Risk Seeking in Losses: Why People Gamble to Get Even

Below the reference point the value curve is still flattening, so each further rupee lost registers less than the one before it. A gamble that might wipe the loss out therefore looks cheap on its bad side and enormous on its good side. The person who took the safe option in gains reaches for the risky one here.

There is a moment almost everybody recognises. A cricket bet has gone wrong, a scheme has fallen, a card table has taken more than was ever meant to be on it, and the sentence that arrives is not stop but one more, and I am back where I started. The sentence arrives in careful people. The same sentence arrives in people who, an hour earlier, would not have taken a coin toss for a thousand rupees. The interesting fact is not that the sentence arrives at all; it is that it arrives in exactly the people who were cautious when the same numbers were pointing the other way.

The reversal has a mechanism behind it, and the mechanism is worth having before any warning arrives. There is at least one situation in which reaching for more risk after a loss is the correct answer, and a blanket warning would have made that situation invisible.

Why does the same person who avoids a gamble in gains reach for one in losses?

The finding is cleaner than any explanation of it, so start there. The finding is called the reflection effectPreferences flipping between gains and losses of the same size., and it is set out in Kahneman and Tversky, Prospect Theory: An Analysis of Decision under Risk, published in Econometrica in 1979. Offer somebody a choice between a certain amount and a gamble with a slightly better average. Most people take the certain amount. Now flip every number in that pair from a gain to a loss of the same size, changing nothing else at all, and most people take the gamble.

The word reflection is doing precise work here, so read the finding again slowly. The choice pair is not made harder, or larger, or more urgent. The pair is held up to a mirror. The odds are the same odds, the amounts are the same amounts, and the difference in average value between the two options is the same difference. Only the sign changed. And the preference between the two options reverses. The sign is not decoration on the choice. The sign is part of the machinery deciding it.

Take this out of finance for a moment. The shape is older than any market. A student is offered a place at a college that is certainly good enough, or an entrance attempt that might land somewhere better and might land nowhere. Most take the certain place. Now take a student who has already failed the year and is looking at repeating it. Offered a safe path that certainly costs another twelve months, or an attempt that might cost nothing and might cost two years, far more of them attempt it. Nobody in either group has changed their appetite for uncertainty. The two groups have changed which outcome counts as the ordinary one.

The two counts come from the Palash decision log, a set of invented records kept by the equally invented Palash Advisory Services Private Limited, covering sixty people who answered a short preference questionnaire on the same afternoon. The gains question and the losses question sat on the same sheet. Nobody was told the second was a mirror of the first, and almost nobody noticed.

The pattern is a finding rather than a curiosity because of what it rules out. If people simply disliked uncertainty, the certain option would have won on both halves of the sheet. If people simply liked uncertainty, the gamble would have won on both. The gamble is the better average in gains and the worse average in losses. If people were following the arithmetic, the gamble would have won the first half and lost the second. No single fixed attitude towards uncertainty produces this pattern. The reference pointThe level that decides which outcomes count as losses. rather than the appetite has to be doing the work.

What exactly did the same sixty people choose on the same afternoon?

The numbers are small enough to hold in mind, and the conclusion depends on their being identical. Both halves of the sheet are worth working through in full. In the first half the offer was a certain Rs 5,000/- against a half chance of Rs 11,000/- and a half chance of nothing. The expected valueThe average outcome, weighting each possibility by how likely it is. of that gamble is half of Rs 11,000/-. Half of Rs 11,000/- is Rs 5,500/-. So the gamble is worth Rs 500/- more on average, and 42 of the 60 turned it down. Sixty less forty two leaves 18, so 18 of 60 took it, being 30.0 per cent.

In the second half the offer was a certain loss of Rs 5,000/- against a half chance of losing Rs 11,000/- and a half chance of losing nothing. The average of that gamble is a loss of Rs 5,500/-, so the gamble is Rs 500/- worse. And 39 of the 60 took it, being 65.0 per cent. The certain loss was chosen by 21 of 60, being 35.0 per cent.

The two Rs 500/- placed side by side give the sentence the whole argument turns on. In gains the crowd handed over Rs 500/- of average value in order to be rid of the uncertainty. In losses the crowd paid Rs 500/- of average value in order to obtain it. The same five hundred rupees was surrendered in one direction and bought in the other. No explanation resting on the amounts themselves survives that. Nothing about the money can produce a reversal when the money is identical. The only thing that differs between the two halves of the sheet is which side of zero the outcomes sat on.

