Loss Aversion: Why Losses Hurt More Than Equivalent Gains

Loss aversion is the finding that a loss is felt more than a gain of the same size. The cohort measured here needed Rs 22,000/- of gain to accept a fifty-fifty gamble against a Rs 10,000/- loss, a coefficient of 2.2. Loss aversion is not the same thing as disliking risk.

Loss aversionFeeling a loss more than a gain of the same size. and risk aversionPreferring a certain amount to a gamble with the same average. get used as if they were two names for one dislike, and they are not. One is about how widely the possible outcomes of a choice are separated. The other is about where a person is standing when they look at them. Risk aversion is a property of a curve that bends the same way throughout. Loss aversion is a property of a change of slope at one particular level. A person can have either without the other. Prospect theory introduces that change of slope, and the measurement below puts a number on it.

What exactly does loss aversion claim?

The claim is narrow, and its narrowness is what makes it useful. The claim says that for one person, with everything else held still, a gain of some size and a loss of the same size do not weigh alike: the loss registers as the larger event. Not the more likely event. Not the more frightening event. The larger one, in whatever internal currency a person uses to weigh outcomes against each other.

The effect is recognisable long before it is formalised. Somebody finds a Rs 500/- note in a coat pocket in the morning and loses a Rs 500/- note out of the same pocket in the evening. In money the day is exactly flat. Almost nobody reports the day as flat. The evening sits on the person all week and the morning is forgotten by lunchtime. The wedding version is sharper still: a caterer who comes in Rs 20,000/- under the quoted figure is a pleasant surprise mentioned once, and a caterer who comes in Rs 20,000/- over is discussed for a year.

Loss aversion does not claim that anybody dislikes uncertainty, or that every loss is frightening, or that the weighting is a fixed multiple that holds at every size. Each of those is a separate proposition and each has been mistaken for this one. The claim is about an asymmetry across a level, and the level matters as much as the asymmetry does. Change where a person thinks they are starting from and the same rupee amount changes sides.

What does it rest on, and what exactly is a kink?

Prospect theory establishes that a person scores outcomes as changes from a reference point rather than as final totals, and that the scoring line has a kinkA change of slope at a single point, as against a curve bending throughout. where the two sides meet. The kink is the subject measured here. A curve that bends is one thing; a curve that snaps to a steeper slope at a single point is another thing entirely, and the difference is not decoration.

Picture two arms leaving the reference point. Walk to the right, into gains, and the line rises. Walk the same distance to the left, into losses, and the line falls further than the right arm rose. The size of the step is identical in rupees. The distance travelled in feeling is not. Loss aversion is simply the statement that the left arm leaves the reference point more steeply than the right arm does, and the coefficient is the number that says by how much.

Two properties of that drawing matter separately. The first is the steepness gap at the meeting point. Loss aversion is that gap and nothing more. The second is that both arms flatten as they run outwards, so the tenth thousand rupees moves a person less than the first thousand did. The second property is not loss aversion and does not measure it, but it is the reason a single coefficient cannot be read as a constant, and that is taken up below.

How is the coefficient measured?

Do not quote the number. Build it. The measurement is a single question asked in a single sitting. The arithmetic is one division, and the trap is entirely in the interpretation.

Each of the 60 investors in the invented Palash decision log was offered a coin toss. Heads, they lose Rs 10,000/-. Tails, they win some amount, and the amount starts small. In money that coin toss is exactly even. At a win of Rs 10,000/- almost nobody takes it. The offered win is raised. At Rs 15,000/- some take it. At Rs 22,000/- half the room has crossed over. The midpoint is the measurement: the point at which the typical person in the room stops refusing.

The coefficientThe ratio of the gain needed to the loss risked, here 2.2. is then the gain needed divided by the loss risked. Rs 22,000/- divided by Rs 10,000/- is 2.2. One division is the entire calculation. A number built that way can be checked against the two amounts it came from rather than taken on trust. The coefficient is also an exchange rateHow much of one side is needed to offset a unit of the other. rather than a measure of unhappiness: it says how much of the gain side buys one unit of the loss side, at this size, on this invented group.

