Loss Aversion
A frequent electronic mail correspondent asked "I’d dear to hear your select on “loss aversion.” I but finished listening to Kahneman’s book." My reply seems worth sharing amongst weblog readers.
Expected Utility
Let’s review expected utility first. The utility you lot larn from consumption or wealth is a concave business office of consumption or wealth. An extra dollar makes you lot to a greater extent than happy than it makes Bill Gates. So, compare either getting C for sure, or a 50/50 bet of getting C+Delta or C-Delta, i.e. having C or betting 50/50 on a money flip. The expected utility of C for sure is but U(C). The expected utility of the bet is
European Union = prob(loss) * U(consumption if loss) + prob(gain) * U(consumption if gain)
European Union = 1/2 * U(C - Delta) + 1/2 * U(C + Delta).
As the graph shows, this is less than the expected utility of C for sure. So, people should turn down fair value bets. They are “risk averse”.
Comments. Behavioral fans (New York times has done this oft inwards its economic science coverage) criticize “classical economics” yesteryear maxim it ignores the fact that people fearfulness losses to a greater extent than than they value gains. That’s absolutely false. Look at the utility function. People fearfulness losses to a greater extent than than they value gains. That’s the whole betoken of expected utility. (You’ll come across the confusion inwards a second).
H5N1 mutual mistake: EU( C) is non the same every bit U [ E(C )]. You exercise non bring out the utility of expected consumption, you lot bring out the expected utility of consumption. In my graph, C is equal to the expected value of C-Delta too C+Delta, too the whole betoken is that the utility of C is bigger than the expected utility of (C-Delta) or (C+Delta). You tin select due east within a linear function, but you lot cannot select due east within a nonlinear function.
Loss aversion
OK, on to loss aversion. In the park form of experiments Kahneman industrial plant life that people seem reluctant to lose money. They receive got a “reference point” too piece of work hard to avoid bets that mightiness pose them below that reference point. He models that every bit expected utility amongst a kink inwards it, every bit inwards the instant drawing.
I was careful to pull the reference betoken every bit dissimilar than C. People exercise non necessarily identify the reference betoken at the expected value of the bet. In fact, unremarkably they don’t. If betting on stocks, the expected value of the bet is to gain 7% per year. The “don’t lose money” betoken would hold upwardly exercise non become below 0, non exercise non become below the mean. Here people are peculiarly afraid exclusively of the real left part of the distribution.
Now, really, how are these models different? Expected utility tin hold upwardly whatever function, too nobody said it doesn’t receive got a kink inwards it. The cardinal distinguishing characteristic of loss aversion – too its Achilles heel – is that the reference betoken shifts around. If you lot brand some money, too play again, too then your kink shifts upwardly to the novel amount of money you lot made. Expected utility is supposed to remain the same business office of consumption or wealth. People mightiness alter demeanour – most probable the utility crimp is flatter at high levels of consumption, thence rich people are less adventure averse. But the crimp itself does non shift. The cardinal supposition that distinguishes loss aversion from expected utility is that the kink betoken shifts approximately every bit you lot gain too lose money.
That’s also the Achilles heel. The commencement work is how exercise you lot grip sequential bets. If I become to the casino, too know I volition play twice, how exercise I recall virtually my strategy? With expected utility this is easy, because the expected utility works backwards. Suppose you lot win the commencement bet, too then figure out what you lot exercise inwards the instant bet. For each of win or loss inwards the commencement bet, then, you lot receive got an expected utility from taking the instant bet. The expected utility of the commencement bet is too then the expected vaule of the expected utilities you lot would receive got if you lot won or lost.
Equations mightiness hold upwardly amend than words. Let Chh, Chl, Clh, too Cll hold upwardly consumption if you lot win twice, win too and then lose, lose too and then win, lose too and then lose, too U(Chh), U(Chl), etc hold upwardly their utilities. So, suppose you lot won the commencement bet. You evaluate the instant bet by
EUh == European Union given you lot won commencement bet = Ph*U(Chh) + Pl*U(Chl).
Similarly, if you lot lost the commencement bet, then
EUl = Eu given you lot lost the commencement bet = Ph*U(Clh) + Pl*U(Lll).
