Chapter 3: Stochastic dominance and behavioural finance

Question 1

What is absolute dominance

Answer 1

When one investment porfolio provides a higher return than another in all possible circumstances

Question 2

State the first order stochastic dominance theorem

Explain what it means in words

Answer 2

Assuming an investor is non-satiated, A will dominate B if:
Cumulative distribution of A <= Cumulative distribution of B
Cumulative distribution of A < Cumulative distribution of B at at least one point

This means that the prob of portfolio B producing a return below a certain value is never less than the prob of A producing a return below that value.

Question 3

Explain first order stochastic dominance in terms of means and variances

Answer 3

If Var[A] = Var[B], and E[A] > E[B]
Then A first order stochastically dominates B

Question 4

State the second order stochastic dominace theorem

Answer 4

Assuming a investor is non-satiated and risk-averse,
A second order stochastically dominates B if:
Integral of cumulative distribution of A <= Integral of cumulative distribution of B
Integral of cumulative distribution of A < Integral of cumulative distribution of B at at least one point

• Integrated from lowest return that both portfolios can provide to some value of x
• An investor will accept a low probabilty of a low absolute return in comparision to the same probabilty of an extra return at a high level

Question 5

Explain second order stochastic dominance in terms of means and variances

Answer 5

If E[A] = E[B] and Var[A] < Var[B],
Then A second order stochastically dominates B

Question 6

What is the main advantage of stochastic dominance

Answer 6

It does not require the explicit formulation of the utility function

Question 7

What are the disadvantages of stochastic dominace

Answer 7

• May be unable to choose between two investments
• Involves pairwise comparison of investment options, which may be problematic if the pool is large

Question 8

What are the disadvantages of stochastic dominace

Answer 8

• May be unable to choose between two investments
• Involves pairwise comparison of investment options, which may be problematic if the pool is large

Question 9

Briefly describe the field of behavioural Finance

Answer 9

Looks at how a variety of mental biases and decision-making errors affect financial decisions

Question 10

Give an example describing how an individual can have different utility functions depending on levels of wealth

Who argued this

Answer 10

Risk aversion at higher levels of wealth as wealthy individuals wish to preserve their levels of wealth - Insurance
Risk-seeking at lower levels of wealth as poor individuals wish to better their financial situation - Gambling

Friedman and Savage (1948)

Question 11

Markowitz criticism of expected utility theory

Answer 11

Utility should be measured in relative to changes from a reference point rather than in absolute values of wealth

Question 12

Describe the two phases of decision making in prospect theory

Who investigated this

Answer 12

1. Editing/Framing phase - Decisions are intially appraised(given) and ordered
   * Leads to a representation of outcomes
2. Evalauation phase - Choosing among appraised decisions

Investigated by Kahneman and Tversky

Question 13

Describe two basic operations associated with the framing phase of the decision-making in prospect theory

Answer 13

Leads to a representation of the acts, outcomes and contigencies associated with a particular choice problem.

Acceptance: People are are unlikely to alter the formulation of the choices given
Segregration: People tend to focus on the most relevent aspects of the decision

Question 14

What are framing effects

Answer 14

The way in which choices among decisions can be affected by the way in which they are initially presented

Question 15

State the observed behavioural patterns in people when evaluating various alternatives

Who observed these ?

Answer 15

• Reference dependence
• Loss aversion
• Endowment effects
• Changing risk attitudes
• Diminishing sensitivity
• Probability weighting
• Certainty effect
• Isolation effect

Kahneman and Tversky

Question 16

Describe the following observed behavioural patterns in people when evaluating various alternatives:
* Reference dependence
* Loss aversion
* Endowment effects
* Changing risk attitudes
* Diminishing sensitivity
* Probability weighting
* Certainty effect
* Isolation effect

Answer 16

Reference dependence
* People weigh alternatives depending on their current level of wealth as opposed to absolute levels of wealth.
* Generates a utility function with a point of inflexion at the reference point.
* Example is initially good terms.

Loss aversion
* People tend to be sensitive to losses as opposed to gains of the same magnitude.
* In experiments, the pain from a loss is estimated to be twice as much as the pleasure of an equivalent gain.
* Utility curve is steeper in the domain of losses than in the domain of gains.

Endowment effects
* When a person’s preferences depend on what they already possess
* Ownership creates satisfacation
* Example is on people not wanting to change their current accounts.

Question 17

Describe the following observed behavioural patterns in people when evaluating various alternatives:

• Reference dependence
• Loss aversion
• Endowment effects
• Changing risk attitudes
• Diminishing sensitivity
• Probability weighting
• Certainty effect
• Isolation effect

Answer 17

Reference dependence
* People weigh alternatives depending on their current level of wealth as opposed to absolute levels of wealth.
* Generates a utility function with a point of inflexion at the reference point.

