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Why Stock Markets Crash

Why Stock Markets Crash. Why stock markets crash?. Sornette’s argument in his book/article is as follows: The motion of stock markets are not entirely random in the ’normal’ sense . Crashes in particular are ’ abnormal ’ and have a certain statistical signature .

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Why Stock Markets Crash

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  1. Why Stock Markets Crash

  2. Why stock markets crash? Sornette’s argument in his book/article is as follows: • The motion of stock markets are not entirelyrandom in the ’normal’ sense. • Crashes in particular are ’abnormal’ and have a certainstatisticalsignature. • A plausible model of trader behaviourduringcrashes is based on ’copying’ or ’herdmentality’. • The statisticalsignatureproduced by suchmodels is close to that seen in the markets. • Fitting parameters of copyingmodels to stock market data gives a reasonablefit. • Sornette and his colleagueshavepredicted the occurance of particularcrashes.

  3. Mathematicsapplied to social sciences Sornette’s argument in his book is as follows: • The motion of stock markets are not entirelyrandom in the ’normal’ sense(observation). • Crashes in particular are ’abnormal’ and have a certainstatisticalsignature(observation/statistics). • A plausible model of trader behaviourduringcrashes is based on ’copying’ or ’herdmentality’ (model). • The statisticalsignatureproduced by suchmodels is close to that seen in the markets (solution). • Fitting parameters of copyingmodels to stock market data gives a reasonablefit(data fitting). • Sornette and his colleagueshavepredicted the occurance of particularcrashes(prediction).

  4. Mathematicsapplied to social sciences Sornette’s argument in his book is as follows: • The motion of stock markets are not entirelyrandom in the ’normal’ sense(observation). • Crashes in particular are ’abnormal’ and have a certainstatisticalsignature(observation/statistics). • A plausible model of trader behaviourduringcrashes is based on ’copying’ or ’herdmentality’ (model). • The statisticalsignatureproduced by suchmodels is close to that seen in the markets (solution). • Fitting parameters of copyingmodels to stock market data gives a reasonablefit(data fitting). • Sornette and his colleagueshavepredicted the occurance of particularcrashes(prediction).

  5. Course Outline • Short, Medium and Long Term Fluctuations • Pricing Derivatives (Johan Tysk) • Positive feedbacks, negative feedbacks and herd behaviour. • Networks and phase transitions. (Andreas Grönlund) • Log-periodicity and predicting crashes. • Stock Market Crash Day.

  6. The Dow Jones 1790-2000

  7. The Dow Jones 1980-1987

  8. Short, Medium & Long Term Fluctuations in Returns Returns are usually defined as (p(t+dt)-p(t))/p(t).

  9. Short term fluctations

  10. Autocorrelation

  11. Trading strategy • Can use correlation with past to predict the expected future. • Profit is determined by standard deviation of return fluctuations (say approx 0.03%). • Invest $10,000, 20 trades a day, 250 days a year: 10000*(1.0003)5000 =$44,806 (!). • But transaction cost must be less than $3 per $10,000.

  12. Medium term fluctations

  13. Medium term fluctations

  14. Efficient market hypothesis (Samuelson 1965)

  15. Example: .

  16. Efficient market hypothesis • Axiom of expected price formation based on rational, all-knowing agents. • Noise generated by underlying noise in the value of the world (similar variance). • Any irrational, ill-informed agents will generate more noise, but will over time be pushed out the market by rational agents. • Relies on agents not using Yt in their pricing of futures (no copying each other).

  17. Long time scale patterns

  18. Hidden patterns? • Autocorrelation does not detect all patterns.

  19. Hidden patterns? • Autocorrelation does not detect all patterns. • Look at drawdowns instead.

  20. Drawdown distribution

  21. Drawdown distribution

  22. Largest drawdowns

  23. Constructing a confidence interval • Take all days of time series and reshuffle them. • Find the distribution of resulting drawdowns.

  24. Confidence interval

  25. Stretched exponential model

  26. Power laws (Mantegna & Stanley, 1995)

  27. Power laws (Mantegna & Stanley, 1995)

  28. Summary • Costs too high to gain from short term correlations. • Medium term fluctations are usually exponentially distributed. • In the long term there are occasional drawdowns (crashes) which are inconsistent with the exponential model. • Other apparent structures in the market.

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