Advanced Finance – 2026
PART I – Behavioral Finance
Introduction to behavioral finance
Behavioral finance is about making the best possible financial decisions, how people make these
decisions in real life. We need to take into account a certain level of uncertainty and also the
actions of others. It is about making predictions.
People make financial decisions using models, which are a simplified representation of reality.
But how do you model human decision making? We start from the standard that human are
rational and make the assumption of an economic man (homo economicus).
The economic man
The economic man is a rational man, who is assumed to have knowledge of relevant aspects of
his environment. This knowledge, if not complete, is at least clear and extensive. He possesses a
well-organized and stable system of preferences and has computational skills that allow him to
evaluate alternative courses of action, and determine which option maximizes his preference
satisfaction.
By combining knowledge, a stable system of preferences and skills, people can rank decisions
and this way act in their own best way, and thus make decisions that are best for themselves.
(At best) bounded rationality
In reality you cannot be fully rational, and
people tend to have a bounded rationality.
People’s rationality is limited by the cognitive
limitations of the mind, the time and
information available to make decisions.
This leads to us making sub-optimal decisions, referring to the fact that it is not optimal and thus
not possible to be fully rational.
Computation skills
Someone with good computation skills should not make any cognitive mistakes. Cognitive
mistakes are systematic errors in thinking that cause people to make irrational decisions,
because of flawed reasoning or information processing.
A very well-known example is the following where you ask people which
one of the two lines is the shortest. People with good computation skills
should quickly and correctly identify the problem, without being misled
by illusions or distractions. Another example is one where we have 3
cards in a pocket. One is red on both sides, one green on both sides, and
one has a green and red side. You reach in the pocket and grab a red card.
What is the probability of the other side being green? Answer: 1/2.
1
,Conclusion
It is difficult to give the right answer on spot because people are overloaded. Besides that, t also
depends on external factors, like people being around you. Some people will even decide to not
answer when such questions are being asked, and will only listen because they feel like it is better
not to talk.
Other people will act like sheep. They will move together as a group and follow each other, which
we call herding. People have the tendency to follow the behavior of a larger group, and tend to
adopt opinions because they see others doing the same. A perfect example of this, is the fact that
everyone started ‘hamsteren’ toilet paper during the COVID-19 outbreak.
Overconfidence of managers and investors
This is called the “better-than-average-effect” of managers and investors, who think of
themselves that they do better than average managers or investors. Overconfident people do not
only overestimate their own capabilities, but also ignore those of their rivals.
Overconfidence is not always bad. It may allow organizations to function better, because an
overconfident team member overestimates his marginal productivity, which makes him work
harder. Consequently, the other members will also work harder, and the organization will benefit
from this. So, for a business for example, it could be good to be overconfident since it may push
your team to work better and make a good carrier.
Loss aversion
People tend to focus more on where they are losing, rather than focusing on where they are
winning, because they hate losing much more than they love winning.
Behavioral finance
Behavioral finance, or also called the financial decision making by normal people. Normal people
make mistakes, are influenced by emotions, copy the behavior of others, and can be irrational.
You, as a person, are the decision architect, and by knowing about these biases you can set rules
to avoid them and exploit the mistakes of others.
Nudging
Nudging is any aspect of the choice architecture that alters people’s behavior in a predictable
way, without forbidding any options or significantly changing their economic incentive. Nudges
are small interventions where people still are free to do what they want, but by having these small
interventions you can encourage people towards a certain behavior that you want to see.
Marketing is all about nudging and exploiting people’s biases to encourage them making decisions
that are best for you. We see for example here two burgers. If people were fully rational, they would
2
,not prefer one or the other. In reality their
preferences are determined by the presentation
of things, and they will choose for the “best”
presentation because they get influenced by the
nudges of marketing.
Richard Thaler (Nobel prize winner)
This 2017 Nobel prize winner in terms of rational
behavior did an experiment at an airport. He put a fly in the men’s urinal pots, which led to a
reduction of the spillage of urine on the men’s room floor by almost 80%. It had men putting more
focus into it while peeing and made them spill less. This is maybe not an economic example, but
perfectly shows how very little nudges can completely change things up.
