Prospect Theory: Why the Fear of Loss Drives Risk-Taking

We’ve all heard stories like this: someone loses money in a casino, or gets stuck in the stock or crypto market. Instead of cutting their losses and leaving, they desperately double down. They bet all their savings, or even borrow money to add leverage… they lose more and more, eventually going bankrupt or even becoming fugitives.

People often say “greed blinds the mind,” but have you ever thought about it? A normal person wouldn’t place such heavy bets for unreliable gains.

We previously discussed the Kelly Criterion. Whether you place a bet should only depend on whether you have an edge. Your betting proportion should be determined by the formula based on the edge and the odds… In fact, the most common mistake most people make is not being too risky, but not daring to take risks.

So, what exactly makes those gamblers take such desperate risks?

It’s the mindset. It’s being “red-eyed” from losing. It’s the unwillingness to accept the previous loss.

People often take risks not out of greed for more, but to “get their money back.” Conversely, if they haven’t lost money yet, they tend to be hesitant when facing real profit opportunities, fearing they might lose what they already have.

This mental tool is called “Prospect Theory,” and it explains a host of decision-making biases.

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Prospect Theory was proposed by Daniel Kahneman and Amos Tversky in 1979 [1]. It was this theory that later earned Kahneman the Nobel Prize.

Traditional economics assumes that when people decide whether to do something or take a risk, they should be guided by the “Expected Utility” of the action, which depends on the final wealth value.

But Prospect Theory says no—people don’t decide based on expected utility—they look at whether they are winning or losing relative to a “Reference Point” in their minds.

The reference point is usually your psychological expectation of the status quo; you can think of it as a psychological zero point. Through the reference point, Prospect Theory draws an asymmetric S-shaped curve, as shown in the figure below—

The horizontal axis of the curve represents gains or losses relative to the reference point; the vertical axis represents the psychological value brought by this result. We can see that to the right of the reference point (the gain zone), the curve rises slowly; to the left (the loss zone), the curve drops rapidly.

What does this mean? For the same $100, the pain of losing $100 is far greater than the joy of winning $100.

This is the famous “Loss Aversion.” A common saying in academia is that pain is about twice as intense as joy… actually, this ratio varies from person to person and case to case, but the key is the “asymmetry” between gain and loss.

The reference point is your psychological expectation of the status quo, and your actual situation may not necessarily align with that reference point.

If your current situation is exactly at the reference point, or to the right of it—meaning you are satisfied with the status quo, or it has even exceeded your expectations—would you want to take a risk? You wouldn’t. Because any risk could change the status quo, and there’s a chance to either win or lose. According to the curve, the joy of winning is far less than the pain of losing, so why take the risk?

But what if you are currently to the left of the reference point? You are very dissatisfied with the status quo; you feel you should have been in a much better situation! You are already losing; wouldn’t losing a bit more just be more pain? But if there’s a chance to get back to zero, that feeling would be fantastic. So, of course, you want to gamble.

This is the “nothing to lose” mentality. Ancients said “a desperate army is bound to win.” Today, athletes say “we need to throw the burden to the opponent; we can’t play to win but fear to lose.” It means if your current situation is below your psychological expectation, you will have a greater willingness to take risks, and your approach will be more aggressive.

People are not driven to madness by greed, but by the refusal to admit defeat.

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By grasping the “Reference Point,” you can explain many diverse “cognitive biases” in behavioral economics using Prospect Theory. Let’s look at the most classic four:

First is “Loss Aversion.” The asymmetry of the S-curve tells us that the fear of losing something is far greater than the desire to gain the same thing.

This is why some people would rather be stuck in a losing stock for over a decade than admit a loss, why some stay in a wrong relationship for half their lives, why some clutter their expensive living spaces with junk, and why people feel the sting of a $20 shipping fee but accept the same price if it’s “free shipping” with the product price increased by $20…

Second is “Status Quo Bias.” People usually take the status quo as the reference point and thus tend to maintain it.

Even if conditions in big cities are significantly better, many people prefer to stay in their hometowns. Even if they are unhappy at work, they are unwilling to change jobs. Knowing that their current bank package is not cost-effective, people are too lazy to switch or even cancel auto-renewals. Company processes are clearly inefficient, yet everyone follows the old ways because reform feels unsettling. You might call it “stability above all,” but you’re just used to it.

Third is the “Endowment Effect.” Once something belongs to you, its psychological price immediately rises— “owning it” has become your reference point, and selling it becomes a loss.

