Chapter 2 Utility Theory Flashcards
Study Theory
Define utility in economics.
Utility is the satisfaction that an individual obtains from a particular course of action.
Utility Function
Function showing the level of utility associated with different levels of wealth
Role is to describe the manner in which an investor derives utility for given choices.
Describes investors risk return preference
Expected Utility Theorem
1) The EUT states that a function U(w) can be constructed as representing an investor’s utility of wealth, w at some future date.
2) Decisions are made in a manner to maximize the expected value of utility given the investor’s particular beliefs about the probability of different outcomes.
Axioms of Utility
1) Comparability
An investor can state a preference between all avaliable certain outcomes.
2) Transitivity
If A is preferred to B and B is preferred to C, then A is preferred to C.
3) Independence
If an investor is indifferent between two outcomes, A and B, then they are also indifferent between the following two gambles:
i) A with probability p and C with probability (1-p)
ii)B with probability p and C with probability (1-p)
4) Certainty Equivalent
Suppose that A is preferred to B and B is preferred to C. Then there exists a unique probability p such that the investor is indifferent between B and gamble giving A with probability p and C with probability (1-p).
B is known as the certaintu equivalent of the above gamble.
Non-satiation
Assumption that people prefer more to less.
U’(w) >0
Risk Preference
Risk Averse investor values an incremental increase in wealth less highly that an incremental decrease and will reject a fair gamble.
U’‘(w) <0
Risk seeking investor values an incremental increase in wealth more highly than an incremental decrease and will seek a fair gamble.
U’‘(w) >0
Risk neutral investor is indifferent between a fair gamble and the status quo.
U’‘(w) =0
Why is it necessary to have state dependent utility functions?
Sometimes it may be inappropriate to model an investors behavior over all possible levels of wealth with a single utility function.
What is a state dependent utility function?
It models the situation where there is a discontinuous change in the state of the investor at a certain level of wealth.
Describe an approach to constructing a utility function
One approach to constructing a utility function involves questioning individuals about their preferences.
The questioning may be direct of indirect.
Indirect questioning may be framed in terms of how much an individual would be prepares to pay for insurance against various risks.
Maximum premium a policyholder will pay
E[U(a-X)] =U(a-P)
a=initial wealth
P=minimum premium policyholder is willing to pay to avoid the potential loss
X=potential loss
Minimum premium an insurer will accept
E[U(a+Q-Y)] =U(a)
a=initial wealth
Q=minimum premium an insurer could charge to cover potential damages
Y=potential damages
Limitations of Utility Theorem
1) We need to know the precise form and shape of the individuals utility function.
2) The expected Utility theorem cannot be applied seperatly to each of the several sets of risky choices facing an individual.
3) For corporate risk management, it may not be possible to consider a utility function for the firm as though the firm was an individual.
Aim of utility theory
To measure utility at differing levels of wealth when facing uncertain outcomes, trying to model financial outcome and investor preference.