So now, the expected utility of the commencement bet is but a one-stage bet, amongst these expected utilities every bit payoffs.
European Union = Ph *Euh + Pl*EUl
I won’t become through to a greater extent than equations, but the same thing holds for decisions. You tin piece of work optimal decisions backwards.
Now, this all gets to hold upwardly a large work amongst loss aversion. The cardinal question: Do loss averse people inwards phase 1 recall virtually the fact that if they win or lose inwards phase 1 that volition alter their reference betoken for phase 2? Again, the reference betoken must shift, or nosotros but receive got expected utility. If people ignore that their actions today shift the reference betoken tomorrow, too then they’re unbelievably dumb. If people don’t, too then nosotros receive got a mess on our hands. Since your preferences today disagree amongst your preferences tomorrow, you lot mightiness deed strategically, deliberately winning or losing today to shift the reference betoken for tomorrow too influence how you lot volition bear tomorrow. There receive got been brave papers trying to piece of work this out (Barberis, Huang too Santos) but the lawsuit has been, inwards my view, thence complex that it hasn’t come upwardly inwards to mutual use.
But really to hold upwardly useful inwards economic science or finance, nosotros receive got to receive got a model that does non apply but to wake up, brand a bet, eat, die, but that describes how people brand decisions over a lifetime, too amongst noesis that they volition bet many times.
Some to a greater extent than problems amongst loss aversion: We sure as shooting come across lots of private demeanour that suggests reference points. People larn really reluctant to sell houses for less than they bought them for, for example. The work hither is that expected utility refers to your overall wealth. You don’t heed losing on your house, say, if you lot gained inwards your stocks, or if the novel menage you lot desire to purchase also went downwards inwards price, every bit your overall wealth or consumption does non change. Now, to apply loss aversion, it seems nosotros demand to define loss aversion every bit a business office of each private purchase, non overall consumption. You demand “mental accounting” every bit well, of which items become into which pot, too a dominion non to lose on private pots, every bit good every bit loss aversion.
A deeper skepticism virtually "irrationality"
I receive got a deeper skepticism virtually the rush to label people irrational (and us researchers oh thence much smarter). What’s thence irrational virtually next a dominion or heuristic that says, avoid losing money on your trades? Another widely adduced “irrationality” is that people tend to merchandise besides much. Given that prices oft exercise bounce back, the heuristic “don’t lose money on your trades” mightiness hold upwardly a useful guide. Most buying too selling oft involves a negotiation. Don’t sell at a loss helps you lot to avoid sudden negotiators. It’s also a skilful precommitment device. Real estate agents continue telling us “well, they won’t select that offering because they’d sell at a loss” fifty-fifty when they bought at the peak inwards 2007.
Likewise, “when people inwards lab coats come upwardly too tell you lot what the probabilities of things are too offering you lot bets on them, don’t believe them because they’re trying to fob you” is a pretty skilful heuristic inwards life. You are going to run inwards to a lot to a greater extent than people playing iii bill of fare monte or offering Bernie Madoff investments, too people inwards lab coats trying to essay you’re a moron, than you lot are going to run inwards to honest researchers explaining how the game really works.
Apparently irrational rules are inwards fact oft skilful rules for actual life. “Don’t pay attending to sunk costs” say economists, but if you lot run away from every one-half finished projection because it’s a sunk cost, you lot don’t larn anything done inwards life. Paying attending to sunk costs is a skilful agency to brand sure you lot really complete writing, revising, too publishing papers! We alive inwards a deeply information overload environment, too nosotros receive got express processing capacity. H5N1 lot of obviously irrational demeanour seems to me decent rules of pollex for daily life, that look irrational when extrapolated out of context to cleverly constructed environments that people receive got never seen earlier too receive got piddling experience with.
Mental accounting is similar. The accounting subdivision of the University of Chicago Booth school, domicile of efficient markets, subdivides the school’s money into thousands of separate budget items amongst a dominion that you can’t lose money on whatever private one. If you lot purchase too extra bottle of vino on the seminar budget, you lot can’t offset that fifty-fifty if at the destination of the yr in that location is money left over inwards the Pizzas for MBAs budget. Such budgeting is a practically universal method of controlling costs inwards all large organizations. It sure feels stupid, but is it really given the information problems?
