* PILLARS
People are rational and seek to maximize their expected utility
Markets are efficient, with no arbitrage opportunities

ANOMALIES
These are not confirmed in real life, so we study the reason behind the anomalies in the models using:
Field data
Lab experiments
Computer simulations
Brain scans

* STUDY TOPICS
Alternatives to Expected Utility Theory
Time Preferences
Predicting Human Behavior in Strategic Situations
Self-Confidence
Cognitive Biases & Consequences
Using Experiments to Test Finance Theories

Saint Petersburg Paradox
Coin-flipping; payoff for the first heads that appears; payoff doubles for every coin flip.
How much are you willing to pay to play this game?
Expected utility is ∞, but people aren’t willing to pay much
E = ½ (1) + ¼ (2) + ⅛ (4) + ...
E = ½ + ½ + ½ + ... + ½
E = ∞

Expected Utility Theory
Indifference Curve: combination of goods & services that maintain a certain level of satisfaction
People maximize their well-being
The roll of government is to maximize social well-being
Pareto Efficiency (most outward point as possible)

Utility cannot be measured or observed directly, but are revealed through preferences and through experiments. Remember: preferences are not necessarily choice, but a probability of choosing that.
Cardinal preferences – objects are given values
Ordinal preferences – objects are ranked against others
Be careful: you can’t compare utility across individuals

Axioms
Completeness – if you have a preference for alternative A against B, you always prefer this alternative, given the chance.
Transitivity – if you prefer A to B and B to C, then you prefer A to C.
Continuity – if the above is true, there is a combination of A and C that are equivalent in utility to B. ( B = p*A + (1-p)*C )
Independence – one “lottery” does not affect another one

Violations (2 Kinds)
Those that have possible explanations in alternative theories regarding preferences
Those that challenge the very axioms on which the theory is built

Ellsberg’s Paradox
An urn containing 30 red balls and 60 green and blue balls (of unknown proportions); subjects are asked to compare bets on which color balls will be drawn.
Gamble A: bet on red draw
Gamble B: bet on green draw
Gamble C: bet on red or blue draw
Gamble D: bet on green or blue draw
Most people prefer Gamble A to B and D to C. Why?
People are risk averse.
Betting on red is the “safe” bet, since there might be zero green balls and 60 blue balls.
Betting on green or blue is guaranteed to have a 60/90 (66,6%) chance, since there might be zero blue balls and 60 green balls.
Even though this is reasonable, the choice of bets is contradictory, since they are based on opposite rationalizations (fear of having zero green balls, fear of having zero blue balls)

Explanation: when people have too little information (or ambiguous information), they take the worst-case scenario (minimum expected utility) in the set when evaluating a bet.

Bad news affects decisions more than good news; shocks to information quality. People don’t like poor information quality. Shocks to information quality (9/11, for example) have persisting negative effects on prices.

Allais’ Paradox
Set 1: Choose between
(a) certain amount of 1 million
(b) lottery that pays 5 million with 10% chance, 1 million with 89% chance or zero with 1% chance
Set 2: Choose between
(c) 1 million with 11% chance or zero with 89% chance
(d) 5 millions with 10% chance or zero with 90%

People tend to prefer (a) and (d), which is contradictory. In the first set, people are risk averse, so the 1% chance of losing their guaranteed 1 million causes them to not take the lottery, even if the EU = 1.39 million. In the second set, the 1% greater chance of losing the lottery doesn’t keep people from choosing option d.
Pessimism: People tend to either neglect the possibility of unlikely positive events, or overweigh them if negative.

Framing: Asian Disease
The US is preparing for an outbreak of an Asian disease which is expected to kill 600 people.
Headline A: “200 people will be saved.” (72% preference)
Headline B: “There is one-third probability that 600 people will be saved, and a two-thirds probability that no one will be saved.”
Headline C: “400 people will die.”
Headline D: “There is a one-third probability that no one will die, and a two-third probability that 600 people will die” (78% preference)
Explanation: people like the certainty of positive outcomes, but not of negative ones (they prefer if framed in a different way).

Prospect Theory
Utility is defined over gains and losses rather than the final wealth (else a person’s original wealth affects their judgment); we consider zero wealth to be our reference point; however people are also influenced by references and expectations.
Examples: a reference might be last year’s earnings, someone might have a positive expectation for the future.

