1. Directional Changes A new way to summarize price movements Edward Tsang Centre for Computational Finance and Economic Agents University of Essex

2. Acknowledgements Ran Tao Profiling Richard Olsen Inventor Han Ao Demonstrator

3. How History Is Recorded By key events –1918: £, US$, Franc, … unlinked with gold –1926: £ tied to gold, but only exchangeable in bars –1931: Floating exchange rates –1944: Bretton Woods: US$ as exchange standard –1971.08.15: US$ unlinked with gold –1971.12.18: Smithsonian Agreement: fixed exchange rate –1973: Fluctuating fiat currencies Not by snapshots at end of each year

4. How Price Movements Are Recorded Interval-based summary

5. Problem with interval-based Summary Important movements not captured

6. Directional Changes Richard Olsen Inventor Attempt to capture significant changes Where significance is user-defined

7. Directional Changes Definition Threshold (%)Directional ChangesOvershoots See video for more information http://www.youtube.com/watch?v=mbSbUKpWOnohttp://www.youtube.com/watch?v=mbSbUKpWOno

8. DC-based Summary Threshold (%)Directional ChangesOvershoots Down- ward Trend Upward Trend Down- ward Trend See video for more information http://www.youtube.com/watch?v=mbSbUKpWOnohttp://www.youtube.com/watch?v=mbSbUKpWOno

9. Why Directional Changes?

10. DC vs Interval Coastline With the same number of points DC captures significant changes missed by Intervals FTSE 100 June 2007 to October 2012

11. Potential for Profits Given perfect foresight: (Buy low, sell high) –Interval based return: 171% –DC-based return: 304% FTSE 100 June 2007 to October 2012

12. Potential for Profits Given perfect foresight: (Buy low, sell high) –Interval based return: 171% –DC-based return: 304% FTSE 100 June 2007 to October 2012 DC-based summaries have longer coastlines

13. Potential for Profits Given perfect foresight: (Buy low, sell high) –Interval based return: 171% –DC-based return: 304% FTSE 100 June 2007 to October 2012 DC-based summaries have longer coastlines Longer coastline  potential for higher profit

14. DC-based Market Analysis Tools Olseninvest.com

15. Statistical Properties Observed Average overshoot: same as threshold (approx.) Average overshoot time: approx. to 2×DC time t ≈2t t θ ≈θ θ DC OS Reference: Glattfelder, J.B., Dupuis, A. & Olsen, R. Patterns in high-frequency FX data: discovery of 12 empirical scaling laws, Quantitative Finance, Volume 11 (4), 2011, 599-614

16. DC-based Algorithmic Trading Can trading algorithms be derived around DC? Research in progress BuySell

17. Current Research Profiling –Stereo vision into the market Physical vs Event time Forecasting –What variables are relevant? Algorithmic trading –Data drive –What are the independent variables?

18. Conclusion History recorded by events, not snapshots at fixed intervals; so should market prices! Directional Change (DC) events defined –They capture ‘significant changes’ Useful for summarising price movements –DC give new perspectives in price movements DC enables discovery of regularities not captured by interval-based summaries –A rich, new world to be explored

19. Supplementary Information

20. 5% Directional Changes (DC) Day 1 104 102 100 94 98 96 92 90 110 108 106 Day 3Day 5Day 7Day 2Day 4Day 6Day 8Day 9Day 10Day 11Day 12 Directional Change Event Overshoot Event Increased >5%; DC confirmed Decreased >5%; DC confirmed Extreme point confirmed in hindsight (on Day 6) Upward Trend Downward Trend Confirmed extreme point Overshoot Event Directional Change Event Confirmation point Downward Trend Confirmation point This example shows what Directional Changes are, and how to find them

21. Definitions

22. Directional Change Events Overshoot Events

23. Directional Changes (DC) A Directional Change Event can be a –Downturn Event or an –Upturn Event. A Downward Run is a period between a Downturn Event and the next Upturn Event. An Upward Run is a period between an Upturn Event and the next Downturn Event.

24. DC in Different Time Systems Downturn Event Downward Overshoot Event Upturn Event Upward Overshoot Event Event-based system Point-based system Downturn Point Downturn Confirmation Point Upturn Point Upturn Confirmation Point Physical Time Line Downturn Event Interval Downturn Overshoot Interval Upturn Event Interval Upturn Overshoot Interval Interval- based system

25. Resources OANDA Tools –http://fxtrade.oanda.com/analysis/labs/http://fxtrade.oanda.com/analysis/labs/ Long-short ratios Order book Heatmap (based on directional changes) Heatmap (weekly, monthly, yearly) OlsenScale

26. Striking observation 17 scaling laws discovered so far, e.g. –When a directional change of r% occurs, it is on average followed by an overshoot of r% –The time for the overshoot to happen is also highly correlated to the time taken for the change of direction to happen! Further observation and analysis needed Machine learning needed for function fitting

27. Shaimaa Masry Deciphering Market Activity Along Intrinsic Time

28. Diminishing Activities in a Trend

29. NsDC(θ, d, k, t), Definition Directional Change Event Overshoot Event Upward Trend Directional Change Event θ T θ T/2 EXT NsDC(θ,2,2,0)NsDC(θ,2,2,1) Now NsDC(θ, d, k, t) = NDC(θ÷d, [Now-(T÷k)*(t+1), Now-(T÷k)*t] where NDC( ,  ) = number of DCs of threshold  over time period 

30. NsDC(θ, d, k, t), Definition Directional Change Event Overshoot Event Upward Trend Directional Change Event θ T θ θ/2 EXT NsDC(θ,2,2,0) NsDC(θ,2,2,1) Now NsDC(θ, d, k, t) = NDC(θ÷d, [Now-(T÷k)*(t+1), Now-(T÷k)*t] where NDC( ,  ) = number of DCs of threshold  over time period 

31. Theory of fractals Financial markets are fractal: statistical properties are self similar.

32. How Long is a Coastline?

33. Length of coastline Maximum profit opportunity after transaction costs with no leverage and perfect foresight Long coast line (>2,000%) means huge opportunities to be exploited! opportunities

34. Case Study Contrasting Time Series and Directional Changes

35. Daily Closing Analysis BTHSBCRDS Sept 2014 Daily Log Returns -0.000878-0.001842-0.001980 Standard Deviation 0.0074020.0083780.006893 Feb 2015 Daily Log Returns 0.004330-0.0027220.002344 Standard Deviation 0.0171760.0133470.015423

36. Daily Closing Prices Analysis

37. DC Profiles BT September 2014 BT February 2015 HSBC September 2014 HSBC February 2015 RDS September 2014 RDS February 2015 # Trades117,694208,920228,248256,000110,551188,581 # Trends59103559146124 Price changes 99%108%96%95%96%104% μ OSV EXT (in θ) 0.99181.00960.83710.91720.93300.9283 μ T (in sec) 120546317140457140157835204 Coastline (in θ) 115.52205.0699.17172.5186.96237.22