Kahneman and others conducted a famous “mug experiment” [2]: some participants were given mugs, while others were not. When asked how much they would pay for the mug, the non-owners bid at most $3. But when the owners were asked how much they would sell it for, they said they wouldn’t sell even for $7.

This is why it’s so hard for a car seller and a buyer to agree on a price. The seller is selling an “old buddy” who has been with them for years; the buyer is buying a used car.

Fourth is the “Framing Effect.” A frame is your narrative style—it can determine others’ reference points, thereby manipulating their choices. There are too many classic cases here.

For example, the “Default Option Effect,” where people tend to stick with the default options on a form… you probably already know this.

Another is the “Asian Disease Problem” designed by Kahneman and Tversky [3]: Facing a disease expected to kill 600 people, which of two treatments do you choose?

For one group of participants, the description was: Program A: 200 people will be saved for sure. Program B: A 1/3 probability that 600 people will be saved, and a 2/3 probability that no one will be saved. Result: 72% chose Program A; we don’t take risks; we want to ensure these people are saved.

For the other group, the description was: Program A: 400 people will die for sure. Program B: A 1/3 probability that nobody will die, and a 2/3 probability that 600 people will die. Result: 78% chose Program B; how can we watch so many people die for sure?

But think about it: these two descriptions are mathematically identical! For the same thing, if the frame induces you to consider survival, you are conservative; if it induces you to consider death, you take risks.

Believe it or not, in medical settings, a study found [4] that when patients were choosing a lung cancer treatment, if the doctor said “the one-month survival rate after surgery is 90%,” the vast majority chose surgery. But if the doctor said “the one-month mortality rate after surgery is 10%,” many were terrified and refused.

Life-and-death decisions can depend on how a sentence is phrased; such is the magic of narrative.

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It’s not just about feeling comfortable psychologically; wrong decisions bring real losses.

One study I particularly like is about New York City taxi drivers [5].

Logically, on rainy days when more people need taxis and business is good, drivers should take the opportunity to work more and earn more; on sunny days when business is slow, they should finish early and rest. But the survey found they don’t do that. They stop early on rainy days and stay on the streets for over a dozen hours on sunny days. Why? Because drivers set a “daily target income” as their reference point. It’s easy to reach the target on rainy days, so they feel the task is done and it’s not worth working more; on sunny days, they can’t reach the goal, and “a real man doesn’t go home” until he does!

Looking back at the stock market, there’s a classic retail investor style called the “Disposition Effect” [6].

Logically, whether to sell a stock should only be decided by its expected future, unrelated to your original purchase price. But in reality, the purchase price is the strongest reference point for retail investors.

When the price rises a little, to experience the certainty of “making money,” retail investors rush to sell and lock in profits. When the price drops, they think as long as they don’t sell, it’s not a real loss. When the price has plummeted, their risk-taking spirit is ignited, and they decisively add to their position! This is why retail investors always miss the big gains but always experience the entire crash.

Another interesting application is in PR crises [7].

Suppose you are a public figure and a small mistake is exposed. Logically, if you just admit it, there won’t be much of a problem, and it’ll pass in a few days. But your reference point is that you have a perfect image, so you try to cover it up—not realizing that covering up is a very risky move.

People usually don’t invent good deeds they’ve done, but they often hide mistakes they’ve made. However, as in the Nixon Watergate or Clinton Monica Lewinsky scandals, the public will find your cover-up more detestable than the original mistake, and your collateral damage will be huge.

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Ultimately, that reference point is purely your subjective imagination. It’s a narrative! Losing down to $200k from $10M might make some people jump off a building, but for someone else, suddenly having $200k would be cause for immense joy.

An expert should be able to set their own reference points freely. It doesn’t have to be the status quo, nor does it have to be a high point you reached in the past. It can be your long-term goal or anything else. It should be a motivation, not a shackle.

One good method is “Mental Accounting” [8].

For instance, you buy a movie ticket for $100 and find you lost it at the door. In this case, would you buy another? Many wouldn’t. But think from another perspective: would you skip the movie just because you lost $100 from your wallet? In experiments, most people still chose to buy the ticket.

The fundamental reason for this difference is that you recorded “watching a movie” and “general wallet” as two separate mental accounts—when in fact, it’s all your money.

In that case, why not set up a $2,000 annual “Risk Exploration Account” or “Tuition Account”? For any unexpected losses, deduct them from this account. If there’s a surplus at the end of the year, donate it. Since it’s not “your money” anyway, any loss becomes irrelevant to you.

You can also set reference points for others.

