Loss Aversion
A frequent e-mail correspondent asked "I’d dearest to hear your pick out on “loss aversion.” I simply finished listening to Kahneman’s book." My response seems worth sharing alongside 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 simply 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 spend upwards fair value bets. They are “risk averse”.
Comments. Behavioral fans (New York times has done this oftentimes inward its economic science coverage) criticize “classical economics” past times 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 run into the confusion inward a second).
H5N1 mutual mistake: EU( C) is non the same every bit U [ E(C )]. You practise non uncovering the utility of expected consumption, you lot uncovering the expected utility of consumption. In my graph, C is equal to the expected value of C-Delta as well as C+Delta, as well as the whole betoken is that the utility of C is bigger than the expected utility of (C-Delta) or (C+Delta). You tin forcefulness out pick out due east within a linear function, but you lot cannot pick out due east within a nonlinear function.
Loss aversion
OK, on to loss aversion. In the commons kind of experiments Kahneman institute that people seem reluctant to lose money. They direct maintain a “reference point” as well as piece of work hard to avoid bets that powerfulness pose them below that reference point. He models that every bit expected utility alongside a kink inward it, every bit inward the mo drawing.
I was careful to pull the reference betoken every bit dissimilar than C. People practise non necessarily identify the reference betoken at the expected value of the bet. In fact, commonly 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 last practise non larn below 0, non practise non larn below the mean. Here people are peculiarly afraid alone of the real left constituent of the distribution.
Now, really, how are these models different? Expected utility tin forcefulness out last whatever function, as well as nobody said it doesn’t direct maintain a kink inward it. The cardinal distinguishing characteristic of loss aversion – as well as its Achilles heel – is that the reference betoken shifts around. If you lot brand some money, as well as play again, as well as thus your kink shifts upwards to the novel amount of money you lot made. Expected utility is supposed to remain the same business office of consumption or wealth. People powerfulness modify demeanour – most probable the utility crimp is flatter at high levels of consumption, thus rich people are less jeopardy 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 as well as lose money.
That’s also the Achilles heel. The start work is how practise you lot handgrip sequential bets. If I larn to the casino, as well as know I volition play twice, how practise I yell upwards nigh my strategy? With expected utility this is easy, because the expected utility plant backwards. Suppose you lot win the start bet, as well as thus figure out what you lot practise inward the mo bet. For each of win or loss inward the start bet, then, you lot direct maintain an expected utility from taking the mo bet. The expected utility of the start bet is as well as thus the expected vaule of the expected utilities you lot would direct maintain if you lot won or lost.
Equations powerfulness last amend than words. Let Chh, Chl, Clh, as well as Cll last consumption if you lot win twice, win as well as and thus lose, lose as well as and thus win, lose as well as and thus lose, as well as U(Chh), U(Chl), etc last their utilities. So, suppose you lot won the start bet. You evaluate the mo bet by
EUh == European Union given you lot won start bet = Ph*U(Chh) + Pl*U(Chl).
Similarly, if you lot lost the start bet, then
EUl = Eu given you lot lost the start bet = Ph*U(Clh) + Pl*U(Lll).
So now, the expected utility of the start bet is simply a one-stage bet, alongside these expected utilities every bit payoffs.
European Union = Ph *Euh + Pl*EUl
I won’t larn through to a greater extent than equations, but the same thing holds for decisions. You tin forcefulness out piece of work optimal decisions backwards.
Now, this all gets to last a large work alongside loss aversion. The cardinal question: Do loss averse people inward phase 1 yell upwards nigh the fact that if they win or lose inward phase 1 that volition modify their reference betoken for phase 2? Again, the reference betoken must shift, or nosotros simply direct maintain expected utility. If people ignore that their actions today shift the reference betoken tomorrow, as well as thus they’re unbelievably dumb. If people don’t, as well as thus nosotros direct maintain a mess on our hands. Since your preferences today disagree alongside your preferences tomorrow, you lot powerfulness human activity strategically, deliberately winning or losing today to shift the reference betoken for tomorrow as well as influence how you lot volition deport tomorrow. There direct maintain been brave papers trying to piece of work this out (Barberis, Huang as well as Santos) but the outcome has been, inward my view, thus complex that it hasn’t come upwards inward to mutual use.
