Behavioural Finance
Lecture 03 Part 01
Finance Markets Behaviour
Recap
• Neoclassical theory of individual behaviour irrational
– Even if pretend it’s OK, theory of market demand
proven wrong by neoclassical economists
• Demand curve can have any shape even if all
individuals have “well-behaved” demand curves
• Theory of supply irrational
– Definition of profit-maximising behaviour provably
wrong
• When corrected, profit-maximising firms don’t set
Price=Marginal Cost
• Can’t derive supply curve
• This week: even if pretend the above is OK, definition of
“rational behaviour” in finance also irrational…
Rational Choice in Finance Markets
1. Choose between
Your Choices?
A. $1000 with certainty; OR
Gamble
A
B
Number
B. 90% odds of $2000 & 10%
odds of -$1000
1
8
7
2. Choose between
A. $0 with certainty; OR
2
B. 50% odds of $150 and 50%
odds of -$100
3
3. Choose between
A. -$100 with certainty; OR
Total for
each option
B. 50% odds of $50; 50% odds
of -$200
• Take your time to work out which one to choose…
• Write down why you made your choices
Rational Choice in Finance Markets
• Tally of class
choices:
• Most people
choose:
Class Choices
Gamble
A
Common Choices
B
“Rational” Choice
Gamble
A
B
Gamble
A
1
1
A
1
B
2
2
A
2
B
3
3
B
3
B
Total
Total
1
Total
2
• So most people are irrational???
B
• Economic theory
says rational is…
0
3
Rational Choice in Finance Markets
• Why? A“rational person” maximises expected return:
– Sum of probabilities times returns:
Choices and Expected Return
Gamble
A
B
ER
1
1x1,000=
+$1,000
0.9x$2,000+ 0.1x-$1,000=
+$1,700
B>A
2
1x$0=
$0
.5x$150 + .5x-$100=
+$25
B>A
3
1x-$100=
-$100
.5x$50+.5x-$200=
-$75
B>A
• Why do most people not make these choices?
– Write down your guess as to why…
Rational Choice in Finance Markets
•
Straw Poll: Reasons for not “being rational”…
No.
Reason…
Parramatta Day
Parramatta Evening
1
2
3
4
• Now an experiment: exactly the same choices EXCEPT
– Whichever option you choose is repeated 100 times
Rational Choice in Finance Markets
Class Choices
1. Choose between 100 repeats of
Gamble
A
B
A. $1000 with certainty; OR
B. 90% odds of $2000 & 10%
1
odds of -$1000
2. Choose between 100 repeats of
2
A. $0 with certainty; OR
B. 50% odds of $150 and 50%
3
odds of -$100
3. Choose between 100 repeats of
Total
A. -$100 with certainty; OR
B. 50% odds of $50 and 50%
odds of -$200
• Take your time to work out which one to choose…
• Write down why you made your choices
Rational Choice in Finance Markets
• Tally of class choices • This time •
economic
Class Choices
theory gets
Gamble
A
B
it right:
• You’re
1
(almost!)
all
rational…
2
Economic theory
says rational is…
“Rational” Choice
Gamble
Number
A
B
1
B
2
B
3
3
B
Total
Total
0
3
Rational Choice in Finance Markets
•
Subjective vs objective probability
– In a single gamble, you get one outcome OR the other
– Subjective expectations are still the given odds:
• E.g. One-off game with Gamble 1
A. $1000 with certainty; OR
B. 90% chance of $2000 & 10% chance of -$1000
– Actual outcome of A is “expected return” of $1,000
– Actual outcome of B is either $2,000 or -$1,000:
• You don’t get the “expected return” of $1,700
– Repeated gamble, you do get the expected return
• 100 repeats of gamble 1
A. 100x1000=$1,000 certain outcome per play; OR
B. 90x2000+10x-1000=$1,700 average per play
Rational Choice in Finance Markets
• Why the difference?
– One-off gamble fundamentally uncertain
• Probability of $2,000 in Gamble 3B is 90%...
• But outcome of single throw will be +$2K or -$1K
• Probability can’t tell you which one will occur
– Subjectively, odds are 90% you’ll get $2,000
– Objectively, you can’t tell which one will occur
• Outcome not “probable” but “uncertain”
• Problem of uncertainty key to failings of finance theory
• First, background to development of finance theory:
– Flawed use of “theory of games” developed by
physicist John von Neumann & economist Oscar
Morgenstern…
Rational Choice in Finance Markets
• von Neumann & Morgenstern developed “Expected
Return/Expected Utility” approach in Theory of Games
and Economic Behavior
– Intended to use “theory of games” to make economic
concepts like utility measureable
• Model then “borrowed” by economists to develop CAPM
• von Neumann & Morgenstern were
– Aware of distinction between objective & subjective
probability
– Insisted on using objective probability:
Rational Choice in Finance Markets
• “Probability has often been visualized as a subjective
concept more or less in the nature of estimation.
