Questions: Prospect Theory: Loss Aversion and Reference Dependence

Question 1

You own a stock currently worth $500. You are offered a trade: exchange it for another stock that has equal odds of being worth $400 or $700. According to prospect theory, most people will:

• A. Decline the trade — the potential loss of $100 (relative to the $500 reference point) looms roughly twice as large as the potential gain of $200, making the gamble subjectively unattractive despite its positive expected value
• B. Accept the trade — rational agents always accept gambles with positive expected value, and prospect theory does not change this
• C. Be indifferent — prospect theory only applies when the amounts are very large or very small
• D. Accept the trade — probability weighting overweights the 50% chance of gaining $200, making the gamble attractive

Answer: (A)

Loss aversion, estimated at roughly 2:1, means the pain of a $100 loss is weighted about twice as heavily as the pleasure of a $200 gain. Even though the gamble has a positive expected value of $50 relative to keeping the current stock, the asymmetric value function makes most people prefer the certain $500. This is not irrational within prospect theory's framework — it reflects genuine subjective disutility of losses. The expected-value argument (option B) describes behavior under standard expected utility theory, not prospect theory.

Question 2

A participant in a study is offered a choice: (A) a certain gain of $500, or (B) a 50% chance of gaining $1,000. The same participant, given a separate choice between (C) a certain loss of $500 or (D) a 50% chance of losing $1,000, prefers option D. Which pattern of behavior does this illustrate?

• A. The reflection effect — people are risk-averse for gains (preferring A over B) but risk-seeking for losses (preferring D over C), because the value function is concave above the reference point and convex below it
• B. Loss aversion — the participant is simply avoiding any outcome involving a loss, which is why they prefer the gamble in the loss domain
• C. Probability weighting — overweighting the 50% probability makes the gamble attractive in both domains equally
• D. Reference dependence — the participant's reference point shifts between the two problems, making A and D both 'gains' from their subjective perspective

Answer: (A)

The reflection effect is one of prospect theory's key predictions. In the gain domain, the value function is concave — diminishing marginal sensitivity means a certain $500 feels better than a coin flip for $1,000 (risk aversion). In the loss domain, the value function is convex — the certain loss of $500 feels worse than the coin flip for $1,000, because the first $500 of loss hurts more than the next $500 (risk seeking). The two choices are mirror images across the reference point. Loss aversion (option B) is a distinct concept — it concerns the asymmetry between gains and losses at the reference point, not the within-domain curvature.

Question 3

According to prospect theory, a person who loses $100 when they have $10,000 in savings experiences approximately the same decrease in subjective value as a person who loses $100 when they have $1,000,000 in savings.

• T. True
• F. False

Answer: True

This follows directly from prospect theory's reference dependence: the value function is defined over changes from the current reference point (typically the status quo), not over final wealth levels. A $100 loss is a $100 loss regardless of initial wealth — the value function responds to the magnitude of the change, not the ending position. This contrasts sharply with standard expected utility theory, where a risk-averse agent with $1,000,000 would suffer less disutility from a $100 loss than a person with $10,000, because the marginal utility of wealth is lower at higher wealth levels.

Question 4

Prospect theory's probability weighting function implies that people systematically overweight most probabilities that differ from the extremes of 0 and 1.

• T. True
• F. False

Answer: False

The probability weighting function is not uniformly above the 45-degree line. It overweights small probabilities (transforming, say, 1% into a subjective weight of 5%) but underweights large probabilities (transforming, say, 90% into a subjective weight of 70%). The weighting function typically crosses the 45-degree line at some intermediate probability. This explains why people simultaneously buy lottery tickets (overweighting a tiny chance of a large gain) and purchase insurance (overweighting a tiny chance of a large loss), but also exhibit the certainty effect — strongly preferring a guaranteed outcome over a near-certain one, because moving from, say, 99% to 100% probability receives a large subjective jump.

Question 5

Why does prospect theory predict that the same person might both buy a lottery ticket and purchase insurance against a rare disaster? What single feature of the theory explains both behaviors?

Model answer: Both behaviors are driven by the probability weighting function, which overweights small probabilities. A lottery ticket involves a tiny probability of a large gain — overweighting this small probability makes the ticket's subjective expected value seem higher than its objective expected value, making it attractive despite being a bad bet. Insurance involves a tiny probability of a large loss — overweighting this small probability makes the disaster feel more likely subjectively, so the insurance premium seems worthwhile. Standard expected utility with risk aversion predicts insurance but not lottery-buying; prospect theory's probability weighting explains both with a single mechanism.

This is a case where prospect theory is genuinely more parsimonious than standard theory: it resolves an apparent contradiction (the same person being risk-averse and risk-seeking) by showing both behaviors stem from the same distortion in probability perception rather than from inconsistency or irrationality.