This is an extensive summary of all the course contents of the course Behavioural Finance 2024. It includes the content of all the lectures and of all the mandatory articles.
Behavioral Finance Theory:
- Irrational people possible
- Assets can be mispriced
Standard Model
The “Standard Model”: individuals are assumed to make decisions today (and at any point in
the future) to maximize the present value of their expected lifetime utility:
𝑚𝑎𝑥 ∑𝑇𝑡=1 𝑒 −𝛾𝑡 ∑𝑠𝑡 ∈𝑆𝑡 𝑝(𝑠𝑡 )𝑢(𝑥𝑡 |𝑠𝑡 , 𝑤)
𝑤∈𝑊
- 𝑤: a strategy within the set of all possible strategies 𝑊
- 𝑠𝑡 : state of the world within the set of all possible states 𝑆
- 𝑝(𝑠𝑡 ): rational beliefs (probabilities) given the state
- 𝑢(𝑥𝑡 |𝑠𝑡 , 𝑤): the utility over outcome 𝑥𝑡 given state 𝑠𝑡 and strategy 𝑤
- 𝛾: discount rate
The rational/standard model assumes that individuals:
- Have rational/objective/correct beliefs: they know the probabilities of certain states:
𝑝(𝑠𝑡 )
- Have standard (CARA: constant absolute risk aversion) preferences over final levels
of outcomes: 𝑢(𝑥𝑡 |𝑠𝑡 , 𝑤)
- Maximize their expected utility over all possible strategies W: 𝑚𝑎𝑥
𝑤∈𝑊
- Are self-interested: 𝑢(𝑥𝑡 |𝑠𝑡 , 𝑤)
- Are able to process all available information immediately
- are Bayesian information processors: they incorporate prior knowledge, beliefs, and
experiences into their decision-making processes
When new information becomes available, they revise update their beliefs
accordingly, taking into account both the prior information and the new evidence
Behavioral approach aims to improve realism by acknowledging deviations from these
assumptions
- It is widely acknowledged that the rational model fails to capture many important
economic phenomena
E.g. bubbles and crashes, high trading volume, asset pricing anomalies etc.
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, Important for investment managers, for macroeconomic consequences and for
policy implications
- The deviations:
Biased beliefs (optimism and overconfidence): long-lasting
Biased updating of beliefs (overreaction, underreaction): transitory
Limits to (the speed of) information processing
Non-standard preferences like loss aversion and reference dependence
Non-Standard Preferences
From “standard” to “non-standard” preferences 𝑢(𝑥𝑡 |𝑠𝑡 , 𝑤)
- Individuals are assumed to make decisions by maximizing expected utility
Classic (expected) utility:
- Individuals have preferences (utility functions) over levels of wealth/consumption
- The utility function is concave: people are risk-averse
- Individuals have stable preferences (stable over time and situations)
From “standard” to “non-standard” preferences: in case of risky choices, people do not
maximize classic expected utility
- People typically respond to changes of circumstances much more than to levels ⇒
financial outcomes should be evaluated based on changes relative to some
reference point
Prospect theory:
1. Preference reversals: people typically have different preferences over (perceived) gains
vs losses
- Risk averse over gains: diminishing sensitivity to gains
- Risk seeking over losses: diminishing sensitivity to losses
2. Loss aversion: displeasure associated with losing a sum of
money is greater than pleasure of winning the same amount
−𝑣(−𝑥) ≥ 𝑣(𝑥)
- Value function is steeper over losses than over gains
- Leads to the Disposition Effect: investors tend to hold
losing investments too long and sell winning investments
too soon
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,What is the “right” reference point?
- Often the price at which you bought something
- Sometimes more random: past peak prices, year-beginning or year-end prices etc.
Non-Standard Beliefs
From “standard” to “non-standard” beliefs 𝑝(𝑠): in the standard model agents know and use
the true probability distribution and use Bayes’ rule to update new information
- In practice people are overconfident (variance estimate 𝑉𝑎𝑟 ̂ (𝑥) is too low) and
̂
overoptimistic (expectation estimate 𝐸[𝑥] is too high)
Leads to excessive trading: people update their beliefs too much in light of new (private)
information 𝑠, so they will trade too much:
- If the info is positive, they become too optimistic: overestimate 𝐸̂ [𝑅|𝑠] > 𝐸[𝑅|𝑠]
- If the info is negative, they become too pessimistic: underestimate 𝐸̂[𝑅|𝑠] < 𝐸[𝑅|𝑠]
Cognitive limits
From “standard” to “non-standard” maximization problem: in the standard model we
maximize over the set of all possible choices 𝑊, but in the behavioral model people don’t
consider all possible choices
- People have limited attention: they neglect less salient information and information
that is harder to process
Objections to the Behavioral Approach
There are some arguments against the behavioral approach
1. Learning and expertise
- People with “wrong” beliefs will learn over time from their mistakes
- Large-stake transactions are done by experts who are less subject to biases in
beliefs, limits to cognitive capacity, etc.