Moreover, if people exercise bear this way, in that location is a agency to brand a huge amount of money off of them. Asset prices are smoothen functions of gains or losses. Suppose your reference betoken is, you lot don’t desire to lose to a greater extent than than $1000 on stocks. By buying stocks too options, I tin create a portfolio that volition never lose to a greater extent than than $1000. The cost of the downside insurance is a smoothen business office of that loss point, thence it volition hold upwardly cheaper for me to purchase that downside insurance than it volition hold upwardly for me to sell it to you. Or you lot tin purchase it for yourself. There is a lot of behavioral report of people’s portfolios too the nutty investments they make, but nosotros exercise non come across pervasive buying of such downside insurance options, nor exercise nosotros come across the large prices such options would receive got if people were all loss averse.
In sum, I prefer when seeing odd demeanour to inquire a flake harder "just what interrogation is this the correct respond to?" earlier rushing to say people are dumb too inquire the authorities to nudge them my way.
Habits too others
Since I worked on it, I receive got to holler i halfway alternative – habits. See the graph. Suppose people receive got a lower storey of consumption that they really don’t desire to become below. The obvious lower fountain is starvation, but nosotros all prepare habits of consumption that would hold upwardly super-painful to change. A hedge fund manager’s married adult woman i time said at a cocktail political party “I’d sooner go than wing commercial again,” too that tin hold upwardly represented yesteryear the habit storey every bit well.
Now, every bit it is, that’s but some other expected utility function. But hither too, nosotros brand the habit betoken motion approximately depending on experience. The hedge fund manager’s married adult woman was i time middle storey similar us too idea the peanuts on Southwest were a grand treat. As you lot swallow more, or every bit you lot notice your neighbors too friends swallow more, the minimum acceptable storey of consumption rises. It tin also model debts too fixed costs -- don't lose thence much money that you lot receive got to sell the menage too motion into an apartment.
One argue this is dissimilar than loss aversion is that it turns out to hold upwardly much to a greater extent than tractable for the dynamic interrogation – how exercise you lot care for multiple bets. Not having a kink wandering approximately helps a lot. The strategic chemical factor is there. If the habit depends on your consumption, non your neighbor’s, too then when you lot swallow to a greater extent than you lot reset your habits. You mightiness know this ahead of time, too nosotros tin piece of work out easily how you lot behave. Habits brand consumption an addictive good, thence when thinking virtually eating to a greater extent than today, you lot recognize that it volition influence how you lot experience tomorrow. When you lot potable some other cappuccino today, you lot know it volition brand you lot desire some other i tomorrow, too are less probable to potable today every bit a result. We tin piece of work those things out easily.
That doesn’t address the mental accounting issues, the vogue to care for bets inwards isolation rather than every bit parts of a portfolio, too thence forth. But it does capture the vogue to really avoid large losses, too how what a loss is shifts over fourth dimension inwards reply to gains too losses inwards wealth.
Two other pop approaches model a lot of challenging demeanour every bit well. Recursive or Epstein-Zin utility is a non-expected utility model that captures lab experiments too is also analytically tractable, thence it's becoming real mutual inwards macroeconomics too property pricing. Lars Hansen is also been on a long enquiry agenda of fifty-fifty to a greater extent than full general utility functions that are "ambiguity averse," capturing that people shrink away from incertitude that they really don't know the probabilities of. Alas, i time in that location is a clear too tractable mathematical model, people similar this seem non welcome inwards the behavioral finance club, which says to a greater extent than virtually academic politics than virtually noun matters.
I promise that helps!
PS to all: Grumpy is back! I was traveling a lot making frequent weblog posts difficult.
Update: An electronic mail correspondent writes
Expected Utility
Let’s review expected utility first. The utility you lot larn from consumption or wealth is a concave business office of consumption or wealth. An extra dollar makes you lot to a greater extent than happy than it makes Bill Gates. So, compare either getting C for sure, or a 50/50 bet of getting C+Delta or C-Delta, i.e. having C or betting 50/50 on a money flip. The expected utility of C for sure is but U(C). The expected utility of the bet is
European Union = prob(loss) * U(consumption if loss) + prob(gain) * U(consumption if gain)
European Union = 1/2 * U(C - Delta) + 1/2 * U(C + Delta).