Loss aversion
* People tend to be sensitive to losses as opposed to gains of the same magnitude.
* In experiments, the pain from a loss is estimated to be twice as much as the pleasure of an equivalent gain.
* Utility curve is steeper in the domain of losses than in the domain of gains.

Endowment effects
* When a person’s preferences depend on what they already possess
* Ownership creates satisfacation

Question 18

Describe the following observed behavioural patterns in people when evaluating various alternatives:
* Reference dependence
* Loss aversion
* Endowment effects
* Changing risk attitudes
* Diminishing sensitivity
* Probability weighting
* Certainty effect
* Isolation effect

Answer 18

Reference dependence
* People weigh alternatives depending on their current level of wealth as opposed to absolute levels of wealth.
* Generates a utility function with a point of inflexion at the reference point.

Loss aversion
* People tend to be sensitive to losses as opposed to gains of the same magnitude.
* In experiments, the pain from a loss is estimated to be twice as much as the pleasure of an equivalent gain.
* Utility curve is steeper in the domain of losses than in the domain of gains.

Endowment effects
* When a person’s preferences depend on what they already possess
* Ownership creates satisfacation

Question 19

Describe the following observed behavioural patterns in people when evaluating various alternatives:
* Reference dependence
* Loss aversion
* Endowment effects
* Changing risk attitudes
* Diminishing sensitivity
* Probability weighting
* Certainty effect
* Isolation effect

Answer 19

Changing risk attitudes
* Individuals tend to be risk-seeking in the domain of losses and risk averse in the domain of gains - think about the solvency example.

Diminishing sensitivity
* Marginal utility decreases as you gain or lose more
* Convex for losses
* Concave for gains

Probability weighting
* People do not weigh outcomes by their objective probabilities, but by their transformed probabilities
* Generally, low probabilities are overweighted and high probabilities are underweighted - like people playing the lotto.

Certainty effect
* When an outcome is certain but becomes less probable, the impact on utility is less than a decrease in probability of an outcome that was previously not certain

Isolation effect
* People often disregard components that alternatives share and instead focus on what sets them apart
* Since different choices can be decomposed differently, it leads to inconsistent choices.

Question 20

Describe the following observed behavioural patterns in people when evaluating various alternatives:
* Reference dependence
* Loss aversion
* Endowment effects
* Changing risk attitudes
* Diminishing sensitivity
* Probability weighting
* Certainty effect
* Isolation effect

Answer 20

Changing risk attitudes
* Individuals tend to be risk-seeking in the domain of losses and risk averse in the domain of gains - think about the solvency example.

Diminishing sensitivity
* Marginal utility decreases as you gain or lose more
* Convex for losses
* Concave for gains

Probability weighting
* People do not weigh outcomes by their objective probabilities, but by their transformed probabilities
* Generally, low probabilities are overweighted and high probabilities are underweighted - like people playing the lotto.

Certainty effect
* When an outcome is certain but becomes less probable, the impact on utility is less than a decrease in probability of an outcome that was previously not certain

Isolation effect
* People often disregard components that alternatives share and instead focus on what sets them apart
* Since different choices can be decomposed differently, it leads to inconsistent choices.

Question 21

Describe the following observed behavioural patterns in people when evaluating various alternatives:
* Reference dependence
* Loss aversion
* Endowment effects
* Changing risk attitudes
* Diminishing sensitivity
* Probability weighting
* Certainty effect
* Isolation effect

Answer 21

Changing risk attitudes
* Individuals tend to be risk-seeking in the domain of losses and risk averse in the domain of gains - think about the solvency example.

Diminishing sensitivity
* Marginal utility decreases as you gain or lose more
* Convex for losses
* Concave for gains

Probability weighting
* People do not weigh outcomes by their objective probabilities, but by their transformed probabilities
* Generally, low probabilities are overweighted and high probabilities are underweighted - like people playing the lotto.

Certainty effect
* When an outcome is certain but becomes less probable, the impact on utility is less than a decrease in probability of an outcome that was previously not certain

Isolation effect
* People often disregard components that alternatives share and instead focus on what sets them apart
* Since different choices can be decomposed differently, it leads to inconsistent choices.

Question 22

Describe the following observed behavioural patterns in people when evaluating various alternatives:
* Reference dependence
* Loss aversion
* Endowment effects
* Changing risk attitudes
* Diminishing sensitivity
* Probability weighting
* Certainty effect
* Isolation effect

Answer 22

Changing risk attitudes
* Individuals tend to be risk-seeking in the domain of losses and risk averse in the domain of gains - think about the solvency example.

Diminishing sensitivity
* Marginal utility decreases as you gain or lose more
* Convex for losses
* Concave for gains

Probability weighting
* People do not weigh outcomes by their objective probabilities, but by their transformed probabilities
* Generally, low probabilities are overweighted and high probabilities are underweighted - like people playing the lotto.

