Chapter 2: Utility Theory

Question 1

Expected Utility Theorem

Answer 1

• A function, U(w) can be constructed representing an investor’s utility of wealth, w, at some future date
• Decisions are made on the basis of maximising the expected value of utility under the investor’s particular beliefs about the probability of different outcomes.

Question 2

4 Axioms of utility theorem

Answer 2

• Comparability
• Transitivity
• Independence
• Certainty equivalence

Question 3

Comparability

Answer 3

An investor can state a preference between all available certain outcomes.

Question 4

Transitivity

Answer 4

If A is preferred to B and B is preferred to C, then A is preferred to C.

Question 5

Independence

Answer 5

If an investor is indifferent between two certain outcomes, A and B, then he is also indifferent between the following two gambles:

• A with probability p and C with probability (1-p)
• B with probability p and C with probability (1-p)

Question 6

Certainty Equivalence

Answer 6

Suppose A is preferred to B, and B is preferred to C.
Then there is a unique probability, p, such that the investor is indifferent between B and a gamble giving A with probability p and C with probability (1-p).
B is known as the certainty equivalent of the gamble.

Question 7

Non-satiation

Answer 7

The principle of assuming that people prefer more wealth to less.
U’(w)>0

Question 8

Risk Averse investor

Answer 8

Values an incremental increase in wealth less highly than an incremental decrease and will reject a fair gamble.
U’‘(w)<0

Question 9

Risk-seeking investor

Answer 9

Values incremental increase in wealth more highly than an incremental decrease and will seek a fair gamble.
U’‘(w)>0

Question 10

Risk-neutral investor

Answer 10

Indifferent between a fair gamble and the status quo.

U’‘(w)=0

Question 11

Absolute risk aversion

Answer 11

A(w) = -U’‘(w)/U’(w)

Question 12

Relative risk aversion

Answer 12

R(w) = -w U’‘(w)/U’(w)

Question 13

State-dependent utility functions

Answer 13

Used to model the situation where there is a discontinuous change in the state of the investor at a certain level of wealth.

Question 14

Limitations of utility theory (3)

Answer 14

• We need to know the precise form and shape of the individual’s utility function.
• The theorem cannot be applied separately to each of several sets of risky choices facing an individual.
• For corporate risk management, it may not be possible to consider a utility function for the firm as though the firm was an individual.