By understanding how people function in an economic context, what decisions they make and
why, we can stimulate an environment that supports better economic decisions. For example, a
professor (prof. De Neve) decided to rewrite letters that the tax administration was sending to
households when people were late with their payments. Just by changing the words, it encouraged
households to pay their bills.
3
,Explaining financial decisions under uncertainty: theory
Decisions have financial consequences and future payoffs that are random. This theory requires
a model, which at its turn requires assumptions. We want to obtain a model, a simplified
representation of the reality in which we explain financial decisions under uncertainty. We make
the assumption that people try to make the “best” decision according to a certain criterion.
Changing this criterion will lead to different predicted decisions. All models are wrong but some
are useful, it should help us understand reality.
Assumptions about the decision problem
You know the choices. The decision is between different contracts (prospects), for example the
decision between two jobs. You have to choose one or the other. Depending on the prospect
chosen, the wealth one has at the end of the period is different. Your decisions have an impact on
your wealth. The actual value will depend on the state of the world, for example if there has been
a recession or not.
Assumptions about the world
You know the uncertainty of the cashflows based on a choice. Consider a world with ‘n’ possible
states, and in each state the wealth received from the prospect can be different from the other.
Each single state has a certain probability of happening:
𝐩𝐢 & 𝐢 = 𝟏, … , 𝐧 𝐰𝐢𝐭𝐡 𝐩𝟏 + ⋯ + 𝐩𝐧 = 𝟏
If you choose prospect 1 and the
world is in state 1, then your wealth
will be w1. If you choose prospect 1
but the world is in state 2, your
wealth will be w2.
Wealth is thus a random variable
for which the distribution depends on the choice of prospect. You will choose for prospect 1 when
the outcome (expected wealth) of that prospect is bigger than the outcome for prospect 2. The
outcome is in this case the sum of all probabilities, times the sum of all expected wealth.
Assumptions about the individual’s optimality criterion
What is understood by “best”, we need to consider three possibilities:
- Maximize expected wealth.
- Maximize expected utility.
- Maximize weighted perceived value (prospect theory).
4
,Decision rule 1: maximize expected wealth
The expected wealth is the expected value of wealth. Under our model of the world we have
discrete outcomes w1, w2, …, wn with probability p1, p2, …, pn. With this in mind we can then say
that the expected wealth is:
𝐧
𝐄[𝐰] = ∑ 𝐩𝐢 𝐰𝐢
𝐢=𝟏
When looking back at the table we saw under the assumptions about the world, we would choose
prospect 1 if: ∑𝐧𝐢=𝟏 𝐩𝐢 𝐰𝐢 > ∑𝐧𝐢=𝟏 𝐩𝐢 𝐯𝐢
Issues with expected wealth as a decision criterion
Sometimes the expected wealth is the same for the lottery and the sure outcome. You would be
indifferent between the different states if you would only care about expected wealth.
State of the world Probability Wealth under Wealth under sure
“lottery” outcome
1 0,5 0 50
2 0,5 100 50
𝟎, 𝟓 𝐱 𝟎 + 𝟎, 𝟓 𝐱 𝟏𝟎𝟎 = 𝟓𝟎
𝟎, 𝟓 𝐱 𝟓𝟎 + 𝟎, 𝟓 𝐱 𝟓𝟎 = 𝟓𝟎
It doesn’t matter which prospect you choose, you will get the same outcome for expected wealth
no matter the prospect. This decision-making method does not take into account the risk
preferences when you only look at the expected wealth. The decision maker can be different. The
impact on the decision depends on the risk preferences of the risk taker. For a risk neutral person
nothing will be change, but someone can also be risk averse (preference for sure outcome) of risk
seeking (preference for the lottery).
The issue with the expected wealth as a decision criterion is that it doesn’t account for risk
preferences. A second issue is that it assumes that individuals weight each outcome with the
probability of outcome. The expected utility theory makes the same assumption, while the
prospect theory allows for “normal” people and weights with perceived probabilities.
Decision rule 2: maximize expected utility
It is not the level of wealth that counts in each state, but the utility received from this. It is not the
level of expected wealth that determines the decision, but the expected utility due to the decision.
We decides such that the decision yields the highest expected utility.
