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A behavioral Model of financial Crisis

A behavioral Model of financial Crisis. Taisei Kaizoji International Christian University, Tokyo. Advance in Computational Social Science National Chengchi University, Taipei, November 3, 2010. The Aim. To propose a behavioral model of bubble and crash.

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A behavioral Model of financial Crisis

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  1. A behavioral Model of financial Crisis Taisei Kaizoji International Christian University, Tokyo Advance in Computational Social Science National Chengchi University, Taipei, November 3, 2010

  2. The Aim • To propose a behavioral model of bubble and crash. • To give a theoretical interpretation why bubbles is • born and is unavoidably collapsed • To give a possible solution on Risk Premium Puzzle

  3. Internet Bubble and Crash in 1998-2002 Period I Period II Internet Stocks: 10 (1998/1/2) 140 (2000/3/6): Peak 3 (2002/10/9): Bottom 14 1/50 Non-Internet Stocks: 10 (1998/1/2) 14 (2000/3/3): Peak 9.8 (2002/10/9) 1.4 0.7 Period I: 1998/1/2-2000/3/9 Period II: 2000/3/10-2002/12/31

  4. Price Changes Internet Stocks: Mean Variance Period I 0.2 4.1 Period II -0.2 2.5 Period I Period II Non-Internet Stocks: Mean Variance Period I 0.007 0.01 Period II -0.004 0.02 Covariance: Period I 0.09 Period II 0.13 Period I: 1998/1/2-2000/3/9 Period II: 2000/3/10-2002/12/31

  5. Probability Distributions of Price-Changes Abnormality of Internet stocks • leptokurtic • fat-tailed

  6. Who Invested in Internet Stocks? Empirical Evidence (1) • Hedge funds: • Ex. Soros Fund Management, Tiger Management, • Omega Advisors, Husic Capital Management, and • Zweig Di-Menna Associates • Brunnermeier and Nagel (2004) • “Hedge Funds and the Technology Bubble,” • Journal of Finance LIX, 5.

  7. Riding Bubble? “Hedge Funds captured the upturn, but, by reducing their positions in stocks that were about to decline, avoided much of the downturn.” Brunnermeier and Nagel (2004)

  8. Who Invested in Internet Stocks? Empirical Evidence (2) Inexperienced young fund manager Inexperienced Investors and Bubbles Robin Greenwood and Stefan Nagel (2008), forthcoming Journal of Financial Economics.

  9. Who invested in internet stocks? • Younger managers are more heavily invested in technology stocks than older managers. • Younger Managers increase their technology holdings during the run-up, and decrease them during the downturn. • Young managers, but not old managers, exhibit trend-chasing behavior in their technology stock investments. Robin Greenwood and Stefan Nagel (2008)

  10. Who invested in internet stocks?Experimental Evidence Traders’ Expectations in Asset Markets: Experimental Evidence Haruvy, E., Lahav, Y., and C. Noussair, Forthcoming in the American Economic Review (2009)

  11. Bubbles and Crashes in Experimental Markets (a) The bubble/crash pattern is observed when traders are inexperienced. (b) The magnitude of bubbles decreases with repetition of the market, converging to close to fundamental values in market 4. Haruvy, E., Lahav, Y., and C. Noussair (2009)

  12. Experimental Evidence Participants’ beliefs about prices are adaptive. Haruvy, E., Lahav, Y., and C. Noussair (2009)

  13. Experimental Evidence The existence of adaptive dynamics suggests the mechanism whereby convergence toward fundamental values occurs. Haruvy, E., Lahav, Y., and C. Noussair (2009)

  14. Participants’ beliefs about prices are adaptive. Haruvy, E., Lahav, Y., and C. Noussair (2009)

  15. Answer I: Noise Trader Approach J. De Long, A. Shliefer, L. Summers and R. Waldmann: Positive Feedback Investment Strategies and Stabilizing Rational Speculation, Journal of Finance 45-2 (1990) pp. 379-395. In DSSW (1990), rational investors anticipate demand from positive feedback traders. If there is good news today, rational traders buy and push the price beyond its fundamental value because feedback traders are willing to take up the position at a higher price in the next period. Synchronization Failure: D. Abreu, and M. K. Brunnermeier, Bubbles and crashes, Econometrica 71, 2003, 173–204.

