Prospect Theory - University of Warwick · Prospect Theory, 10 of 44. ... Violation of the Independence axiom ... Prospect Theory Empirical Evidence Finance The Equity Premium Puzzle

Prospect Theory

Warwick Economics Summer School

Prospect Theory

Eugenio Proto

University of Warwick, Department of Economics

July 19, 2016

Prospect Theory, 1 of 44

Prospect Theory

Outline

1 General Introduction

2 The Expected Utility Theory

3 Main Departures from Expected Utility

4 Prospect Theory

5 Empirical EvidenceFinanceEconomic DevelopmentHousing MarketsLabor MarketDomestic Violence

6 Summary


Prospect Theory

General Introduction

Behavioral Economics

Economics and Psychology were not separated

Adam Smith: The theory of Moral Sentiments

Jeremy Bentham, the psychological underpinnings of Utility

Francis Edgeworth, concept of envy in Utility Functions


Prospect Theory


Behavioral Economics, cont’d

Neoclassical Revolution separated clearly Psychology andEconomics

Economics like a natural (and not a social) science

Psychology has too unsteady foundations

Utility can be defined as an ordinal (and not a cardinal) object

Rejection of the hedonistic assumptions of Benthamite Utility

Neoclassical economists expunged the psychology fromeconomics


Prospect Theory


Behavioral Economics, cont’d

Some early Criticism to the neoclassical economy from IrwingFisher, J.M. Keynes,, Herbert Simon

More from Allais (1953), Ellsberg (1961), Markowitz (1952),Strotz (1955), following the Expected Utility Theory and thediscounted utility models

Kahneman and Tversky (1979) on expected utility, Thaler(1981) and Loewenstain and Prelec (1992) (on discountedutility), Happiness Economics on Hedonic foundations ofUtility

Neuroscience looks for the bases of Individual Behavior

Neuroscience gives steadier foundations to psychology

Toward a unique discipline?


Prospect Theory

The Expected Utility Theory

Outline




4 Prospect Theory


6 Summary


Prospect Theory


Expected Utility

Individuals generally, ceteris paribus, prefer certainty touncertainty

a prospect is a vector of probabilities and Consequences(q = (x1, p1, ..., xn, pn))

they take decision over a prospect H, p; L, (1 − p), following autility function

Eu = pu(H) + (1 − p)u(L) (1)

1 is defined Expected Utility

Individuals prefer r1 = (800, 1) to r2 = (1000, 0.85; 0, 0.15)

note that E (r1) < E (r2).


Prospect Theory


Main Tenets of EU

1 The overall Utility of a prospect is the expected Utility, Eu

2 The Utility is defined over final wealth rather than gain andlosses

3 Risk aversion: u is concave (u′′ < 0)

4 Preferences are independent on the manner the prospects aredescribed


Prospect Theory

Main Departures from Expected Utility

Outline




4 Prospect Theory


6 Summary


Prospect Theory


Main Departures from EU

1 Non Linear Decision Weights

2 Individuals reason in terms of loss and gains rather than finaloutcome

3 Loss aversion

4 Framing Effects


Prospect Theory


Non Linear Decision Weights

Expected Utility requires a linear response to variation ofprobability

Experimentally: raising the probability from 0.39 to 0.40 hasmuch less impact than increasing the probability from 0.99 to1, or 0 to 0.01 (certainty effect)


Prospect Theory


Non Linear Decision Weights: Allais Paradox

Problem 1: A = (2500, 0.33; 2400, 0.66; 0, 0.01) orB = (2400, 1)

Problem 2: C = (2500, 0.33; 0, 0.67) orD = (2400, 0.34; 0, 0.66)

choosing B and C is not consistent with EU theory,

u(2400) > 0.33u(2500) + 0.66u(2400) or0.34u(2400) > 0.33u(2500)

The second inequality is inconsistent with C > D (assumeu(0) = 0)

Problem 2 is obtained from Problem 1, by eliminating .66 ofwinning 2400

Eliminating a large chance of winning alters the ordering


Prospect Theory


Non Linear Decision Weights: Allais Paradox; cont’d

Problem 3: A = (4000, .80) or B = (3000, 1)

Problem 4: C = (4000, 0.20) or D = (3000, 0.25)


Problem 4 is obtained from Problem 3, by dividing allprobabilities of a positive outcome by 4

Reducing the probability of winning from 1 to .25 has agreater effect than reducing it from .8 to .2