𝐧
𝐄𝐔 = ∑ 𝐩𝐢 𝐔(𝐰𝐢 )
𝐢=𝟏
The more wealth, the more utility you have. Utility is an increasing function of wealth. Pay attention
to decreasing marginal utility, which means that the first million will make you happier than the
5
, second one does, and so on. When
considering the following table, we will
choose prospect one when the following
condition holds:
𝐧 𝐧
∑ 𝐩𝐢 𝐔(𝐰𝐢 ) > ∑ 𝐩𝐢 𝐔(𝐯𝐢 )
𝐢=𝟏 𝐢=𝟏
The utility function
The utility function has a positive slope for the first order derivative, because more wealth is
always preferred to less wealth: 𝐢𝐟: 𝐰𝐢 > 𝐯𝐢 , 𝐭𝐡𝐞𝐧: 𝐔(𝐰𝐢 ) > 𝐔(𝐯𝐢 ). The utility function U(w) should
be strictly increasing for the first derivative. The curvature depends on the risk preference and risk
profile of the risk taker. There are three option, as we already saw.
In all cases the first derivative is positive, but the difference lays in the second derivative.
Whenever the second derivative is positive, we are situated in the first case, where the risk taker
is risk seeking and the utility function is convex. The second graph is the other way around, a
concave utility function. Here we are risk averse, and the second derivative is negative. In the last
graph where the utility function is linear, we are risk neutral and the second derivative equals 0.
- Risk seeking: u’’ > 0 - Risk averse: u’’ < 0 - Risk neutral: u’’ = 0
People will make different choices depending on their preferences, even if everything has the
same outcome and the average wealth is the same. The average wealth is the same, but the
distribution is different, which will affect the utility.
𝐧 𝐧
𝐔(∑ 𝐩𝐢 𝐰𝐢 ) 𝐯𝐞𝐫𝐬𝐮𝐬 ∑ 𝐩𝐢 𝐔(𝐰𝐢 )
𝐢=𝟏 𝐢=𝟏
On one side we got the expected utility sure outcome (has only one outcome) and on the other
side the expected utility lottery outcome (multiple possibilities depending on the state).
Linear utility function
This is where the function is a straight line and where the preferences of the risk taker are neutral,
the economic agent is risk neutral and the second derivative is equal to 0. This means that both
6
PART I – Behavioral Finance
Introduction to behavioral finance
Behavioral finance is about making the best possible financial decisions, how people make these
decisions in real life. We need to take into account a certain level of uncertainty and also the
actions of others. It is about making predictions.
People make financial decisions using models, which are a simplified representation of reality.
But how do you model human decision making? We start from the standard that human are
rational and make the assumption of an economic man (homo economicus).
The economic man
The economic man is a rational man, who is assumed to have knowledge of relevant aspects of
his environment. This knowledge, if not complete, is at least clear and extensive. He possesses a
well-organized and stable system of preferences and has computational skills that allow him to
evaluate alternative courses of action, and determine which option maximizes his preference
satisfaction.
By combining knowledge, a stable system of preferences and skills, people can rank decisions
and this way act in their own best way, and thus make decisions that are best for themselves.
(At best) bounded rationality
In reality you cannot be fully rational, and
people tend to have a bounded rationality.
People’s rationality is limited by the cognitive
limitations of the mind, the time and
information available to make decisions.
This leads to us making sub-optimal decisions, referring to the fact that it is not optimal and thus
not possible to be fully rational.
Computation skills
Someone with good computation skills should not make any cognitive mistakes. Cognitive
mistakes are systematic errors in thinking that cause people to make irrational decisions,
because of flawed reasoning or information processing.
A very well-known example is the following where you ask people which
one of the two lines is the shortest. People with good computation skills
should quickly and correctly identify the problem, without being misled
by illusions or distractions. Another example is one where we have 3
cards in a pocket. One is red on both sides, one green on both sides, and
one has a green and red side. You reach in the pocket and grab a red card.
What is the probability of the other side being green? Answer: 1/2.
1
,Conclusion
It is difficult to give the right answer on spot because people are overloaded. Besides that, t also
depends on external factors, like people being around you. Some people will even decide to not
answer when such questions are being asked, and will only listen because they feel like it is better
not to talk.
Other people will act like sheep. They will move together as a group and follow each other, which
we call herding. People have the tendency to follow the behavior of a larger group, and tend to
adopt opinions because they see others doing the same. A perfect example of this, is the fact that
everyone started ‘hamsteren’ toilet paper during the COVID-19 outbreak.
