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Behavioural Finance

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.

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Behavioural Finance

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  1. Behavioural Finance Lecture 03 Part 02 Finance Markets Behaviour

  2. 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)

  3. 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…

  4. 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:

  5. Thrill seeker... Risk neutral… Highly risk-averse The Capital Assets Pricing Model

  6. 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:

  7. Capital market line The Capital Assets Pricing Model Range of efficient assetcombinations after market price adjustments: more than just one efficient portfolio

  8. 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”

  9. 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

  10. 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:

  11. Risk peculiar to asset i Higher return for assets more strongly affected by trade cycle (systematic risk) The Capital Assets Pricing Model

  12. 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.”

  13. 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…

  14. 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...

  15. 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)

  16. 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?

  17. The CAPM: Evidence • Volatile but superficially exponential trend • As it should be if economy growing smoothly But looking more closely...

  18. 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

  19. 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”…

  20. The CAPM: Evidence 21 years ahead of trend... • 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 Tracking sideways for a decade... 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 1949-1966: Minsky’s “financial tranquility” CAPM fit to this data looks pretty good!

  21. 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

  22. Anomalies mount… • Behavioural “anomalies”—people not maximising expected return—initially explained by “preference for risk” • “Choose between • $1000 with certainty; OR • 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”…

  23. Anomalies mount… • Problem 1: Choose between two alternatives: • A: do nothing • B a gamble with: • 50% chance of winning $150; • 50% chance of losing $100. • Problem 2: Choose between two alternatives: • A: Lose $100 with certainty • B: a gamble with: • 50% chance of winning $50; • 50% chance of losing $200 • Record your choices…

  24. Anomalies mount… • Did they look like this?: • Or this? • Or this? • 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…

  25. 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:

  26. 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…

  27. Anomalies mount… • Problem 3. Choose between: • A: Lose $45 with certainty • B: 50% chance of -$100 and 50% chance of $0 • Problem 4. Choose between: • A: 10% chance of -$45 and 90% chance of $0 • B: 5% chance of -$100 and 95% chance of $0 • A is “rational choice” in both cases: • A/B choice pair gives expected utility reversal…

  28. 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

  29. 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

  30. 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…

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