As the graph shows, this is less than the expected utility of C for sure. So, people should turn down fair value bets. They are “risk averse”.
Comments. Behavioral fans (New York times has done this oft inwards its economic science coverage) criticize “classical economics” yesteryear maxim it ignores the fact that people fearfulness losses to a greater extent than than they value gains. That’s absolutely false. Look at the utility function. People fearfulness losses to a greater extent than than they value gains. That’s the whole betoken of expected utility. (You’ll come across the confusion inwards a second).
H5N1 mutual mistake: EU( C) is non the same every bit U [ E(C )]. You exercise non bring out the utility of expected consumption, you lot bring out the expected utility of consumption. In my graph, C is equal to the expected value of C-Delta too C+Delta, too the whole betoken is that the utility of C is bigger than the expected utility of (C-Delta) or (C+Delta). You tin select due east within a linear function, but you lot cannot select due east within a nonlinear function.
Loss aversion
OK, on to loss aversion. In the park form of experiments Kahneman industrial plant life that people seem reluctant to lose money. They receive got a “reference point” too piece of work hard to avoid bets that mightiness pose them below that reference point. He models that every bit expected utility amongst a kink inwards it, every bit inwards the instant drawing.
I was careful to pull the reference betoken every bit dissimilar than C. People exercise non necessarily identify the reference betoken at the expected value of the bet. In fact, unremarkably they don’t. If betting on stocks, the expected value of the bet is to gain 7% per year. The “don’t lose money” betoken would hold upwardly exercise non become below 0, non exercise non become below the mean. Here people are peculiarly afraid exclusively of the real left part of the distribution.
Now, really, how are these models different? Expected utility tin hold upwardly whatever function, too nobody said it doesn’t receive got a kink inwards it. The cardinal distinguishing characteristic of loss aversion – too its Achilles heel – is that the reference betoken shifts around. If you lot brand some money, too play again, too then your kink shifts upwardly to the novel amount of money you lot made. Expected utility is supposed to remain the same business office of consumption or wealth. People mightiness alter demeanour – most probable the utility crimp is flatter at high levels of consumption, thence rich people are less adventure averse. But the crimp itself does non shift. The cardinal supposition that distinguishes loss aversion from expected utility is that the kink betoken shifts approximately every bit you lot gain too lose money.
That’s also the Achilles heel. The commencement work is how exercise you lot grip sequential bets. If I become to the casino, too know I volition play twice, how exercise I recall virtually my strategy? With expected utility this is easy, because the expected utility works backwards. Suppose you lot win the commencement bet, too then figure out what you lot exercise inwards the instant bet. For each of win or loss inwards the commencement bet, then, you lot receive got an expected utility from taking the instant bet. The expected utility of the commencement bet is too then the expected vaule of the expected utilities you lot would receive got if you lot won or lost.
Equations mightiness hold upwardly amend than words. Let Chh, Chl, Clh, too Cll hold upwardly consumption if you lot win twice, win too and then lose, lose too and then win, lose too and then lose, too U(Chh), U(Chl), etc hold upwardly their utilities. So, suppose you lot won the commencement bet. You evaluate the instant bet by
EUh == European Union given you lot won commencement bet = Ph*U(Chh) + Pl*U(Chl).
Similarly, if you lot lost the commencement bet, then
EUl = Eu given you lot lost the commencement bet = Ph*U(Clh) + Pl*U(Lll).
So now, the expected utility of the commencement bet is but a one-stage bet, amongst these expected utilities every bit payoffs.
European Union = Ph *Euh + Pl*EUl
I won’t become through to a greater extent than equations, but the same thing holds for decisions. You tin piece of work optimal decisions backwards.