People have a greater sensitivity to losses than to gains. (Value function is concave in the domain of gains and convex in the domain of losses.) (a) * * * Gains * * * Losses * * *
People overweigh small probabilities. The smaller the value of β the larger the distortion. β=1 gives linearity (b)
Π(p) > p for small p;
Π(p) < p for large p. * * * * * * * *

People tend to evaluate gambles separately, which might maximize utility locally rather than optimizing the “big picture"
Example: a lottery paying 60 by head and -59 by tail and a lottery B paying -59 by head and 60 by tail would be rejected if evaluated separately, even though if you played both simultaneously, you’d have a guaranteed profit of 1. *
People keep the losers and sell the winners.
People are reluctant to sell stocks below purchase price and are more likely to sell stocks that have gone up in value.
Explanation: investors are reluctant to realize their losses *
The Equity-Premium Puzzle
The average spread of stocks to bonds is 8% people would have to be absurdly risk-averse to demand such a high premium.
Explanation: people are not averse to variability, but to loss. Stocks have more negative returns than bonds do; people demand a higher premium out of the fear of losing money in a year (myopic horizon).

Intertemporal choices (decisions involving trade-offs among costs and benefits occurring at different times) are all over:
Borrowing & Savings
Diet & Exercise
Human Capital Accumulation

Marshmallow Example
Preschoolers had to wait 15 minutes to get another marshmallow; which measured their ability to delay gratification, or perhaps their time preference. This matters for life outcomes.

Discounted Utility Model
DU model specifies a decision maker’s intertemporal preferences over consumption profiles (ct, … , cT)

u(ct+k) is a person’s utility in a certain time
D(k) is the discount function, the relative weight that she attaches in period t to her well being in t+k ρ represents the individual’s pure rate of time preference (her discount rate)
If ρ = 0, there is no time preference
If ρ = 1, she prefers it 1x more, etc. *
Interpretations
A person’s well-being in period t+k is independent of his consumption in any other period.
The distribution of utility across time makes no difference beyond that dictated by discounting. That is to say, if two consumption profiles have equal utility, even if one is a “rollercoaster” and the other is flat, the person is indifferent towards them, even though we know that people prefer the “flat” consumption profile (because they are loss averse).
Diminishing marginal utility (u(ct) is concave)
Positive time preference (ρ) (preference for consuming today)
Time consistancy – discount rate is fixed between two consecutive periods.

Anomalies

Declining rate of preference (hyperbolic discounting)
Strong preference for consuming today, but as time goes on, this preference isn’t so strong.
Example: waiting one day to consume something is tough, but is waiting one year vs. one year and one day just as tough?
Example: Receive $15 now. How much money makes you indifferent to receiving $15 now, in one month, in one year or in 10 years?
1 month: $20 (345% a year)
1 year: $50 (120% a year)
10 years: $100 (19% a year)

The “sign” effect
Losses are discounted at a lower rate than gains
Many times, people prefer to incur a loss immediately rather than delay it
Ex: how much are you willing to pay to delay the payment of a traffic ticket? (not much)

The “magnitude” effect
Small outcomes are discounted more than large ones.
Example: Thaler’s subjects are indifferent between:
$15 now, $60 in a year (139%)
$350 now, $250 in a year (34%)
$3000 now, $4000 in a year (29%) *
The “delay-speedup” asymmetry
Discount rates vary if the change in delivery time of an outcome is framed as an acceleration or a delay (expectations)
In the VCR example, respondents that were told that they would receive a VCR in a year would pay $54 to receive it now; others that expected to receive it now demanded $126 to delay its receipt by a year. *
Preference for improving sequences
Rather than declining ones
Example: wages
Example: headache (flat, improving or worsening?)

Preference for spread

Is the dynamically inconsistent person aware that her preferences will change over time?
A “naïve” person will believe their future preferences will be identical to her current ones.
A “sophisticated” person will correctly predict how her preferences will change over time.
A “partially naïve” consumer is aware of his quasi-hyperbolic preferences, but underestimates his self-control problem.

Applications
Overconsumption / Insufficient Saving
Procrastination (people tend to put off an onerous activity more than they would have liked to from a prior point of view)
Addiction
Decision to acquire information (free) – if you know that more information will affect your behavior in a negative way.

Procrastination: Setting One’s Deadlines
MIT students had to write 3 papers for one class and were given two choices:
The professor chooses the deadlines (10%)
The student chooses the deadlines (90%)
80% of students chose evenly-spaced deadlines (evidencing preference for commitment)
20% of students chose to put everything at the end of the semester
The penalty for delay was 1% per day late
The students who showed a preference for commitment did better than those who had chosen to delay the deadlines, despite the less amount of time.

Savings: Golden Eggs (Laibson 1997)
Use of illiquid assets prevent overconsumption in the short term
The consumer is essentially “playing a game” with their future self by putting their money in an illiquid asset. (They don’t trust their future self to know what’s good for them.)
There was a decline in saving in the US since the 1980s caused by the rapid expansion of the use of credit cards.

