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

Acknowledgements Ran Tao Profiling Richard Olsen Inventor Han Ao Demonstrator

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 – : US$ unlinked with gold – : Smithsonian Agreement: fixed exchange rate –1973: Fluctuating fiat currencies Not by snapshots at end of each year

How Price Movements Are Recorded Interval-based summary

Problem with interval-based Summary Important movements not captured

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

Directional Changes Definition Threshold (%)Directional ChangesOvershoots See video for more information

DC-based Summary Threshold (%)Directional ChangesOvershoots Down- ward Trend Upward Trend Down- ward Trend See video for more information

Why Directional Changes?

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

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

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

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

DC-based Market Analysis Tools Olseninvest.com

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,

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

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?

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

Supplementary Information

5% Directional Changes (DC) Day 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

Definitions

Directional Change Events Overshoot Events

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.

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

Resources OANDA Tools – Long-short ratios Order book Heatmap (based on directional changes) Heatmap (weekly, monthly, yearly) OlsenScale

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

Shaimaa Masry Deciphering Market Activity Along Intrinsic Time

Diminishing Activities in a Trend

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 

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 

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

How Long is a Coastline?

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

Case Study Contrasting Time Series and Directional Changes

Daily Closing Analysis BTHSBCRDS Sept 2014 Daily Log Returns Standard Deviation Feb 2015 Daily Log Returns Standard Deviation

Daily Closing Prices Analysis

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 # Trends Price changes 99%108%96%95%96%104% μ OSV EXT (in θ) μ T (in sec) Coastline (in θ)