FOUNDATIONS OF FINANCE
FROM
BEHAVIORAL FINANCE: PSYCHOLOGY, DECISION-MAKING, AND
MARKETS
BY LUCY. F. ACKERT & RICHARD DEAVES
FOUNDATIONS OF FINANCE I
EXPECTED UTILITY THEORY
Investors are irrational
and
markets are inefficient
NEOCLASSICAL (STANDARD) ECONOMICS
Main assumptions:
1. People have rational preferences across possible outcomes
or states of nature
2. People maximize utility and firms maximize profits
3. People make independent decisions based on all relevant
information
ASSUMPTİON 1: RATİONAL PREFERENCES
Suppose there are two outcomes to choose: 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).
ASSUMPTİON 1: RATİONAL PREFERENCES
Two axioms for a choice to be rational are:
1. Completeness
A person can compare all possible choices and assess preference or
indifference.
2. Transitivity
If there are three outcomes, x ≻ y and y ≻ z, then x ≻ z
ASSUMPTİON 2: UTİLİTY MAXİMİZATİON
• 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?
An individual considers all possible bundles of goods that satisfy her budget
constraint (based on wealth or income), and then chooses the bundle that
maximizes her utility.
As income increases individuals gain a
correspondingly smaller increase in satisfaction
and happiness.
Diminishing marginal utility of
income and wealth
ASSUMPTİON 3: RELEVANT
INFORMATİON
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
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».
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.
AXİOMS OF THE EXPECTED
UTİLİTY THEORY
1. Completeness: People can compare all possible outcomes and assess
preference or indifference. (x>y or x<y or x~y)
2. Transitivity: People’s choices are transitive (x ≥y ≥ z)
3. 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)
AXİOMS OF THE EXPECTED
UTİLİTY THEORY
4. 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.
5. 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.
EXPECTED UTILITY THEORY
• Expected utility theory is set up to deal with risk, not uncertainty.
• Risk vs. Uncertainty (What is the difference?)
EXPECTED UTILITY THEORY
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 In uncertainty no previous knowledge is possible.
known in advance.
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
P1 (0.40, $50,000, $1,000,000)
Probabilities assigned:
Low wealth 40%
High weath 60%
EXPECTED UTILITY THEORY
2. Suppose there are only two states of nature (two outcomes):
• Low wealth $100,000
• High wealth $1,000,000
P2 (0.50, $100,000, $1,000,000)
Probabilities assigned:
Low wealth 50%
High weath 50%
EXPECTED UTILITY THEORY
• P1 (0.40, $50,000, $1,000,000)
• P2 (0.50, $100,000, $1,000,000)
Given these two prospects, two risky alternatives, which one of them you would prefer?
Let’s calculate the expected utilities of the prospects! Remember: u(w) = ln(w)
E[u(P1)] = U(P1) = 0.40*u($50,000) + 0.60*u($1,000,000)
= 0.40*1.6094 + 0.60*4.6052 = 3.0469 P2 is superior to
P1
E[u(P2)] = U(P2) = 0.50*u($100,000) + 0.50*u($1,000,000) So choose P2!
= 0.50*2.3026 + 0.50*4.6052 = 3.4539
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.
Stock Expected Risk
Return
Stock A 10% 20%
Stock B 10% 15%
• Tell which one you would like to invest in?
RISK ATTITUDE
Individuals’ attitudes towards risk may show difference.
Types of Investors:
• Risk averse
• Risk seeker or Risk lover
• Risk neutral
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.
RISK ATTITUDE
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.
RISK ATTITUDE
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 certainty.
RISK ATTITUDE
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
ALLAIS PARADOX
• A contradiction to expected utility theory Allais Paradox
ALLAIS PARADOX
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)
ALLAIS PARADOX
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)
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
QUIZLET
Review the chapter with Quizlet
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