Now, this all gets to hold upwardly a large work amongst loss aversion. The cardinal question: Do loss averse people inwards phase 1 recall virtually the fact that if they win or lose inwards phase 1 that volition alter their reference betoken for phase 2? Again, the reference betoken must shift, or nosotros but receive got expected utility. If people ignore that their actions today shift the reference betoken tomorrow, too then they’re unbelievably dumb. If people don’t, too then nosotros receive got a mess on our hands. Since your preferences today disagree amongst your preferences tomorrow, you lot mightiness deed strategically, deliberately winning or losing today to shift the reference betoken for tomorrow too influence how you lot volition bear tomorrow. There receive got been brave papers trying to piece of work this out (Barberis, Huang too Santos) but the lawsuit has been, inwards my view, thence complex that it hasn’t come upwardly inwards to mutual use.
But really to hold upwardly useful inwards economic science or finance, nosotros receive got to receive got a model that does non apply but to wake up, brand a bet, eat, die, but that describes how people brand decisions over a lifetime, too amongst noesis that they volition bet many times.
Some to a greater extent than problems amongst loss aversion: We sure as shooting come across lots of private demeanour that suggests reference points. People larn really reluctant to sell houses for less than they bought them for, for example. The work hither is that expected utility refers to your overall wealth. You don’t heed losing on your house, say, if you lot gained inwards your stocks, or if the novel menage you lot desire to purchase also went downwards inwards price, every bit your overall wealth or consumption does non change. Now, to apply loss aversion, it seems nosotros demand to define loss aversion every bit a business office of each private purchase, non overall consumption. You demand “mental accounting” every bit well, of which items become into which pot, too a dominion non to lose on private pots, every bit good every bit loss aversion.
A deeper skepticism virtually "irrationality"
I receive got a deeper skepticism virtually the rush to label people irrational (and us researchers oh thence much smarter). What’s thence irrational virtually next a dominion or heuristic that says, avoid losing money on your trades? Another widely adduced “irrationality” is that people tend to merchandise besides much. Given that prices oft exercise bounce back, the heuristic “don’t lose money on your trades” mightiness hold upwardly a useful guide. Most buying too selling oft involves a negotiation. Don’t sell at a loss helps you lot to avoid sudden negotiators. It’s also a skilful precommitment device. Real estate agents continue telling us “well, they won’t select that offering because they’d sell at a loss” fifty-fifty when they bought at the peak inwards 2007.
Likewise, “when people inwards lab coats come upwardly too tell you lot what the probabilities of things are too offering you lot bets on them, don’t believe them because they’re trying to fob you” is a pretty skilful heuristic inwards life. You are going to run inwards to a lot to a greater extent than people playing iii bill of fare monte or offering Bernie Madoff investments, too people inwards lab coats trying to essay you’re a moron, than you lot are going to run inwards to honest researchers explaining how the game really works.
Apparently irrational rules are inwards fact oft skilful rules for actual life. “Don’t pay attending to sunk costs” say economists, but if you lot run away from every one-half finished projection because it’s a sunk cost, you lot don’t larn anything done inwards life. Paying attending to sunk costs is a skilful agency to brand sure you lot really complete writing, revising, too publishing papers! We alive inwards a deeply information overload environment, too nosotros receive got express processing capacity. H5N1 lot of obviously irrational demeanour seems to me decent rules of pollex for daily life, that look irrational when extrapolated out of context to cleverly constructed environments that people receive got never seen earlier too receive got piddling experience with.
Mental accounting is similar. The accounting subdivision of the University of Chicago Booth school, domicile of efficient markets, subdivides the school’s money into thousands of separate budget items amongst a dominion that you can’t lose money on whatever private one. If you lot purchase too extra bottle of vino on the seminar budget, you lot can’t offset that fifty-fifty if at the destination of the yr in that location is money left over inwards the Pizzas for MBAs budget. Such budgeting is a practically universal method of controlling costs inwards all large organizations. It sure feels stupid, but is it really given the information problems?
Moreover, if people exercise bear this way, in that location is a agency to brand a huge amount of money off of them. Asset prices are smoothen functions of gains or losses. Suppose your reference betoken is, you lot don’t desire to lose to a greater extent than than $1000 on stocks. By buying stocks too options, I tin create a portfolio that volition never lose to a greater extent than than $1000. The cost of the downside insurance is a smoothen business office of that loss point, thence it volition hold upwardly cheaper for me to purchase that downside insurance than it volition hold upwardly for me to sell it to you. Or you lot tin purchase it for yourself. There is a lot of behavioral report of people’s portfolios too the nutty investments they make, but nosotros exercise non come across pervasive buying of such downside insurance options, nor exercise nosotros come across the large prices such options would receive got if people were all loss averse.