Certainty effect


Prospect Theory


Non Linear Decision Weights

Problem 7: A = (6000, 0.45) or B = (3000, 0.90)

Problem 8: C = (6000, 0.001) or D = (3000, 0.002)


Problem 8 is obtained from Problem 7, by dividing allprobabilities of a positive outcome by 45

Violation of the Independence axiom

With high probability of winning individuals are risk aversewith low individuals are more risk seekers


Prospect Theory


Willingness to Pay vs Willingness to Accept (Kahneman,Knetsch and Thaler 1990)

Markets for: Tokens and Mugs

Willingness to Pay is the maximum price an individuals wantto pay a good

Willingness to Accept is the minimum compensationdemanded by the owner to sell a good

Standard Assumptions imply that WTA ≈ WTP


Prospect Theory


Willingness to Pay vs Willingness to Accept

Market for Tokens and Mugs (6 USD)

in an experiment involving the exchange of a mug (6 USDvalue), some individuals were endowed with a mug, someother with the money to buy this mug

at a price 8.75 I will sell I will not sell

at a price 8.25 I will sell I will not sell

For the token: WTP = WTA

for the mug the Median WTP = 2.75 and the Median WTA= 5.25

Similar Experiments were conducted with pens, foldingbinoculars, lottery tickets etc.


Prospect Theory


Willingness to Pay vs Willingness to Accept

Why WTA >WTP?

Endowment Effect

Mugs belong to sellers’ endowment but not to the Buyers’endowment

A manifestation of Loss aversion


Prospect Theory


Framing Effects and status quo

The EU theory implies that choices are invariant to the wayoptions are described. An outbreak of a disease is expected to kill600 people.

Program A : 200 people will be saved (72%)

Program B : 1/3 probability to save 600 people, 2/3probability that no people will be saved (28%)

Program A (reframed) : 400 people will die (22%)

Program B (reframed) : 1/3 probability that nobody will die,2/3 that no people will be saved (78%)

In the first version the reference is:“everybody will die”. In thesecond version is “nobody will die”.

Individuals prefer the status quo.


Prospect Theory


Framing of Gains and Losses

Decision frames: Individuals evaluates outcome separatelyrather than jointly

Hedonic Frames: Individuals aggregate losses and segregategains :

who is happier someone who win 50 and 25 in two lotteries(64%) or someone that wins 75 in one lottery (36%)?


Prospect Theory

Prospect Theory

Outline




4 Prospect Theory


6 Summary


Prospect Theory

Prospect Theory

Prospect Theory

“Transforming” the EU theory to accommodate some of the aboveanomalies

V = pu(x) + (1 − p)u(y) is the value function for theExpected Utility

V = π(p)v(x) + (1 − π(p))v(y)

where π(p) is a decision weight which reflect the overallimpact of p on the value of the prospect

v is a function different from utility u


Prospect Theory

Prospect Theory

Prospect Theory: the function v

Individuals reason in terms of loss and gains, they are risk averse ingains and risk lovers in losses,

A difference between a gain of 100 to 200 appears larger thana difference between 1100 and 1200

The difference between a loss of -100 and -200 appears largerthan difference between -1100 and -1200

The effect of a change diminishes with the distance to thereference point: principle of diminishing sensitivity

Hence v ′′(x) < 0 for x > 0 and v ′′(x) > 0 for x < 0


Prospect Theory

Prospect Theory

Prospect Theory : the function v cont’d


Prospect Theory

Prospect Theory

Prospect Theory : the weighting function π(p)

the principle principle of diminishing sensitivity applies to π(p)

The natural reference for p are certainty p = 1 andimpossibility p = 0

an increase of 0.1 in the probability of winning a prize hasmore impact when it changes to probability from 0.9 to 1 orfrom 0 to 0.1 than from 0.5 to 0.6

diminishing sensitivity gives rise to a weighting function π(p)concave near 0 and convex near 1

implies subadditivity for unlikely event and superadditivitynear certainty


Prospect Theory : the weighting function π(p)

Prospect Theory

Empirical Evidence

Outline




4 Prospect Theory


6 Summary


Prospect Theory

Empirical Evidence

Finance

The Equity Premium Puzzle (Benartzi and Thaler 1995)

Stocks’ returns are more volatile than bonds’ returns

The average return to stocks is 8% higher than the averagereturn to bonds

this would imply an unrealistically high degree of risk aversion,i.e. lotteries (51.2K , 1) and (50K , 1/2; 100K , 1/2) should beequivalent

Since stocks have negative returns more often than bonds,this can be explained with the loss aversion.


