A frequent electronic mail correspondent asked "I’d dear 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 refuse fair value bets. They are “risk averse”.
Comments. Behavioral fans (New York times has done this ofttimes inward its economic science coverage) criticize “classical economics” yesteryear proverb 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 cry for of expected utility. (You’ll come across the confusion inward a second).
Influenza A virus subtype H5N1 mutual mistake: EU( C) is non the same every bit U [ E(C )]. You exercise 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 together with C+Delta, together with the whole cry for is that the utility of C is bigger than the expected utility of (C-Delta) or (C+Delta). You tin 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 flora that people seem reluctant to lose money. They receive got a “reference point” together with piece of work hard to avoid bets that mightiness position them below that reference point. He models that every bit expected utility alongside a kink inward it, every bit inward the minute drawing.
I was careful to push clit the reference cry for every bit dissimilar than C. People exercise non necessarily identify the reference cry for 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” cry for would go exercise non larn below 0, non exercise non larn below the mean. Here people are particularly afraid solely of the real left component division of the distribution.
Now, really, how are these models different? Expected utility tin go whatever function, together with nobody said it doesn’t receive got a kink inward it. The primal distinguishing characteristic of loss aversion – together with its Achilles heel – is that the reference cry for shifts around. If you lot brand some money, together with play again, thus 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 plication is flatter at high levels of consumption, thus rich people are less direct chances averse. But the plication itself does non shift. The primal supposition that distinguishes loss aversion from expected utility is that the kink cry for shifts to a greater extent than or less every bit you lot gain together with lose money.
That’s also the Achilles heel. The starting fourth dimension work is how exercise you lot handgrip sequential bets. If I larn to the casino, together with know I volition play twice, how exercise I retrieve most my strategy? With expected utility this is easy, because the expected utility industrial plant backwards. Suppose you lot win the starting fourth dimension bet, thus figure out what you lot exercise inward the minute bet. For each of win or loss inward the starting fourth dimension bet, then, you lot receive got an expected utility from taking the minute bet. The expected utility of the starting fourth dimension bet is thus the expected vaule of the expected utilities you lot would receive got if you lot won or lost.
Equations mightiness go improve than words. Let Chh, Chl, Clh, together with Cll go consumption if you lot win twice, win together with thus lose, lose together with thus win, lose together with thus lose, together with U(Chh), U(Chl), etc go their utilities. So, suppose you lot won the starting fourth dimension bet. You evaluate the minute bet by
EUh == European Union given you lot won starting fourth dimension bet = Ph*U(Chh) + Pl*U(Chl).
Similarly, if you lot lost the starting fourth dimension bet, then
EUl = Eu given you lot lost the starting fourth dimension bet = Ph*U(Clh) + Pl*U(Lll).
So now, the expected utility of the starting fourth dimension 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 piece of work optimal decisions backwards.
Now, this all gets to go a large work alongside loss aversion. The primal question: Do loss averse people inward phase 1 retrieve most the fact that if they win or lose inward phase 1 that volition alter their reference cry for for phase 2? Again, the reference cry for must shift, or nosotros simply receive got expected utility. If people ignore that their actions today shift the reference cry for tomorrow, thus they’re unbelievably dumb. If people don’t, thus nosotros receive got a mess on our hands. Since your preferences today disagree alongside your preferences tomorrow, you lot mightiness deed strategically, deliberately winning or losing today to shift the reference cry for for tomorrow together with influence how you lot volition acquit tomorrow. There receive got been brave papers trying to piece of work this out (Barberis, Huang together with Santos) but the consequence has been, inward my view, thus complex that it hasn’t come upwardly inward to mutual use.
But really to go useful inward economic science or finance, nosotros receive got to receive got 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, together with alongside noesis that they volition bet many times.
Some to a greater extent than problems alongside loss aversion: We surely 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 hear losing on your house, say, if you lot gained inward your stocks, or if the novel household you lot desire to purchase also went downwards 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, together with a dominion non to lose on private pots, every bit good every bit loss aversion.
