Lecture 12: Cumulative Prospect Theory

Question 1

PT - Violation of stochastic dominance

Answer 1

Under PT a lottery where each outcome is below a given sure payment might be preferred over the sure payment due to overvaluation of small probabilities and diminishing marginal utility.
-> Stochastic dominance is violated!

Solution: Cumulative Prospect Theory

Question 2

Cumulative Prospect Theory

Answer 2

Uses transformation of the cumulative probability instead of separate probabilities.

PT: overweighting of unlikely events
CPT: overweighting of extreme outcomes

Question 3

What is the difference between PT and CPT?

Answer 3

PT: All unlikely events (low probability) receive the same overweighting

CPT: Overweighting differs although the probabilities are equal -> highest for the most extreme outcome (high deviation from reference point)

Question 4

Cumulative Prospect Theory - Steps

Answer 4

1. Valuation of outcomes: a(i) -> v[a(i)]
2. Calculate transformed probabilities: p(i) -> w[p(i)]
3. Calculate CPT value: Sum v[a(i)] * w[p(i)]

Question 5

Probability weighting function for positive prospects

Answer 5

• risk neutral: points are on the diagonal
• risk averse: points are below the diagonal
• risk prone: points are above the diagonal

Question 6

Probability weighting function for negative prospects

Answer 6

• risk neutral: points are on the diagonal
• risk averse: points are above the diagonal
• risk prone: points are below the diagonal

Question 7

Characteristics of CPT

Answer 7

• Stochastic dominance is not violated
• Cumulative instead of individual probabilities are transformed
• Decision weights don’t have to add up to one

Question 8

Examples of prospect theory in real life

Answer 8

1. Consumer goods:
   - Asymmetric price elasticities
   - price increase = loss; price decrease = gain
   - Losses are weighted more heavily -> demand responses are more elastic to price increases
2. Stock market:
   - Disposition effect
   - Holding losers to long and winners to short because the purchase price is used as reference point