Prospect Theory

Empirical Evidence

Finance

The Disposition Effect (Shefrin and Statman 1985)

Individuals hold stock that have lost value too long and areeager to sell stocks that have gained value

following the standard theory, price expectation should drivethis choice

trading volumes for stocks that have fallen in price is lowerthan for stocks that have risen

in a field experiment from a brokerage firm investors heldlosing stocks a median of 124 days and held winners only 104days

a similar effect exists in the housing market: when the houseprice falls the volume of the sales fall as well.


Prospect Theory

Empirical Evidence

Finance

The Disposition Effect: Finance (Odean (JF, 1998))

Do investors sell winning stocks more than losing stocks?

Individual trade data from Discount brokerage house(1987-1993)

Share of realized gains:

PGR =RealizedGains

RealizedGains + PaperGains(2)

Share of realized Losses:

PLR =RealizedLosses

RealizedGains + PaperGains(3)


Prospect Theory

Empirical Evidence

Finance

The Disposition Effect, Odean (JF, 1998))

PGR and PLR for the Entire Data Set

This table compares the aggregate Proportion of Gains Realized ~PGR! to the aggregate Pro- portion of Losses Realized ~PLR!, where PGR is the number of realized gains divided by the number of realized gains plus the number of paper ~unrealized! gains, and PLR is the number of realized losses divided by the number of realized losses plus the number of paper ~unrealized! losses. Realized gains, paper gains, losses, and paper losses are aggregated over time ~1987– 1993! and across all accounts in the data set. PGR and PLR are reported for the entire year, for December only, and for January through November. For the entire year there are 13,883 realized gains, 79,658 paper gains, 11,930 realized losses, and 110,348 paper losses. For December there are 866 realized gains, 7,131 paper gains, 1,555 realized losses, and 10,604 paper losses. The t-statistics test the null hypotheses that the differences in proportions are equal to zero assuming that all realized gains, paper gains, realized losses, and paper losses result from independent decisions.

Entire Year December Jan.–Nov.

PLR 0.098 0.128 0.094 PGR 0.148 0.108 0.152 Difference in proportions -0.050 0.020 -0.058 t-statistic -35 4.3 -38


Prospect Theory

Empirical Evidence

Finance

The Disposition Effect, Odean (JF, 1998))


Prospect Theory

Empirical Evidence

Economic Development

Mental Accounting effects For the Poor (Bertrand,Mullainathan, Shafir. 2004

Money is not fungible

Liquidity, current account , assets are perceived differently

Differential marginal propensities to consume (MPC)

current income (where MPC is high), current assets (whereMPC is intermediate), future income (where MPC is low).

Consumption functions thus end up being overly dependenton current income,

Importance to induce poor people to open a saving account

Savings, help investments and efficiently smooth consumptions


Prospect Theory

Empirical Evidence

Housing Markets

Loss Aversion in the Housing market (Genesove-Mayer ,2001)

For houses sales, natural reference point is previous purchaseprice, P0

Loss Aversion: Unwilling to sell house at a loss

General Prediction, when aggregate prices are low

Higer prices P relative to fundamentals

Bunching at purchase price P0

Lower probability of sale p(P)

Longer waiting on market


Prospect Theory

Empirical Evidence

Housing Markets

Loss Aversion in the Housing market (cont’d)

Listing price Li ,t

Lossi ,t = P̂i .t − P0

P̂ is the real market value (estimated)

Listing price increases with the Loss


Prospect Theory

Empirical Evidence

Housing Markets

Loss Aversion in the Housing Market (cont’d)

LOSS AVERSION AND LIST PRICES

DEPENDENT VARIABLE: LOG (ORIGINAL ASKING PRICE), OLS equations, standard errors are in parentheses.