What does 2.2 mean, and what does it not mean?

Now the hard part, and the part that gets dropped when a number travels. A coefficient of 2.2 does not mean anybody is 2.2 times as unhappy about anything. Unhappiness has no units and nobody measured any. The measurement is a rate at which one side of a level trades against the other, at one particular size, on one particular afternoon, for one invented group of 60 people.

The coefficient also does not mean the ratio holds at every size. Both arms of the kink flatten as they run outwards: the second Rs 10,000/- of a loss moves a person less than the first Rs 10,000/- did, and the same is true of gains. Nothing forces the two arms to flatten at the same rate. Because the two sides flatten at their own rates, the ratio between them changes with the size of the stake, so a coefficient measured at Rs 10,000/- is a reading at Rs 10,000/- and not a constant of human nature.

And it does not mean every one of the 60 answered 2.2. The 2.2 is a median. Some would have taken the toss at Rs 12,000/-, some would have refused at Rs 40,000/-, and the log does not report the range because it was not designed to. Quoting the midpoint as though it were the distribution states more than the measurement supports. Three qualifications, then, and they travel with the number wherever it goes: this size, this cohort, and a shape that is not linear.

What gain would actually be needed before the toss was taken?

The coefficient becomes real the moment it is turned back into rupees. Hold the loss fixed at Rs 10,000/- and the required gain is the coefficient multiplied by that loss. At a coefficient of 1.0 the required gain is Rs 10,000/-. The 1.0 setting is the anchor the whole scale should be read against: at 1.0 the two sides weigh exactly the same, there is no loss aversion at all, and an even coin toss is even in feeling as well as in money. At 1.5 the required gain is Rs 15,000/-. At 2.2, the measured median, it is Rs 22,000/-. At 3.0 it is Rs 30,000/-.

The same arithmetic gives a second reading worth having. Half of Rs 22,000/- less half of Rs 10,000/- is Rs 6,000/-, so a person at a coefficient of 2.2 will only take the toss when it carries Rs 6,000/- of expected money. The coefficient is therefore a statement about how large a money advantage a person needs before an even chance becomes acceptable, and at 1.0 that advantage is zero. A fixed offer of Rs 15,000/- against the same Rs 10,000/- risk is accepted by anybody below 1.5, refused by anybody above it, and exactly balanced at 1.5 itself.

Loss Aversion Vs Risk Aversion: what actually separates them?

The distinction is between two different objects rather than two degrees of one thing.

Risk aversion is about spreadHow widely the possible outcomes of a choice are separated.. A risk averse person, offered a certain amount and a gamble with the same average, takes the certain amount. Notice what is absent from that sentence: any mention of a level, a starting point or a reference. Risk aversion applies wherever the choice is put. Above the reference point, below it, in a person's first year of saving and their thirtieth, the same preference for the narrower spread shows up.

Loss aversion is about the reference point. Loss aversion says nothing at all about spread. Loss aversion says that one particular level divides the outcome space into two halves that get weighed on different scales, and that the lower half is weighed more heavily. Risk aversion ranks two whole gambles against each other by how widely their outcomes are spread. Loss aversion says where the dividing line sits and how much steeper the far side of it is. Neither statement implies the other.

The household version. A person who will not put savings into anything that moves is showing something about spread; they would refuse a wide gamble whether it was framed as a chance to grow the reserve or a chance to shrink it. A person who is perfectly comfortable with a scheme that moves about but cannot bring themselves to sell one holding for less than they paid for it is showing something about a level. Two different people, two different conversations, and the second conversation is useless on the first person.

How can somebody have one without the other?

If the two were the same thing there would be two kinds of person and the table below would have two filled cells. There are four, and each one describes decisions a reader has seen.

