Behavioural Finance

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 • Choose between • $1000 with certainty; OR • 90% odds of $2000 & 10% odds of -$1000 • Choose between • $0 with certainty; OR • 50% odds of $150 and 50% odds of -$100 • Choose between • -$100 with certainty; OR • 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: • Economic theory says rational is… • So most people are irrational???

Rational Choice in Finance Markets • Why? A“rational person” maximises expected return: • Sum of probabilities times returns: • 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”… • Now an experiment: exactly the same choices EXCEPT • Whichever option you choose is repeated 100 times

Rational Choice in Finance Markets • Choose between 100 repeats of • $1000 with certainty; OR • 90% odds of $2000 & 10% odds of -$1000 • Choose between 100 repeats of • $0 with certainty; OR • 50% odds of $150 and 50% odds of -$100 • Choose between 100 repeats of • -$100 with certainty; OR • 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 • Economic theory says rational is… • This time economic theory gets it right: • You’re (almost!) all rational… Why the Difference?

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 • $1000 with certainty; OR • 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 • 100x1000=$1,000 certain outcome per play; OR • 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

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… Utility of 2 bananas… Utility of 3 bananas…

Rational Choice in Finance Markets • A numeric measure of utility & marginal utility: • 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”…

“Efficient” opportunities on the edge Increasing utility: Higher expected returns & lower risk Optimal combination for this investor The Capital Assets Pricing Model Investment opportunities Z inferior to C (lower ER) and B (higher sR) Indifference curves Border (AFBDCX) is Investment Opportunity Curve (IOC)

Variance due to A Perceived correlation of A with B (varies between -1 & +1) The Capital Assets Pricing Model • IOC reflects correlation of separate investments. Consider 3 investments A, B, C: • A contains investment A only • Expected return is ERa, • Risk is sRa • B contains investment B only • Expected return is ERb, • Risk is sRb • C some combination of a of A & (1-a) of B • ERc=aERa + (1-a)ERb

This is 1 This can be factored The Capital Assets Pricing Model • If rab=1, C lies on straight line between A & B: Straight line relation for risk, and also for expected return:

The Capital Assets Pricing Model

The Capital Assets Pricing Model • If rab=0, C lies on curved path between A & B: This is zero Hence this is zero Straight line relation Hence lower risk for diversified portfolio (if assets not perfectly correlated)

The Capital Assets Pricing Model Fall in sR due to diversification when investments are not perfectly correlated

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

Fred Nurk Jane Nguyen Bill Gates sR sR sR Z Z Z CSR IBM IBM BHP CSR IBM BHP BHP CSR ER ER ER P P P 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… • How to go from theory of individual investor to theory of market?... • You guessed it… • Sharpe assumes all investors are (almost!) identical...

Behavioural Finance