Behavioural Finance
Lecture 03 Part 02
Finance Markets Behaviour
The Capital Assets Pricing Model
• “In order to derive conditions for equilibrium in the capital market
we invoke two assumptions.
• First, we assume a common pure rate of interest, with all investors
able to borrow or lend funds on equal terms.
• Second, we assume homogeneity of investor expectations:
– investors are assumed to agree on the prospects of various
investments—the expected values, standard deviations and
correlation coefficients described in Part II.
• Needless to say, these are highly restrictive and undoubtedly
unrealistic assumptions.
• However, since the proper test of a theory is not the realism of its
assumptions but the acceptability of its implications,
• and since these assumptions imply equilibrium conditions which form
a major part of classical financial doctrine,
• it is far from clear that this formulation should be rejected—
especially in view of the dearth of alternative models leading to
similar results.” (Sharpe 1964, pp. 433-434)
The Capital Assets Pricing Model
• Defended by appeal to Friedman’s “Instrumentalism”:
– “the proper test of a theory is not the realism of its
assumptions but the acceptability of its implications”
• Bad version of a bad methodology (discussed in
History of Economic Thought lecture—click for link)
• Another example of “proof by contradiction”
– IF have to assume identical investors to get a Capital
Assets Market Line
– THEN there can’t be a Capital Assets Market Line
• Could have been heuristic step to more general model
– See History of Economic Thought methodology lecture
• And next lecture slides 38-43
– But instead…
The Capital Assets Pricing Model
• CAPM based on absurd counter-factual assumptions that
all investors:
– Agree with each other about every stock; AND
– Have limitless ability to borrow at risk-free rate; AND
– Their expectations about the future are correct!
• Consequence of identical accurate expectations and
identical access to limitless borrowing “assumptions”:
– spectrum of available investments/IOC identical for
all investors
– P same for all investors
– PfZ line same for all investors
– Investors only differ by preferences for risk:
• distribute along line by borrowing/lending according
to own risk preferences:
The Capital Assets Pricing Model
Thrill seeker...
Risk neutral…
Highly
risk-averse
The Capital Assets Pricing Model
• Next, the (perfect) market mechanism
– Price of assets in f will rise
– Price of assets not in f will fall
– Price changes shift expected returns
– Causes new pattern of efficient investments aligned
with PfZ line:
The Capital Assets Pricing Model
Capital market line
Range of efficient asset
combinations after
market price adjustments:
more than just one
efficient portfolio
The Capital Assets Pricing Model
• Theory so far applies to combinations of assets
• Individual assets normally lie above capital market line
(no diversification)
• Can’t relate between ERi & si
• Can relate ERi to “systematic risk”:
• Investment i can be part of efficient combination g:
– Can invest (additional) a in i and (1-a) in g
• a=1 means invest solely in i;
• a=0 means some investment in i (since part of
portfolio g);
• Some a<0 means no investment in i;
• Only a=0 is “efficient”
The Capital Assets Pricing Model
Single investment
i which is part of
portfolio g
Efficient
combination g
Additional investment
in i is zero (a=0) here
The Capital Assets Pricing Model
• Slope of IOC and igg’ curve at tangency can be used to
derive relation for expected return of single asset
E Ri  P  rig
s Ri
s Rg

 E Rg  P

• This allows correlation of variation in ERi to
variation in ERg (undiversifiable, or systematic, or
“trade cycle” risk)
• Remaining variation is due to risk inherent in i:
The Capital Assets Pricing Model
Risk peculiar
to asset i
Higher return for assets more strongly
affected by trade cycle (systematic risk)
The Capital Assets Pricing Model
• Efficient portfolio enables investor to minimise asset
specific risk
• Systematic risk (risk inherent in efficient portfolio) can’t
be diversified against
• Hence market prices adjust to degree of responsiveness
of investments to trade cycle:
– “Assets which are unaffected by changes in economic
activity will return the pure interest rate; those which
move with economic activity will promise appropriately
higher expected rates of return.”
The Capital Assets Pricing Model
• Crux/basis of model: markets efficiently value
investments on basis of expected returns/risk tradeoff
• Modigliani-Miller extend model to argue valuation of
firms independent of debt structure
• Combination: the “efficient markets hypothesis”
• Focus on portfolio allocation across investments at a
point in time, rather than trend of value over time
• Argues investors focus on “fundamentals”:
– Expected return; Risk; Correlation
• So long as assumptions are defensible…
– common pure rate of interest
– homogeneity of investor expectations
• Sharpe later admits to qualms…
The CAPM: Reservations
• “People often hold passionately to beliefs that are
far from universal.
• The seller of a share of IBM stock may be
convinced that it is worth considerably less than
the sales price.
• The buyer may be convinced that it is worth
considerably more.” (Sharpe 1970)
• However, if we try to be more realistic:
– “The consequence of accommodating such
aspects of reality are likely to be disastrous in
terms of the usefulness of the resulting
theory...
