Questions: Loss Aversion

Question 1

A person is offered a coin flip: heads they win $120, tails they lose $100. Most people reject this bet despite its positive expected value ($10). This rejection is best explained by...

• A. Risk aversion due to a concave utility function over wealth
• B. Loss aversion — the pain of losing $100 exceeds the pleasure of gaining $120
• C. Inability to calculate expected values
• D. Distrust of the person offering the bet

Answer: (B)

Standard risk aversion (concave utility) cannot explain rejection of small-stakes gambles — the curvature of the utility function over total wealth is negligible for $100-$120 changes. Loss aversion provides the explanation: with a loss aversion coefficient of ~2, losing $100 is psychologically equivalent to losing ~$200 in gain terms, making the subjective expected value of the gamble negative. This is one of the cleanest demonstrations that loss aversion operates independently of diminishing marginal utility.

Question 2

Loss aversion implies that people always avoid risk.

• T. True
• F. False

Answer: False

Loss aversion makes people risk-averse for mixed gambles (involving both potential gains and losses) because the potential loss is psychologically amplified. However, prospect theory predicts risk-seeking behavior in the domain of pure losses — when all options involve losses, people gamble to avoid a certain loss. Additionally, loss aversion can actually increase risk-taking in some contexts: an investor who is 'in the hole' may take large risks to get back to their reference point (break-even). Loss aversion shapes risk attitudes in context-dependent ways, not uniformly toward risk avoidance.

Question 3

Why does loss aversion pose a challenge for standard expected utility theory?

Model answer: Expected utility theory evaluates outcomes as final wealth states, so gaining $100 and losing $100 are symmetric changes in wealth with symmetric utility implications (assuming a smooth utility function). Loss aversion — the asymmetry between gains and losses — cannot emerge from a smooth utility-of-wealth function because the evaluation depends on the direction of change from a reference point, not on the final wealth level. Incorporating loss aversion requires reference-dependence, which is outside the standard framework.

Rabin (2000) provided a formal proof of this challenge: if people reject small gambles due to concavity of utility over wealth (the only mechanism available in expected utility), they would have to reject absurdly favorable large gambles as well — which they do not. Loss aversion resolves this by operating on a different mechanism: it is about the kink in the value function at the reference point, not about curvature over total wealth. This makes loss aversion a genuinely new psychological mechanism, not just a special case of risk aversion.