1. CHAPTER 1 FOUNDATIONS OF FINANCE I: EXPECTED UTILITY THEORY

2. Investors are irrational (not rational) and markets are inefficient (not efficient)

3. NEOCLASSICAL ECONOMICS
Main assumptions:
People have rational preferences across possible outcomes or states of nature
People maximize utility and firms maximize profits
People make independent decisions based on all relevant information

4. Assumption 1: Rational Preferences
Suppose there are two outcomes: x and y
If x > y, then individual prefers x to y (strict preference).
If x ~ y, then individual is indifferent between x and y (indifference).
If x ≥ y, then individual prefers x or is indifferent between two choices (weak preference).

5. Assumption 1: Rational Preferences
Two axioms for a choice to be rational are:
Completeness
Transitivity

6. Assumption 2: Utility Maximization
Utility theory is used to describe preferences
Utility can be described as «the satisfaction received from a particular outcome»
Ex: For an individual, if
U( 2 bread, 1 water) > U(1 bread, 2 water)
What does that mean?

7. An individual considers all possible bundle of goods (outcomes) that satisfy his/her needs and desires under the budget constraint (which is based on level of wealth or income), and then chooses the bundle that maximizes his/her utility.

10. Diminishing marginal utility of
As income increases individuals gain a correspondingly smaller increase in satisfaction and happiness.
Diminishing marginal utility of
income and wealth

11. Assumption 3: Relevant Information
Individuals maximize their utility by using full information of the choice set.
In theory it is assumed that there are no costs of information
BUT
In practice, there is COST of
Acquiring
Assimilating
Understanding
the INFORMATION

12. EXPECTED UTILITY THEORY
In financial decision making process, people face with uncertainty of outcomes and they have to deal with it in order to make decisions.
The origins of the expected utility theory dates back to 18th century. The theory was orginally advanced by Daniel Bernoulli in his paper(1738) «Exposition of a New Theory on the Measurement of Risk»
Bernoulli discussed individuals do not always make rational decisions under risky situations. (Remember St. Petersburg Paradox!) When there is uncertainty, individuals tend to be risk averse.
Later, the theory was developed by John von Neumann and Oskar Morgenstern (1944) in their book «Theory of Games and Economic Behavior».

13. EXPECTED UTILITY THEORY
The expected utility theory deals with the analysis of situations where individuals must make a decision without knowing which outcomes may result from that decision, this is, decision making under uncertainty.
These individuals will choose the act that will result in the highest expected utility, being this the sum of the products of probability and utility over all possible outcomes. 

14. Axioms of the Expected Utility Theory
Completeness: People can compare all possible outcomes and asses preference or indifference. (x>y or x<y or x~y)
Transitivity: People’s choices are transitive (x ≥y ≥ z)
Continuity: Given any certain level w* between highest (wH)and lowest (wL), there exists one and only one u* such that ;
w* ~ P(u*, wH, wL)
Rationality:   A gamble which assigns a higher probability to a preferred outcome will be preferred to one which assigns a lower probability to a preferred outcome.
Independence:  If a decision-maker is indifferent between two possible outcomes, then she/he will be indifferent between two gambles which offer them with equal probabilities.

15. EXPECTED UTILITY THEORY
Expected utility theory is set up to deal with risk, not uncertainty.
Risk vs. Uncertainty (What is the difference?)
RISK
UNCERTAINITY
Risk is a measurable uncertainty.
Uncertainity is an unknown risk.
Risk can be quantitavely measured.
Uncertainity cannot be quantitavely measured.
Risk can be transferred.
Uncertainity cannot be transferred.
Risk is objective
Uncertainty is subjective
In risk, all the possible alternatives of a problem are known in advance.
In uncertainty no previous knowledge is possible.