But really to last useful inward economic science or finance, nosotros direct maintain to direct maintain a model that does non apply simply to wake up, brand a bet, eat, die, but that describes how people brand decisions over a lifetime, as well as alongside cognition that they volition bet many times.
Some to a greater extent than problems alongside loss aversion: We sure enough run into 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 hear losing on your house, say, if you lot gained inward your stocks, or if the novel family you lot desire to purchase also went downwardly inward 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 larn into which pot, as well as a dominion non to lose on private pots, every bit good every bit loss aversion.
A deeper skepticism nigh "irrationality"
I direct maintain a deeper skepticism nigh the rush to label people irrational (and us researchers oh thus much smarter). What’s thus irrational nigh next a dominion or heuristic that says, avoid losing money on your trades? Another widely adduced “irrationality” is that people tend to merchandise also much. Given that prices oftentimes practise bounce back, the heuristic “don’t lose money on your trades” powerfulness last a useful guide. Most buying as well as selling oftentimes involves a negotiation. Don’t sell at a loss helps you lot to avoid sudden negotiators. It’s also a proficient precommitment device. Real estate agents go on telling us “well, they won’t pick out that offering because they’d sell at a loss” fifty-fifty when they bought at the peak inward 2007.
Likewise, “when people inward lab coats come upwards as well as tell you lot what the probabilities of things are as well as offering you lot bets on them, don’t believe them because they’re trying to fox you” is a pretty proficient heuristic inward life. You are going to run inward to a lot to a greater extent than people playing iii carte du jour monte or offering Bernie Madoff investments, as well as people inward lab coats trying to examine you’re a moron, than you lot are going to run inward to honest researchers explaining how the game really works.
Apparently irrational rules are inward fact oftentimes proficient 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 inward life. Paying attending to sunk costs is a proficient means to brand sure you lot really complete writing, revising, as well as publishing papers! We alive inward a deeply information overload environment, as well as nosotros direct maintain express processing capacity. H5N1 lot of evidently 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 direct maintain never seen earlier as well as direct maintain piffling experience with.
Mental accounting is similar. The accounting subdivision of the University of Chicago Booth school, abode of efficient markets, subdivides the school’s money into thousands of separate budget items alongside a dominion that you can’t lose money on whatever private one. If you lot purchase as well as extra bottle of vino on the seminar budget, you lot can’t offset that fifty-fifty if at the destination of the twelvemonth in that location is money left over inward the Pizzas for MBAs budget. Such budgeting is a practically universal method of controlling costs inward all large organizations. It sure feels stupid, but is it really given the information problems?
Moreover, if people practise deport this way, in that location is a means to brand a huge amount of money off of them. Asset prices are polish 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 as well as options, I tin forcefulness out create a portfolio that volition never lose to a greater extent than than $1000. The toll of the downside insurance is a polish business office of that loss point, thus it volition last cheaper for me to purchase that downside insurance than it volition last for me to sell it to you. Or you lot tin forcefulness out purchase it for yourself. There is a lot of behavioral report of people’s portfolios as well as the nutty investments they make, but nosotros practise non run into pervasive buying of such downside insurance options, nor practise nosotros run into the large prices such options would direct maintain if people were all loss averse.
In sum, I prefer when seeing odd demeanour to inquire a chip harder "just what interrogation is this the correct response to?" earlier rushing to say people are dumb as well as inquire the authorities to nudge them my way.
Habits as well as others
Since I worked on it, I direct maintain to advert i halfway alternative – habits. See the graph. Suppose people direct maintain a lower storey of consumption that they really don’t desire to larn below. The obvious lower fountain is starvation, but nosotros all prepare habits of consumption that would last super-painful to change. A hedge fund manager’s married adult woman i time said at a cocktail political party “I’d sooner pop off than wing commercial again,” as well as that tin forcefulness out last represented past times the habit storey every bit well.
Now, every bit it is, that’s simply some other expected utility function. But hither too, nosotros brand the habit betoken motility approximately depending on experience. The hedge fund manager’s married adult woman was i time middle storey similar us as well as idea the peanuts on Southwest were a grand treat. As you lot swallow more, or every bit you lot uncovering your neighbors as well as friends swallow more, the minimum acceptable storey of consumption rises. It tin forcefulness out also model debts as well as fixed costs -- don't lose thus much money that you lot direct maintain to sell the family as well as motility into an apartment.