A deeper skepticism most "irrationality"
I receive got a deeper skepticism most the rush to label people irrational (and us researchers oh thus much smarter). What’s thus irrational most 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 ofttimes exercise bounce back, the heuristic “don’t lose money on your trades” mightiness go a useful guide. Most buying together with selling ofttimes involves a negotiation. Don’t sell at a loss helps you lot to avoid precipitous negotiators. It’s also a skilful precommitment device. Real estate agents continue 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 upwardly together with tell you lot what the probabilities of things are together with offering you lot bets on them, don’t believe them because they’re trying to fob you” is a pretty skilful heuristic inward life. You are going to run inward to a lot to a greater extent than people playing three carte du jour monte or offering Bernie Madoff investments, together with people inward lab coats trying to essay 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 ofttimes 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 inward life. Paying attending to sunk costs is a skilful means to brand sure you lot really complete writing, revising, together with publishing papers! We alive inward a deeply information overload environment, together with nosotros receive got express processing capacity. Influenza A virus subtype H5N1 lot of patently 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 together with receive got lilliputian 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 together with extra bottle of vino on the seminar budget, you lot can’t offset that fifty-fifty if at the goal of the yr at that topographic point 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 exercise acquit this way, at that topographic point is a means to brand a huge amount of money off of them. Asset prices are shine functions of gains or losses. Suppose your reference cry for is, you lot don’t desire to lose to a greater extent than than $1000 on stocks. By buying stocks together with 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 shine business office of that loss point, thus it volition go cheaper for me to purchase that downside insurance than it volition go 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 together with 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 chip harder "just what enquiry is this the correct response to?" earlier rushing to say people are dumb together with inquire the regime to nudge them my way.
Habits together with others
Since I worked on it, I receive got to get upwardly 1 halfway alternative – habits. See the graph. Suppose people receive got a lower storey of consumption that they really don’t desire to larn below. The obvious lower jump is starvation, but nosotros all educate habits of consumption that would go super-painful to change. A hedge fund manager’s married adult woman in 1 trial said at a cocktail political party “I’d sooner conk than wing commercial again,” together with that tin go represented yesteryear 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 cry for movement to a greater extent than or less depending on experience. The hedge fund manager’s married adult woman was in 1 trial middle storey similar us together with idea the peanuts on Southwest were a grand treat. As you lot eat more, or every bit you lot uncovering your neighbors together with friends eat more, the minimum acceptable storey of consumption rises. It tin also model debts together with fixed costs -- don't lose thus much money that you lot receive got to sell the household together with movement into an apartment.
One argue this is dissimilar than loss aversion is that it turns out to go much to a greater extent than tractable for the dynamic enquiry – how exercise you lot care for multiple bets. Not having a kink wandering to a greater extent than or less helps a lot. The strategic chemical component is there. If the habit depends on your consumption, non your neighbor’s, thus when you lot eat to a greater extent than you lot reset your habits. You mightiness know this ahead of time, together with nosotros tin piece of work out easily how you lot behave. Habits brand consumption an addictive good, thus when thinking most 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 1 tomorrow, together with are less probable to drinkable today every bit a result. We tin piece of work those things out easily.
That doesn’t address the mental accounting issues, the style to care for bets inward isolation rather than every bit parts of a portfolio, together with thus forth. But it does capture the style to really avoid large losses, together with how what a loss is shifts over fourth dimension inward response to gains together with 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 together with is also analytically tractable, thus it's becoming real mutual inward macroeconomics together with property pricing. Lars Hansen is also been on a long inquiry agenda of fifty-fifty to a greater extent than full general utility functions that are "ambiguity averse," capturing that people shrink away from doubt that they really don't know the probabilities of. Alas, in 1 trial at that topographic point is a clear together with tractable mathematical model, people similar this seem non welcome inward the behavioral finance club, which says to a greater extent than most academic politics than most 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 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 refuse fair value bets. They are “risk averse”.
Comments. Behavioral fans (New York times has done this ofttimes inward its economic science coverage) criticize “classical economics” yesteryear proverb 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 cry for of expected utility. (You’ll come across the confusion inward a second).