Certainty effect
* When an outcome is certain but becomes less probable, the impact on utility is less than a decrease in probability of an outcome that was previously not certain

Isolation effect
* People often disregard components that alternatives share and instead focus on what sets them apart
* Since different choices can be decomposed differently, it leads to inconsistent choices.

Question 23

Describe the following observed behavioural patterns in people when evaluating various alternatives:
* Reference dependence
* Loss aversion
* Endowment effects
* Changing risk attitudes
* Diminishing sensitivity
* Probability weighting
* Certainty effect
* Isolation effect

Answer 23

Changing risk attitudes
* Individuals tend to be risk-seeking in the domain of losses and risk averse in the domain of gains - think about the solvency example.

Diminishing sensitivity
* Marginal utility decreases as you gain or lose more
* Convex for losses
* Concave for gains

Probability weighting
* People do not weigh outcomes by their objective probabilities, but by their transformed probabilities
* Generally, low probabilities are overweighted and high probabilities are underweighted - like people playing the lotto.

Certainty effect
* When an outcome is certain but becomes less probable, the impact on utility is less than a decrease in probability of an outcome that was previously not certain

Isolation effect
* People often disregard components that alternatives share and instead focus on what sets them apart
* Since different choices can be decomposed differently, it leads to inconsistent choices.

Question 24

Outline the key findings of prospect theory

Answer 24

• Utility is based on gains and losses relative to some reference point
• The reduction in utility from a loss is typically twice as much as the increase in utility frome the same sized monetary gains
• People are typically risk seeking in the domain of losses and risk averse in the domain of gains relative to a reference point.
• People experience diminishing sensitivity to gains and losses, so, for example, amn initial gaim has greater impact than the subsequent gain of the same size

Question 25

Name some heuristics (mental shortcut) that violate the axioms underpinning prospect theory

Answer 25

• Anchoring and adjustments
• Representativeness
• Availability
• Familiarity

Result of system 1 thinking

Question 26

Explain the anchoring and adjustment heuristic

Answer 26

People tend to start with an intial estimate (anchor) and adjust away from it to arrive at their final judgement

Question 27

Explain the representativeness heuristic and relate it to the law of small numbers

Answer 27

Explaination
* People base the probability of occurence on a statistically unrepresentative sample to make sense of a situation
* Reprentativeness an lead to a decision on whether or not to invest.

Law of small numbers
* People assess the probability of an event occuring based on a small statistically-unrepresentative sample due to the desire to make sense of an uncertain situation.

Question 28

Explain the availability heuristic

Answer 28

Assessing the probability of an event by the ease at which its occurrences come to mind

Question 29

Explain the familiarity heuristic

Answer 29

People favour outcomes or situations that are familiar, ie. investing in industries that you know

Question 30

Differentiate between the familiarity and availability heuristic

Answer 30

For availability, you are weighing probabilities based on what you can come up with in your mind. Whereas with familiarity, you are given options, and are more likely to choose what you are familiar with, ie. investing in your home country.

Question 31

What is the difference between a heuristic and a bias

Answer 31

Heuristic stems from a mental shortcut, caused by system 1 thinking.
Bias stems from the interaction between system 1 and system 2

Question 32

List the behavioural biases that are exhibited by investors

Answer 32

• Overconfidence
• Self-serving
• Status quo
• Herd-behaviour

Question 33

Explain the overconfidence bias and biases that may cause it with it

Answer 33

Overconfidence
When people systematically overestimate their capabilities, judgements and abilities. This may be a result of hindsight bias and confirmation bias

Hindsight bias
Events that have occured being believed to have been predictable prior to their occurence

Confirmation bias
People tend to look for evidence that confirms their point of view, and disregard confidence that contradicts it

Question 34

Explain the following biases:
* Self-serving
* Status quo
* Herd-behaviour

Answer 34

Self-serving
When people credit achievements to their own capabilities and failures to external factors

Status quo
People tend to stick to their current situation even when presented with better alternatives at no transaction costs - due to loss aversion and endowment effects

Herd-behaviour
People tend to follow or mimic decisions made by others
- Can lead t financial bubbles (think Steinhoff)

Question 35

Outline the Equity Premium Puzzle as formulated by Metha and Prescott

Answer 35

• The puzzle is related to the gap in return from risk bearing stocks when compared to the returns earned from lower-risk government bonds and treasury bills.
• The standard solution is that the premium reflects the difference in the level of risk associated with equities relative to bonds and T-bills , with higher risk securities requiring higher returns to attract investors.
• The difference is too large to be explained by risk-aversion using CAPM models

Question 36

What does the equity risk premium then comprise of ?

Answer 36

• Return for the risk of stocks over bonds and T bills
• As well as return to overcome the loss aversion of investors

Question 37

What was Metha and Prescott’s solution to the Equity Premium Puzzle

Answer 37

Myopic loss aversion
* investors review their allocations annually
* this frames a one-year view - myopic loss aversion
* if a long-term view was taken, there would be far greater investment in equities and a lower ERP
* Probability of capital loss decreases over time