Behavioral finance
Part 2: Lecture 1
Utility and prospect theories
You should invest is
1. ETF
2. Real estate (rent is very little taxed)
3. Pension plans
(On exam)
Stock market ineCiciency post earnings PEAD
For CEO to meet expectations he can use money from the firm (lecture 5)
Markets are ineCicient because they are driven by emotions
Law a large numbers/ Bernoulli’s Theorem
As the population grows, the average comes closer to the expected value. As n gets bigger,
the variance will decrease.
Expected value
Probability-weighted sum of the possible values
Fair game
Chance for a gain or a loss, the E(x) should be zero. After a large number of independent
repetitions, neither the player nor the casino has an advantage over each other.
Though most people will only play is the expected gain > expected loss. Or even some
people play with a negative expected profit, ex. Lottery. These are not fair games.
1
,St. Petersburg paradox
Prize is 2! , with n the total flips till you got heads
1 1 1
𝐸(𝑌) = 2 ∙ + 4 ∙ + 8 ∙ … = ∞
2 4 8
Entrance fee: a rational gambler plays if the price of entry is less than the expected value,
so the entrance fee should be ∞. But no one will do this
Marginal utility
Any increase in wealth ∆𝑥 will always result in an increase in utility ∆𝑈 which is inversely
proportionate to the quantity of goods x already possessed
𝑎
∆𝑈 = ∙ ∆𝑥
𝑥
Marginal utility decreases as the quantity consumed increase, each additional good
consumed is less satisfying than the previous one.
Gamblers only enter the St. Petersburg game for a modest amount of entry. This is because
they can not evaluate whether the expected value of the game is positive, which is equal to
the expected value of the gain – expected value of the loss (entrance fee).
They decide by comparing the utility of the loss (certain loss) and the utility of the gain
(uncertain). When U(gain) > U(loss), a gambler is rational. They do not look at the expected
value anymore.
𝐸(𝑥) = 3 𝑥" ∙ 𝑝(𝑥" )
𝐸 [𝑈(𝑥)] = 3 𝑈(𝑥" ) ∙ 𝑝(𝑥" )
2
, The theory of rationality
- There is a set of conceivable actions which everyone undertakes and which leads to
certain consequences
- Individuals have an order of preferences concerning all the consequences of their
actions
- They evaluate the consequences and decide upon a particular action
- Ration individuals make their choice coherently with their preferences. The choice
is the oucome of calculations, their complexity does matter
- Disregarding from the problems with the calculations, the theory suggests for
economic actors the best way to achieve their goals
Kahneman and Tversky: four assumptions on expected utility theory
When all these are satisfied, an individual is said to be rational and their preference can be
represented by a utility function (von Neumann-Morgenstern axioms)
1. Comparability: always X > Y or X < Y or indiCerent
2. Transitivity: if X > Y and Y > Z, then X > Z, if X = Y and Y = Z, then X = Z
3. Strong independence: preference should not depend on the context
4. Measurability: if X > Y > Z, then Y = 𝛼 X + (1 - 𝛼) Z
Individuals choose the highest expected utility, which is not always the highest expected
value. Play the gamble of getting $100 with p = 1/8 or nothing, or the guaranteed payment
of $1. Though the expected value of the gamble is $1.25, some people are risk averse and
will prefer the sure thing.
Quasi-rational individuals
1. Problem decomposition: solve components sequentially and simplify complex
problems. This can cause interactions being ignored and overlook relevant info
2. Framing: preference is not independent of the way the alternatives are presented
3. Mental accounting: evaluate an outcome by creating separate accounts
3
Part 2: Lecture 1
Utility and prospect theories
You should invest is
1. ETF
2. Real estate (rent is very little taxed)
3. Pension plans
(On exam)
Stock market ineCiciency post earnings PEAD
For CEO to meet expectations he can use money from the firm (lecture 5)
Markets are ineCicient because they are driven by emotions
Law a large numbers/ Bernoulli’s Theorem
As the population grows, the average comes closer to the expected value. As n gets bigger,
the variance will decrease.
Expected value
Probability-weighted sum of the possible values
Fair game
Chance for a gain or a loss, the E(x) should be zero. After a large number of independent
repetitions, neither the player nor the casino has an advantage over each other.
Though most people will only play is the expected gain > expected loss. Or even some
people play with a negative expected profit, ex. Lottery. These are not fair games.
1
,St. Petersburg paradox
Prize is 2! , with n the total flips till you got heads
1 1 1
𝐸(𝑌) = 2 ∙ + 4 ∙ + 8 ∙ … = ∞
2 4 8
Entrance fee: a rational gambler plays if the price of entry is less than the expected value,
so the entrance fee should be ∞. But no one will do this
Marginal utility
Any increase in wealth ∆𝑥 will always result in an increase in utility ∆𝑈 which is inversely
proportionate to the quantity of goods x already possessed
𝑎
∆𝑈 = ∙ ∆𝑥
𝑥
Marginal utility decreases as the quantity consumed increase, each additional good
consumed is less satisfying than the previous one.
Gamblers only enter the St. Petersburg game for a modest amount of entry. This is because
they can not evaluate whether the expected value of the game is positive, which is equal to
the expected value of the gain – expected value of the loss (entrance fee).
They decide by comparing the utility of the loss (certain loss) and the utility of the gain
(uncertain). When U(gain) > U(loss), a gambler is rational. They do not look at the expected
value anymore.
𝐸(𝑥) = 3 𝑥" ∙ 𝑝(𝑥" )
𝐸 [𝑈(𝑥)] = 3 𝑈(𝑥" ) ∙ 𝑝(𝑥" )
2
, The theory of rationality
- There is a set of conceivable actions which everyone undertakes and which leads to
certain consequences
- Individuals have an order of preferences concerning all the consequences of their
actions
- They evaluate the consequences and decide upon a particular action
- Ration individuals make their choice coherently with their preferences. The choice
is the oucome of calculations, their complexity does matter
- Disregarding from the problems with the calculations, the theory suggests for
economic actors the best way to achieve their goals
Kahneman and Tversky: four assumptions on expected utility theory
When all these are satisfied, an individual is said to be rational and their preference can be
represented by a utility function (von Neumann-Morgenstern axioms)
1. Comparability: always X > Y or X < Y or indiCerent
2. Transitivity: if X > Y and Y > Z, then X > Z, if X = Y and Y = Z, then X = Z
3. Strong independence: preference should not depend on the context
4. Measurability: if X > Y > Z, then Y = 𝛼 X + (1 - 𝛼) Z
Individuals choose the highest expected utility, which is not always the highest expected
value. Play the gamble of getting $100 with p = 1/8 or nothing, or the guaranteed payment
of $1. Though the expected value of the gamble is $1.25, some people are risk averse and
will prefer the sure thing.
Quasi-rational individuals
1. Problem decomposition: solve components sequentially and simplify complex
problems. This can cause interactions being ignored and overlook relevant info
2. Framing: preference is not independent of the way the alternatives are presented
3. Mental accounting: evaluate an outcome by creating separate accounts
3