The CAPM: Reservations
• “The capital market line no longer exists.
• Instead, there is a capital market curve–linear over
some ranges, perhaps, but becoming flatter as [risk]
increases over other ranges.
• Moreover, there is no single optimal combination of
risky securities; the preferred combination depends
upon the investors’ preferences...
• The demise of the capital market line is followed
immediately by that of the security market line.
• The theory is in a shambles.” (Sharpe, W. F., 1970,
Portfolio Theory and Capital Markets, McGraw-Hill,
New York, pp. 104-113 emphasis added)
The CAPM: Evidence
• Sharpe’s qualms ignored & CAPM took over economic
theory of finance
• Initial evidence seemed to favour CAPM
– Essential ideas:
• Price of shares accurately reflects future earnings
– With some error/volatility
• Shares with higher returns more strongly
correlated to economic cycle
– Higher return necessarily paired with higher
volatility
• Investors simply chose risk/return trade-off that
suited their preferences
– Initial research found expected (positive) relation
between return and degree of volatility
– But were these results a fluke?
The CAPM: Evidence
• Volatile but superficially exponential trend
– As it should be if economy growing smoothly
12000
DJIA 1920-2001
10000
8000
6000
4000
2000
0
11/25/1921
-2000
8/4/1935
4/12/1949
12/20/1962
8/28/1976
5/7/1990
1/14/2004
The CAPM: Evidence
• Sharpe’s CAPM paper published 1964
• Initial CAPM empirical research on period 1950-1960’s
– Period of “financial tranquility” by Minsky’s theory
• Low debt to equity ratios, low levels of speculation
– But rising as memory of Depression recedes…
• Steady growth, high employment, low inflation…
• Dow Jones advance steadily from 1949-1965
– July 19 1949 DJIA cracks 175
– Feb 9 1966 DJIA sits on verge of 1000 (995.15)
• 467% increase over 17 years
– Continued for 2 years after Sharpe’s paper
• Then period of near stagnant stock prices
The CAPM: Evidence
• Dow Jones “treads water” from 1965-1982
– Jan 27 1965: Dow Jones cracks 900 for 1st time
– Jan 27 1972: DJIA still below 900! (close 899.83)
• Seven years for zero appreciation in nominal terms
• Falling stock values in real terms
– Nov. 17 1972: DJIA cracks 1000 for 1st time
• Then “all hell breaks loose”
– Index peaks at 1052 in Jan. ‘73
– falls 45% in 23 months to low of 578 in Dec. ’74
– Another 7 years of stagnation
– And then “liftoff”…
The CAPM: Evidence
• Fit shows average exponential growth 1915-1999:
• index well above or below except for 1955-1973
Log of Dow Jones Industrial Average 1915-1999 plus last ten years...
4.5
4
3.5
y = 6E-05x + 1.4228
R2 = 0.9031
Crash of ’73: 45%
fall in 23 months…
Sharpe’s paper published
Jan 11 ’73: Peaks at 1052
Log Closing Value
3
Dec 12 1974: bottoms at 578
2.5
Bubble takes off in ‘82…
2
CAPM fit doesn’t look so hot any more…
1.5
1
Steady above trend growth 19491966: Minsky’s “financial tranquility”
CAPM fit to this data looks pretty good!
0.5
0
7/5/1914
4/13/1926
1/20/1938
10/29/1949
8/7/1961
5/16/1973
Date
2/22/1985
12/1/1996
9/9/2008
6/18/2020
Anomalies mount…
• For CAPM to describe reality:
– At the individual level
• All investors have to maximise expected utility
– Exhibit risk-return tradeoff
– At the systemic level
• Stock market has to follow “random walk with drift”
• Only determinant of stock’s price can be market
(efficient) return, riskless return, and stock’s beta
• Experiments like earlier ones challenge individual rule
– Most individuals breach risk/return tradeoff rule…
– Reaction of economists & psychologists to breaches
gave rise to “Behavioural Economics & Finance”
• But even here misunderstanding of what vN&M
tried to do distorted development of alternative
Anomalies mount…
•
Behavioural “anomalies”—people not maximising expected
return—initially explained by “preference for risk”
1. “Choose between
A. $1000 with certainty; OR
B. 90% odds of $2000 & 10% odds of -$1000”
– “Rational” person would choose B (expected return
$1700) over A
– Vast majority choose A over B
– Explanation: majority is “risk averse”
– Actively dislikes risk, chooses A to minimise it
– Problem: “risk preference reversal”…
Anomalies mount…
• Problem 1: Choose between two
alternatives:
– A: do nothing
Your Choices?
– B a gamble with:
Choice
• 50% chance of winning $150; Problem
Number
A
B
• 50% chance of losing $100.
