Week 1 - Limits to arbitrage

Question 1

What criteria does rational choice meets?

Answer 1

1.It is based on decision maker’s current assets.
2. Based on the possible consequences of the choice (no effect of framing).
3. Agents make choices consistent with the expected utility framework.
· Consider different possible future outcomes.
· Decide how good or bad each outcome will make him feel.
· Weight each outcome by its probability and sum up.
4. When agents receive new information, they update their expectations correctly, as described by Bayes law.

Question 2

What is a market efficiency

Answer 2

An efficient market is one in which prices equal fundamental value:
Prices equal the discounted sum of expected future cash flows.
The discount rate is consistent with a normatively acceptable preference
specification.
Prices incorporate all relevant available information.
Forms of market efficiency:
Strong form - prices incorporate all public and private information.
Semi-strong form - prices incorporate all public information.
Weak form - prices incorporate only past public information.

Question 3

What does Behavioural finance says?

Answer 3

Some agents are not fully rational:
- Fail to update beliefs correctly (fail to incorporate all available information).
- Make choices that are normatively unacceptable.
Limits to arbitrage:
- Rational agents cannot always correct the irrationality of other investors.
- Irrationality (mispricing) can have substantial and long impact.
Behavioral biases (psychology):
- The irrational decisions are not random.
- Systematic form of irrationality that creates a mispricing.
- Belief formation - how agents form expectations.
- Decision-making (preferences) - how agents evaluate risky decisions.

Question 4

What risks allows the mispricing to continue?

Answer 4

Fundamental risk:
- The risk that the asset held by an investor loses value.
- Finding a perfect hedge (substitute) is usually impossible.
2 Noise trader risk:
- Mispricing worsens further in the short run due to investor sentiment.
- Can force arbitrageurs to liquidate their positions prematurely.
3 Implementation costs:
- All costs that make it less attractive to exploit the mispricing.
- Transaction costs, short-sale constrains, and information costs.
- Horizon risk.
- Synchronization risk.

Question 5

What are the Sufficient condiditons to limit arbitrage?

Answer 5

Arbitrageurs are risk averse and have short horizons.
- Arbitrageurs cannot afford to be patient.
- Creditors and investors evaluate the arbitrageur based on his returns.
- Forced closure of a short position.
Noise trader risk is systematic.
- Whatever investor sentiment is causing one asset to be undervalued
relative to the other, it could also cause the mispricing to increase in the
short term.

Question 6

What are twin shares?

Answer 6

Dual listed companies:
Two corporations function as a single operating business.
They retain separate stock exchange listings.
Their shares represent claims on exactly the same underlying cash flows
(same fundamental).
Examples: Unilever, Reed Elsevier, Royal Dutch Shell etc.

Question 7

What are other examples of limits to arbitrage?

Answer 7

1.Index inclusions of stocks (S&P500, Russell 1000):
- When a stock is added to the index, it jumps even though its fundamental
value does not change.
- Fundamental risk and noise trader risk.
2 Closed-end funds:
- Mutual funds that issue a fixed number of shares that are traded on exchanges.
- Fund share prices differs from the net asset value (NAV).
- Mainly noise trader risk.
- Lee, Shleifer and Thaler (1991).
3 Bubbles:
- Limited short-selling (implementation costs) during the DotCom bubble.
- Housing bubble - short selling is not directly possible.
- Griffin, Harris, Shu and Topaloglu (2011).
4 Equity carve-outs:
- Lamont and Thaler (2003).

Question 8

What is a behavioural bias? How they form and how they are evaluated?

Answer 8

Decisions of irrational agents are not random and can create mispricings.
1 Beliefs - how agents form expectations:
- Representativeness.
- Overconfidence and overoptimism (wishful thinking).
- Belief perseverance and confirmation bias.
- Anchoring.
- Availability bias.
2 Decision-making (preferences) - how agents evaluate risky decisions:
- Prospect theory.
- Ambiguity aversion.

Question 9

What is representativness and what biases does it create?

Answer 9

Definition based on Kahneman and Tversky (1974): Agents determine whether
an event or sample is representative based on:
Similarity of sample to the parent population.
Reflection of randomness (appear random).
Two biases generated by representativeness:
Sample size neglect, i.e. belief in the law of small numbers.
Base rate neglect.

is what we associate with something. e.g. the odds that someone
fulfills one statement is equal or greater than that someone fulfills two statements

Question 10

What is the belief in the law of small numbers, and what is its application in finance?

Answer 10

Definition of sample size neglect bias:
People expect that even a small sample will reflect the properties of the
model that generated it.
Agents tend to infer the model on the basis of too few data points.
Mistake - small sample typically is not enough to infer the overall model.
Applications in finance: people see trends too quickly in random data.
Stock market fluctuations.
Momentum and return reversals.
Return-chasing behavior among mutual fund investors (Franzzini and
Lamont, 2008; Goyal and Wahal, 2008).
Formation of asset bubbles.

Question 11

What is the volatility puzzle?

Answer 11

The volatility of returns is higher than the volatility of earnings growth.
Stock price is a present value of all future earnings.
Variation in the price-earnings ratio can come from:
Variation in the expected earnings growth g.
Variation in the discount rate r

Question 12

What are the potential explanations for the volatility puzzle?

