Chapter 3: Stochastic dominance and behavioural finance Flashcards
What is absolute dominance
When one investment porfolio provides a higher return than another in all possible circumstances
State the first order stochastic dominance theorem
Explain what it means in words
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.
Explain first order stochastic dominance in terms of means and variances
If Var[A] = Var[B], and E[A] > E[B]
Then A first order stochastically dominates B
State the second order stochastic dominace theorem
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
Explain second order stochastic dominance in terms of means and variances
If E[A] = E[B] and Var[A] < Var[B],
Then A second order stochastically dominates B
What is the main advantage of stochastic dominance
It does not require the explicit formulation of the utility function
What are the disadvantages of stochastic dominace
- May be unable to choose between two investments
- Involves pairwise comparison of investment options, which may be problematic if the pool is large
What are the disadvantages of stochastic dominace
- May be unable to choose between two investments
- Involves pairwise comparison of investment options, which may be problematic if the pool is large
Briefly describe the field of behavioural Finance
Looks at how a variety of mental biases and decision-making errors affect financial decisions
Give an example describing how an individual can have different utility functions depending on levels of wealth
Who argued this
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)
Markowitz criticism of expected utility theory
Utility should be measured in relative to changes from a reference point rather than in absolute values of wealth
Describe the two phases of decision making in prospect theory
Who investigated this
- Editing/Framing phase - Decisions are intially appraised(given) and ordered
* Leads to a representation of outcomes - Evalauation phase - Choosing among appraised decisions
Investigated by Kahneman and Tversky
Describe two basic operations associated with the framing phase of the decision-making in prospect theory
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
What are framing effects
The way in which choices among decisions can be affected by the way in which they are initially presented
State the observed behavioural patterns in people when evaluating various alternatives
Who observed these ?
- Reference dependence
- Loss aversion
- Endowment effects
- Changing risk attitudes
- Diminishing sensitivity
- Probability weighting
- Certainty effect
- Isolation effect
Kahneman and Tversky
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
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.
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
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
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
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
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
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.
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
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.
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
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.
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
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.
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
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.
Outline the key findings of prospect theory
- 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
Name some heuristics (mental shortcut) that violate the axioms underpinning prospect theory
- Anchoring and adjustments
- Representativeness
- Availability
- Familiarity
Result of system 1 thinking
Explain the anchoring and adjustment heuristic
People tend to start with an intial estimate (anchor) and adjust away from it to arrive at their final judgement
Explain the representativeness heuristic and relate it to the law of small numbers
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.
Explain the availability heuristic
Assessing the probability of an event by the ease at which its occurrences come to mind
Explain the familiarity heuristic
People favour outcomes or situations that are familiar, ie. investing in industries that you know
Differentiate between the familiarity and availability heuristic
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.
What is the difference between a heuristic and a bias
Heuristic stems from a mental shortcut, caused by system 1 thinking.
Bias stems from the interaction between system 1 and system 2
List the behavioural biases that are exhibited by investors
- Overconfidence
- Self-serving
- Status quo
- Herd-behaviour
Explain the overconfidence bias and biases that may cause it with it
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
Explain the following biases:
* Self-serving
* Status quo
* Herd-behaviour
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)
Outline the Equity Premium Puzzle as formulated by Metha and Prescott
- 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
What does the equity risk premium then comprise of ?
- Return for the risk of stocks over bonds and T bills
- As well as return to overcome the loss aversion of investors
What was Metha and Prescott’s solution to the Equity Premium Puzzle
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