Overconfidence of managers and investors
This is called the “better-than-average-effect” of managers and investors, who think of
themselves that they do better than average managers or investors. Overconfident people do not
only overestimate their own capabilities, but also ignore those of their rivals.
Overconfidence is not always bad. It may allow organizations to function better, because an
overconfident team member overestimates his marginal productivity, which makes him work
harder. Consequently, the other members will also work harder, and the organization will benefit
from this. So, for a business for example, it could be good to be overconfident since it may push
your team to work better and make a good carrier.
Loss aversion
People tend to focus more on where they are losing, rather than focusing on where they are
winning, because they hate losing much more than they love winning.
Behavioral finance
Behavioral finance, or also called the financial decision making by normal people. Normal people
make mistakes, are influenced by emotions, copy the behavior of others, and can be irrational.
You, as a person, are the decision architect, and by knowing about these biases you can set rules
to avoid them and exploit the mistakes of others.
Nudging
Nudging is any aspect of the choice architecture that alters people’s behavior in a predictable
way, without forbidding any options or significantly changing their economic incentive. Nudges
are small interventions where people still are free to do what they want, but by having these small
interventions you can encourage people towards a certain behavior that you want to see.
Marketing is all about nudging and exploiting people’s biases to encourage them making decisions
that are best for you. We see for example here two burgers. If people were fully rational, they would
2
,not prefer one or the other. In reality their
preferences are determined by the presentation
of things, and they will choose for the “best”
presentation because they get influenced by the
nudges of marketing.
Richard Thaler (Nobel prize winner)
This 2017 Nobel prize winner in terms of rational
behavior did an experiment at an airport. He put a fly in the men’s urinal pots, which led to a
reduction of the spillage of urine on the men’s room floor by almost 80%. It had men putting more
focus into it while peeing and made them spill less. This is maybe not an economic example, but
perfectly shows how very little nudges can completely change things up.
By understanding how people function in an economic context, what decisions they make and
why, we can stimulate an environment that supports better economic decisions. For example, a
professor (prof. De Neve) decided to rewrite letters that the tax administration was sending to
households when people were late with their payments. Just by changing the words, it encouraged
households to pay their bills.
3
,Explaining financial decisions under uncertainty: theory
Decisions have financial consequences and future payoffs that are random. This theory requires
a model, which at its turn requires assumptions. We want to obtain a model, a simplified
representation of the reality in which we explain financial decisions under uncertainty. We make
the assumption that people try to make the “best” decision according to a certain criterion.
Changing this criterion will lead to different predicted decisions. All models are wrong but some
are useful, it should help us understand reality.
Assumptions about the decision problem
You know the choices. The decision is between different contracts (prospects), for example the
decision between two jobs. You have to choose one or the other. Depending on the prospect
chosen, the wealth one has at the end of the period is different. Your decisions have an impact on
your wealth. The actual value will depend on the state of the world, for example if there has been
a recession or not.
Assumptions about the world
You know the uncertainty of the cashflows based on a choice. Consider a world with ‘n’ possible
states, and in each state the wealth received from the prospect can be different from the other.
Each single state has a certain probability of happening:
𝐩𝐢 & 𝐢 = 𝟏, … , 𝐧 𝐰𝐢𝐭𝐡 𝐩𝟏 + ⋯ + 𝐩𝐧 = 𝟏
If you choose prospect 1 and the
world is in state 1, then your wealth
will be w1. If you choose prospect 1
but the world is in state 2, your
wealth will be w2.
Wealth is thus a random variable
for which the distribution depends on the choice of prospect. You will choose for prospect 1 when
the outcome (expected wealth) of that prospect is bigger than the outcome for prospect 2. The
outcome is in this case the sum of all probabilities, times the sum of all expected wealth.
Assumptions about the individual’s optimality criterion
What is understood by “best”, we need to consider three possibilities:
- Maximize expected wealth.
- Maximize expected utility.
- Maximize weighted perceived value (prospect theory).