If the company’s profits are good this year, the boss says everyone will get a $50k raise… The HR says that won’t do. If this money is counted as a raise, employees will consider it a reference point they are entitled to. Then, if the company’s performance is poor next year and you can’t continue the raise, employees won’t thank you for this year’s generosity but will feel a sense of stagnation or deprivation, potentially leading to them quitting. The correct approach: make $20k a raise and $30k a performance bonus.

The folk saying “Give a bowl of rice and you’re a savior; give a sack of rice and you’re an enemy” is also a reference point issue: the former is something that shouldn’t have been given, but you did, so it’s a surprise; the latter is because you always gave it, so they think you should, and the one time it’s inconvenient and you don’t, you are resented.

Cynical philosophy might say then we should never help unrelated people… but there is a solution here: manage the reference points. One is “work for relief”—you must pay a price to get a benefit. Another is to say the “ugly words” first to lower expectations. Another is to change a fixed salary into occasional rewards—this is called “de-regularizing benevolence.”

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Finally, let me mention something big.

The Xuanhe Northern Expedition of the Northern Song Dynasty—taking advantage of the Jin attacking the Liao to “ally with Jin against Liao”—was one of the greatest strategic disasters in Chinese history. Emperor Huizong and his ministers were double-minded, wanting to fight one moment and hesitating the next, wanting to recover the Yan-Yun territories but not daring to bear the cost of full-scale war… eventually inviting wolves into the house, leading to the humiliation of Jingkang. What were they thinking?

Yu Haiyang and Shen Chaoyong of Jilin University argued in a paper [9] that the key was that the Song had not one, but two reference points:

One was the “Real Security Reference Point.” Peace had lasted for over a hundred years between Song and Liao. Keeping the status quo and paying some tribute each year for peace—wasn’t that good? The pro-peace faction said why take risks when things are fine?

The other was the “Historical Territory Reference Point.” The Yan-Yun Sixteen Prefectures were ancestral lands of the Han and Tang! If we don’t recover them, how can we face our ancestors? To make up for this huge historical loss, why not take a gamble now that there’s a chance?

These two reference points left the court without a clear objective function. One side pushed the country toward adventure, while the other pulled back, refusing to risk everything. How could the generals execute? You neither had the courage of a gambler to win, nor the steadiness of an honest man to endure. The result was inevitably failing to hurt the enemy and failing to protect yourself—the worst possible outcome.

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Prospect Theory rewrites “humans are interest-seeking animals” into “humans are reference-point-guarding animals.” There has never been absolute rationality. When on the right side of the reference point, we are conservative; when on the left, we bet.

Your bravery and cowardice are often not from character, but from coordinates.

In a sense, this is reasonable. Shouldn’t an animal foraging on the African savanna, like a NYC taxi driver, stop after being full for the day? After all, food cannot be stored for long.

It’s just that the rules of some games have changed today. Then we must change the reference point from default to active choice.

注释

[1] Kahneman, Daniel, and Amos Tversky. 1979. “Prospect Theory: An Analysis of Decision under Risk.” Econometrica 47 (2): 263–291.

[2] Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler. 1990. “Experimental Tests of the Endowment Effect and the Coase Theorem.” Journal of Political Economy 98 (6): 1325–1348.

[3] Tversky, Amos, and Daniel Kahneman. 1981. “The Framing of Decisions and the Psychology of Choice.” Science 211 (4481): 453–458.

[4] McNeil, Barbara J., Stephen G. Pauker, Harold C. Sox Jr., and Amos Tversky. 1982. “On the Elicitation of Preferences for Alternative Therapies.” New England Journal of Medicine 306 (21): 1259–1262.

[5] Camerer, Colin F., Linda Babcock, George Loewenstein, and Richard H. Thaler. 1997. “Labor Supply of New York City Cabdrivers: One Day at a Time.” The Quarterly Journal of Economics 112 (2): 407–441.

[6] Shefrin, Hersh, and Meir Statman. 1985. “The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence.” The Journal of Finance 40 (3): 777–790.

[7] Painter, Richard W. 2000. “Lawyers’ Rules, Auditors’ Rules and the Psychology of Concealment.” Minnesota Law Review 84 (6): 1399–1468.

[8] Thaler, Richard H. 1985. “Mental Accounting and Consumer Choice.” Marketing Science 4 (3): 199–214.

[9] Yu Haiyang, Shen Chaoyong, 2021. “Victory of Failure: Multiple Reference Dependence and Decision Defects of the Xuanhe Northern Expedition.” World Economics and Politics 2021 Issue 12.