• Problem 2: Choose between two
1
alternatives:
2
– A: Lose $100 with certainty
Total for
– B: a gamble with:
each option
• 50% chance of winning $50;
• 50% chance of losing $200
• Record your choices…
Anomalies mount…
• Did they look like this?:• Or this? • Or this?
1. Risk Averse
Problem
Number
Choice
A
1
X
2
Total
2. Risk Seeking
B
Problem
Number
A
1
X
1
X
X
2
X
2
2
Total
2
Total
B
Problem
Number
Choice
3. Risk Reversal
A
Choice
B
X
1
1
• Most people looked like 3:
– “Irrational” re risk too:
• Risk avoiding in one case
• Risk seeking in the other…
• Result didn’t make sense in either neoclassical (“risk
averse vs risk seeking”) or vN&M (numerical utility)
terms…
Anomalies mount…
• If people normally choose A over B in Problem 1 then:
– U($0) > U(0.5x$150+0.5x-$100)
• Using vN&M axioms we can rewrite this as:
– U($0) > 0.5xU($150)+0.5xU(-$100)
– “Utility of zero exceeds 0.5 times utility of
$150 plus 0.5 times utility of -$100”
• If people normally choose B over A in Problem 2 then:
– U(-$100) < U(0.5x$50+0.5x-$200)
• Using vN&M axioms we can rewrite this as:
– U(-$100) < 0.5xU($50)+0.5xU(-$200)
– “Utility of zero is less than 0.5 times utility of
$50 plus 0.5 times utility of -$200”
• Inconsistent in vN&M terms because axioms are linear in
money: adding fixed sum shouldn’t alter outcome:
Anomalies mount…
• If U(-$100) < U(0.5x$50+0.5x-$200), then add $100:
• Then U($0) < U(0.5x$150+0.5x-$100)
– U($0) < 0.5xU($150)+0.5xU(-$100)
• So if someone chooses A over B in Problem 1, vN&M say:
– U($0) > 0.5xU($150)+0.5xU(-$100)
• And if they choose B over A in Problem 2, vN&M say:
– U($0) < 0.5xU($150)+0.5xU(-$100)
• These are inconsistent:
• Preference reversal even in vN&M terms!
• May look like “cheating” to add $100;
– But same result turns up in single experiment…
Anomalies mount…
Your Choices?
• Problem 3. Choose between:
Problem
Choice
– A: Lose $45 with certainty
A
B
– B: 50% chance of -$100 and 50%
3
chance of $0
4
• Problem 4. Choose between:
Total
– A: 10% chance of -$45 and 90%
chance of $0
Commonest Choice
– B: 5% chance of -$100 and 95%
Problem
Choice
chance of $0
A
B
• A is “rational choice” in both cases:
3
Expected return
Problem
Choice
A
B
3
-$45
0.5x-$100=-$50
4
0.1x-$45=-$4.5
0.05x-$100=-$5
X
4
X
Total
1
1
• A/B choice pair
gives expected
utility reversal…
Anomalies mount…
•
•
•
•
•
•
Choosing 3B implies that:
U(-$45) < U(0.5x-$100+0.5x$0); or
1.0xU(-$45) < 0.5xU(-$100) + 0.5xU($0)
Choosing 4A implies that:
U(0.1x-$45 + 0.9x$0) > U(0.05x-$100 + 0.95x$0); or
0.1xU(-$45) + 0.9xU($0) > 0.05xU(-$100) + 0.95xU($0)
– Subtract 0.9xU($0) from both sides to yield:
• 0.1xU(-$45) > 0.05xU(-$100) + 0.05xU($0)
– Multiply both sides by 10 to yield:
• 1.0xU(-$45) > 0.5xU(-$100) + 0.5xU($0)
• Since most people choose 3B and 4A, this implies
• 1.0xU(-$45) < 0.5xU(-$100) + 0.5xU($0) AND
• 1.0xU(-$45) > 0.5xU(-$100) + 0.5xU($0): contradiction
Anomalies mount…
• Or is it?
– “Contradiction” disappears if
examples applied as vN&M
insisted they should be…
• Problem 5. Choose between 100
repeats of either:
– A: Lose $45 with certainty
OR
– B: 50% chance of -$100 and
50% chance of $0
• Problem 6. Choose between 100
repeats of either:
– A: 10% chance of -$45 and
90% chance of $0 OR
– B: 5% chance of -$100 and
95% chance of $0
Your Choices?
Problem
Choice
A
B
5
6
Total
Expected Return over 100
plays
Problem
Choice
A
B
5
-$4500
-$5000
6
-$450
-$500
From risk to uncertainty
• vN&M framework intended to derive numeric alternative
to indifference curves
– Suffers same core problem (impossibility of forming
complete set of preferences);
– But valid with repeated choices to derive model of
utility
• NOT devised to handle “one-off” choices where even
given probability data, each single outcome is
fundamentally uncertain
• A model of behaviour in finance must consider
uncertainty
– Next week…