Twenty one people is a useful way to hold it. Thirty nine less eighteen is twenty one, so at least twenty one of the sixty answered the two halves of that sheet in ways that cannot both be produced by one settled attitude towards uncertainty. Some who took the gamble in gains may have taken the certain loss afterwards, so the count could be more than twenty one. Fewer than twenty one is impossible. The sixty were not confused and they were not careless. Asked afterwards, most of them could restate both offers correctly. Nothing in the way a person reads an offer flags the sign as the thing to watch, so what none of them could do was notice that the second offer was the first one reflected.

What does the shape of the curve below the reference point predict?

Now the explanation. Prospect theory sets out the value curve: outcomes are read as gains or losses from a reference point rather than as totals, and the curve through them bends. The property doing the work below the reference point is called diminishing sensitivityThe idea that rupee number ten thousand lands more softly than rupee number one, in whichever direction the travel runs., and it is the half of the idea that most often goes missing. Diminishing sensitivity runs in both directions. Diminishing sensitivity flattens the curve above the reference point and flattens it below the point too, symmetrically in shape if not in steepness.

Above the point, flattening is the familiar idea and it has a comfortable name. The second lakh of gain feels smaller than the first, so a certain gain now beats a bigger gain that might not arrive, and the person looks prudent. Below the point, the identical property produces something nobody thinks of as prudent. The second lakh of loss also feels smaller than the first. And a further loss that is felt as smaller is, in the only currency the decision actually runs on, a cheaper thing to risk.

Feel it in a household first. A month in which the electricity bill arrives Rs 400/- higher than expected is a month somebody talks about. A month in which the roof has already gone and thirty thousand rupees of repair is already committed is a month in which another Rs 400/- of anything simply disappears into the hole. Nobody decided to stop caring about four hundred rupees. The four hundred rupees stopped registering. The four hundred arrived on top of a number that had already used up the capacity to be shocked.

The claim is narrower than it looks, so the ten bars repay careful reading. Nobody is saying the tenth ten thousand rupees costs less. The tenth ten thousand costs exactly the same ten thousand rupees, and the bank statement will not distinguish it in any way from the first. The change is in what that tenth instalment registers as, and the next decision is made from the registering rather than from the rupees.

So the prediction the shape makes is precise. Somebody standing well below their reference point is standing in a region where the downside of a gamble is discounted by the shape of the curve, and where the one outcome that is not discounted at all is the outcome that returns them to the point. The curve does not make people brave. The curve makes the bad half of a gamble look cheaper than it is. Looking cheaper is a different thing from being brave, and a more troubling one.

Does the same arithmetic really produce both answers?

The same arithmetic does produce both answers, and the production is worth watching once rather than taking on trust. Score the two options from the questionnaire on a single bent curve, using the same illustrative power of 0.80 as the drawing above, and let the curve do the choosing. In gains, the certain Rs 5,000/- scores 0.258 in felt units. The half chance of Rs 11,000/- scores half of 0.486, or 0.243. The certain amount wins. In losses, the certain Rs 5,000/- loss scores minus 0.574. The half chance of losing Rs 11,000/- scores half of minus 1.079, or minus 0.540. Minus 0.540 is the better of the two, so the gamble wins.

One curve, one power, one gamble, and two opposite recommendations, produced by nothing more than the sign of the numbers going in. Something else is not doing the work here. The gain side of the drawing is scaled down against the loss side by the kink, and loss aversion measures that kink at a coefficient of 2.2. The scaling multiplies both options in the gain comparison equally, so it cancels out of that comparison entirely. The reversal is produced by the bend alone.

Flattening is where somebody who has been treating it as bookkeeping usually sits up. Flattening is not a footnote to the theory. Flattening above the point is the reason careful people bank a gain early, and flattening below the point is the reason those same careful people sit in front of a position that has gone wrong and reach for the one action they would have refused a month earlier. Flattening is one property with two faces, and the reference point decides which face appears.

What is break-even chasing, and why is it so specific a target?

Take the mechanism to the case. On 30 September the eight-quarter valuation was struck across Meera Sundaram's four holdings. Kesari Logistics Limited had been bought for Rs 3,00,000/- and stood at Rs 1,95,000/-. Three lakh less one lakh ninety five thousand is Rs 1,05,000/-. On a cost of Rs 3,00,000/- that is 35.0 per cent down. On 12 October she sold Suvarna Chemicals Limited whole and kept Kesari, and the sentence she gave her adviser Devika Rao was that she would sell Kesari when it got back to Rs 3,00,000/-.