A person low on both takes the wide gamble and does not mind which side of the purchase cost they sell on. A person high on risk aversion and low on loss aversion refuses wide spreads everywhere but will book a loss without flinching. The loss is just an outcome and not a border being crossed. A person low on risk aversion and high on loss aversion is the one advisers describe as contradictory: perfectly happy holding something that moves violently, completely unable to sell it below cost. The fourth cell, high on both, is the only one that the two words describe identically. Running them together seems to work until it suddenly does not.

The four cells are not a taxonomy for their own sake. The grid is the reason a single risk questionnaire cannot locate a person. The invented practice's questionnaire runs 12 questions scored 1 to 5, so 60 is the maximum, and Meera Sundaram scores 44. The score of 44 is a reading on spread. The score has nothing to say about where her dividing line sits, and her dividing line is what the decision of 12 October actually turned on.

Why does treating them as one thing break the analysis?

Now the cost of the confusion, and the invented log settles it without argument.

Fear vs Risk Aversion: is being frightened the same as disliking spread?

There is a third thing in the room, and it is neither of the two above. FearA feeling about a specific outcome, which is not the same as a preference over spread. is a feeling that attaches to one particular outcome. Risk aversion is a preference that ranks whole gambles. Fear and risk aversion are different kinds of object, and mixing them wastes conversations.

An investor who says she is frightened of a scheme is usually pointing at something specific: that the whole amount could go, that she would have to explain the decision to somebody, that the money is needed in eleven years and this is the eleven year money. Each of those worries is a statement about one outcome. A risk averse investor, by contrast, is making a comparison: this gamble against that one, and the narrower one wins.

Reassurance works on a particular outcome, and risk aversion is a ranking over whole gambles rather than a worry about any one of them. Reassurance therefore addresses fear and changes nothing about risk aversion. Telling a frightened person that the outcome she is picturing is unlikely may solve her problem entirely. She was never claiming the bad outcome was likely, so telling a risk averse person the same thing does not touch her preference. She was saying she would rather have the narrower distribution at the same average.

And loss aversion is a third object again, indifferent to both. Loss aversion does not point at an outcome and does not rank spreads. Loss aversion says where the line is.

Why does the distinction change what would be done about it?

Because each of the three has a different handle, and pulling the wrong one is not merely useless. Pulling the wrong handle is often taken as evidence that the person is being difficult.

If fear is running, the thing to address is the specific outcome. Name it out loud, work out what would actually happen if it occurred, and see whether the feeling survives contact with the arithmetic. If risk aversion is running, the thing to change is the spread: a different mixture, a smaller amount at stake, a longer stretch of time over which the spread narrows. If loss aversion is running, neither of those helps, and the thing to examine is the reference point itself. Where did the line come from? The purchase cost, in the case of Meera Sundaram on 12 October, when she kept a holding until it returned to Rs 3,00,000/-. The purchase cost is a fact about a past transaction and nothing else.

Each of the three has a different handle, and the wrong handle does nothing at all when it is pulled. Naming which one is running is therefore not a diagnosis for its own sake. Two definitions that look like pedantry pay for themselves there.

Where is weighting losses more heavily simply correct?

Loss aversion is called a bias when the two sides really are symmetric and a person treats them as though they were not. Where the two sides are genuinely asymmetric, weighting the loss more heavily is not a bias. The heavier weight is accurate.

Take the invented household in the case. Monthly outgo is Rs 55,000/- and the reserve is Rs 1,10,000/-, exactly two months deep. A gain of Rs 55,000/- takes the reserve to three months, and three months is pleasant. A loss of Rs 55,000/- takes the reserve to one month, and one month is a different kind of event: the point at which the next unexpected bill has to be met by borrowing. The same rupee amount, and the consequences are not mirror images of each other.

