Prospect Theory

Question 1

What is the traditional approach in choices under risk and uncertainty?

Answer 1

• Expected Utility Theory = EUT.
  Behavioral finance is critical about descriptive value of expected utility theory.

Prospect theory is a positive theory about choices under risk and uncertainty.

Question 2

What is prospect theory and who developed it?

Answer 2

Kahnemand and Tversky developed prospect theory, based on simple choice experiment to identify how people make choices in the face of risk.

They use experimental evidence to support their theory. 2 important elements:

1) Value function
2) Probabilitity weighting

Question 3

What is the value function?

Answer 3

• People’s valuations depend on gains and losses relative to a reference point. The reference point is often the status quo.

This is in contrast with expected utility theory which presumes that we care about absolute levels of wealth, not changes relative to a reference point.

People treat losses differently compared to comparable gains.
- Loss aversion: People dislike losses more than they like comparable gains, losses loom larger than comparable gains.

Question 4

What are the key features of the value function?

Answer 4

People sometimes exhibit risk aversion and sometimes risk seeking behaviour depending on the nature of the problem.

People’s valuations depend on gains and losses relative to a reference point, that reference point is often the status quo.

Loss aversion: people dislike losses more than they like comparable gains. Losses loom larger than comparable gains.

Diminishing marginal sensititivity implies risk aversion in the domain of gains and risk seeking in the domain of losses.

Question 5

What is the common ratio effect?

Answer 5

Expected utility says that choices are invariant to common ratios. Violation of this is called the common ratio effect.

Kahneman & Tversky’s explanation:

• Underweighing of small probabilities
• Degree of relative over-weighitng increases the smaller the probabilities

Question 6

What is subcertainty?

Answer 6

Choices involving certainty are relatively more attractive. This implies that the weighting function must be quite steep close to certainty.

Question 7

What is prospect theory?

Answer 7

Prospect theory is a theory that describes decisions under risk and uncertainty.

The model is descriptive. It tries to model how people make choices in real life, rather than how they should take optimal decisions

Formally prospect theory consists of a specification of:

(1) Mental accounts
(2) A value function defined over losses and gains
(3) A probability weighting function

Question 8

What is the 2 step process?

Answer 8

Prospect theory models choices as a 2 step process:

1) Editing phase:
- Prospects are transformed into simpler representations
- Heuristic rules and operations are appliced to organize, reforumulate and narrow down the options on the table
- Operations include coding, segregation, cancellation, simplification and the detection of dominance

2) Evaluation process in phase 2: gamble with highest value is chosen.

Question 9

What is coding

Answer 9

Gambles / prospects are coded in terms of losses and gains relative to a reference point.

Question 10

What is combination?

Answer 10

Prospects can sometimes be simplified by combining the probabilities associated with identical outcomes.

Q= (100,0.3; 100,0.3: 0,0.4) –> q’ = (100, 0.6; 0, 0,4)

Question 11

What is segregation?

Answer 11

Some prospects contain a riskless component that can be segregated from the risk component. So you get a gamble and a riskless component.

Question 12

What is cancellation?

Answer 12

When different prospects share identical components, these components may be discarded or ignored

Question 13

What is simplification?

Answer 13

Prospect might be simplified by rounding either outcomes or probabilities

Prospect q=(99, 0.51: 0, 0.49) is likely to be coded as an even chance to win 100: q’=(100, 0,5; 0, 0,5)

Question 14

What is detection of dominance

Answer 14

Finding the dominating choice between 2 prospect: outcomes of first components could be the same but probabilities higher.

Question 15

What is the evaluation stage?

Answer 15

Decision makers evaluate prospects and are assumed to choose the one with the highest value.

Overall value of an edited prospect is function v, expressed in v(x) and pii(p).

V(x) assigns to each outcome x a number which reflects the value of that outcome.

Pii(p) assigns to each probability p a decision weight which reflects the impact of p on the overall value of the prospect.

Question 16

What is the value function?