4
,Decision rule 1: maximize expected wealth
The expected wealth is the expected value of wealth. Under our model of the world we have
discrete outcomes w1, w2, …, wn with probability p1, p2, …, pn. With this in mind we can then say
that the expected wealth is:
𝐧
𝐄[𝐰] = ∑ 𝐩𝐢 𝐰𝐢
𝐢=𝟏
When looking back at the table we saw under the assumptions about the world, we would choose
prospect 1 if: ∑𝐧𝐢=𝟏 𝐩𝐢 𝐰𝐢 > ∑𝐧𝐢=𝟏 𝐩𝐢 𝐯𝐢
Issues with expected wealth as a decision criterion
Sometimes the expected wealth is the same for the lottery and the sure outcome. You would be
indifferent between the different states if you would only care about expected wealth.
State of the world Probability Wealth under Wealth under sure
“lottery” outcome
1 0,5 0 50
2 0,5 100 50
𝟎, 𝟓 𝐱 𝟎 + 𝟎, 𝟓 𝐱 𝟏𝟎𝟎 = 𝟓𝟎
𝟎, 𝟓 𝐱 𝟓𝟎 + 𝟎, 𝟓 𝐱 𝟓𝟎 = 𝟓𝟎
It doesn’t matter which prospect you choose, you will get the same outcome for expected wealth
no matter the prospect. This decision-making method does not take into account the risk
preferences when you only look at the expected wealth. The decision maker can be different. The
impact on the decision depends on the risk preferences of the risk taker. For a risk neutral person
nothing will be change, but someone can also be risk averse (preference for sure outcome) of risk
seeking (preference for the lottery).
The issue with the expected wealth as a decision criterion is that it doesn’t account for risk
preferences. A second issue is that it assumes that individuals weight each outcome with the
probability of outcome. The expected utility theory makes the same assumption, while the
prospect theory allows for “normal” people and weights with perceived probabilities.
Decision rule 2: maximize expected utility
It is not the level of wealth that counts in each state, but the utility received from this. It is not the
level of expected wealth that determines the decision, but the expected utility due to the decision.
We decides such that the decision yields the highest expected utility.
𝐧
𝐄𝐔 = ∑ 𝐩𝐢 𝐔(𝐰𝐢 )
𝐢=𝟏
The more wealth, the more utility you have. Utility is an increasing function of wealth. Pay attention
to decreasing marginal utility, which means that the first million will make you happier than the
5
, second one does, and so on. When
considering the following table, we will
choose prospect one when the following
condition holds:
𝐧 𝐧
∑ 𝐩𝐢 𝐔(𝐰𝐢 ) > ∑ 𝐩𝐢 𝐔(𝐯𝐢 )
𝐢=𝟏 𝐢=𝟏
The utility function
The utility function has a positive slope for the first order derivative, because more wealth is
always preferred to less wealth: 𝐢𝐟: 𝐰𝐢 > 𝐯𝐢 , 𝐭𝐡𝐞𝐧: 𝐔(𝐰𝐢 ) > 𝐔(𝐯𝐢 ). The utility function U(w) should
be strictly increasing for the first derivative. The curvature depends on the risk preference and risk
profile of the risk taker. There are three option, as we already saw.
In all cases the first derivative is positive, but the difference lays in the second derivative.
Whenever the second derivative is positive, we are situated in the first case, where the risk taker
is risk seeking and the utility function is convex. The second graph is the other way around, a
concave utility function. Here we are risk averse, and the second derivative is negative. In the last
graph where the utility function is linear, we are risk neutral and the second derivative equals 0.
- Risk seeking: u’’ > 0 - Risk averse: u’’ < 0 - Risk neutral: u’’ = 0
People will make different choices depending on their preferences, even if everything has the
same outcome and the average wealth is the same. The average wealth is the same, but the
distribution is different, which will affect the utility.
𝐧 𝐧
𝐔(∑ 𝐩𝐢 𝐰𝐢 ) 𝐯𝐞𝐫𝐬𝐮𝐬 ∑ 𝐩𝐢 𝐔(𝐰𝐢 )
𝐢=𝟏 𝐢=𝟏
On one side we got the expected utility sure outcome (has only one outcome) and on the other
side the expected utility lottery outcome (multiple possibilities depending on the state).
Linear utility function
This is where the function is a straight line and where the preferences of the risk taker are neutral,
the economic agent is risk neutral and the second derivative is equal to 0. This means that both
6
