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  1. 1. Why Stock Markets Crash
  2. 2. Why stock markets crash? <ul><li>Sornette’s argument in his book/article is as follows: </li></ul><ul><li>The motion of stock markets are not entirely random in the ’normal’ sense. </li></ul><ul><li>Crashes in particular are ’abnormal’ and have a certain statistical signature. </li></ul><ul><li>A plausible model of trader behaviour during crashes is based on ’copying’ or ’herd mentality’. </li></ul><ul><li>The statistical signature produced by such models is close to that seen in the markets. </li></ul><ul><li>Fitting parameters of copying models to stock market data gives a reasonable fit. </li></ul><ul><li>Sornette and his colleagues have predicted the occurance of particular crashes. </li></ul>
  3. 3. Mathematics applied to social sciences <ul><li>Sornette’s argument in his book is as follows: </li></ul><ul><li>The motion of stock markets are not entirely random in the ’normal’ sense (observation) . </li></ul><ul><li>Crashes in particular are ’abnormal’ and have a certain statistical signature (observation/statistics) . </li></ul><ul><li>A plausible model of trader behaviour during crashes is based on ’copying’ or ’herd mentality’ (model) . </li></ul><ul><li>The statistical signature produced by such models is close to that seen in the markets (solution) . </li></ul><ul><li>Fitting parameters of copying models to stock market data gives a reasonable fit (data fitting) . </li></ul><ul><li>Sornette and his colleagues have predicted the occurance of particular crashes (prediction) . </li></ul>
  4. 4. Mathematics applied to social sciences <ul><li>Sornette’s argument in his book is as follows: </li></ul><ul><li>The motion of stock markets are not entirely random in the ’normal’ sense (observation) . </li></ul><ul><li>Crashes in particular are ’abnormal’ and have a certain statistical signature (observation/statistics) . </li></ul><ul><li>A plausible model of trader behaviour during crashes is based on ’copying’ or ’herd mentality’ (model) . </li></ul><ul><li>The statistical signature produced by such models is close to that seen in the markets (solution) . </li></ul><ul><li>Fitting parameters of copying models to stock market data gives a reasonable fit (data fitting) . </li></ul><ul><li>Sornette and his colleagues have predicted the occurance of particular crashes (prediction) . </li></ul>
  5. 5. Course Outline <ul><li>Short, Medium and Long Term Fluctuations </li></ul><ul><li>Pricing Derivatives (Johan Tysk) </li></ul><ul><li>Positive feedbacks, negative feedbacks and herd behaviour. </li></ul><ul><li>Networks and phase transitions. (Andreas Grönlund) </li></ul><ul><li>Log-periodicity and predicting crashes. </li></ul><ul><li>Stock Market Crash Day. </li></ul>
  6. 6. The Dow Jones 1790-2000
  7. 7. The Dow Jones 1980-1987
  8. 8. Short, Medium & Long Term Fluctuations in Returns <ul><li>Returns are usually defined as (p(t+dt)-p(t))/p(t) . </li></ul>
  9. 9. Short term fluctations
  10. 10. Autocorrelation
  11. 11. Trading strategy <ul><li>Can use correlation with past to predict the expected future. </li></ul><ul><li>Profit is determined by standard deviation of return fluctuations (say approx 0.03%). </li></ul><ul><li>Invest $10,000, 20 trades a day, 250 days a year: 10000*(1.0003) 5000 =$44,806 (!). </li></ul><ul><li>But transaction cost must be less than $3 per $10,000. </li></ul>
  12. 12. Medium term fluctations
  13. 13. Medium term fluctations
  14. 14. Efficient market hypothesis <ul><li>(Samuelson 1965) </li></ul>
  15. 16. Example: .
  16. 17. Efficient market hypothesis <ul><li>Axiom of expected price formation based on rational, all-knowing agents. </li></ul><ul><li>Noise generated by underlying noise in the value of the world (similar variance). </li></ul><ul><li>Any irrational, ill-informed agents will generate more noise, but will over time be pushed out the market by rational agents. </li></ul><ul><li>Relies on agents not using Y t in their pricing of futures (no copying each other). </li></ul>
  17. 18. Long time scale patterns
  18. 19. Hidden patterns? <ul><li>Autocorrelation does not detect all patterns. </li></ul>
  19. 20. Hidden patterns? <ul><li>Autocorrelation does not detect all patterns. </li></ul><ul><li>Look at drawdowns instead. </li></ul>
  20. 21. Drawdown distribution
  21. 22. Drawdown distribution
  22. 23. Largest drawdowns
  23. 24. Constructing a confidence interval <ul><li>Take all days of time series and reshuffle them. </li></ul><ul><li>Find the distribution of resulting drawdowns. </li></ul>
  24. 25. Confidence interval
  25. 26. Stretched exponential model
  26. 27. Power laws (Mantegna & Stanley, 1995)
  27. 28. Power laws (Mantegna & Stanley, 1995)
  28. 29. Summary <ul><li>Costs too high to gain from short term correlations. </li></ul><ul><li>Medium term fluctations are usually exponentially distributed. </li></ul><ul><li>In the long term there are occasional drawdowns (crashes) which are inconsistent with the exponential model. </li></ul><ul><li>Other apparent structures in the market. </li></ul>

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