How do we make decision under uncertainty?

Behavioral finance uses psychological insights to inform financial theory. Behavioral finance holds that we do not behave like the rational and self-interested agent of economic theories. Homo Sapiens is not Homo Economicus. We have emotions. We are influenced by the others. We have cognitive bias. This papers aims to help you better understand how these psychological factors affect your financial decisions under risk.


Understanding the cognitive mechanism of financial decisions

Daniel Kahneman, one of the most influential figures of behavioral finance, developed the powerful “two minds: System 1/System 2” framework to describe our decision-making process.

System 2: Deliberate, slow and effortful. We use this system when solving analytically complex problems such as multiplying 47*89. Even if we can be quick, we are aware of the reasoning we use to solve the problem. We can explain and debate it.

System 1: Intuitive, fast and effortless. We use this system when performing automatic tasks such as driving or solving 2+2. These automatic tasks can be however highly complex. A business angel may have a gut feeling for a start-up after a 1-minute pitch. An art expert can recognize in a fraction of seconds the author of a masterpiece. System 1 uses shortcuts, heuristics and automatisms rather than deliberation. This is a very powerful tool to make quick decisions in a complex environment. That’s why most of our decisions are made by System 1.

However, they are prone to cognitive bias.

What is cognitive bias?

Which stick is the longest?


Have a careful look! Measure them! This may be not the one you think…

Optical illusion is an example of cognitive bias. Have a look again…you may still feel that the second stick is the longest, even if rationally you know they are the same length. Similarly, we often unconsciously use mental shortcuts to make quick decisions. These rules work well under most circumstances, but they can lead to systematic deviations from logic or reality. These deviations are called cognitive biases. Like optical illusions, even when we know we have a bias, it is not always easy to avoid being influenced by it.


There are tons of cognitive biases. The table displays some common cognitive biases in financial decisions

Decision under risk: Greed, Fear and Pessimism

Let’s imagine you can invest in a bet with a 50% chance of getting either $100 or $0. How much are you willing to pay for this bet?

One investment strategy is to calculate the expected value (EV) of the bet and invest only if the EV is greater than the price of the bet. Most of us however are risk-averse and are willing to gamble only if the EV is greater than $50. Moreover, the higher the outcome, the less sensitive we become to an outcome increase. Getting a $10 free gift coupon, this is a big deal. But winning $11k at casino instead of $10k may not make you so much happier… To account for this first psychological parameter, we can say that the utility we attribute to financial gains is often concave. We are rarely greedy. Instead we underestimate gains and our marginal utility is diminishing.

Now, what if I asked you to choose between paying $50, and placing a bet where you have 50% chance of paying either $100 or nothing? In this case, most of us prefer to gamble. There is some hope not to lose. We try our chances. Even for $25, we may be ready to gamble. Most of us are afraid of losing. On average, we are twice more sensitive to losses than to gains. Moreover, we are much more sensitive to a change in small losses than in big losses. If you expected to pay $10 for your meal and get a $20 bill, you may become very upset. But if you finally buy your house $1.1M instead of $1M, it may not really matter. In a nutshell, our valuation of losses is often convex.

Loss aversion is one of the most fundamental heuristics in our financial decisions. It is also present among very young children and capuchin monkeys (Chen, 2006). We can speculate that this makes sense from an evolutionary point of views. Our hot-headed and fearless ancestor may not have survived long in the savannah…

Finally, you may not care about buying a pill with a 90% or 90.5% chance of success. But you may strongly prefer a 100% safe pill over a pill with a 0.5% risk. To sum things up, we tend to distort probabilities. Small probabilities are over weighed. Large probabilities are underweighted. 30% is most of the time the limit. One of the most famous illustrations of probability distortion is the Allais paradox (1953).

We are also more or less optimist or confident in our financial decisions. If you drive a car for the first time and are told that 1M+ people die each year on the road, you may be quite scared and over weigh the probability of crashing. If you are an experienced driver, you may on the contrary be overconfident and under weigh the risk.

Prospect Theory is a decision-making model under risk which takes into account these psychological factors. Developed by the Nobel Prize winners Daniel Kahneman and Amos Tversky in 1979, Prospect Theory is at the heart of behavioral finance (Kahneman & Tversky, 1979; Wakker, 2011).