- Counterarguments:
● Some deceptions are hard-wired in our brains, and very hard to correct ⇒ also
plausible for finance contexts
● Confirmation bias (inattention and misinterpretation of evidence that contradicts
ones own prior beliefs) hinders learning
2. Arbitrage: behavioral biases do not matter in aggregate markets, because deviations
from fundamentals are quickly corrected by rational traders (“arbitrageurs”): deviations
from fundamentals occur ⇒ a profit opportunity arises ⇒ rational traders take counter-
position ⇒ price adjusts
- Counterargument: real world arbitrage is limited, so prices can deviate from the
fundamental value for extended periods of time
● Mispricing almost never creates risk-free, profitable investment opportunities:
“arbitrage” strategies are in reality often risky and costly
● Due to margin calls and short squeezes, arbitrage can sometimes move prices
further away from fundamental values
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,Example: VW common-preferred stock: common shares were getting much more expensive
relative to preferred shares
- People took a long-short position in preferred-common:
● Long position: buy an asset with the expectation that its value will increase over
time
● Short position: sell an asset you do not own (typically borrowing it from a broker)
with the intention of buying it back at a lower price in the future
- A short squeeze occurred: the price of the shorted stock/asset experiences a rapid
price increases ⇒ short sellers are forced to buy back their positions to limit their
losses ⇒ price increases even further
Week 2
Lecture 2
Non-Standard preferences
The standard economist conception of human behavior is
𝑚𝑎𝑥 ∑𝑇𝑡=1 𝑒 −𝛾𝑡 ∑𝑠𝑡 ∈𝑆𝑡 𝑝(𝑠𝑡 )𝑢(𝑥𝑡 |𝑠𝑡 , 𝑤)
𝑤∈𝑊
1
- 𝑢(𝑥|𝑠) = 𝑢(𝑥) = 𝑥 1−𝛾 is the standard specification of preferences
1−𝛾
Standard: CRRA: constant relative risk aversion: as wealth increases, the
marginal utility of wealth decreases at a constant rate
There are non-standard specifications of 𝑢(𝑥) possible
Risk preferences
The shape of the utility function says something about the risk preference:
- Concave utility function: risk averse: 𝐸[𝑢(𝑥)] < 𝑢(𝐸[𝑥])
- Convex utility function: risk seeking: 𝐸[𝑢(𝑥)] > 𝑢(𝐸[𝑥])
With concave utility there is much to lose on the downside but not much to gain on the
upside
We can determine risk preferences from gambles:
1
- Assume standard CRRA utility 𝑢(𝑥𝑖 |𝑠) = 𝑢(𝑥𝑖 ) = 𝑥𝑖 1−𝛾
1−𝛾
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, - Parameter 𝛾 determines the curvature = the risk aversion
- You can obtain 𝛾 by having people choose the risk premium 𝜋 that makes them
indifferent between two lotteries
● Example: you can have 0.5 − 𝜋 with certainty or either 1 or 0 with prob. 0.5: solve
0.5 ⋅ 𝑢(1) + 0.5 ⋅ 𝑢(0) = 𝑢(0.5 − 𝜋) for 𝛾
Prospect theory
Prospect theory consists of 5 key components:
1. Narrow framing: differences relative to reference point matter more than levels
2. Concavity (risk aversion) over gains
3. Convexity (risk seeking) over losses
4. Loss aversion
5. Probability weighting
People look at gains and losses separately, not at total wealth ⇒ they seem to be sensitive
to how a situation is framed in terms of gains and losses (1-3)
- Example:
● Problem 1: You have been given $1000. Now choose between A = (1000, 0.5; 0,
0.5) and B = (500,1) ⇒ people usually choose the safer option B
● Problem 2: You have been given $2000. Now choose between C = (-1000,0.5; 0,
0.5) and D = (-500, 1) ⇒ people usually choose the riskier option C
● Both problems have wealth proposition A = C = (W=2000, p=0.5; W=1000,
p=0.5) and B = D = (W=1500, p=1), but people choose inconsistently
S-shaped utility function around the reference point (4)
- Risk aversion in the region of gains: concave: diminishing
sensitivity to gains
- Risk-seeking in the region of losses: convex: diminishing
sensitivity to losses
- Loss aversion: losses decrease the utility more than gains of the same magnitude
increase it ⇒ function is steeper in the region of losses than in the region of gains
Probability weighting: people overweight small probabilities (5)
- Example:
Problem 1: You have to choose between A = (5000, 0.001; 0, 0.999) and B = (5,
1) ⇒ people usually choose the riskier option A
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, Problem 2: You have to choose between A = (-5000, 0.001; 0, 0.999) and B = (-5,