Influenza A virus subtype H5N1 mutual mistake: EU( C) is non the same every bit U [ E(C )]. You exercise 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 together with C+Delta, together with the whole cry for is that the utility of C is bigger than the expected utility of (C-Delta) or (C+Delta). You tin 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 flora that people seem reluctant to lose money. They receive got a “reference point” together with piece of work hard to avoid bets that mightiness position them below that reference point. He models that every bit expected utility alongside a kink inward it, every bit inward the minute drawing.
I was careful to push clit the reference cry for every bit dissimilar than C. People exercise non necessarily identify the reference cry for 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” cry for would go exercise non larn below 0, non exercise non larn below the mean. Here people are particularly afraid solely of the real left component division of the distribution.
Now, really, how are these models different? Expected utility tin go whatever function, together with nobody said it doesn’t receive got a kink inward it. The primal distinguishing characteristic of loss aversion – together with its Achilles heel – is that the reference cry for shifts around. If you lot brand some money, together with play again, thus 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 plication is flatter at high levels of consumption, thus rich people are less direct chances averse. But the plication itself does non shift. The primal supposition that distinguishes loss aversion from expected utility is that the kink cry for shifts to a greater extent than or less every bit you lot gain together with lose money.
That’s also the Achilles heel. The starting fourth dimension work is how exercise you lot handgrip sequential bets. If I larn to the casino, together with know I volition play twice, how exercise I retrieve most my strategy? With expected utility this is easy, because the expected utility industrial plant backwards. Suppose you lot win the starting fourth dimension bet, thus figure out what you lot exercise inward the minute bet. For each of win or loss inward the starting fourth dimension bet, then, you lot receive got an expected utility from taking the minute bet. The expected utility of the starting fourth dimension bet is thus the expected vaule of the expected utilities you lot would receive got if you lot won or lost.
Equations mightiness go improve than words. Let Chh, Chl, Clh, together with Cll go consumption if you lot win twice, win together with thus lose, lose together with thus win, lose together with thus lose, together with U(Chh), U(Chl), etc go their utilities. So, suppose you lot won the starting fourth dimension bet. You evaluate the minute bet by
EUh == European Union given you lot won starting fourth dimension bet = Ph*U(Chh) + Pl*U(Chl).
Similarly, if you lot lost the starting fourth dimension bet, then
EUl = Eu given you lot lost the starting fourth dimension bet = Ph*U(Clh) + Pl*U(Lll).
So now, the expected utility of the starting fourth dimension 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 piece of work optimal decisions backwards.
Now, this all gets to go a large work alongside loss aversion. The primal question: Do loss averse people inward phase 1 retrieve most the fact that if they win or lose inward phase 1 that volition alter their reference cry for for phase 2? Again, the reference cry for must shift, or nosotros simply receive got expected utility. If people ignore that their actions today shift the reference cry for tomorrow, thus they’re unbelievably dumb. If people don’t, thus nosotros receive got a mess on our hands. Since your preferences today disagree alongside your preferences tomorrow, you lot mightiness deed strategically, deliberately winning or losing today to shift the reference cry for for tomorrow together with influence how you lot volition acquit tomorrow. There receive got been brave papers trying to piece of work this out (Barberis, Huang together with Santos) but the consequence has been, inward my view, thus complex that it hasn’t come upwardly inward to mutual use.
But really to go useful inward economic science or finance, nosotros receive got to receive got 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, together with alongside noesis that they volition bet many times.
Some to a greater extent than problems alongside loss aversion: We surely 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 hear losing on your house, say, if you lot gained inward your stocks, or if the novel household you lot desire to purchase also went downwards 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, together with a dominion non to lose on private pots, every bit good every bit loss aversion.
