Notes: Prospect Theory in the WildPaper by Colin F. Camerer

Review and finish up of Prospect Theory

The Man Himself

Kahneman Nobel Lecture: 9:00-22:15 and 31:50-end

Changes are salient and maintained states are mostly ignored. What does this mean?

What does he mean when he says that “framing outcomes in terms of wealth is psychologically unrealistic but normatively appropriate (19:30)?”

Why would indifference curves have kinks?

What is the point of the colonoscopy experiment?

What does PT add?• K and T introduce the value function.

• Carriers of value are changes in wealth or welfare, rather than final states.

• “When we respond to attributes such as brightness, loudness, or temperature, the past and present context of experience defines an adaptation level, or reference point, and stimuli are perceived in relation to this reference point.”

• Value should be treated as a function in two arguments:• 1. The asset position that serves as a reference point• 2. The magnitude of the change (positive or negative) from that

reference point.

Property that the Value Function proposes: • “Many sensory and perceptual dimensions share the property

that the psychological response is a concave function of the magnitude of physical change.”

• Ex: Temperature change from 3 degrees to 6 degrees VERSUS a temperature change of 13 degrees to 16 degrees

• EX: value of a gain of 100€ to 200€ VERSUS a change of 1,100€ to 1,200€

• Ex: value of a loss of 100€ to 200€ VERSUS a loss of 1,100€ to 1,200€

Concave and Convex• The value function for changes in wealth:• Concave above the reference point• Convex below it

• And that the marginal value of both gains and losses generally decreases with their magnitude

The Value Function

GainsLosses

Value

Summary of the Value Function• 1. it is defined on deviations from the reference point – that

reference point may be:• The status quo• An individual’s “endowment”

• 2. It is generally concave for gains and commonly convex for losses

• 3. It is steeper for losses than for gains (this is the idea of “loss aversion”)

Add: The Weighting Function• In Prospect Theory, the value of each outcome is multiplied by

a decision weight.• Decision weights are inferred from choices between prospects

much as subjective probabilities are inferred from preferences

• K and T propose that very low probabilities are generally over-weighted

• Because people are limited in their ability to comprehend and evaluate extreme probabilities, highly unlikely events are either ignored or overweighted, and the difference between high probability and certainty is either neglected or exaggerated

• The following is a hypothetical weighting function

The Probability Weighting Function

Actual Probability

Perceived Probability

0.00 0.25 0.50 0.75 1.00

0.00

0.25

0.50

0.75

Weighting function

Misperceiving Probability

Misperceiving Probability

Ten Anomalies in Naturally-Occurring Data: Colin Camerer

• Anomalies for EUT but can be explained by three simple elements of prospect theory:• Loss aversion• Reflection effects• Nonlinear weighting of probability

• Along with the assumption that people isolate decisions (or edit them) from others they may be grouped with

1. Finance: The Equity Premium• Stocks or equities tend to have more variable annual price changes

(or returns) than do bonds.

• Result: the average return to stocks is higher, as a way of compensating investors for the additional risk they bear.

• Avg: 8% higher per year return

• This was accepted a as a reasonable return premium for equities

until Mehra and Prescott (1985) asked how large a degree of risk-aversion is implied by this premium?

Why is the equity premium strange?• The assumption is that the equity premium is the excess

return one would get from investing in a stock (a risky bet) versus a bond (a risk free bet).

• Imagine that the RoR on a three-month U.S. Treasury Bill (T Bill – the risk-free rate) is 0.17 percent.

• Imagine a RoR on a stock, say 3 percent.• Subtracting the risk-free rate from the RoR on the risky

investment should determine the equity risk premium.

• Here’s the math for this example:• 3% - 0.17% = 2.83%

But stocks perform on average 8% better than bonds...• So, now assuming

• Risky – Risk Free = 8 percent

• What kind of attitude toward risk does this imply?

• A person with enough risk-aversion to explain the equity premium would be indifferent between a coin flip paying either $50,000 or $100,000 and a sure amount of $51,329

• (See “The Equity Premium: A Puzzle” by Rajnish Mehra and Edward C. Prescott, 1985)

Benartzi and Thaler (1997)• Investors are not averse to the variability of returns, they are

averse to a loss (the chance that their returns are negative).

• The high return is compensation for the much higher chance of losing money in a year

• To calculate, B&T assumed investors take a short horizon over which stocks are more likely to lose than bonds.

• Find the expected prospect values of stock and bond returns over various horizons using estimates of investor utility functions

• Include a loss-aversion coefficient of 2.25 (i.e. The disutility of a small loss is 2.25 times as large as the utility of an equal gain)

• Over a one-year horizon, the prospect values of stock and bond returns are about the same if stocks return 8% more than bonds

2. Finance: The disposition effect• Investors tend to hold on to stocks that have lost value

(relative to their purchase price) too long and will be eager to sell stocks that have risen in value.

• Anomalous because the purchase price of a stock should not matter much for whether you decide to sell it

• If you think it will rise, you should keep it.• If you think it will fall, you should sell it.

Evidence from Odean• Found investors held losing stocks a median of 124 days• Held winners 104 days

• Losers returned 5% in the subsequent year• Winners returned 11.6% in the subsequent year

Labor Supply• Camerer, Babcock, Loewenstein and Thaler talked to cab

drivers in NYC about when they decide to quit driving each day.

• Drivers lease cabs for a fixed fee for up to 12 hours.

• Many set an income target for the day and quit when they reach that target.

• Implication? Drivers work long hours on bad days when per-hour wage is low and quit earlier on good, high-wage days.

• Standard theory predicts the opposite.

