# Directional Changes A new concept for summarising price movements Edward Tsang Presenter Richard Olsen Inventor Han Ao Demonstrator.

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Directional Changes A new concept for summarising price movements Edward Tsang Presenter 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 –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 years

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

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, 599-614

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 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

Directional Change Example (1) First we define what we consider a significant price change –Suppose we consider 5% to be significant Suppose the price of an asset in day 1 is 100 We don’t know whether we are in an upward or downward trend If the price goes to 105, then we conclude that the market is in an upward trend If price goes to 95, we’re in a downward trend

Directional Change Example (2) Suppose on day 2, price is 95. So we are on a downward trend In a downward trend, we record the lowest price –Currently, the lowest price is 95 Suppose on day 3 the price goes up to 98 –It is not 5% above 95, hence no directional change Suppose price drops to 90 on day 4 –We are still in a downward trend –We record 90 as the lowest price Let price go up to 92 on day 5 –We are still in a downward trend

Directional Change Example (3) If price goes to 96, then we conclude that a directional change has happened –Because 96 is >5% above 90 Now we confirm that 90 (day 4) was an extreme point At day 4, the downward trend ended –At day 4, the upward trend started In an upward trend, we record the highest price –Currently the highest price is 96 –(Not 100 in day 1) We are now looking for a downturn directional change

Directional Change Example (4) Suppose subsequent price change are: 99, 97, 105, 110, 108, 104 104 is more than 5% below 110, the highest recorded price So we conclude at 104 a downturn directional change –110 was an extreme point We define the price changes from 90 to 95 a directional change event The price changes from 95 to 110 an overshooting event These events summarise market movements

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.

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

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 –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

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

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