The case already contains the numbers. Beside the reserve sits Rs 1,80,000/- of card borrowing at 36.0 per cent and a Rs 2,40,000/- deposit at 6.5 per cent. If a loss forces Rs 55,000/- onto the card for a year, that costs Rs 19,800/-. If a gain of Rs 55,000/- goes into the deposit for a year, that earns Rs 3,575/-. The loss costs about 5.5 times what the identical gain earns, so a household weighting the downside more heavily is not showing a bias at all, it is reading its own arithmetic correctly.

What does a whole holding look like once the losses are weighted?

One last calculation, and it is the reason a statement can feel unbearable while the number at the bottom of it is small. On 30 September the invented holding stood at a cost of Rs 13,00,000/- against a value of Rs 12,46,000/-, so it was down Rs 54,000/-, or 4.2 per cent. Two positions were in gain by Rs 36,000/- and Rs 60,000/-, being Rs 96,000/- together, and two were in loss by Rs 45,000/- and Rs 1,05,000/-, being Rs 1,50,000/- together. Ninety six thousand less one hundred and fifty thousand is the same minus Rs 54,000/-, so the two readings reconcile.

Now apply the measured coefficient as if it were constant, knowing that it is not. The gains still count Rs 96,000/-. The losses count Rs 1,50,000/- multiplied by 2.2, giving Rs 3,30,000/-. Ninety six thousand less three hundred and thirty thousand is minus Rs 2,34,000/-. The statement that reads as down Rs 54,000/- in money reads as down Rs 2,34,000/- in felt weight, about 4.3 times as large. The gap is the whole reason a mildly disappointing statement can produce an urgent decision. The coefficient was read at one size only, so the multiplication illustrates the direction rather than measuring it.

How does an adviser, or somebody deciding alone, actually use this?

Devika Rao, the adviser at the invented Palash Advisory Services Private Limited, does not use the coefficient as a score. She uses the distinction as a sorting question, asked before anything is proposed. When a client resists, there are exactly three things it can be, and one sentence usually separates them. Ask what specifically worries them. If the answer names one outcome, that is fear. If the answer compares two options and says the steadier one is preferred, that is risk aversion and the mixture is what needs changing. If the answer contains a level, and it usually does because levels sound like reasons, then loss aversion is in the room and the level is the thing to look at.

For somebody deciding alone, with no adviser and no committee, there is nobody else to catch the mistake, so the same three way sort matters more rather than less. The test is to write down the sentence that would justify not selling something, and then underline any number in it. A number that is a purchase cost, a previous high or a round figure is a reference point, and the fact that a level appears in the sentence at all is the signal.

The coefficient itself is never the useful output, having been measured on 60 invented people at one size. Knowing which of the three attitudes is producing the resistance is the useful output, and anybody can settle that in one sentence. A number that cannot be measured for one person can still be an excellent reason to ask a better question.

What does this not explain?

Quite a lot, and the limits are worth stating because loss aversion gets used as a universal solvent. Loss aversion does not explain why somebody would take a gamble in losses that they refused in gains; that follows from the same curve read on its other side, and risk seeking in losses is a separate subject. Loss aversion does not explain the structure the kink sits inside. The structure is prospect theory, as Daniel Kahneman and Amos Tversky set it out in Econometrica in 1979, and prospect theory is treated on its own. Loss aversion does not explain the pattern of selling winners and keeping losers. The disposition effect covers that pattern, and it needs the trading record rather than the preference measurement.

Loss aversion also has a version with no gamble in it at all. Amos Tversky and Daniel Kahneman set out loss aversion in riskless choice in the Quarterly Journal of Economics in 1991, where no probabilities appear anywhere: the asymmetry shows up in straight exchanges of one thing for another. The riskless version shows the effect does not need uncertainty to appear, and that is the strongest single reason to say loss aversion is not a form of risk aversion wearing a different name.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited and the Palash decision log are invented.
Educational material. Not advice on any investment, tax, budget or market position.