• Since we propose to use it in constructing an individual,
numerical estimation of utility [more on this shortly…],
– the above view of probability would not serve our
purpose.
• The simplest procedure is, therefore, to insist upon the
alternative, perfectly well founded interpretation of
probability as
– frequency in long runs.” (von Neumann & Morgenstern
1944: 19 [Emphases added])
• This directive (and much else!) ignored by economists who
developed “Modern Finance Theory”…
Rational Choice in Finance Markets
• von Neumann & Morgenstern (abbreviated to vN&M)
– Critical of economic theory in general
– In particular rejected “indifference curves”:
• “the treatment by indifference curves implies
either too much or too little:
– if the preferences of the individual are not at all
comparable
• then the indifference curves do not exist.
– If the individual’s preferences are all
comparable
• then we can even obtain a (uniquely defined)
numerical utility
• which renders the indifference curves
superfluous.” (19-20)”
Rational Choice in Finance Markets
• Developed numerical measure of utility instead
– Argued that non-numerical economic concept of utility
was “immature”
– Gave examples of pre-numerical concepts in physics
– Measurement there resulted from good theory:
• “The precise measurement of the quantity and
quality of heat (energy and temperature) were the
outcome and not the antecedents of the
mathematical theory” (p. 3)
– i.e., develop a good theory, and what is currently
“ordinal” (ranking of preferences via
indifference curves) can become “cardinal”
(quantitative measure for utility)
Rational Choice in Finance Markets
• Their idea:
– Use gambles and objective probability to provide
numeric scale for utility
• “Numerical utility” model has same “curse of
dimensionality” problem as indifference curves
• But unlike economists, vN&M were aware of problem:
– “one may doubt whether a person can always decide
which of two alternatives—with the utilities u, v—he
prefers.
– But, whatever the merits of this doubt are, this
possibility—i.e. the completeness of the system of
(individual) preferences—must be assumed even for
the purposes of the ‘indifference curve method’.” (pp.
28-29)
Rational Choice in Finance Markets
• Model mirrored “Revealed Preference” numerically:
– Allowed precise statement of extend to which
consumer preferred one “shopping trolley” to another
Samuelson’s “Revealed Preference”
vN&M’s “Numerical Utility”
“Completeness”: Given any 2 bundles
of commodities A & B , consumer
can decide whether prefers A to B
(A≻B), B to A (B≻A), or is
indifferent between them (B≈A)
Ditto but now: if A≻B then there
is some numerical conversion of
utility v() such that v(A) greater
than v(B); Can put a numeric value
on utility of A and B
“Transitivity”: If (A≻B) and (B≻C)
then (A≻C)
Ditto but now: if A≻B then there
is some probability 0<a<1 such
that av(A) =v(B)
“Non-satiation”: More is preferred
to less
Probable (but not necessary)
consequences of numerically
measured utility
“Convexity”:Marginal utility positive
but falling as consumption of any
good rises
Rational Choice in Finance Markets
• Basic Idea:
– Arbitrarily assign value
• 0 to zero bananas
• 1 to 1 banana
– (just like setting freezing point of fresh
water=32ºF & freezing point of salt water=0ºF
in Fahrenheit scale)
– Then offer consumer repeated gamble of
• 1 banana for certain; OR
• a% odds of 2 bananas vs (1-a)% odds of no bananas
• If consumer accepts gamble when (say) a=0.7, then
utility of 1 banana = 0.7 times utility of 2 bananas:
Rational Choice in Finance Markets
• U(1 banana) = 1 “util”
• Accept repeated gamble between 1 for certain and 60%
chance of 2 versus 40% chance of none:
– 1 banana gives you 60% the utility of 2 bananas
– 1 = 0.6 x U(2)
– U(2) = 1/0.6=1.67
– Marginal Utility of 2nd banana = 0.67
• Repeat same exercise
– Repeated gamble between
• 2 for certain and gamble between (0 and 3),
• 3 for certain and gamble between (0 and 4
bananas), etc.…
– Use odds at which gamble accepted to calculate
numerical utility for bananas:
Rational Choice in Finance Markets
• Adding up the bananas…
Number of Numeric Marginal Odds at which
bananas for “utils”
Utility
gamble for one
certain
more accepted
Calculation
0
0
0
N/A
N/A
1
1
1
60% odds of 2
bananas vs 40% of
no banana
1/0.6=1.67
2
1.67
0.67
78% odds of 3
1.67/0.78=2.141
3
2.141
0.471
92% odds of 4
2.141/0.92
4
2.327
0.186
97% odds of 5
2.327/0.97
5
2.399
0.072
99% odds of 6
2.399/0.99
Rational Choice in Finance Markets
• A numeric measure of utility & marginal utility:
Cardinal Utility from Odds of Gamble
3.00
Utility
2.50
Change in Utility
Utility
2.00
1.50
1.00
0.50
0.00
0
1
2
3
4
5
Number of bananas
• So “cardinal expected utility” meant to be a replacement
for “ordinal utility” indifference curve analysis…
Rational Choice in Finance Markets
• Instead, economists
– Ignored numeric utility proposal
– Combined new vN&M ideas:
• Expected Return
• Expected Utility etc.