Multiple-Self Model
View that intertemporal choices are the outcome of a conflict between multiple selves
Thaler and Shefrin (1981) proposed a model which evidences a series of myopic doers (caring only about their immediate gratification) interacting with a single planner, who cares equally about the present and the future. (Freud’s Id, Ego & Superego)

Health: Going to the Gym (Dellavigna and Malmendier 2004)
Cost (c) associated with going to the gym in t=1 and benefit (b) associated in t=2.
Not going to the gym results in cost and payoff zero in t=1 and 2
A consumer decides to go to the gym in t=0 if the benefit (discounted by one period) exceeds the cost. (δb≥c)
But, in fact, the time-inconsistent consumer will only go to the gym if the benefit exceeds the cost by βδ

Habit Formation & Reference Points
Utility from current and future consumption can be affected by the level of past consumption
Our reference points can include:
Past consumptions
Expectations
Social Comparison
Status-Quo

Anticipation
People derive utility not only from current consumption, but also from anticipating future consumption (?)
If dreading future bad outcomes is a stronger emotion than savoring future good outcomes, utility from anticipation would generate a sign effect (anxiety)
Anxiety creates a taste for risk-free assets and aversion to risky assets.

An economic agent is supposed to be fully rational and aware of his performance level and the accuracy of his knowledge, but we know this is not true.

Overconfidence: an overly optimistic self-assessment (consistently superior to actual performance)

Calibration: ability to assign subjective probabilities to outcomes that correspond to the objective frequency of those outcomes.
Applies to a large set of judgments
Confidence Interval (for 90% confidence, 90/100 questions should be correct, with a margin of error)
Calibration = Average Confidence – Correct Answers
Zero = Perfect Calibration
Positive = Overconfident
Negative = Underconfident

Discrimination: ability to distinguish when you are correct from when you are incorrect.
Applies to a large set of judgments
Discrimination: Average confidence with correct item – Average confidence with incorrect items
Zero: No Discrimination
The higher the number, the better the discrimination

Applications
In a financial market context, poor calibration leads to poor performance
Overconfident managers and CEOs tend to be poor managers and heads of companies.
Traders found to be more overconfident than most people; males more so than females, which leads to overtrading (45% more) and thus poor performance.
Glass ceiling effect
Gender wage gap
Men and women react similarly to information, but women are fed different signals (stereotypes, discrimination, etc.) and start with different priors (differences in preferences, abilities, etc.), which leads to the different processing of information.
Conservatism: Subjects update their information less in response to both positive and negative new information.
Assymetry: Subjects adjust more to positive information than negative information
Women tend to be more conservative
Biases less pronounced when the ego is not at stake *
Gender & Competition
How do people choose to compete?
Differences in performance
Beliefs about relative performance
Risk attitudes
Feedback aversion
Taste for Competition
Women are less likely to compete
Example: Tournament ($2 for winner) vs. Price-Rate (50¢ per correct answer); groups of 4 people.
Why? Lack of confidence in one’s ability, aversion to feedback, risk aversion, etc.

Cognitive Heuristics are the biases that we have that “help” us process large amounts of complex information more easily. It’s the quick associations we make that help us in our day-to-day lives, but that can end up being faulty under certain circumstances.
Representativeness: past performance is indicative of future performance.
Conservatism
Confirmatory Bias: that which you see confirms your already preexisting notions; you “select” information that confirms your bias, and “discard” that which doesn’t. Insufficient learning.
Illusion of Control: belief that one has control over random events (ex: most people prefer to roll I die themselves or to pick out their lottery numbers)
Rationalization of Randomness: Trying to rationalize that which cannot be rationalized.
Flipping a coin: if the past three outcomes of a die was heads, do you believe the next one is tails? If not, do you believe that is a fair coin? Do you believe it’s more likely that a coin would come out three times head and three times tails rather than six times only heads?
In reality, a coin must be 50% heads and 50% negative only for an infinite sequence. The shorter the sequence, the less “fair” it has to be.
Lottery numbers: gamblers avoid last week’s winning numbers in the current week’s bet.
“Hot Hand”: “one should always pass the ball to a team-player who just scored several times in a row.”
People believe repetitive patterns are not random.
Ex: head, tail, head, tail, head, tail…
Availability: people believe that that which they see most often is what is more likely. People overestimate the frequency of rare risks (publicity in the media) and underestimate the frequency of common risks (no publicity). Also, we tend to remember things more the stronger the emotional attachment.
Anchoring: people start with an initial value (or notion) that they update, yet since they react insufficiently to new information (positive or negative) and have confirmatory bias, they never reach the correct final value.
Wishful Thinking: the formation of beliefs or making decisions based on what might be pleasing to imagine rather than appealing in evidence, rationality or reality.

Monty Hall Problem (elaborate)

Sometimes, you have to anticipate the other person’s movement in order to make your own.

