Behavioral Finance · Decision Theory
Prospect Theory Explained
The Nobel Prize-winning model that explains why losing £100 feels worse than gaining £100 feels good — and why this asymmetry shapes every financial decision you make.
Imagine you’re offered two choices: (A) a guaranteed £50, or (B) a 50% chance of £100. Standard expected utility theory says both have the same expected value — and a risk-neutral person should be indifferent. Now change the frame: (A) a guaranteed loss of £50, or (B) a 50% chance of losing £100. Experimentally, most people switch from preferring the certain option to preferring the gamble — even though the expected values are identical. Prospect Theory explains this reversal.
📘 Key Term
Prospect Theory (Kahneman and Tversky, 1979) is a descriptive model of decision-making under risk. It posits that people evaluate outcomes as gains or losses relative to a reference point, not as absolute wealth states. Losses are felt more intensely than equivalent gains (loss aversion), and probabilities are weighted non-linearly — small probabilities are overweighted and large probabilities underweighted.
The Three Core Features of Prospect Theory
1. Reference Dependence
People evaluate outcomes relative to a reference point (typically the status quo or purchase price), not in terms of final wealth. A portfolio worth £90,000 feels like a loss if you started with £100,000 — even though £90,000 is objectively significant wealth.
People evaluate outcomes relative to a reference point (typically the status quo or purchase price), not in terms of final wealth. A portfolio worth £90,000 feels like a loss if you started with £100,000 — even though £90,000 is objectively significant wealth.
2. Loss Aversion
The psychological pain of losing £X is approximately twice as intense as the pleasure of gaining £X. Kahneman and Tversky estimated the loss aversion coefficient (λ) at approximately 2.25 — meaning a gain must be 2.25× larger than a loss to produce equal emotional impact.
The psychological pain of losing £X is approximately twice as intense as the pleasure of gaining £X. Kahneman and Tversky estimated the loss aversion coefficient (λ) at approximately 2.25 — meaning a gain must be 2.25× larger than a loss to produce equal emotional impact.
Value function v(x):
v(x) = x^α if x ≥ 0 (gains)
v(x) = −λ(−x)^β if x < 0 (losses), where λ ≈ 2.25, α ≈ β ≈ 0.88
3. Probability Weighting
People do not use objective probabilities — they use a weighting function π(p) that overweights small probabilities (explaining why people buy lottery tickets and insurance simultaneously) and underweights moderate-to-high probabilities.
People do not use objective probabilities — they use a weighting function π(p) that overweights small probabilities (explaining why people buy lottery tickets and insurance simultaneously) and underweights moderate-to-high probabilities.
💡 Key Insight
The value function in Prospect Theory is S-shaped: concave in the gain domain (diminishing sensitivity to gains) and convex in the loss domain (diminishing sensitivity to losses). This explains the classic fourfold pattern of risk attitudes: risk-averse for moderate gains, risk-seeking for moderate losses, risk-seeking for small probability gains (lottery), and risk-averse for small probability losses (insurance).
Real-World Applications
📉 The Disposition Effect: Investors sell winning stocks too early (to lock in gains) and hold losing stocks too long (to avoid realising losses). This is prospect theory in action — loss aversion makes realising losses psychologically painful.
🏠 Housing Markets: Homeowners are reluctant to sell at a loss relative to their purchase price — even if the opportunity cost is high. Reference dependence anchors their decision to the purchase price.
💼 Salary Negotiations: A pay cut of £5,000 feels worse than not receiving a £5,000 raise — even though both leave you £5,000 worse off than you could have been. Framing effects driven by loss aversion.
⚠️ Common Error
Prospect Theory is a descriptive model — it describes how people actually behave, not how they should behave. It is not a normative theory. Students sometimes confuse it with Expected Utility Theory (which is normative — it tells us what a rational agent should do). Prospect Theory explains systematic deviations from rational expected utility maximisation.
Q1. Using Prospect Theory, explain why an investor might hold a losing stock longer than a rational model would predict. [6 marks]
Answer: Prospect Theory predicts that investors evaluate outcomes relative to a reference point — in this case, the purchase price of the stock. Selling the stock at a loss means realising a loss, which triggers loss aversion: losses feel approximately 2× more painful than equivalent gains. To avoid this psychological pain, the investor holds the losing stock in the hope of a recovery to their reference point (purchase price), even if the expected return from holding is inferior to alternative investments. This is the disposition effect — one of the best-documented anomalies in behavioural finance and a direct prediction of Prospect Theory.
References
1. Kahneman, D. and Tversky, A. (1979) ‘Prospect Theory: An Analysis of Decision Under Risk’, Econometrica, 47(2), pp. 263–292.
2. Tversky, A. and Kahneman, D. (1992) ‘Advances in Prospect Theory: Cumulative Representation of Uncertainty’, Journal of Risk and Uncertainty, 5(4), pp. 297–323.
3. Shefrin, H. and Statman, M. (1985) ‘The Disposition to Sell Winners Too Early and Ride Losers Too Long’, Journal of Finance, 40(3), pp. 777–790.
4. Thaler, R.H. (1980) ‘Toward a Positive Theory of Consumer Choice’, Journal of Economic Behavior and Organization, 1(1), pp. 39–60.
5. Kahneman, D. (2011) Thinking, Fast and Slow. Farrar, Straus and Giroux.