4. Asymmetric price elasticities of consumer goods• Price elasticity: percentage change in the quantity demanded

divided by the percentage change in price• Tons of studies estimate elasticities – effects of how much

quantity demanded responds to own prices, cross prices etc.• Elasticities of labor supply... Etc.• If we take PT into consideration we can expect that loss

aversion might affect elasticities: loss-averse consumers might dislike price increases more than they like the windfall gain from price cuts • We might see larger elasticities after a price increase than a price

decrease

Hardie, Johnson, and Fader (1993) on price elasticities• Looked at the possibility that consumers compare a goods

current price to some reference price (the price they last paid) • Found that consumers get more disutility from buying when

prices have risen than the extra utility they get when prices have fallen

• For OJ, estimate the coefficient of loss aversion to be 2.4

5. Savings and Consumption• Economic models of lifetime savings and consumption: people

have different utility functions over each period of life, and discount factors which weight future consumption less than current consumption.

• Implication: because workers expect to earn larger and larger incomes throughout their lives, people will spend more than they earn when they are young (perhaps borrowing) and then earn more than they spend when they are older.

• What people really do? They spend a fixed fraction of their current income, and it doesn’t vary across the life cycle.

• Consumption drops steeply after retirement because people didn’t save enough.

PT can help explain• Bowman, Minehart and Rabin (1994) explain with a stylized

tow-period consumption-savings model in which workers have reference-dependent utility.

• The utility they get from consumption in each period exhibits loss aversion and a reflection effect

• “ Our main conclusion is that, when there is sufficient income uncertainty, a person resists lowering consumption in response to bad news about future income, and this resistance is greater than the resistance to increase consumption in response to good news.”

6. Status Quo Bias, Endowment Effects and buying-selling gaps• Samuelson and Zeckhauser (1988) coined the term “status quo

bias” to refer to an exaggerated preference for the status quo.• Example: Harvard U added new health-care plan options.• Previously hired faculty members could switch to new options.• Assume: old and new faculty members have same preferences

for health care plans• Implication: the distribution of plans elected by new and old

faculty should be the same• S and Z found that older faculty tended to stick to previous

plans

Default Choices• When there is no status quo, people may have an exaggerated

preference for whichever option is the default choice.

• Johnson, Hershey, Meszaros and Kunreuther (1993) showed this in decisions involving insurance purchases.

• Pennsylvania and New Jersey passed similar forms of limited insurance policies but chose different default options.

• Penn: limited-rights insurance was the default• NJ: unlimited-rights insurance was the default

• Result: people stuck with the default

Endowment Effect• In Class Experiment

The Endowment Effect

Buying and Selling Prices are often quite different.

Kahneman, Knetsch and Thaler (1990): some subjects are endowed (randomly) with coffee mugs and others are not.

Those who are given the mugs demand a price about 2-3 times as large as the price that those without mugs are willing to pay

But the prices should be extremely close together... Why?

More papers on the Endowment Effect for your Perusal• Kahneman, Daniel, Jack L. Knetsch, Richard H. Thaler

. 1991. Anomalies: The Endowment Effect, Loss Aversion and Status Quo Bias. The Journal of Economic Perspectives, Vol. 5 (1): 193-206.

• Kahneman, Daniel, Jack L. Knetsch and Richard H. Thaler. 1990. “Experimental Tests of the Endowment Effect and the Coase Theorem.” Journal of Political Economy. Vol. 98(6): 1325-1348.

7. Racetrack Betting: The favorite-longshot bias• “In parimutuel betting on horse races, there is a pronounced

bias toward betting on longshots, horses with a relatively small chance of winning.”

• Horses with 2% of the total money bet on them win only about 1% of the time.

• Implication is that favorites are underbet. The problem is that the return for a dollar bet is low on favorites and people dislike those types of bets.

Explanations for favorite-longshot bias• Gambler’s fallacy: longshots are due• Overweighting of low probabilities of winning• Losing on a heavy favorite is particularly dissapointing (as

opposed to losing on a long-shot or winning on a long-shot)

The End-of-the-day effect• McGlothlin (1956) and Ali (1977) a racetrack anomaly which

points to the central role of reference points.

• Betters tend to shift their bets toward longshots later in the racing day.

• Because the track takes a big bite out of each dollar, most bettors are behind by the last race of the day.

• These bettors prefer longshots because a small longshot bet can generate a large enough profit to cover earlier losses, enabling them to break even.

• PT: assume people open a mental account a the beginning of the day, close it at the end, and hate closing an account in red.

9. State Lotteries• Lotto: players choose six different numbers from a set of 40-50

numbers. • They win a jackpot if their six choice match six numbers which

are randomly drawn in public. If no one wins, the jackpot is rolled over and added to the next week’s jackpot.

• Cook and Clotfelter (1993): people are more sensitive to the large jackpot than to the correspondingly low probability of winning

• Ticket sales are correlated with the size of a state’s population which is correlated with jackpot size

• PT explanatino: overweighting of and insensitivity to very low probabilities

Conclusion....• Is this stuff in our brain???

10 Ways we get it wrong• 1. we fear snakes, not cars• 2. We fear spectacular, unlikely events• 3. We fear cancer but not heart disease• 4. No pesticide in my backyard—unless I put it there (i.e. Risks

are okay if I can control them)• 5. We speed up when we put our seat belts on• 6. Teens may think to much about risk—and not feel enough

(sometimes rational thought leads us into bad actions)• 7. Why young men will never get good rates on car insurance• 8. We worry about teen pot but not about teen sports• 9. We love sunlight but fear nuclear power• 10. We should fear fear itself