoping to avoid realizing loss (risk-seeking)

#Numerical Example

Scenario: You hold a position bought at $0.60. Current price:$0.50. True probability: 50%.

Rational analysis:

• Expected value at current price = 50% × $1 =$0.50
• Position is fairly priced
• No action required on EV basis

Prospect theory prediction:

• Reference point: $0.60 (purchase price)
• Current frame: -$0.10 loss (unrealized)
• Loss aversion kicks in: Selling feels like "accepting defeat"
• Probability weighting: 50% feels closer to 40%
• Result: Hold the position hoping for recovery, despite no positive EV

This explains why traders often hold losers—they're in the loss domain where risk-seeking behavior dominates.

#Examples

Favorite-longshot bias: Prediction markets often show this pattern: very low probability outcomes (1-5%) are slightly overpriced, while near-certainties (95-99%) are slightly underpriced. Prospect theory explains this through probability weighting—small probabilities feel bigger than they are, making long shots feel more attractive.

Refusing to sell losers: A trader bought "Candidate wins primary" at $0.70. The candidate stumbles, and price drops to$0.35. Rather than selling, the trader holds, hoping for recovery. The purchase price creates a reference point; selling feels like admitting defeat. Prospect theory predicts this behavior even when the rational action is to sell.

Early profit-taking: A trader buys at $0.30, price rises to$0.55. Despite believing true probability is 65%, they sell to "lock in profits." They've switched to the gain domain where risk aversion dominates—they prefer a certain $0.25 gain to risking it for additional upside.

Hedging low-probability disasters: A trader holds a large position that wins unless a specific low-probability event occurs. Despite the hedge being priced at negative expected value, they buy it anyway—probability weighting makes the 5% disaster feel more threatening than 5% should.

#Risks and Common Mistakes

Loss aversion holding: Refusing to close positions at a loss leads to poor capital allocation. Money trapped in bad positions can't be deployed to better opportunities.

Premature profit-taking: Selling winners too early limits upside. If true probability exceeds market price, selling to "lock in gains" sacrifices expected value.

Overweighting small probabilities: Buying long shots because they "feel" more likely than they are leads to negative expected value trading.

Reference point anchoring: Using purchase price as a reference point makes trading decisions about your psychology rather than market probabilities. The market doesn't care what you paid.

Assuming others are rational: If you assume other traders follow expected value reasoning, you'll be surprised by persistent mispricings caused by prospect theory effects.

#Practical Tips for Traders

• Use EV as your reference: Frame positions by expected value, not purchase price. The question is "Is this position +EV at current price?" not "Am I up or down?"

• Set exit rules in advance: Decide exit criteria before entering positions, when you're not emotionally attached. This combats loss aversion holding.

• Fade long shots when appropriate: If probability weighting causes long shots to be overpriced, selling them may offer positive expected value.

• Be skeptical of "sure things": If near-certainties are underpriced due to probability weighting, buying them at 95 cents for something 98% likely may be +EV.

• Recognize the feeling of loss aversion: When you feel reluctant to sell a losing position, that feeling may be loss aversion rather than rational analysis. Examine your reasoning carefully.

• Track your behavioral patterns: Do you consistently hold losers too long? Sell winners too early? Identifying your personal prospect theory tendencies enables correction.

• Reframe losses as learning: Reducing the psychological pain of losses helps combat loss aversion. A closed losing position is information, not just failure.

#Related Terms

• Heuristics
• Expected Value (EV)
• Risk Management
• Herd Instinct
• Hindsight Bias
• Kelly Criterion
• Drawdown
• Vibe Trading

#FAQ

#What is prospect theory in simple terms?

Prospect theory says people make decisions differently than pure math would suggest. We hate losses about twice as much as we enjoy gains. We treat probabilities weirdly—overweighting small chances and underweighting large ones. And we evaluate outcomes relative to a reference point rather than in absolute terms. Together, these explain many "irrational" trading behaviors.

#How does loss aversion affect prediction market trading?

Loss aversion makes traders hold losing positions too long (hoping to avoid realizing the loss) and sell winning positions too early (to lock in gains). This is backwards from an expected value perspective—you should hold positions when price is below true probability and sell when price is above, regardless of your entry price.

#What is the favorite-longshot bias?

The favorite-longshot bias is the empirical finding that low-probability outcomes tend to be overpriced and high-probability outcomes tend to be underpriced. Prospect theory's probability weighting explains this: people treat 5% as if it's more than 5% and 95% as if it's less than 95%, causing them to overpay for long shots and underpay for favorites.

#Can understanding prospect theory improve my trading?

Yes. By recognizing these biases, you can: (1) avoid holding losers irrationally, (2) avoid selling winners prematurely, (3) identify mispricings caused by others' biases, and (4) make decisions based on expected value rather than emotional reference points. Self-awareness of prospect theory effects is the first step to countering them.

#Is prospect theory always relevant in prediction markets?

It's most relevant for individual trading behavior and in markets with significant retail participation. Professional traders and sophisticated participants may exhibit less prospect theory bias, making some markets more efficient. However, even experienced traders show these effects under stress or with personally significant positions.