16. EXPECTED UTILITY THEORY
Prospect (P): A series of wealth outcomes, each of which is associated with a probability.
1. Suppose there are only two states of nature (two outcomes):
Low wealth  $50,000
High wealth  $1,000,000
Probabilities assigned:
Low wealth  40%
High weath  60%
P1 (0.40, $50,000, $1,000,000)

17. EXPECTED UTILITY THEORY
2. Suppose there are only two states of nature (two outcomes):
Low wealth  $100,000
High wealth  $1,000,000
Probabilities assigned:
Low wealth  50%
High weath  50%
P2 (0.50, $100,000, $1,000,000)

18. EXPECTED UTILITY THEORY
Given these two prospects, two risky alternatives, which of one them you would prefer?
Lets calculate the expected utilities of the prospects! Remember: u(w) = ln(w)
E[u(P1)] = U(P1) = 0.40*u($50,000) *u($1,000,000)
= 0.40* * =
E[u(P2)] = U(P2) = 0.50*u($100,000) *u($1,000,000)
= 0.50* * =
P2 is superior to P1
So choose P2!

19. RISK ATTITUDE Most evidence show that people are RISK AVERSE
Individuals do not want to take risk unless they are paid for it.
Suppose there are two stocks with same expected returns and different risk levels.
Tell which one you would like to invest in?
Stock
Expected Return
Risk
Stock A
10%
%20
Stock B
%15

20. RISK ATTITUDE Types of Investors: Risk averse
Individuals’ attitudes towards risk may show difference.
Types of Investors:
Risk averse
Risk seeker or Risk lover
Risk neutral

21. RISK ATTITUDE
Risk averse people dislike risk and prefer the expected value of a prospect to the prospect itself. u[E(P)] > E[u(P)] Someone who is risk averse has a concave utility function. This type of person would take the expected value of a prospect with certainity than actually take a gamble on an uncertain outcome.

22. RISK ATTITUDE

23. RISK ATTITUDE
Risk seeker people like risk and prefer the prospect to the expected value of a prospect. u[E(P)] < E[u(P)] Someone who is risk seeker has a convex utility function. This type of person would rather gamble on the uncertain outcome than take the expected value of a prospect with certainity.

24. RISK ATTITUDE

25. RISK ATTITUDE
Risk neutral people are insensitive to risk. u[E(P)] = E[u(P)] Someone who is risk neutral has a linear utility function. This type of person would be indifferent between choosing a gamble on an uncertain outcome and a prospect with certainity.

26. RISK ATTITUDE

27. RISK ATTITUDE
Certainity equivalent (CE) is a certain wealth level that leads the decision-maker to be indifferent between this certain wealth level and a particular prospect.
Risk Premium (RP) = E (P) – CE
As risk aversion of an individual increases, the risk premium demanded for any given risky outcome will also increase.
CE < E (P)  Risk averse
CE > E(P)  Risk seeker
CE = E(P)  Risk neutral

28. ALLAIS PARADOX
A contradiction to expected utility theory  Allais Paradox

29. ALLAIS PARADOX If people choose A, then;
E[u(A)] = u($1,000,000)
E[u(A*)] = (0.01)u($0) + (0.89)u($1,000,000) + (0.10)u($5,000,000)
If people choose A, then;
u($1,000,000) > (0.89) u($1,000,000) + (0.10) u($5,000,000)
(0.11) u($1,000,000) > (0.10) u($5,000,000)

30. ALLAIS PARADOX If people choose B*, then;
E[u(B)] = (0.89) u($0) + (0.11) u($1,000,000)
E[u(B*)] = (0.90) u($0) + (0.10) u($5,000,000)
If people choose B*, then;
(0.10) u($5,000,000) > (0.11) u($1,000,000)

31. ALLAIS PARADOX Allais Paradox
For Question 1, people preferred Prospect A to prospect A*, which means:
(0.11) u($1,000,000) > (0.10) u($5,000,000)
For Question 2, people preferred Prospect B* to prospect B, which means:
(0.10) u($5,000,000) > (0.11) u($1,000,000)
Allais Paradox
shows that, individuals’ decisions can be inconsistent with Expected Utility Theory