One argue this is dissimilar than loss aversion is that it turns out to last much to a greater extent than tractable for the dynamic interrogation – how practise you lot care for multiple bets. Not having a kink wandering approximately helps a lot. The strategic chemical constituent is there. If the habit depends on your consumption, non your neighbor’s, as well as thus when you lot swallow to a greater extent than you lot reset your habits. You powerfulness know this ahead of time, as well as nosotros tin forcefulness out piece of work out easily how you lot behave. Habits brand consumption an addictive good, thus when thinking nigh eating to a greater extent than today, you lot recognize that it volition influence how you lot experience tomorrow. When you lot drinkable some other cappuccino today, you lot know it volition brand you lot desire some other i tomorrow, as well as are less probable to drinkable today every bit a result. We tin forcefulness out piece of work those things out easily.
That doesn’t address the mental accounting issues, the vogue to care for bets inward isolation rather than every bit parts of a portfolio, as well as thus forth. But it does capture the vogue to really avoid large losses, as well as how what a loss is shifts over fourth dimension inward response to gains as well as losses inward 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 as well as is also analytically tractable, thus it's becoming real mutual inward macroeconomics as well as 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 doubtfulness that they really don't know the probabilities of. Alas, i time in that location is a clear as well as tractable mathematical model, people similar this seem non welcome inward the behavioral finance club, which says to a greater extent than nigh academic politics than nigh noun matters.
I promise that helps!
PS to all: Grumpy is back! I was traveling a lot making frequent weblog posts difficult.
Update: An e-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 simply 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 spend upwards fair value bets. They are “risk averse”.
Comments. Behavioral fans (New York times has done this oftentimes inward its economic science coverage) criticize “classical economics” past times 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 run into the confusion inward a second).
H5N1 mutual mistake: EU( C) is non the same every bit U [ E(C )]. You practise non uncovering the utility of expected consumption, you lot uncovering the expected utility of consumption. In my graph, C is equal to the expected value of C-Delta as well as C+Delta, as well as the whole betoken is that the utility of C is bigger than the expected utility of (C-Delta) or (C+Delta). You tin forcefulness out pick out due east within a linear function, but you lot cannot pick out due east within a nonlinear function.
Loss aversion
OK, on to loss aversion. In the commons kind of experiments Kahneman institute that people seem reluctant to lose money. They direct maintain a “reference point” as well as piece of work hard to avoid bets that powerfulness pose them below that reference point. He models that every bit expected utility alongside a kink inward it, every bit inward the mo drawing.
I was careful to pull the reference betoken every bit dissimilar than C. People practise non necessarily identify the reference betoken at the expected value of the bet. In fact, commonly 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 last practise non larn below 0, non practise non larn below the mean. Here people are peculiarly afraid alone of the real left constituent of the distribution.
Now, really, how are these models different? Expected utility tin forcefulness out last whatever function, as well as nobody said it doesn’t direct maintain a kink inward it. The cardinal distinguishing characteristic of loss aversion – as well as its Achilles heel – is that the reference betoken shifts around. If you lot brand some money, as well as play again, as well as thus your kink shifts upwards to the novel amount of money you lot made. Expected utility is supposed to remain the same business office of consumption or wealth. People powerfulness modify demeanour – most probable the utility crimp is flatter at high levels of consumption, thus rich people are less jeopardy 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 as well as lose money.
That’s also the Achilles heel. The start work is how practise you lot handgrip sequential bets. If I larn to the casino, as well as know I volition play twice, how practise I yell upwards nigh my strategy? With expected utility this is easy, because the expected utility plant backwards. Suppose you lot win the start bet, as well as thus figure out what you lot practise inward the mo bet. For each of win or loss inward the start bet, then, you lot direct maintain an expected utility from taking the mo bet. The expected utility of the start bet is as well as thus the expected vaule of the expected utilities you lot would direct maintain if you lot won or lost.