In sum, I prefer when seeing odd demeanour to inquire a flake harder "just what interrogation is this the correct respond to?" earlier rushing to say people are dumb too inquire the authorities to nudge them my way.
Habits too others
Since I worked on it, I receive got to holler i halfway alternative – habits. See the graph. Suppose people receive got a lower storey of consumption that they really don’t desire to become below. The obvious lower fountain is starvation, but nosotros all prepare habits of consumption that would hold upwardly super-painful to change. A hedge fund manager’s married adult woman i time said at a cocktail political party “I’d sooner go than wing commercial again,” too that tin hold upwardly represented yesteryear the habit storey every bit well.
Now, every bit it is, that’s but some other expected utility function. But hither too, nosotros brand the habit betoken motion approximately depending on experience. The hedge fund manager’s married adult woman was i time middle storey similar us too idea the peanuts on Southwest were a grand treat. As you lot swallow more, or every bit you lot notice your neighbors too friends swallow more, the minimum acceptable storey of consumption rises. It tin also model debts too fixed costs -- don't lose thence much money that you lot receive got to sell the menage too motion into an apartment.
One argue this is dissimilar than loss aversion is that it turns out to hold upwardly much to a greater extent than tractable for the dynamic interrogation – how exercise you lot care for multiple bets. Not having a kink wandering approximately helps a lot. The strategic chemical factor is there. If the habit depends on your consumption, non your neighbor’s, too then when you lot swallow to a greater extent than you lot reset your habits. You mightiness know this ahead of time, too nosotros tin piece of work out easily how you lot behave. Habits brand consumption an addictive good, thence when thinking virtually eating to a greater extent than today, you lot recognize that it volition influence how you lot experience tomorrow. When you lot potable some other cappuccino today, you lot know it volition brand you lot desire some other i tomorrow, too are less probable to potable today every bit a result. We tin piece of work those things out easily.
That doesn’t address the mental accounting issues, the vogue to care for bets inwards isolation rather than every bit parts of a portfolio, too thence forth. But it does capture the vogue to really avoid large losses, too how what a loss is shifts over fourth dimension inwards reply to gains too losses inwards wealth.
Two other pop approaches model a lot of challenging demeanour every bit well. Recursive or Epstein-Zin utility is a non-expected utility model that captures lab experiments too is also analytically tractable, thence it's becoming real mutual inwards macroeconomics too property pricing. Lars Hansen is also been on a long enquiry agenda of fifty-fifty to a greater extent than full general utility functions that are "ambiguity averse," capturing that people shrink away from incertitude that they really don't know the probabilities of. Alas, i time in that location is a clear too tractable mathematical model, people similar this seem non welcome inwards the behavioral finance club, which says to a greater extent than virtually academic politics than virtually noun matters.
I promise that helps!
PS to all: Grumpy is back! I was traveling a lot making frequent weblog posts difficult.
Update: An electronic mail correspondent writes
If a domicile was purchased at $500,000 amongst a mortgage of $450,000, too it is straightaway sold for less than fifty-fifty $475,000, too then afterward commissions too closing costs, the seller has less than $450,000 inwards mitt too volition hold upwardly required to “bring cash to the closing” inwards monastic say to fully pay off the bank. Generally, families amongst homes selling for below mortgage value receive got problem raising whatever cash at all. All this is farther complicated yesteryear the work of where too how tin the seller motion to side yesteryear side if all his cash is pose into getting out of the electrical flow mortgage? No money for novel downwards payment, or commencement month’s rent too deposit. The electrical flow possessor is really stuck at an to a higher identify marketplace offering price.This is a skilful point. Fixed costs too transactions costs tin give ascension to the extra costs of a loss, too arrive at a kink. People who prepare rules of pollex inwards that circumstance may non notice the lab experiment is cleverly designed non to receive got the actual costs of many real-world losses.
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