Behavioural Finance Lecture 03 Finance Markets Behaviour Reading

Behavioural Finance Lecture 03 Finance Markets Behaviour

Reading Assignments Update • Assignments now linked to sources • When you open it and get 2 readings assigned: – Right click on each link & save them to your computer – Take detailed notes in Word (or equivalent) • As if reading them to prepare for an exam • Copy graphics etc. if needed – Once you’ve finished • Copy and paste your notes into v. UWS • Don’t worry if formatting, graphics lost etc. • Click on “Save” then “Finish” • I will simply scan to make sure you have read them both • If so you will get 2 marks • Purpose of assessment to have you read the references

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 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: Common Choices Class Choices “Rational” Choice Gamble A B Gamb le A 1 1 A 1 B 2 2 A 2 B 3 3 B Total 1 Total Gamble A B 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 1 x 1, 000= +$1, 000 0. 9 x$2, 000+ 0. 1 x-$1, 000= +$1, 700 B>A 2 1 x$0= $0 . 5 x$150 +. 5 x-$100= +$25 B>A 3 1 x-$100= -$100 . 5 x$50+. 5 x-$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”… N o. Reason… Campbelltown Class 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 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 B

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… Economic theory says rational is… “Rational” Choice Gamble Number A B 1 B 2 2 B 3 3 B 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. 100 x 1000=$1, 000 certain outcome per play; OR B. 90 x 2000+10 x-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 3 B is 90%. . . • But outcome of single throw will be +$2 K or -$1 K • 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 v. N&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, v. N&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” v. N&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 2 nd 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 1 1 1 2 1. 67 0. 67 3 2. 141 0. 471 4 2. 327 5 2. 399 N/A 60% odds of 2 1/0. 6=1. 67 bananas vs 40% of s… a n a 2 b f no banana o y t ili Ut i 78% odds of 3 1. 67/0. 78=2. 141 … s a n a b 3 Utility of 92% odds of 4 2. 141/0. 92 0. 186 97% odds of 5 2. 327/0. 97 0. 072 99% odds of 6 2. 399/0. 99

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 v. N&M ideas: • Expected Return • Expected Utility etc. – With existing economic theory • Indifference curves, etc. – To develop “Modern Finance Theory” in 1950 s & 60 s… • 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 appeared 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) s. R – 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 s. R) 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 s. Ra Perceived correlation of A – B contains investment B only with B • Expected return is ERb, (varies between -1 • Risk is s. Rb & +1) – C some combination of a of A & (1 -a) of B • ERc=a. ERa + (1 -a)ERb

The Capital Assets Pricing Model • If rab=1, C lies on straight line between A & B: This is 1

The Capital Assets Pricing Model • If rab=1, C lies on straight line between A & B: This can be factored

The Capital Assets Pricing Model • If rab=1, C lies on straight line between A & B: Identical to straight line relation 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

The Capital Assets Pricing Model • If rab=0, C lies on curved path between A & B:

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

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

The Capital Assets Pricing Model • Sharpe assumes riskless asset P with ERP=pure interest rate, s. RP=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 Pf. Z 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 s. R Z CSR IBM BHP P s. R IBM Z BHP CSR ER P ER s. R 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. . .

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 methodology lecture… • 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 – Pf. Z 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 Pf. Z 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 • 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. ” [OREF II]

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 (see OREF II) • 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 1970 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

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 1 st 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 1 st 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 Crash of ’ 73: 45% fall in 23 months… Sharpe’s paper published Jan 11 ’ 73: Peaks at 1052 Dec 12 1974: bottoms at 578 Bubble takes off in ‘ 82… CAPM fit doesn’t look so hot any more… Steady above trend growth 19491966: Minsky’s “financial tranquility” CAPM fit to this data looks pretty good!

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 v. N&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? 1. Risk Averse Problem Number Choice A 1 X 2 Total 2. Risk Seeking B Problem Number A 1 X X 2 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 v. N&M (numerical utility) terms…

Anomalies mount… • If people normally choose A over B in Problem 1 then: – U($0) > U(0. 5 x$150+0. 5 x-$100) • Using v. N&M axioms we can rewrite this as: – U($0) > 0. 5 x. U($150)+0. 5 x. U(-$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. 5 x$50+0. 5 x-$200) • Using v. N&M axioms we can rewrite this as: – U(-$100) < 0. 5 x. U($50)+0. 5 x. U(-$200) – “Utility of zero is less than 0. 5 times utility of $50 plus 0. 5 times utility of -$200” • Inconsistent in v. N&M terms because axioms are linear in money: adding fixed sum shouldn’t alter outcome:

Anomalies mount… • If U(-$100) < U(0. 5 x$50+0. 5 x-$200), then add $100: • Then U($0) < U(0. 5 x$150+0. 5 x-$100) – U($0) < 0. 5 x. U($150)+0. 5 x. U(-$100) • So if someone chooses A over B in Problem 1, v. N&M say: – U($0) > 0. 5 x. U($150)+0. 5 x. U(-$100) • And if they choose B over A in Problem 2, v. N&M say: – U($0) < 0. 5 x. U($150)+0. 5 x. U(-$100) • These are inconsistent: • Preference reversal even in v. N&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. 5 x-$100=-$50 4 0. 1 x-$45=-$4. 5 0. 05 x-$100=-$5 X 4 X Total 1 1 • A/B choice pair gives expected utility reversal…

Anomalies mount… • • • Choosing 3 B implies that: U(-$45) < U(0. 5 x-$100+0. 5 x$0); or 1. 0 x. U(-$45) < 0. 5 x. U(-$100) + 0. 5 x. U($0) Choosing 4 A implies that: U(0. 1 x-$45 + 0. 9 x$0) > U(0. 05 x-$100 + 0. 95 x$0); or 0. 1 x. U(-$45) + 0. 9 x. U($0) > 0. 05 x. U(-$100) + 0. 95 x. U($0) – Subtract 0. 9 x. U($0) from both sides to yield: • 0. 1 x. U(-$45) > 0. 05 x. U(-$100) + 0. 05 x. U($0) – Multiply both sides by 10 to yield: • 1. 0 x. U(-$45) > 0. 5 x. U(-$100) + 0. 5 x. U($0) • Since most people choose 3 B and 4 A, this implies • 1. 0 x. U(-$45) < 0. 5 x. U(-$100) + 0. 5 x. U($0) AND • 1. 0 x. U(-$45) > 0. 5 x. U(-$100) + 0. 5 x. U($0): contradiction

Anomalies mount… Your Choices? • Or is it? Choice – “Contradiction” disappears if Problem A B examples applied as v. N&M insisted they should be… 5 • Problem 5. Choose between 100 6 repeats of either: Total – A: Lose $45 with certainty OR Expected Return over 100 – B: 50% chance of -$100 and plays 50% chance of $0 Problem Choice • Problem 6. Choose between 100 A B repeats of either: 5 -$4500 -$5000 – A: 10% chance of -$45 and 6 -$450 -$500 90% chance of $0 OR – B: 5% chance of -$100 and 95% chance of $0

From risk to uncertainty • v. N&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…