Introduction to Prospect Theory

Let’s take a bet, L, that pays x with a probability of either p or y. x and y can be positive or negative. How do people value this bet? As discussed above, the Expected Value does not take into account personal preferences and cognitive bias.


We assume that each person has her own value function U to evaluate the bet L:

U(L) = w(p)u(x) + (1 −w(p))u(y)

With u her utility function:

u(x) = xα, x > 0,

u(x) =  − λ( − x)α, x < 0

α is the concavity/convexity or “Greed” parameter. λ is the loss aversion or “Fear” parameter.



w is the probability weighting function with two parameters:

w(p) = (exp( − ( − ln p)σ))β

with β>0 the elevation/pessimism parameter and σ>0 the curvature/likelihood insensitivity parameter. If 0<β<1, the probability weighting function captures optimism. If β > 1 the probability weighting function captures pessimism. If 0<σ<1, the function reflects inverse s-shape pattern where small probabilities are over weighed and large probabilities are under weighed.

Contrary to the classical framework, there is no one specific parameter for risk-taking in Prospect Theory. A risk-averse behavior results from the combination of loss aversion, concavity of the utility function, and pessimism and likelihood insensitivity of the probability function.

Most empirical studies show that we tend to exhibit a fourfold pattern with risk-aversion for large probabilities and risk-seeking for small probabilities in the gain domain, risk-aversion for small probabilities and risk-seeking for large-probabilities in the loss domain.

There is however a high variability at the level of the individual.

I’m biased, this is serious?

The basics of behavioral finance are that we don’t behave like the rational and self-interested agent of classical finance. Our decisions are strongly influenced by emotions, social pressure and cognitive fallacies. We prefer to use heuristics than deliberation. Such mental shortcuts are often presented as “bad things” which prevent us from rationality. However, heuristics is a wide term which covers many different cognitive mechanisms. Even what we mean by rationality is not always clear. Is it a deviation from individual profit maximization? From logics? From wisdom? From reality? From evolutionary optimum?

For some bias, like logical fallacies, such as base rate fallacy (ignoring prior when calculating conditional probabilities), the answer is quite straightforward. They lead to mathematical error and we’d better get rid of them.

For others, the answer is more complicated.

Let’s consider the question of risk-taking. Risk-taking behavior depends on loss aversion, greed and optimism. In other words, it depends on how much risk we are willing to take to win more, to loose less and how we perceive the probabilities of outcomes. Loss aversion and greed are more a question of preference. You refuse to bet with your friend because, even if you are quite sure you are right, you know you hate losing. You can make this choice deliberatively. It is not rational or irrational to do so. Some preferences may be of course more appropriate according to the situation. If you are a medical doctor, loss aversion is required. You deal with lives. If you are a wealth manager, you should adapt to your clients preferences. If you are a trader, neutrality may be effective if you want to maximize expected value. But this may be of course challenged by external constraints like corporate governance, bonus or competition. To cut it short, loss aversion and greed are more a question of personal preferences, personality or wisdom.

For probability distortion, the question is trickier. We do not really choose to over weigh small probabilities and under weigh large probabilities. This is not a question of preference and we can’t help it so easily. Are we irrational if we do so? Again, the answer is not straightforward. Yes we are, as we misperceive the reality. However, probability distortion can be useful in practice. If you are an entrepreneur, a bit of optimism can help inspire your team. The heuristics “If I am not sure, let’s say there is a 50% of chance” can be effective to make super-quick decisions.

What about memory, causality or social biases? Is it irrational to make generalizations considering our past experiences, to prefer to collaborate with people like us, to punish free-riders even if it is costly…? Such biases often make sense from an evolutionary perspective. Using our past experiences helps us make decisions when we lack information. Trusting our kin and punishing free-riders helps the tribe to survive.

Many cognitive biases are heuristics or intuitions which can be very effective in making quick and result-oriented decisions in a complex and uncertain environment. But their solution is often approximate. When we have time and access to more information, a deliberative thought is often a better option.

Author: Tiphaine Saltini




















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