1) ⇒ people usually choose the safer option B
People are usually risk averse over gains and risk seeking over losses, but here it
is reversed ⇒ indicates that small probabilities are overweighted
Reference points
There are few settings (such as lab experiments) where reference points are perfectly
obvious and unambiguous ⇒ in real life, reference points are much less well-defined
- Often they are quite arbitrary and depend on the framing of a decision problem
● E.g. the limit on how many cans customers are allowed to buy influences how
many cans they buy
● E.g. the number a judge rolls with a dice influences the term he sentences
someone to
Strategies with reference points:
- If you can, move first ⇒ if you can’t, be aware of the influence
- Try to “think the opposite”
Reference dependence in M&A
In the bargaining process, an (arbitrary) reference point is the focus: peak prices are natural
anchors (beliefs) or reference points (preferences)
- Bidder:
● Recent peak prices might form a bidder anchor for what the firm is worth under
ideal management
● Recent peak prices might provide reassurance to financiers and bidder
shareholders who are themselves anchored
- Target:
● Recent peak prices might form a reference point for target shareholders due to
their salience
● Recent peak prices provide legal cover or a negotiating/entrenchment strategy
for the target board/management
Past peak prices are quite arbitrary ⇒ a plausible anchor in mergers is the 52-week high
Reference dependence model
Simple model of reference dependence: 𝑚𝑎𝑥 {𝑝𝑟𝑜𝑏(𝑃)𝑢(𝑃) + (1 − 𝑝𝑟𝑜𝑏(𝑃))𝑢̄ }
𝑃
- There’s a trade-off: a higher asking price P lowers the takeover probability 𝑝𝑟𝑜𝑏(𝑃)
but increases (the utility of) the acquisition premium
- FOC: 𝑝𝑟𝑜𝑏(𝑃∗ )𝑢′(𝑃∗ ) = −𝑝𝑟𝑜𝑏′(𝑃∗ ){𝑢(𝑃∗ ) − 𝑢̄ }: marginal benefit = marginal cost
, In many cases MB>MC for 𝑃 < 𝑃52 and MB < MC for 𝑃 ≥ 𝑃52:
- Marginal benefit of acquiring another company is higher than marginal cost if the
price is below the 52-week high
- Marginal cost is higher than marginal benefit if the price is above the 52-week high
Some predictions based on this:
- Deals “bunch” at 𝑃 = 𝑃52
- Asking and offer prices rise with the 52-week high (reflects the perception that the
target company's value has appreciated)
- The success rate (prob. that offer is accepted) increases when the offer price
exceeds the 52-week high
- Merger waves coincide with 52-week market highs: bidders will find it easier to pay
the 52-week high when it is at a relatively small premium to current price
- Market reaction: acquirer’s stock price falls with the 52-week high (not shown):
investors may perceive acquisitions made at or near the 52-week high as overvalued
or risky ⇒ downward pressure on the acquirer's stock price
Attractive reference price points are usually round numbers: easier to process and suggests
that you have left some premium for the target (instead of trying to extract every last penny
from them)
Reference dependence in the housing market
Logic of reference points in M&A can be applied to housing markets (the target shareholder
is the seller of the house)
- Same maximization problem: 𝑚𝑎𝑥 {𝑝𝑟𝑜𝑏(𝑃)𝑢(𝑃) + (1 − 𝑝𝑟𝑜𝑏(𝑃))𝑢̄ }
𝑃
- Plausible reference points: purchase price, highest value since purchase
When taking into account loss aversion, we get the same predictions as for mergers:
- Sales prices “bunch” around the purchase price: sellers are reluctant to sell at a price
lower than what they initially paid, as it would result in a perceived loss
- Higher asking price when in the loss region: sellers may be reluctant to accept a
selling price that would result in a loss relative to their purchase price
- Lower probability of sale (⇒ longer time on the market) when in the loss region
These predictions can explain two key features of the real estate market:
- Positive correlation between price-volume: when the fundamental market prices are
relatively high, more people want to sell, because they don’t experience loss aversion
(the price is not below their reference point (the purchase price))
- Negative correlation between price-time on the market: when fundamental market
prices are relatively low, many people are in a loss region and because they are loss
averse, they ask a relatively too high selling price ⇒ lower probability of sale ⇒
longer time on the market
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