– With existing economic theory
• Indifference curves, etc.
– To develop “Modern Finance Theory” in 1950s & 60s…
• Vision of investors maximising non-numerical utility
given budget constraints…
“Modern” Finance?
• “Modern Finance Theory” has many components:
– Sharpe’s “Capital Asset Pricing Model” (CAPM)
– Modigliani-Miller’s “Dividend Irrelevance Theorem”
– Markowitz’s risk-averse portfolio optimisation model
– Arbitrage Pricing Theory (APT)
• “Modern” as compared to pre-1950 theories that
emphasised behaviour of investors as explanation of
stock prices, value investing, etc.
– Initially seemed to explain what “old finance” could not
– But 50 years on, not so crash hot…
• Foundation is Sharpe’s CAPM:
• Objective: To “predict the behaviour of capital
markets”
The Capital Assets Pricing Model
• Method: Extend theories of investment under certainty
– to investment under conditions of risk
– Based on neoclassical utility theory:
• investor maximises utility subject to constraints where
utility is:
– Positive function of expected return ER
– Negative function of risk (standard deviation) sR
– Constraints are available spectrum of investment
opportunities as perceived by individual investor:
• Expectation of return on stock over time including
expected volatility of return & correlation with other
assets
– E.g. “I expect IBM to give a 6% return, with a
standard deviation of 3% & a minus 67% correlation
with CSR”…
The Capital Assets Pricing Model
Z inferior
to C
(lower ER)
and B
(higher
sR)
Investment
opportunities
“Efficient”
opportunities
on the edge
Indifference
curves
Increasing utility:
Higher expected
returns & lower risk
Optimal
combination
for this
investor
Border (AFBDCX) is Investment Opportunity Curve (IOC)
The Capital Assets Pricing Model
• IOC reflects correlation of separate investments.
Consider 3 investments A, B, C:
– A contains investment A only
Variance due to A
• Expected return is ERa,
• Risk is sRa
Perceived
correlation of A
– B contains investment B only
with B
• Expected return is ERb,
(varies between -1
• Risk is sRb
& +1)
– C some combination of a of A & (1-a) of B
• ERc=aERa + (1-a)ERb
s Rc  a .s Ra  (1  a ) s Rb  2. rab .a . 1  a .s Ra .s Rb
2
2
2
2
The Capital Assets Pricing Model
• If rab=1, C lies on straight line between A & B:
This is 1
s Rc  a 2 .s Ra 2  (1  a ) 2 s Rb 2  2. rab .a . 1  a .s Ra .s Rb
s Rc  a 2 .s Ra 2  (1  a )2 s Rb 2  2.a . 1  a  .s Ra .s Rb
This can be factored
s Rc 
a.s Ra  (1 a ).s Rb 
Straight line relation
for risk, and also for
expected return:
2
 a.s Ra  (1 a )s Rb
The Capital Assets Pricing Model
sR
W h en rab= 1
B
In v e sm
t en t
O ppo r tun ity C
C u rv e
A
ER
a
a
The Capital Assets Pricing Model
• If rab=0, C lies on curved path between A & B:
This is zero
s Rc  a 2 .s Ra 2  (1  a ) 2 s Rb 2  2. rab .a . 1  a .s Ra .s Rb
s Rc  a 2.s Ra2  (1 a )2s Rb2
s Rc 
a.s Ra  (1 a )s Rb 
2
Hence this is zero
Straight line relation
Hence lower risk for diversified portfolio
(if assets not perfectly correlated)
The Capital Assets Pricing Model
sR
W h en rab< 1
In v e sm
t en t
O ppo r tun ity C
C u rv e
B
Fall in sR due to
diversification
when investments
are not perfectly
correlated
A
ER
a
a
The Capital Assets Pricing Model
• Sharpe assumes riskless asset P with ERP=pure interest
rate, sRP=0.
– Assumes limitless borrowing/lending at riskless
interest rate = return on asset P
• Investor can form portfolio of P with any other
combination of assets
– Investor can therefore move to anywhere along PfZ
line by borrowing/lending…
The Capital Assets Pricing Model
•
•
Efficiency: maximise expected return & minimise risk given constraints
One asset combination will initially dominate all others:
Only asset combination
which can efficiently
be combined with
riskless asset P in
a portfolio
The Capital Assets Pricing Model
• To this point, Sharpe has theory of a single investor
• However…
– “Riskless” lending rate will differ for each investor
– Expectations of future returns will differ too…
Fred Nurk
Jane Nguyen
Bill Gates
sR
Z
CSR
IBM
BHP
P
sR
IBM Z
BHP
CSR
ER
P
ER
sR
Z
IBM
BHP
CSR
P
ER
• How to go from theory of individual investor to theory of
market?...
– You guessed it…
– Sharpe assumes all investors are (almost!) identical...