The sentence she gave is break-even chasingRefusing to close a position until it returns exactly to its starting level., and break-even chasing is the most specific thing anybody says in this whole subject. Look at the number. Not Rs 2,90,000/-, a level that would leave a small loss and free the money. Not Rs 3,10,000/-, a level that would at least ask for a margin over what was paid. Rs 3,00,000/-, to the rupee. The precision is the tell. No fact about Kesari Logistics Limited would ever land on the exact amount that one particular buyer happened to hand over for it.

The sentence deserves fairness before it is taken apart. A person who says they will sell at what they paid is not being stupid, and they are usually not even being stubborn. Such a person is answering a question that feels natural: how do I get out of this without having been wrong? Break-even is the only level at which the whole episode nets to nothing, so break-even is the only level in the entire range that answers that question. Every other level requires admitting an amount. Break-even is not chosen as a valuation; it is chosen as the one number that lets the episode close without a verdict.

The same instinct turns up at a wedding. A hall was booked, the caterer took an advance, the date has to move, and the household is quoted a change fee. Half the argument that follows is not about the fee at all. The argument is about not being the people who lost the advance. A way to move the date at exactly no net cost stops the argument instantly, even if it takes more effort than paying the fee would have.

Break-even needs a boundary drawn round it. Break-even appears twice in this sequence, and the two appearances are not the same idea. Mental accounting treats break-even as an account that has been opened and must be closed at zero, a story about how money gets sorted into separate mental boxes. Below the reference point break-even is instead a targetThe specific level at which somebody has decided they will act. produced by the shape of the curve. The account explains why the episode needs closing; the curve explains why the closing is defended with a gamble rather than with patience. Either one alone accounts for half the behaviour.

So what does the shape actually do to Kesari? Meera stands Rs 1,05,000/- below the reference point. Suppose the position could go two ways from here in equal measure: either it comes all the way back to Rs 3,00,000/-, or it falls by another Rs 1,05,000/-. In rupees that is a coin toss worth exactly nothing on average. In felt units it is not close to nothing. Doubling the loss to Rs 2,10,000/- adds 4.86 units of pain. Erasing the loss removes all 6.56 units that are already there. The bad half adds only 74.1 per cent of what the good half takes away.

The third bar of the ledger above carries the sentence a lot of people spend years not saying out loud, so read it once more. The average of the two halves, in felt units, is positive. A gamble whose money value is exactly zero has a positive value in the currency the decision actually runs on. Nobody in this situation is choosing to be reckless; they are correctly maximising the wrong quantity. The distinction shows where to look, and knowing where to look is worth more than any warning. The error is not in the courage. The error is in the units.

How large does a loss have to be before the effect appears?

Here is where a lot of second-hand accounts go wrong. Such accounts describe risk seekingPreferring a gamble to a certain amount with the same or better average. in losses as though it were a switch: above the line cautious, below the line reckless, with the flip happening the instant a position goes one rupee into the red. The shape does not say that, and the log does not show it. The curve flattens gradually, so the discount it applies to a further loss also arrives gradually.

Take the two ends the log actually measured. At the reference point itself, the position the gains half of the questionnaire describes, 30.0 per cent took the gamble. At a distance of Rs 1,05,000/- below the point, exactly where Kesari stood, 65.0 per cent took it. Between those two ends the log has nothing, so any share quoted at a middle distance is an interpolation rather than a reading. The direction matters, and so does the fact that the low end is not zero. At the reference point almost a third of the sixty still reached for the gamble, the same share as in gains.

A straight line between the two measured ends makes the steps come out unusually tidy. Each further Rs 35,000/- of distance moves the share by 11.7 percentage points. On sixty people 11.7 percentage points is seven people exactly. Eighteen at the point, twenty five at Rs 35,000/- below, thirty two at Rs 70,000/- below, thirty nine at Rs 1,05,000/- below. Nobody should read seven as a law of nature; it is the arithmetic of the two ends and the interpolation between them. The seven is useful for holding on to the idea of a climb rather than a switch.

A climb rather than a switch changes what there is to look for, and the practical consequence is worth stating plainly. If the effect were a switch, the thing to look for would be the moment somebody crossed into loss. Since it is a climb, the moment tells almost nothing and the distance tells almost everything. A position that has drifted a little below cost is a very different decision environment from one that has fallen a long way below it, even though both are described by the same word.

What does this do to a decision that would otherwise be straightforward?

