Loss Aversion Simulator: Prospect Theory & Why Losses Hurt More

simulator beginner ~8 min
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Certainty equivalent ≈ -$12.50 — a fair coin flip for $100 feels like losing $12.50

With lambda=2.25, a 50/50 gamble to win or lose $100 has zero expected value but feels like a $12.50 loss due to loss aversion. Most people reject this mathematically fair bet.

Formula

Prospect theory value: v(x) = x^alpha if x >= 0, -lambda * (-x)^alpha if x < 0
Certainty equivalent: CE such that v(CE) = p * v(gain) + (1-p) * v(-loss)
Risk premium = Expected Value - Certainty Equivalent

Why Losses Hurt More

Flip a coin: heads you win $100, tails you lose $100. The expected value is exactly zero. A rational agent should be indifferent. But almost everyone rejects this bet — because losing $100 feels about twice as bad as winning $100 feels good. This asymmetry, called loss aversion, is one of the most fundamental discoveries in behavioral economics. Daniel Kahneman and Amos Tversky documented it in their landmark 1979 paper introducing prospect theory.

The Value Function

The simulation displays prospect theory's characteristic S-shaped value function: concave above the reference point (diminishing sensitivity to gains) and convex below it (diminishing sensitivity to losses), with the loss side steeper by a factor of lambda. The default lambda of 2.25 means a $100 loss produces 2.25 times the psychological impact of a $100 gain. This simple asymmetry explains an enormous range of human behavior, from the endowment effect to the disposition effect in investing.

Animated Coin Flips

Watch the simulation run hundreds of coin flips. The running profit/loss tracker shows the random walk of cumulative outcomes. Even when the gamble has positive expected value, the psychological experience is dominated by the sharp pain of losses. The green gain bars and red loss bars are scaled by lambda, making the asymmetry visible. Notice how your gut reaction to each loss is stronger than your reaction to each gain — that is loss aversion at work, even in a simulation.

Real-World Implications

Loss aversion is not merely a laboratory curiosity. It explains why people hold losing stocks (selling would 'realize' the loss), why homeowners refuse to sell below their purchase price even in a down market, why negotiators anchor on their current position, and why the pain of a tax increase exceeds the pleasure of an equivalent tax cut. Benartzi and Thaler showed that loss aversion, combined with frequent portfolio evaluation, explains the equity premium puzzle — why stocks must offer such high returns relative to bonds. Understanding lambda is understanding why humans are not the rational agents that classical economics assumes.

FAQ

What is loss aversion?

Loss aversion is the psychological phenomenon where losses feel roughly twice as painful as equivalent gains feel good. Discovered by Kahneman and Tversky (1979), it means losing $100 feels as bad as gaining $200 feels good. The typical loss aversion coefficient (lambda) is 2.0-2.5.

What is prospect theory?

Prospect theory (Kahneman & Tversky, 1979) describes how people actually make decisions under risk, replacing expected utility theory. It has three key features: loss aversion (losses weighed more than gains), diminishing sensitivity (the value function is concave for gains, convex for losses), and probability weighting (overweighting small probabilities, underweighting large ones).

What is the certainty equivalent?

The certainty equivalent is the guaranteed amount that would make you indifferent between taking the gamble and taking the sure thing. For a loss-averse person, the certainty equivalent of a fair 50/50 gamble for $100 is negative — they would pay to avoid the gamble.

How does loss aversion affect real decisions?

Loss aversion explains the endowment effect (overvaluing what you own), status quo bias (preferring current state), the disposition effect (selling winners too early, holding losers too long), and insurance overpurchasing. It is one of the most robust findings in behavioral economics.

Sources

Embed

<iframe src="https://homo-deus.com/lab/behavioral-economics/loss-aversion/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub