Bias of judgement

Photo by David Clode on Unsplash

Notes from the paper from Daniel Kahneman and Mark W Piece “Aspects of Investor Psychology”; source: https://www.turtletrader.com/investor-psychology.pdf

Some of these elements are also covered in Nassim Taleb’s work or in the book “Psychology of Money”

Overconfidence

People tend to be overconfident in their ability to do prediction, even if when picking a very large range of values. For example, we ask financial experts to select the best estimate value of the Dow Jones one month from today. We then ask them to choose a high and low value where they are 99% sure that the Dow Jones won’t be above or below that number (the confidence interval boundaries). In theory we should expect to encounter approximately 1% of high surprises — real outcome that could be even higher than your high estimate — and 1% of low surprises which are outcome that could be lower than your low estimate. “A vast amount of research documents a highly systematic bias in subjective confidence intervals; there are far too many surprises, indicating that the intervals were set too tightly. A typical outcome in many studies is a surprise rate of 15–20%, where accurate calibration would yield 2%. This phenomenon, known as overconfidence, is widespread and robust”.

“In general, if you are told that someone is 99% sure, you might be well-advised to assume that the relevant probability is 85%.”

Professionals which are able to be well calibrated (like meteorologists) have the following characteristics:

1. they face similar problems every day
2. they make explicit probabilistic predictions
3. they obtain swift and precise feedback on outcomes

Conditions for good calibration may be satisfied for some finance professionals; they are never satisfied for non-professional investors, who are therefore prone to display overconfidence.

This difficulties to predict is also discussed across Nassim Taleb’s work where he suggests to be ready for whatever comes and potentially benefit from it: “what you do is that you don’t have a forecast but instead have a collection of things that can happen in the world and you make sure that you are ok across these possible events. You don’t need to have a precise forecast”. It can also relate to dollar-cost averaging technique: by buying the same ETF at a regular frequency with the same purchase amount, you don’t try to predict the market but rather focus on what is under your control, which is the saving aspect.

Optimism

Optimism is another powerful bias of judgement. A famous example is 80% of drivers believing that they are above the average. “Optimists also underestimate the likelihood of bad outcomes over which they have no control”. Furthermore, they are more likely to believe they are in control as “they tend to underestimate the role of chance in human affairs and to misperceive games of chance as games of skill”.

“The combination of overconfidence and optimism is a potent brew, which causes people to overestimate their knowledge, underestimate risks and exaggerate their ability to control events. It also leaves them vulnerable to statistical surprises”

Hindsight

“Psychological evidence indicates that people can rarely reconstruct, after the fact, what they thought about the probability of an event before it occurred. Most are honestly deceived when they exaggerate their earlier estimate of the probability that the event would occur”. Furthermore, events that the best-informed experts did not anticipate often appear almost inevitable after they occur (point also discussed by Nassim Taleb). Hindsight bias can boost overconfidence.

“Within an hour of the market closing every day, experts can be heard on the radio explaining with high confidence why the market acted as it did. A listener could well draw the incorrect inference that the behavior of the market was so reasonable that it could have been predicted earlier in the day”.

Over-Reaction to chance Events

The following sequences were generated by tossing a fair coin : HHHTTT and HTHTTH. We are more likely to believe that the latter was randomly generated while the former appear systematic (and therefore less likely to appear). However, both sequences have the same probability to occur. “More important, many people will be far too quick to perceive causal regularity in random sequences of events”. We often have this case in data analytics when you are likely to “see” some patterns which may be in fact random. This effect is also called the “hot hand” fallacy (from the basketball notion that players may have “hot” or “cold” hands).

“The human mind is a pattern-seeking device, and it is strongly biased to adopt the hypothesis that a causal factor is at work behind any notable sequence of events”

The risk of this judgment bias is that you may overreact to information or perceive trends that don’t exist. An example of this effect was studied by Odean where he “reports a striking pattern of results in his analysis of hundreds of thousands of individual transactions made with a brokerage firm. He finds that when individual investors sold a stock and quickly bought another, the stock they sold outperformed the stock they bought by 3.4 percentage points in the first year, on average (excluding the costs of transactions). This costly overtrading may be explained in terms of two of the biases that we have discussed: people perceive patterns where none exist, and they have too much confidence in their judgments of uncertain events”

Error of preference

You are facing a chance for a gain of $20,000. You do not know the exact probability. Consider the three pairs of outcomes: A. The probability is either 0 or 1% B. The probability is either 41% or 42% C. The probability is either 99% or 100% Are the three differences, A, B and C, equally significant to a decision-maker? Could you order them by their impact on preferences?

“The theory of rational choice tells us that uncertain prospects should be evaluated by a weighted average of the utilities of possible outcomes, each weighted by its probability. Weighting by probability implies that a possible outcome that has a probability of 1% should be weighted ten times as much as an outcome that has a probability of 0.1%. Another implication is that an increment of 1 percentage point in the probability of an event should have the same effect on the weighting of outcomes, whether the initial probability is 0%, 41%, or 99%”. However, in practice, people are more likely to pay to raise the probability of a desirable event from 0% to 1% or from 99% to 100% rather than paying for an increase from 41% to 42%. In particular, people overweight low probabilities and “it explains why people like long shots better than other gambles of equal expected value; long shots are preferred because low probabilities of winning are greatly overweighted. Thus, most people will find a 1% chance to win 1,000 USD more attractive than a 10 USD gift. And most people who have a 99% chance to win 1,000 USD will be willing to pay much more than 10 USD to eliminate the possibility of missing the prize. In general, the non-proportional weighting of probabilities makes people like both lottery tickets and insurance policies”.

People value changes, not state

• Question 6. Imagine that you are richer by 20,000 USD than you are today, and that you face a choice between options: A. receive 5,000 USD or B. a 50% chance to win 10,000 USD and a 50% chance to win nothing.
• Question 7. Now imagine that you are richer by 30,000 USD than you are today, and that you are compelled to choose one of two options: C. lose 5,000 USD or D. a 50% chance to lose 10,000 USD and a 50% chance to lose nothing.

“A fully rational decision-maker would treat the two decision problems as identical, because they are identical when formulated in terms of states of wealth” : be richer of 25,000 USD today or end up richer by 20,000 USD or 30,000 USD with equal probabilities. Nevertheless, people are more likely to focus on the gain/loss aspect (influenced by the related emotions associated with it) rather than wealth which is the final goal. If we were rational, we will choose either the gamble or the sure thing in both Questions 6 and 7 (both are the same so it doesn’t matter), instead of flipping preferences as most people do.

What matters to a perfectly rational decisionmaker is where he or she gets to in the end, not the gains or losses along the way

Conclusion: “it is always possible to frame the same decision problem in broader terms (such as wealth) or in narrower terms (such as gains and losses); broad and narrow frames often lead to different preferences. Second, rationality is best served by adopting broad frames, and by focusing on states (such as wealth) rather than on changes (such as gains and losses).”

Value function

(From wikipedia) “Loss aversion is the tendency to prefer avoiding losses to acquiring equivalent gains. Loss aversion implies that one who loses 100 USD will lose more satisfaction than the same person will gain satisfaction from a 100 USD windfall. Loss aversion is part of prospect theory, a cornerstone in behavioral economics.

Consider two scenarios;

1. 100% chance to gain 450 USD or 50% chance to gain 1000 USD
2. 100% chance to lose 500 USD or 50% chance to lose 1100 USD

Prospect theory suggests that;

• When faced with a risky choice leading to gains agents are risk averse, preferring the certain outcome with a lower expected utility (concave value function). Agents will choose the certain 450 USD even though the expected utility of the risky gain is higher
• When faced with a risky choice leading to losses agents are risk seeking, preferring the outcome that has a lower expected utility but the potential to avoid losses (convex value function). Agents will choose the 50% chance to lose 1100 USD even though the expected utility is lower, due to the chance that they lose nothing at all

These two examples are thus in contradiction with the expected utility theory, which only considers choices with the maximum utility. Also, the concavity for gains and convexity for losses implies diminishing marginal utility with increasing gains/losses. In other words, someone who has more money has a lower desire for a fixed amount of gain (and lower aversion to a fixed amount of loss) than someone who has less money”.

You can see the value function below. Psychology value here has to be understood as happiness / pain. Horizontal and vertical axis cross on the ‘reference point’ (source: https://www.dreamendstate.com/2021/02/15/prospect-theory-why-we-feel-losses-more-intensely-than-gains/)

“Question 8. Someone offers you a bet on the toss of a coin. If you lose, you lose USD 100. What is the minimal gain that would make this gamble acceptable?The answers to Question 8 typically fall in the range 200 to 250 USD — an extraordinarily high ratio of gain to loss. This number reflects the sharp asymmetry between the values that people put on gains and losses. This asymmetry, called loss aversion, explains decisions in many domains”

The shape and attractiveness of gambles

Individuals like gambles that combine a high level of security with some upside potential; these prospects are associated with much hope and little fear. The ideal gamble combines the attractiveness of a lottery ticket (due to overweighting of the small probability of a large gain) and the attractiveness of a sure, smaller gain.