Try the cleanest test available. Put two people in front of the identical holding on the identical day. Kesari Logistics Limited stands at Rs 1,95,000/-, and there is only one of it, so everything anybody could find out about it is the same for both of them. The first person bought at Rs 3,00,000/- and is therefore Rs 1,05,000/- below their reference point. The second bought at Rs 1,50,000/- and is therefore Rs 45,000/- above theirs. On Rs 1,50,000/- that is 30.0 per cent up.

Every fact about the future is shared. The same business, the same prospects, the same everything that could possibly happen next. And yet the first person is standing in the flattened region where a gamble is discounted. The second is standing in the region where a certain outcome is attractive and a gamble is not. Two people facing one identical decision reach opposite conclusions, and the entire difference between them is a number from their own past that has nothing to do with the thing in front of them.

Risk seeking in losses does not make a hard decision harder. There is only one holding and one set of facts about it, so the decision has one answer. The flattening splits that answer in two according to something in the holder's history, and a split of that kind earns a treatment of its own rather than a paragraph in a list of biases. Any process that wants to be robust has to survive that, and the first step in surviving it is being able to see it.

How does somebody deciding for others actually work with this?

The practice, Palash Advisory Services Private Limited, employs an adviser called Devika Rao, and she has no way of seeing inside a client's head. She has instead an ear for one shape of sentence. The shape turns out to be surprisingly easy to catch once it has been named. A target stated to the rupee, matching a number that appears nowhere except in the client's own purchase record, is a stated level with a traceable origin. Her question is never whether the level is right. Her question is where the level came from.

Three checks do the work, and none of them requires knowing anything about the holding. The first: can this level be derived from anything other than what was paid? If it cannot, the level is a reference point wearing the clothes of a plan. The second: how far below the point is this position in rupees? A small distance and a large one are different environments even though both are called a loss. The third, and the sharpest: would this same person take this same action if they had bought the same thing at a different amount? If the answer to the third question is no, the decision is being made by the purchase record rather than by the position.

The same three questions work just as well when there is nobody else in the room at all, no adviser and no committee to answer to. Working alone is why they are written as questions rather than as a procedure. A second person in the room is not required. The third question is what is required, written down somewhere it will actually be read. Nothing else is as impossible to answer dishonestly in the moment, and nothing else is as easy to avoid asking at all.

Where is taking more risk after a loss the correct response?

A warning is the wrong shape for all of this. There is a real situation in which more risk after a loss is the right answer, and a blanket warning would hide it. The situation is this. Somebody has to reach a fixed amount by a fixed date, the amount is not negotiable, the date is not negotiable, and the safe path can be shown not to reach it. In that case the safe path has a known failure and the risky path has an unknown one, and preferring an unknown failure to a certain one is not a bias. The preference is arithmetic.

Notice how different the structure of that is from break-even chasing, and notice that the difference is checkable rather than a matter of judgement. In break-even chasing the requirement did not move. Nothing outside changed at all. The position fell, the reference point stayed where it was, and the gamble became attractive because the curve had flattened underneath it. In the case that is correct, the requirement itself is what makes the safe path insufficient, and the requirement can be written down without mentioning what anything cost. The test is this: state the reason for the extra risk without referring to the purchase price. If the reason survives, it is a requirement. If it evaporates, it was a reference point.

The household version is easy to picture. A deposit has to be paid by a date, and the amount short is known. The safe route is short by a definite sum on a definite day. Taking a route with a range of outcomes, some of which reach the amount, is a response to the deadline rather than to any feeling about what has been lost. Change nothing except the purchase history and the answer does not move. Not moving is precisely what distinguishes it.

Which neighbouring subjects read the same curve for a different purpose?

Four subjects sit close enough to be confused with this one, and the edges between them are worth being clear about. The structure as a whole is covered under prospect theory. The reference point, the value function and the weighting of probabilities are set out there, prospect theory being the stated prerequisite, and the curve used above is borrowed from it rather than derived.

How much worse a loss feels than an equivalent gain is a separate measurement. The measurement is loss aversion, the kink at the reference point, and loss aversion puts the coefficient at 2.2 from the same questionnaire. Risk seeking in losses reads the same curve on the other side of the point, where the flattening rather than the kink is what matters. The disposition effect is covered separately: the disposition effect follows the flattening across many positions and many quarters inside one portfolio.

And no account of the mechanism tells anybody what to do after a loss. The refusal is not modesty. An explanation of why an option looks attractive is a different kind of statement from an instruction about which option to take, and an account that blurs the two has stopped being an explanation.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited, the Palash decision log, the Vindhya index scheme, the Nilgiri mid-cap scheme, Suvarna Chemicals Limited and Kesari Logistics Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.