Equations powerfulness last amend than words. Let Chh, Chl, Clh, as well as Cll last consumption if you lot win twice, win as well as and thus lose, lose as well as and thus win, lose as well as and thus lose, as well as U(Chh), U(Chl), etc last their utilities. So, suppose you lot won the start bet. You evaluate the mo bet by
EUh == European Union given you lot won start bet = Ph*U(Chh) + Pl*U(Chl).
Similarly, if you lot lost the start bet, then
EUl = Eu given you lot lost the start bet = Ph*U(Clh) + Pl*U(Lll).
So now, the expected utility of the start bet is simply a one-stage bet, alongside these expected utilities every bit payoffs.
European Union = Ph *Euh + Pl*EUl
I won’t larn through to a greater extent than equations, but the same thing holds for decisions. You tin forcefulness out piece of work optimal decisions backwards.
Now, this all gets to last a large work alongside loss aversion. The cardinal question: Do loss averse people inward phase 1 yell upwards nigh the fact that if they win or lose inward phase 1 that volition modify their reference betoken for phase 2? Again, the reference betoken must shift, or nosotros simply direct maintain expected utility. If people ignore that their actions today shift the reference betoken tomorrow, as well as thus they’re unbelievably dumb. If people don’t, as well as thus nosotros direct maintain a mess on our hands. Since your preferences today disagree alongside your preferences tomorrow, you lot powerfulness human activity strategically, deliberately winning or losing today to shift the reference betoken for tomorrow as well as influence how you lot volition deport tomorrow. There direct maintain been brave papers trying to piece of work this out (Barberis, Huang as well as Santos) but the outcome has been, inward my view, thus complex that it hasn’t come upwards inward to mutual use.
But really to last useful inward economic science or finance, nosotros direct maintain to direct maintain a model that does non apply simply to wake up, brand a bet, eat, die, but that describes how people brand decisions over a lifetime, as well as alongside cognition that they volition bet many times.
Some to a greater extent than problems alongside loss aversion: We sure enough run into 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 hear losing on your house, say, if you lot gained inward your stocks, or if the novel family you lot desire to purchase also went downwardly inward 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 larn into which pot, as well as a dominion non to lose on private pots, every bit good every bit loss aversion.
A deeper skepticism nigh "irrationality"
I direct maintain a deeper skepticism nigh the rush to label people irrational (and us researchers oh thus much smarter). What’s thus irrational nigh next a dominion or heuristic that says, avoid losing money on your trades? Another widely adduced “irrationality” is that people tend to merchandise also much. Given that prices oftentimes practise bounce back, the heuristic “don’t lose money on your trades” powerfulness last a useful guide. Most buying as well as selling oftentimes involves a negotiation. Don’t sell at a loss helps you lot to avoid sudden negotiators. It’s also a proficient precommitment device. Real estate agents go on telling us “well, they won’t pick out that offering because they’d sell at a loss” fifty-fifty when they bought at the peak inward 2007.
Likewise, “when people inward lab coats come upwards as well as tell you lot what the probabilities of things are as well as offering you lot bets on them, don’t believe them because they’re trying to fox you” is a pretty proficient heuristic inward life. You are going to run inward to a lot to a greater extent than people playing iii carte du jour monte or offering Bernie Madoff investments, as well as people inward lab coats trying to examine you’re a moron, than you lot are going to run inward to honest researchers explaining how the game really works.
Apparently irrational rules are inward fact oftentimes proficient 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 inward life. Paying attending to sunk costs is a proficient means to brand sure you lot really complete writing, revising, as well as publishing papers! We alive inward a deeply information overload environment, as well as nosotros direct maintain express processing capacity. H5N1 lot of evidently 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 direct maintain never seen earlier as well as direct maintain piffling experience with.
Mental accounting is similar. The accounting subdivision of the University of Chicago Booth school, abode of efficient markets, subdivides the school’s money into thousands of separate budget items alongside a dominion that you can’t lose money on whatever private one. If you lot purchase as well as extra bottle of vino on the seminar budget, you lot can’t offset that fifty-fifty if at the destination of the twelvemonth in that location is money left over inward the Pizzas for MBAs budget. Such budgeting is a practically universal method of controlling costs inward all large organizations. It sure feels stupid, but is it really given the information problems?