The purchase price as a reference point

“Question 11. Investor A owns a block of a stock, which he originally bought at 100 USD per share. Investor B owns a block of the same stock for which she paid 200 USD per share. The value of the stock was 160 USD per share yesterday, and today it dropped to 150 USD per share. Who is more upset?

Most readers will agree that B is more upset than A. The reason for this intuition is that investor A will probably treat the bad news as a reduction in a gain, while B will experience the same news as an increased loss. Because the value function is steeper for losses than for gains the difference of $10 in share price is more significant for B than for A. As this example illustrates, we generally expect investors to be aware of the price at which they made a substantial investment in a stock, and to continue for some time to use this price as a reference point. Thus, the initial price determines whether selling the stock now will yield a gain or a loss.

An important consequence of this psychological fact is known as the disposition effect: a marked reluctance of investors to realize their losses. For example, consider an investor who needs cash and must sell one of two stocks that she owns; one of the stocks has gone up and the other has gone down. Odean [1998a] studied trade records for 10,000 individual investors and shows that investors are much more likely to sell the stock that went up”. You should probably “let winners run” and “cut losses” instead….

Narrow Framing

We tend to take decision within a narrow frame without taking the broader perspective into account. “There is an abundance of real-world examples of investors considering decision problems one at a time instead of adopting a broader frame. Some of these are simply mistakes, in which the investor misses an opportunity to diversify, hedge or self-insure. In other cases, narrow framing arises from the common practice of maintaining multiple mental accounts. There might be a budget for current expenses; there may be a special account of saving for a vacation, which is kept separate from saving for the children’s education, and so on. Attitudes toward spending, saving and risk are quite different for different accounts. Thus, people may simultaneously save for the children’s education and borrow to buy a car; they may invest in a risky venture if the cash is drawn from a windfall gain, but not if it is drawn from the savings earmarked for retirement”.

Repeated Gambles and Risk Policies

“Most decision-makers, as we have seen, adopt narrow frames, consider their decision problems one at a time, and are guided by the attractiveness of the options immediately available in making their decisions. In contrast, a rational decision-maker adopts a broader frame for evaluating outcomes, and makes particular decisions in light of a general risk policy. A sound policy also incorporates considerations of the frequency with which further risky opportunities are likely to be encountered”.

Short and Long Views

“Investors who own risky assets must commit themselves psychologically to stay with their investments for some time. […] One expression of commitments is the frequency with which the investor monitors the investment and checks how well it has done. Some nervous investors check very frequently; others are less concerned with short-term fluctuations”. Many individuals like to talk long term and act short term.

Living with the consequences of decisions

1. “Investment decisions have both emotional and financial consequences overtime. There is potential for worry and for pride, for elation and for regret, and sometimes for guilt […]. A financially optimal decision […] is of little use to an investor who cannot live comfortably with uncertainty. And the optimal decision is certainly irrelevant if it is one that means the investor is likely to change course at the wrong time.
2. No one likes to lose, but regret makes losing hurt more. Clearly, the losing investor who believes that he should have anticipated the poor performance of his investment feels worse than if he believes the failure could not have been predicted”.

Regret of Omission and Commission

Question 18. Mr. Paul owned shares in company A. During the past year he considered switching to the stock of company B, but he decided against it. He now finds that he would have been better off by 20,000 USD if he had switched to company B. sr. George owned shares in company B. During the past year he switched to the stock of company A. She now finds that she would have been better off by $20,000 if she had kept her shares of company B. Who is more upset?

“Ms. George was probably more upset than Mr. Paul, although in economic terms their outcomes are the same. The essential difference between them is that Ms. George suffers from a regret of commission: she regrets something she did. In contrast, Mr. Paul suffers the weaker regret of omission: he regrets failing to do something that would have made him better off. The difference between the two occasions for regret is related to the well-documented difference between losses (which people feel acutely) and opportunity costs (failures to gain), which seem to cause relatively little pain”.

Regret and Risk Taking

Question 19. Think of a bad financial decision that you made which you now regret. Was it a decision to do something, or to refrain from doing something? What was the role of chance in the outcome?

Although most people feel more regret about things they did than about things they did not do, there are exceptions, and these exceptions appear to be significant in the context of investment. A study by Kahneman and Thaler showed that “people who regret the opportunities they missed tend to take more risks than people who regret attempts that failed”. The risk takers tended to assign little role to luck as a cause of both outcomes. In the terms we have discussed, the illusion of control helps people take risks and live with them.