A deeper skepticism most "irrationality"
I receive got a deeper skepticism most the rush to label people irrational (and us researchers oh thus much smarter). What’s thus irrational most 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 ofttimes exercise bounce back, the heuristic “don’t lose money on your trades” mightiness go a useful guide. Most buying together with selling ofttimes involves a negotiation. Don’t sell at a loss helps you lot to avoid precipitous negotiators. It’s also a skilful precommitment device. Real estate agents continue 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 upwardly together with tell you lot what the probabilities of things are together with offering you lot bets on them, don’t believe them because they’re trying to fob you” is a pretty skilful heuristic inward life. You are going to run inward to a lot to a greater extent than people playing three carte du jour monte or offering Bernie Madoff investments, together with people inward lab coats trying to essay 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 ofttimes 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 inward life. Paying attending to sunk costs is a skilful means to brand sure you lot really complete writing, revising, together with publishing papers! We alive inward a deeply information overload environment, together with nosotros receive got express processing capacity. Influenza A virus subtype H5N1 lot of patently 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 together with receive got lilliputian 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 together with extra bottle of vino on the seminar budget, you lot can’t offset that fifty-fifty if at the goal of the yr at that topographic point 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 exercise acquit this way, at that topographic point is a means to brand a huge amount of money off of them. Asset prices are shine functions of gains or losses. Suppose your reference cry for is, you lot don’t desire to lose to a greater extent than than $1000 on stocks. By buying stocks together with 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 shine business office of that loss point, thus it volition go cheaper for me to purchase that downside insurance than it volition go 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 together with 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 chip harder "just what enquiry is this the correct response to?" earlier rushing to say people are dumb together with inquire the regime to nudge them my way.
Habits together with others
Since I worked on it, I receive got to get upwardly 1 halfway alternative – habits. See the graph. Suppose people receive got a lower storey of consumption that they really don’t desire to larn below. The obvious lower jump is starvation, but nosotros all educate habits of consumption that would go super-painful to change. A hedge fund manager’s married adult woman in 1 trial said at a cocktail political party “I’d sooner conk than wing commercial again,” together with that tin go represented yesteryear 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 cry for movement to a greater extent than or less depending on experience. The hedge fund manager’s married adult woman was in 1 trial middle storey similar us together with idea the peanuts on Southwest were a grand treat. As you lot eat more, or every bit you lot uncovering your neighbors together with friends eat more, the minimum acceptable storey of consumption rises. It tin also model debts together with fixed costs -- don't lose thus much money that you lot receive got to sell the household together with movement into an apartment.
One argue this is dissimilar than loss aversion is that it turns out to go much to a greater extent than tractable for the dynamic enquiry – how exercise you lot care for multiple bets. Not having a kink wandering to a greater extent than or less helps a lot. The strategic chemical component is there. If the habit depends on your consumption, non your neighbor’s, thus when you lot eat to a greater extent than you lot reset your habits. You mightiness know this ahead of time, together with nosotros tin piece of work out easily how you lot behave. Habits brand consumption an addictive good, thus when thinking most 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 1 tomorrow, together with are less probable to drinkable today every bit a result. We tin piece of work those things out easily.
That doesn’t address the mental accounting issues, the style to care for bets inward isolation rather than every bit parts of a portfolio, together with thus forth. But it does capture the style to really avoid large losses, together with how what a loss is shifts over fourth dimension inward response to gains together with 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 together with is also analytically tractable, thus it's becoming real mutual inward macroeconomics together with property pricing. Lars Hansen is also been on a long inquiry agenda of fifty-fifty to a greater extent than full general utility functions that are "ambiguity averse," capturing that people shrink away from doubt that they really don't know the probabilities of. Alas, in 1 trial at that topographic point is a clear together with tractable mathematical model, people similar this seem non welcome inward the behavioral finance club, which says to a greater extent than most academic politics than most 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 abode was purchased at $500,000 alongside a mortgage of $450,000, together with it is forthwith sold for less than fifty-fifty $475,000, thus subsequently commissions together with closing costs, the seller has less than $450,000 inward mitt together with volition go 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 receive got problem raising whatever cash at all. All this is farther complicated yesteryear the work of where together with how tin the seller movement to adjacent if all his cash is position into getting out of the electrical flow mortgage? No money for novel downwards payment, or starting fourth dimension month’s rent together with deposit. The electrical flow possessor is genuinely stuck at an inward a higher identify marketplace position offering price.This is a skilful point. Fixed costs together with transactions costs tin give ascent to the extra costs of a loss, together with attain a kink. People who educate rules of pollex inward that circumstance may non notice the lab experiment is cleverly designed non to receive got the actual costs of many real-world losses.