(1) All

(2) All

(3) All

(4) All

(5) All

(6) All

Variable listings listings listings listings listings listings

LOSS 0.35 0.25 0.63 0.53 0.35 0.24 (0.06) (0.06) (0.04) (0.04) (0.06) (0.06) LOSS-squared -0.26 -0.26 (0.04) (0.04) LTV 0.06 0.05 0.03 0.03 0.06 0.05 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) Estimated 1.09 1.09 1.09 1.09 1.09 1.09

value in (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 1990

Estimated 0.86 0.80 0.91 0.85 price index (0.04) (0.04) (0.03) (0.03) at quarter of entry

Residual from 0.11 0.11 0.11 last sale (0.02) (0.02) (0.02) price

Months since -0.0002 -0.0003 -0.0002 -0.0003 -0.0002 -0.0003 last sale (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001)

Dummy No No No No Yes Yes variables for quarter of entry

Constant

-0.77

-0.70

-0.84

-0.77

-0.88

-0.86

(0.14) (0.14) (0.13) (0.14) (0.10) (0.10)

R2 0.85 0.86 0.86 0.86 0.86 0.86 Number of 5792 5792 5792 5792 5792 5792

observations


Prospect Theory

Empirical Evidence

Housing Markets

Effect of the experience and loss Aversion

(1) (2) (3) (4)

Variable

All listings

All listings

All listings

All listings

LOSS x owner-occupant 0.50 0.42 0.66 0.58 (0.09) (0.09) (0.08) (0.09) LOSS x investor 0.24 0.16 0.58 0.49

(0.12) (0.12) (0.06) (0.06) LOSS-squared x owner-occupant -0.16 -0.17

(0.14) (0.15) LOSS-squared x investor -0.30 -0.29

(0.02) (0.02) LTV x owner-occupant 0.03 0.03 0.01 0.01

(0.02) (0.02) (0.01) (0.01) LTV x investor 0.053 0.053 0.02 0.02

(0.027) (0.027) (0.02) (0.02) Dummy for investor -0.02 -0.02 -0.03 -0.03

(0.014) (0.01) (0.01) (0.01) Estimated value in 1990 1.09 1.09 1.09 1.09

(0.01) (0.01) (0.01) (0.01) Estimated price index at quarter of 0.84 0.80 0.86 0.82

entry (0.05) (0.04) (0.04) (0.04) Residual from last sale price 0.08 0.08

(0.02) (0.02) Months since last sale -0.0002 -0.0003 -0.0001 -0.0002

(0.0002) (0.00015) (0.0001) (0.0001) Constant -0.80 -0.76 -0.86 -0.84

(0.16) (0.16) (0.14) (0.16)

R2 0.85 0.85 0.86 0.86 Number of observations 3687 3687 3687 3687


Prospect Theory

Empirical Evidence

Labor Market

New York Cab Drivers (Camerer, Babcock, Loewensteinand Thaler, 1997)

cab drivers in New York lease their cabs for a fixed fee for upto 12 hours

They work long hours when there is low demand (sunny days)and short hours when there is high demand (rainy days)

The standard theory would predict the opposite

This is consistent with the loss aversion of cab drivers fix adaily target and are averse to fall short of it.

Inexperienced drivers feature this behavior more thanexperienced ones


Prospect Theory

Empirical Evidence

Labor Market

New York Cab Drivers (Camerer, Babcock, Loewensteinand Thaler, 1997)

FIGURE I Hours-Wage Relationships


Prospect Theory

Empirical Evidence

Domestic Violence

Domestic Violence (Card and Dahl, QJE 2011))

Consider a man in conflicted relationship with the spouse

What is the effect of an event such as the local football teamlosing or winning a game?

With probability h the man loses control and becomes violent

Assume h = h(u) with h′ < 0 and u the underlying utilityDenote by p the ex-ante expectation that the team wins


Prospect Theory

Empirical Evidence

Domestic Violence

Implication from Reference dependent utility)

The more a win is expected, the more a loss is costly in termsof utility, the more likely it is to trigger violence

The (positive) effect of a gain is higher the more unexpected(lower p)


Prospect Theory

Empirical Evidence

Domestic Violence

Data)

Domestic violence (NIBRS)

Football matches by State

Expected win probability from Las Vegas predicted pointspread

Separate matches into

Predicted win (+3 points of spread)Predicted closePredicted loss (-3 points)


Prospect Theory

Empirical Evidence

Domestic Violence

Results


Prospect Theory

Empirical Evidence

Domestic Violence

Results

Unexpected loss increases domestic violence

No effect of expected loss

No effect of unexpected win, if anything increases violence

Effect disappears within a few hours of game end – Emotionsare transient


Prospect Theory

Summary

Summary

Main departures from EU theory

Prospect Theory can accommodate most of them

several applications

FinanceLabor MarketEconomic DevelopmentHousing MarketDomestic Violence


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Prospect Theory - University of Warwick · Prospect Theory, 10 of 44. ... Violation of the Independence axiom ... Prospect Theory Empirical Evidence Finance The Equity Premium Puzzle