Chapter 3 - Stochastic Dominance And Behavioural Finance

Question 1

Absolute dominance

Answer 1

Absolute dominance exists when one investment portfolio provides a higher return than another in all possible circumstances.

Question 2

First-order stochastic dominance

Answer 2

Consider two investment portfolios A and B with cumulative probability distribution functions of returns Fa and Fb respectively.

The first-order stochastic dominance theorem states that, assuming an investor prefers more to less, A will dominate B if:
Fa(x) <= Fb(x) for all x, and
Fa(x) < Fb(x) for some value of x

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In words, this means that the probability of portfolio B producing a return below a certain value is never less than the probability of Portfolio A producing a return below the same value, and exceeds it for at least some value of x.
For example, if two normal distributions have the same variance but different means, the one with the higher mean displays first-order stochastic dominance over the other.

Question 3

Second-order stochastic dominance

Answer 3

We consider two investment portfolios, A and B, with cumulative probability distribution functions of returns Fa and Fb respectively

The second-order stochastic dominance theorem applies when the investor is risk-averse as well as preferring more to less.

In this case the condition for A to dominate B is that
Integral from a to x of Fa(y) dy <=
Integral from a to x of Fb(y) dy for all x
With the strict inequality holding for some value of x, and where a is the lowest return that the portfolios can possibly provide.

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The interpretation of the inequality is that a risk-averse investor will accept a lower probability of a given extra return at a low absolute level of return in preference to the same probability of extra return at a higher absolute level. In other words, a potential gain of a certain amount is not valued as highly as a loss of the same amount.
For example, if two normal distributions have the same mean but different variances, the one with the lower variance displays second order stochastic dominance over the other.

Question 4

Describe the field of behavioural finance

Answer 4

The field of behavioural finance looks at how a variety of mental biases and desicion-making errors affect financial decisions. It relates to the psycology that underlies and drives financial decision-making behaviour. Much of the work to date has concentrated on the impact on prices in capital markets (indeed some “contrarian” infestment funds are run on the basis of taking advantage of errors made by other investors). In investment consultancy, behavioural arguments can be applied to trustees and used to justify proposed investment managment structures.

Question 5

List the eight common themes found in research on behavioural finance

Answer 5

FOAM POEM

1. Anchoring and adjustment
2. Prospect theory
3. Framing (and question wording)
4. Myopic loss aversion
5. Estimating probabilities
6. Overconfidence
7. Mental accounting
8. Effect of options

Question 6

Anchoring and adjustment

Answer 6

Anchoring is a term used to explain how people will produce estimates. They start with the initial idea of the answer (“the anchor”) and then adjust away from this initial anchor to arrive at their final judgement.

{Thus, people base perceptions on past experience or “expert” opinion, which they amend to allow for evident differences to the current conditions. The effects of anchoring are pervasive and robust and are extremely difficult to ignore, even when people are aware of the effect and aware that the anchor is ridiculous.}

Question 7

Prospect theory

Answer 7

Prospect theory is a theory of how people make decisions when faced with risk and uncertainty. It replaces the conventional risk-averse/risk-seeking decreasing marginal utility theory based on total wealth with a concept of value defined in terms of gains and losses relative to a reference point.

{This generates utility curves with a point of inflexion at the chosen reference point.
Prospect theory is therefore associated with the concept of framing.}

Question 8

Framing (and question wording)

Answer 8

The way a choice is presented (“framed”) and, particularly, the wording of a question in terms of gains and losses, can have an enormous impact on the answer given or the decision made. Changes in the way a question is framed of only a word or two can have a profound effect.

{In the same way, “structured response” questions are found to convey an implicit range of acceptable answers.}

Question 9

Myopic loss aversion

Answer 9

This is similar to prospect theory, but considers repeated choices rather than a single “gamble”.

{Research suggests that investors are less “risk-averse” when faced with a multi-period series of “gambles”, and that the frequency of choice / length of reporting period will also be influential.}

Question 10

Estimating probabilities

Answer 10

Issues (other than anchoring) which might affect probability estimates include:

• Dislike of “negative” events - the “valence” of an outcome (the degree to which it is considered as negative or positive) has an enormous influence on the probability estimates of its likely occurence.
• Representative heuristics - people find more probable that which they find easier to imagine. As the amount of detail increases, its apparent likelihood may increase (although the true probability can only decrease steadily)
• Availability - people are influenced by the ease with which something can be brought to mind. This can lead to biased judgments when examples of one event are inherently more difficult to imagine than examples of another.

Question 11

Overconfidence

Answer 11

People tend to overestimate their own abilities, knowledge and skills.

{Moreover, studies show that the discrepancy between accuracy and overconfidence increases, in all but the simplest tasks, as the respondent is more knowledgable! Accuracy increases to a modest degree but confidence increases to a much larger degree}

This may be a result of:

• Hindsight bias: events that happen will be thought of as having been predictable prior to the event; events that do not happen will be thought of as having been unlikely prior to the event.
• Confirmation bias: people will tend to look for evidence that confirms their point of view (and will tend to dismiss evidence that does not justify it)

Question 12

Mental accounting

Answer 12

People show a tendency to separate related events and decisions and find it difficult to aggregate events. Thus, rather than netting out all gains and losses people set up a series of “mental accounts” and view individual decisions as relating to one or another of these accounts.

Question 13

Effect of options

Answer 13

In addition to the “framing” effect described above, other issues include:

• the primary effect - people are more likely to choose the first option presented
• the recency effect - in some instances, the final option that is discussed may be preferred! The gap in time between the presentation of the options and the decision may influence this dichotomy.
• other research suggesting that people are more likely to choose an intermediate option than one at either end
• a greater range of options tends to discourage decision-making. On the other hand, a higher probability is attributed to options explicitly stated than when included in a broader category.
• status quo bias - people have a marked preference for keeping things as they are
• regret aversion - by retaining the existing arrangements, people minimise the possibility of regret (the pain associated with feeling responsible for a loss)
• ambiguity aversion - people are prepared to pay a premium for rules.