Beauty Contest Game
People don’t choose who they believe to be the prettiest, but instead who they believe the others believe the others believe is prettiest. (Average-looking people)

Level-K Model (2/3 Game)
Pick a number between 0 and 100. The winner is the person whose number is closest to 2/3 times the average of all chosen numbers.
Many people don’t play equilibrium (0 = Level ∞) because they are confused. (Level 0 – no strategy, randomness)
Average: 50
Others don’t play equilibrium because they know that that won’t win because they anticipate that others will be confused. (Level 1 – assume all others are level 0)
Average: 33
If you are Level 2, you assume all others are level 1 and play accordingly to their expected average.
Average: 22

Experience & Equilibrium
As players become more experienced, the result tends more to the equilibrium.
But, as new players enter the game, it stops moving towards the new equilibrium.
Experienced players win more than inexperienced players because of this knowledge.

“Any government wanting to kill an opponent would not try it at a meeting with government officials.” (expand)

Centipede Game:
Two players move sequentially, alternating between taking or passing. The reward increases every time the ball is passed.
Equilibrium: no one passes and everyone earns the lowest reward, since everyone anticipates that the other won’t pass.
In reality, people pass, because they know that if the ball is passed at least 2x (high probability) everyone’s reward is greater (cooperation).

Zero Sum Betting
“No rational trader would trade with another rational trader.”
If he’s selling me something, it’s because there’s something wrong with it. It can’t possibly be worth the price he’s asking for it.
Equilibrium: no trading happens.
In reality, we know that people trade for many reasons.

Prisoner’s Dilemma

If people are indifferent towards two objects, they should trade 50% of the time. However, most people prefer to keep what they have; they value what they have more than what the other person has. (Endowment Effect)

WTA = Willingness to Ask
WTP = Willingness to Pay

WTA = λ u(mug)
WTP = u(mug)
WTA = λWTP

This result is accentuated with inexperienced traders who are not forced to trade. As people learn and play more (obligatory) rounds, this gap disappears. Also, if you make people state their absolute lowest WTA price and their absolute highest WTP price (to not risk losing good trades), there is conciliation.

Anonymity affects trades, since, if people believe their objects were given to them as gifts, they are hesitant to trade it and ask for a larger price.

Language affects people’s perceptions
“This mug is a gift.” Vs. “You have a mug.”
“Choose mug or chocolate” vs. “Switch to mug/chocolate?”

Good experiments are simple and don’t allow the experimenter to fool himself into believing what he wants to believe.

Field experiments are “sexier,” done with large numbers of people, yet with less control (more random factors) in real life. You can’t experiment in real life, because that is not considered ethical.

Laboratory Experiments are less “sexy”, but they offer more control and are replicable, although more expensive and not in “real life”. Small incentives have more power in the lab, whereas the same incentives in real life might be overlooked.

Experiments are used to create and to test new models and to detect flaws in current models, which help us rationalize human behavior and create good policies (ex: economic policies based on Micro and Macroeconomic theories and models that were both tested in the field and in the lab).

Most theories are based on people being rational and markets being efficient, but in fact, they’re not. Field data, lab experiments, computer simulations and brain scans all point to this.
There are exceptions to all rules; some can be explained by other rules, while other challenge the very pillars on which we base our conclusions.
People are complex, and being risk averse, they take into consideration not only one expectation, but a set of possibilities, and often “expect the best, but prepare for the worst.” Bad news is more credible than good news, and shocks to information quality might have lasting negative effects (9/11 for example). That 1% risk of something bad happening can often keep people from seeking good opportunities, as they’d rather be “safe than sorry”. They hate to lose.
People are influenced by the world around them and can’t help comparing with others and with their own expectations. Sometimes, they can be myopic and impatient, preferring to consume and have fun today than to delay pleasures. At the same time, they prefer to have a constant consumption over the course of their lifetime. They are willing to wait (and gamble) to earn large sums of money, but forgo the smaller amounts.
Most people are naïve, and don’t know how to plan their time and resources, so there is a “game” of sorts between the wiser “planner” version of oneself (superego) and the more impulsive “doer” version (id). This causes anxiety around procrastination, saving and debt, going to the gym and dieting.
They can be overly optimistic and not reliable to make self-assessments; this overconfidence is more present in men, who also tend to be more competitive (but not in teams, because they don’t trust the other’s judgment… the irony!) This may be due to many cognitive biases, developed in order to help us deal with large amounts of information. Some of these include confirmation bias and the illusion of control.
The fact is, when man learned to live in society, he learned to watch what others do and anticipate their moves. None-the-less, many people consider others to be completely irrational (Level 1), and don’t trust their judgment. Although in certain situations this is true, in most cases, there is good will and cooperation. * However, that leads to people preferring to maintain what is theirs. “It’s better to have one bird in the hand than two flying in the sky.” They value the gifts people give them, and are reluctant to sell them, as tokens of friendship in an unsure environment.