Moreover, if people practise deport this way, in that location is a means to brand a huge amount of money off of them. Asset prices are polish 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 as well as options, I tin forcefulness out create a portfolio that volition never lose to a greater extent than than $1000. The toll of the downside insurance is a polish business office of that loss point, thus it volition last cheaper for me to purchase that downside insurance than it volition last for me to sell it to you. Or you lot tin forcefulness out purchase it for yourself. There is a lot of behavioral report of people’s portfolios as well as the nutty investments they make, but nosotros practise non run into pervasive buying of such downside insurance options, nor practise nosotros run into the large prices such options would direct maintain if people were all loss averse.
In sum, I prefer when seeing odd demeanour to inquire a chip harder "just what interrogation is this the correct response to?" earlier rushing to say people are dumb as well as inquire the authorities to nudge them my way.
Habits as well as others
Since I worked on it, I direct maintain to advert i halfway alternative – habits. See the graph. Suppose people direct maintain a lower storey of consumption that they really don’t desire to larn below. The obvious lower fountain is starvation, but nosotros all prepare habits of consumption that would last super-painful to change. A hedge fund manager’s married adult woman i time said at a cocktail political party “I’d sooner pop off than wing commercial again,” as well as that tin forcefulness out last represented past times the habit storey every bit well.
Now, every bit it is, that’s simply some other expected utility function. But hither too, nosotros brand the habit betoken motility approximately depending on experience. The hedge fund manager’s married adult woman was i time middle storey similar us as well as idea the peanuts on Southwest were a grand treat. As you lot swallow more, or every bit you lot uncovering your neighbors as well as friends swallow more, the minimum acceptable storey of consumption rises. It tin forcefulness out also model debts as well as fixed costs -- don't lose thus much money that you lot direct maintain to sell the family as well as motility into an apartment.
One argue this is dissimilar than loss aversion is that it turns out to last much to a greater extent than tractable for the dynamic interrogation – how practise you lot care for multiple bets. Not having a kink wandering approximately helps a lot. The strategic chemical constituent is there. If the habit depends on your consumption, non your neighbor’s, as well as thus when you lot swallow to a greater extent than you lot reset your habits. You powerfulness know this ahead of time, as well as nosotros tin forcefulness out piece of work out easily how you lot behave. Habits brand consumption an addictive good, thus when thinking nigh eating to a greater extent than today, you lot recognize that it volition influence how you lot experience tomorrow. When you lot drinkable some other cappuccino today, you lot know it volition brand you lot desire some other i tomorrow, as well as are less probable to drinkable today every bit a result. We tin forcefulness out piece of work those things out easily.
That doesn’t address the mental accounting issues, the vogue to care for bets inward isolation rather than every bit parts of a portfolio, as well as thus forth. But it does capture the vogue to really avoid large losses, as well as how what a loss is shifts over fourth dimension inward response to gains as well as losses inward 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 as well as is also analytically tractable, thus it's becoming real mutual inward macroeconomics as well as 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 doubtfulness that they really don't know the probabilities of. Alas, i time in that location is a clear as well as tractable mathematical model, people similar this seem non welcome inward the behavioral finance club, which says to a greater extent than nigh academic politics than nigh noun matters.
I promise that helps!
PS to all: Grumpy is back! I was traveling a lot making frequent weblog posts difficult.
Update: An e-mail correspondent writes
If a abode was purchased at $500,000 alongside a mortgage of $450,000, as well as it is immediately sold for less than fifty-fifty $475,000, as well as thus afterwards commissions as well as closing costs, the seller has less than $450,000 inward paw as well as volition last required to “bring cash to the closing” inward monastic enjoin to fully pay off the bank. Generally, families alongside homes selling for below mortgage value direct maintain problem raising whatever cash at all. All this is farther complicated past times the work of where as well as how tin forcefulness out the seller motility to adjacent if all his cash is pose into getting out of the electrical flow mortgage? No money for novel downwardly payment, or start month’s rent as well as deposit. The electrical flow possessor is genuinely stuck at an to a higher identify marketplace position offering price.This is a proficient point. Fixed costs as well as transactions costs tin forcefulness out give ascension to the extra costs of a loss, as well as range a kink. People who prepare rules of pollex inward that circumstance may non notice the lab experiment is cleverly designed non to direct maintain the actual costs of many real-world losses.
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