Answer 12

1 Variation in the expected dividend growth g:
The P/E ratio should have predict cash-flow growth, but it does not!
Rejected by Shiller (1981), research rewarded with a Nobel prize.
2 Variation in the discount rate r:
Variation in expected future risk-free rate.
- But P/E ratio does not predict interest rates in time series.
Changing forecast of risk.
- Also little evidence that P/E ratio predicts changes in risk.
Changing risk aversion.
- The only remaining rational story.
- Campbell and Cochrane (1999) habit model.
3 Belief-based behavioral models:
Extrapolate trends: if the stock market has done well (poorly) in the past year
or two, some investors think it will keep doing well (poorly).
Such beliefs are incorrect… but can be justified by the law of small numbers.
4 Survey data favours the behavioral model.

Question 13

What are the parts of Overconfidence Bias?

Answer 13

1 Overoptimism and wishful thinking:
- People overestimate their own abilities.
- In surveys, more than 80% believe themselves to be above the median on
various dimensions (driving, humor, exam).
- Systematic planning fallacy (leads to procastination).
- Malmendier and Tate (2005).
2 Overprecision (miscalibration):
- People are too confident in the accuracy of their beliefs.
- 90% confidence intervals contain the correct answer less than 50% of the time.
- Ben-David, Graham and Harvey (2013).
3 Illusion of control.
4 Self-attribution bias.
5 Hindsight bias.

Question 14

What are the other behavioural biases?

Answer 14

Belief perseverance and confirmation bias:
- People hold to opinions too tightly and for too long.
- People are reluctant to search for evidence that contradicts their beliefs.
Anchoring:
- People use arbitrary (irrelevant) value as a reference point.
- Insufficient adjustments afterwards.
- Baker, Pan and Wurgler (2012).
Availability bias:
- When judging the probability of an event, people search their memories for
relevant information.
- Biased estimates because not all memories are equally “available.”

Question 15

What are the different models used for model preferences??

Answer 15

Expected utility theory:
- Normative model of rational choice (how we should behave?)
- Consider different possible future outcomes.
- Decide how good or bad each outcome will make him feel.
- Weight each outcome by its probability and sum up.
Kahneman and Tversky (1979) prospect theory:
- Descriptive model (how we actually behave?)
- Viewed as the best available summary of how people think about risk.

Question 16

What are the 3 parts of the Expected utility framework?

Answer 16

1. Expectation - overall utility of a decision is the expected utility of its
   outcomes weighted by their probabilities.
   U(x1, p1; x2, p2; x3, p3) = p1u(x1) + p2u(x2) + p3u(x3)
2. Asset integration - the utility of a gamble is considered relative to the overall
   wealth position of the agent. A gamble is acceptable if
   U(w + x1, p1;w + x2, p2;w + x3, p3) > U(w)
   where w captures the wealth (asset position).
3. Risk aversion - agents prefer a certain outcome x to any risky outcome with
   expected value x. Risk aversion implies concave utility function.

Question 17

What does the risk aversion tells you?

Answer 17

The utility of the certain outcome is higher than uncertain bet

Question 18

What are the Violations of expected utility framework we mentioned?

Answer 18

1. Certainty effect.
2. Reflection effect.
3. Framing effect.

Question 19

what is a Certainty effect?

Answer 19

Independence axiom of expected utility theory: If B is preferred to A, then any
probability mixture (B, p) must be preferred to the mixture (A, p).

People usually prefer something certain over something risky

Question 20

What does a Reflection effect (Four Fold Pattern) tells you?

Answer 20

Risk aversion in gains is accompanied with risk seeking in the losses.
The certainty effect switches the preferences in both gains and losses.
Certainty increases aversion of losses as well as desirability of gains.

the different risk appetite of individuals when it comes to gains vs losses environment

Question 21

What does a Isolation (framing) effect tells you?

Answer 21

Frame dependance - choices between prospects are not determined solely by the
probabilities of final stages.

if you are presented with the same choice but framed differently you should not be affected by the different framing in your choice

Question 22

What are the stages in prospect theory?

Answer 22

1. Editing and framing stage:
   Reference point:
   - Status quo.
   - Aspiration level.
   - Security level or survival point.
   - Break-even point.
   Coding (gains and losses).
   Combining or segregating outcomes.
   Cancelation, simplification and detection of dominance.
2. Evaluation stage:
   Value function.
   Decision weight function

Question 23

What is Ambiguity aversion, and what are its applications?

Answer 23

Ambiguity aversion - people do not like situations where they are uncertain
about the probability distribution of a gamble; agents prefer known risk over
unknown risks.
Applications:
Equity premium puzzle.
Insufficient diversification:
Familiarity bias.
Local (home) bias.
Investing in company (employers) stocks.

Question 24

What are the explenations of Shefrin and Statman (1984) for investor preference for cash dividends?

Answer 24

1. Self-control - dividends provide a natural rule to prevent overconsumption.
   2.Prospect theory and mental accounting:
   Segregate two gains.
   Integrate two losses.
   Integrate small loss and small gain.
   Segregate large loss and small gain (silver lining).
   3.Regret aversion - frustration that people feel when they imagine having taken an action that would have led to a more desirable outcome.
   Stronger for errors in which people acted and took responsibility.
   Weaker for errors when people followed the rule or failed to act.