  16. Master Equation Approach: Noise traders’ herd behavior Collective Behavior of a large number of agents Weidlich, W. and G. Hagg (1983) Concept and Models of a Quantitative Sociology, Springer. Bubbles and Crashes: Lux, Economic Journal, 105 (1995) Kaizoji, Physica A (2000)

  17. The Setting of the Model • Assets traded • Bubble asset : • ex. Internet stocks • Non-bubble asset: • ex. Large stocks like utility stocks • Risk-free asset: • ex. Government bonds, fixed time deposits

  18. The Setting of the Model • Agents • Rational traders (Experienced managers) • (i) They hold a portfolio of three assets. • (ii) Capital Asset Pricing Model (CAPM). • (Mossin(1966), Lintner (1969)) • Noise traders (Inexperienced managers) • (i) They hold either risk-free asset or bubble asset. • (ii) Maximization of random utility function of • discrete choice (MacFadden (1974))

  19. Rational traders The expected value of wealth The variance of wealth References: John Lintner, The JFQA, Vol. 4, No. 4. (1969), 347-400. Jan Mossin, Econometrica, Vol. 34, No. 4. (Oct., 1966), pp. 768-783.

  20. Rational traders Demand for bubble asset Demand for non-bubble asset Price of bubble asset Price of non-bubble asset Price of risk-free asset Variance of the asset price change Covariance of the asset price change Expected Price of bubble asset

  21. The rational investor’sdemands where

  22. The rational investors’aggregate excess demands where

  23. Noise Traders Their preference: Random Utility Function: : Random variable : Deterministic part

  24. Noise-Trader’s Random Utility Function: : Random variable • Average preference: • Strength of Herding: • Momentum: ( Adaptive expectation)

  25. Probabilities The probability that a utility-maximizing noise trader will choose each alternative: under the Weibull distribution: McFadden, Daniel (1974)

  26. Transition Probabilities:

  27. The Master Equation:

  28. Representative Noise-Trader’s Behavior: The noise trader’s Aggregate Excess demands

  29. Bimodal: Unimodal:

  30. Market-clearing Conditions:

  31. Market-clearing prices：

  32. Maxima of stationary probability density distribution : peaks for maximum for minimum : peaks for maximum for minimum

  33. Unimodal:

  34. Phase Transition

  35. Mechanism of bubble and crash Bubble birth

  36. Mechanism of bubble and crash (continued) Crash!!

  37. A Example of the Model Simulation: s Price on bubble asset (Crash) Return Moment H Price on non-bubble asset

  38. Risk Premium Puzzle: Expected risk premium: E[r] = Risk Premium + Risk Free Rate

  39. A Model Simulation: Risk Premium Realized Return: Expected Discount Rate: The period of bubble: After burst of bubble:

  40. In Summary • Conditions for a bubble’s birth: • (i) to appear any new market and • (ii) a large number of inexperienced investors start to trade • the bubble assets that are listed in the new market. • Under the above conditions, as noise traders’ herd behavior destabilize the rational expectation equilibrium, and give cause to a bubble. • As long as the noise traders adopt a return momentum strategy, bubbles burst as a logical consequence. • After all, the rational investors can make a profit from a long-term investment, while the noise traders lose money.

  41. Example I: Internet Bubble NASDAQ: 1503 (1998/1/5) 5048 (2000/3/6): Peak 1140 (2002/9/23): Bottom 3.3 1/5 NASDAQ S&P500: 927 (1998/1/5) 1527 (2000/3/20): Peak 800 (2002/9/30): Bottom S&P500 1.6 1/2

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