Distribution of EUR/USD daily high and low during a day

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Written by Forex Automaton   
Tuesday, 09 March 2010 12:32

In my personal experience with the Danica system, the same situation repeated itself on multiple occasions: I enter trades, buying and selling at market as soon as possible after the day's forecast becomes available (9:08am Eastern time). Then there is a point when the profit is at a local maximum, usually before noon Eastern time. Things rarely become better after that point, and often keep deteriorating for hours. On the days of drawdowns, most stop-losses are hit during this time span, and then for hours, not much happens. Closing the trades before the nominal time interval of the system ends (day for Danica) is certainly a deviation from the system, but in what direction? Do I really improve the system if I close trades before noon?



Timing of daily high and low, EUR/USD, 2003-2009, CET 1.1 Timing of daily high, EUR/USD, 2003-2009 year by year, CET 1.2 Timing of daily low, EUR/USD, 2003-2009 year by year, CET 1.3

Fig.1. Distribution of time moments when EUR/USD daily high and low are achieved, 2003-2009. 1.1: high and low, all years added; 1.2: high only, all years separately; 1.3: low only, all years separately.

Tokyo 9 1011 1213 14 15 16 17 18 19 20 21 2223 0 1 2 3 4 5 6 7 8
Central Europe 123456789101112 13141516171819202122230
Greenwich 01234567891011 121314151617181920212223
Eastern US 19202122230123456 789101112131415161718

Table 1. Time zone conversion table. Seasonal time shifts, such as daylight saving time, may complicate the picture if the nations choose to enact them on different days, and are ignored.

The worst thing a trader can do is to buy at the day's high and sell at the day's low. (I talk about day scale to be specific but the same general discussion will apply to any time scale). Any deviation from that, such as trying very hard not to buy at the day's high and trying very hard not to sell at the day's low, should result in improvement, although by itself, it does not necessarily guarantee net profit: you may still have to close a trade with a loss, we are talking about not closing it with the greatest loss possible during the day.

The best thing to do is to buy at the day's low and sell at the day's high. The system gives one a fixed entrance point during the day, and with this constraint, the best thing to do is to enter as soon as the forecast is generated and exit at the point of maximum profit. For a long trade, that is day's high. For a short trade, that is day's low. This is more complex than a hypothetic system with a fixed step that has been studied quantitatively so far, since the exit point is not fixed a priori.

The key question is however, how do you know when the day high and day low arrives? It turns out that even though you can't know that for sure, the distribution of these instances in time has a high degree of predictability. Fig.1 histograms the moments of time daily extreme price levels (either low and high) are achieved. The horizontal axis is split into 24 bins, for 24 hours of the day. Bin boundaries are at 00:00, 01:00, and so on -- in Central European time.

Central European time is chosen for the following reason. Forex week begins, roughly speaking (since the volume increase is gradual) on Sunday 5pm and ends Friday 6pm Eastern time. It is convenient to define this week to consist of 5 full days, from 6pm Sunday to 6pm Friday New York time. When it's 6pm in New York, it's midnight in Berlin, Paris, Madrid, Rome, Geneva and Frankfurt. These cities use Central European Time or CET. The convenience of using CET is that one gets 5 non-interrupted, full 24-hour long trading days per week. Table 1 compares four time zones including major trading centers of the world.

The vertical axis of the histogram is simply the number of times, during the period of 2003-2009, when the daily high or low occurred within the specified time bin.

Here are some conclusions. First, there are three major activity peaks corresponding to Japan, Europe and the US. Second, active trading likely begins around 8am in the morning in each of these zones.  8am-9am Tokyo is the most likely time for the day's top or bottom in EUR/USD to be achieved, the hour between 8am and 9am Eastern time (New York) being the close second most likely time. The US activity pattern, in contrast to Japan, is characterized by near constancy for several hours, having a plateau between 8am and 11am Eastern time. A curious feature is that during the European trading, the most likely hour for day's high and the one for day's low are different.

A note added on January 14, 2011: one should be careful not to over-interpret the fact that the extremes of the daily range seem  relatively more likely to be achieved in the first and last hours of trading. The same effect has been seen in random walk data.

The two bottom panels of Fig.1 prove that the activity pattern reproduces itself with a fair degree of stability year after year.

For the hour-scale trading system currently under development, information such as this may help improve the system performance by eliminating time intervals with little profit potential from consideration.

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Last Updated ( Friday, 14 January 2011 13:16 )