Loss aversion (Kahneman & Tversky, Prospect Theory, 1979) — losses are felt approximately 2× more strongly than equivalent gains.
• Hold losers too long (to avoid realizing the painful loss)
• Sell winners too quickly (to lock in the pleasurable gain)
• Refuse to take small calculated losses → small loss becomes catastrophic
• Trading costs and overtrading explain much of retail underperformance (Barber & Odean 2000); loss aversion adds to it
A fair coin: win 110 or lose 100. The expected value is +5, yet with Tversky & Kahneman’s estimates (curvature 0.88, losses weighted 2.25×) it feels like −33. To make losing 100 feel even, the win would have to be about 251. Repeated small bets like this one are where loss aversion costs most: refused one at a time, a profitable series is never played (Benartzi & Thaler’s “myopic loss aversion”).
- “Losses hurt twice as much” is a median from lab gambles, not a constant. Estimates vary widely by person, stakes and method, and some find little loss aversion for small, routine amounts (Gal & Rucker 2018).
- Being careful with losses is not a bias when a loss would ruin you; with real survival constraints, refusing a positive bet can be correct.
- Holding losers and selling winners is a related but separate effect (see Disposition Effect).
def v(x, a=0.88, lam=2.25): # Tversky & Kahneman's (1992) median estimates
return np.where(x >= 0, np.abs(x) ** a, -lam * np.abs(x) ** a)
ev = 0.5 * 110 + 0.5 * -100 # a fair coin: win 110 or lose 100
felt = 0.5 * v(110) + 0.5 * v(-100)
win_needed = 100 * 2.25 ** (1 / 0.88) # the win that makes losing 100 feel evenAssumes import numpy as np and import pandas as pd. Each snippet carries its own example numbers; the comments say which are made up.
- D. Kahneman & A. Tversky, “Prospect Theory: An Analysis of Decision under Risk”, Econometrica 47(2), 1979
- A. Tversky & D. Kahneman, “Advances in Prospect Theory: Cumulative Representation of Uncertainty”, Journal of Risk and Uncertainty 5(4), 1992 — the 0.88 and 2.25 used here
- S. Benartzi & R. H. Thaler, “Myopic Loss Aversion and the Equity Premium Puzzle”, Quarterly Journal of Economics 110(1), 1995
- D. Gal & D. D. Rucker, “The Loss of Loss Aversion: Will It Loom Larger Than Its Gain?”, Journal of Consumer Psychology 28(3), 2018
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1. According to Tversky and Kahneman’s 1992 estimates, a loss feels about how many times as strong as an equal gain?
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B. Later studies find a range of values, but the asymmetry itself is one of the most replicated findings in behavioural economics.
2. Many people refuse a 50/50 bet to lose $100 or win $150. Why?
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C. The expected value is +$25, but with losses weighted about twice, the bet feels like a loss.
3. What is myopic loss aversion?
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C. Benartzi & Thaler (1995) used it to explain why investors demand such a high premium for holding stocks.
- Tversky & Kahneman’s (1992) median estimate: losses weigh about 2.25× as much as equal gains
- In trading: investors tend to hold losers and sell winners — Odean (1998) found individual investors realised gains about 1.5× as readily as losses
- Pre-committed stop-losses and systematic exit rules are a common defence, because they take the decision away from the moment of loss