Why Stock Markets Crash

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)

16. Example: .

17. 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).

18. Long time scale patterns

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

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

21. Drawdown distribution

22. Drawdown distribution

23. Largest drawdowns

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

25. Confidence interval

26. Stretched exponential model

27. Power laws (Mantegna & Stanley, 1995)

28. Power laws (Mantegna & Stanley, 1995)

29. 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.