Prospect theory Flashcards
two ways of having a preference relation
complete: always define preference between x and y transitive: if x>y and y>z then x>z
a preference relation between goods is rational if…
complete or transitive preference relationship
what is monotone
more is preferred to less
what is convex
diminishing marginal rates of substitutions (agents prefer diversification)
what is independence
if x>y then (x,z)>(y,z)
what is continuity
if A>B>C then there is always a p such that A and C weighted equals B (5/31 don’t rly get)
what are main assumptions of expected utility theory
continuity independence linear in probability
what is linear in probability
V(q) = Σpiu(xi)
what are the other assumptions in expected utility theory
utility defined over final wealth rather than gains and losses, preferences are independent on the manner the prospects are described
what are the puzzles of EU theory
framing effects (dying and saving people) loss aversion (losses loom larger than gain), utility not defined over final wealth (100k vs 50k happy 100k vs 500k sad), linear decision weights
what is the Allais paradox (linear decision weights)
A=(4000,.80) or B=(3000,1) C=(4000,0.20) or D=(3000,0.25) people prefer B to A and C to D. C&D obtained by dividing probabilities by 4. reducing probability of winning from 1 to 0.25 has a greater effect than reducing it from 0.8 to 0.2 (certainty effect)
what does it mean that individuals are risk averse in gains and risk lovers in losses
diff between gain of 100 to 200 appears larger than 1100 and 1200, diff between loss of -100 and -200 appears larger than -1100 and -1200. hence v’‘(x)<0 for x>0 and v’‘(x)>0 for x<0
what does risk loving in losses mean
in order to avoid losses you will do crazy things (irrational risk)
what is π(p)
weighting function: probability is a function of π
in prospect theory how is the decision weight used
the value of an uncertain outcome is multiplied by a decision weight π(p) which is a monotonic function of p but is not a probability (in EU just multiplied by probability)
explain mug experiment and who wrote it*
kahneman et al (1990), market for mugs (6 USD) some were endowed a mug some others with money to buy, median WTP=2.75 mediam WTA=5.25
why is mug experiment of note
standard assumptions imply WTA≈WTP, evidence of endowment effect: value things you own more than things you don’t. this type of loss aversion implies asymmetry in treatment of losses and foregone gains
WTP and WTA d
willingness to accept: minimum compensation demanded by owner to sell willingness to pay: max price individuals want to pay for a good
what is the disposition effect in terms of stocks
individuals hold stock that have lost value for too long and are eager to sell stocks that have gained value
first field experiment of brokerage firm*
shefrin and statman (1985) field experiment brokerage firm investors held losing stocks median 124 days and held winners only 104 days
what is another similar example to investors holding stocks that have lost value for too long and sell gainers
similar effect in housing market when house price falls the volume of sales falls as well
Odean (1998)*
info from discount brokerage house 1987-1993. share of realised gains PGR=realisedgains/realisedgains+papergains (PLR opposite)(this controls for the market) PGR greater than PLR people more reluctant to realise losses than gains however in December PLR>PGR because if you have more losses you get taxed less at end of year
why do you need paper gains as well
because if bull market would naturally have more winners than losers. need to look at frequency with which they sell winners and losers relative to their opportunities to sell winners and losers
talk about cab driver paper*
Camerer et al. (1997), cab drivers lease cabs for fixed fee, they work long hours when there is low demand (sunny) and short hours when high demand (rainy), this is consistent with loss aversion: fix a daily target and averse to fall short standard theory says should respond positively to wage changes (work more when wage higher,(leisure cost more))
how does the cab driver link with loss aversion
notion that drivers are averse to falling below a target income, almost consistent with loss aversion
why study NYC cabs
exogenous wage fluctuations due to weather, subway breakdowns etc, make labour supply decisions each day and have a target wage, this motivates study of their behaviour as one-day target predicts negative elasticities.
what is prospect theory
when faced with simple 2 or 3 outcome lotteries, people behave as if maximising S-shaped value function that is defined on gains and losses rather than on levels of wealth
explain shape of prospect theory value function
concave in domain of gains and convex in domain of losses. steeper for losses than gains, implies people are generally risk-averse. critical to value function is the reference point from which gains and losses measured, its usually the status quo but could be expectation or aspiration level
what does certainty effect lead to from Kahneman et al (1990)
contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses
what is the certainty effect and which paper is it from
people overweight outcomes that are considered certain, relative to outcomes that are merely probable
what is the reflection effect
risk aversion in the positive domain is accompanies by risk seeking in the negative domain (people willing to accept risk .8 to lose 4000 over a sure loss of 3000)
what is the isolation effect
in order to simplify the choice between alternatives, people often disregard components that the alternatives share, and focus on the components that distinguish them., this produces inconsistent preferences as prospects can be decomposed in different ways leading to diff choices
what is the key feature of prospect theory
carriers of value are changes in wealth or welfare, rather than final stages
in prospect theory what happens to the value of each outcome
multiplied by a decision weight, decision weights are inferred from choices between prospects
How are decision weights different to probabilities
decision weights measure the impact of events on the desirability of prospects, not merely the perceived likelihood of these events
what is loss aversion
losses loom larger than gains, Status-quo Bias (Endowment represents the status-quo)
PGR PLR
proportion of realised gains/losses
what is the conclusion of the Odean (1998) paper
a large difference in the proportion of realised gains (PGR) and realised losses (PLR) indicates that investors are more willing to realise either gains or losses
what are some properties of π
impossible events are discarded π(0)-0, the function is not well behaved near end points, for low probabilities π(p)>p, thus low probabilities overweighted, moderate and high probabilities underweighted and latter more pronounced than former
what is the principle of diminishing sensitivity
the effect of a change diminishes with the distance to the reference point
what does complete mean
Complete: it is always possible to define preferences between
good x and y
what is transitive
Transitive: if x > y and y > z then x > z