Answer 16

Utility function defined over gains and losses, always measured relative to a reference point (eg. 0, buying price of a stock,…)

Characteristics:

1) Concave in the domain of gains = risk aversion
2) Convex in the domain of losses = risk seeking
3) Point of nondifferentiability at the origin
4) More steeply sloped to the left of the origing than to the right = loss aversion
5) Marginal value of losses and gains decreases = diminishing marginal sensitivity/ This implies risk aversion in the domain of gains and risk seeking in the domain of losses.

Question 17

What is subaddivity?

Answer 17

Subadditivity implies the overweighing of small probabilities.

Question 18

Subcertainty

Answer 18

A sure event is always overweighted, choices involving certainty are relatively more attractive.

Implication: values are less sensitive to variations in probabilities.

An increase in the probability of an event does have a lower impact on the overall value of a prospect than in expected utility theory.

Question 19

What is subproportionality?

Answer 19

For a fixed ratio of probabilities, the ratio of the corresponding decision weights is closer to unity when te probabilities are low than when they are high.

Question 20

What did Olsen examine?

Answer 20

1997: He examines the degree to which investment behaviors of protfolio managers is consistent with the implications of the value function of prospect theory.

3 anonymous mail surveys of professional investement managers (all CFA’s with major responsbilities of an institutional investment portfolio).

First surve: information about investment managers perception of and attitudes toward investment risk.

Second 2 studies were designed to study investment preferences.

Question 21

What conclusion can we make from prospect theory?

Answer 21

Prospect theory is a descriptive model about how people make decisions under risk, based on experimental evidence.

Question 22

What are the applications to finance of prospect theory?

Answer 22

Research connecting prospect theory and finance can be divided into 3 areas:

1) Cross section of average returns
2) Aggregate stock market
3) Trading of financial assets over time

Financial decisions closesly associated with risk, which makes prospect theory an obvious candidate.

Other applications: insurance

Question 23

What does the cross section of average returns mean?

Answer 23

Why do some securities have higer average returns than others.

CAPM postulates that securities with higher betas should have average returns, but this prediction has not received a lot of empirical support: Fama & French

Question: Can prospect theory explain some of the cross section of average returns?

Question 24

What dit Barberis & Huang analyze?

Answer 24

Barberis & Huang (2008) analysed an economy in which investors derive PT utility from the change in the values of their portfolios.

Prospect theory leads to a new prediction: a security’s skewness in the distribution of its returns will be priced (willingness to pay).

In particular: a positively skewed security, a security whose return distribution has a right tail that is longer than its left tail will be overpriced, relative to the price it would command in an economy with expected utility investors and it will earn a lower average return.

Intuition: by taking a significant position in a positively sked stock, investors give themselves a small chance of becoming wealthy should the stock turn out the be the next Google.

Under the probability weighting component of PT, investors overweight the tails of the distribution they are considering = small probabilities. They overweight the unlikely state of the world in which they make a lot of money by investing in the postively skewed stock.

This makes them overprice stock –> which leads to lower average returns.

Question 25

What is the empirical support of the cross section of average returns?

Answer 25

Significant attention and empirical support.

1) Several papers have confirmed the basic prediction that more postively skewed stocks will have lower average returns.

2) Papers also argue that skewness prediction from prospect theory can shed a light on other empirical patterns.
- Eg. Long term average return of stocks that conduct an initial public offering is below that of a control group of stocks (that didn’t do an IPO)

Intitial public offering stocks = highly postively skewed.

Some perform incredibly well. PT says that stocks that do an offering should have lower avergage returns.

Constistent: Green and Hwang (2012) find that, the higher the predicted skewness of an IPO stock, the lower is its long-term avergage return.

Question 26

What is the aggregate stock market and how can PT explain this,

Answer 26

PT can explain the famous equity premium puzzle (Bernatzi & Thaler 1995): an individuel who is thinking about investing in the stock market considers the historical distribution of annual stock market returns.

Annual because the performance of asset classes if often reported in annual terms.

Since investors are loss averse, the high dispersion of this distribution is very unappealing. To compensate for this, and to ensure that the investor is willing to hold his share of the supply of equity, the stock market needs a high average return, that is significantly higher than on a safe asset like a Treasure bill.

Loss aversion can explain non-participation puzzle: historically most households did not participate in stock market. (Dimmock and Kouwenberg (2010))