Revisiting the Day Range Strategy. Part 2.

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Written by Forex Automaton   
Tuesday, 06 July 2010 15:02

Note added on July 28, 2010: the quantitative results presented in this report have been found to be affected by a bug in the analysis code and are consequently incorrect. This report is kept here for the sake of historical completeness only.

This report continues our efforts to document the progress in the Day Range Strategy as the strategy is on its way towards production version. The research version of our system, known as Danica, has demonstrated in the six months of live operation that the high degree of predictability for daily extremes (low and high) is a reality, not a backtesting artefact. The Day Range Strategy is designed to benefit from the high stability of forecasts for daily extremes while minimizing the exposure to the forecast of daily close, by placing a protective stop and a profit target.

The logic of the Day Range trading system is explained in detail in the previous post on the subject (Part 1 of this report). In short,

  • the system gives a "buy" signal when today's low is predicted to be above the yesterday's one, today's high is predicted to be above the yesterday's one, and the distance from today's open (which is the price to enter the market) to yesterday's high (which is the profit target) is somewhat (again, see the details in Part 1) larger than the distance from today's open to yesterday's low (which is the protective stop);

  • the system gives a "sell" signal in the situation which is a mirror reflection of the above.


The requirement of same predicted direction for the upcoming day's low and high will be referred to as L0 trigger.

In the back-testing simulations, we optimize the system by tweaking the parameter responsible for the prediction algorithm, nicknamed Fred. Every step of the back-testing run tests applicability of (then) past data for the (then) future, as at every step of the way the system can only access what is the "past" at that step.

The key good news of Part 1 was that by moving Fred away from the value which maximizes the correlation between predicted and real logarithmic returns (as measured by the Pearson correlation coefficient) towards lower values of Fred, one obtains much better profitability. This post, Part 2 on the subject, brings you the details on what exactly happens.

Three different Fred values are picked to run the backtesting simulations and the results are compared. The data for the 14 most popular forex pairs cover the time interval from 2002/08/20 through 2010/06/10.

Probability distribution of net profit/loss as a fraction of quote price. Tails are included. 1.1 Probability distribution of net profit/loss as a fraction of quote price. Central part of the distribution. 1.2


Fig.1. Probability distribution of net profit/loss as a fraction of quote. 1.1: tails are included. 1.2: central part of the distribution.

This type of variable to histogram, profit/loss relative to price, illustrates some basic features of the profit/loss distribution: the distribution has a two-peak structure and long tails; the tail of profits looks longer than the tail of losses; a loss is a lot more frequent than a profit. By taking frequent small losses and less frequent large gains one can obtain a positive balance. This fact known from the "cut your losses and let your winners run" traders' motto is illustrated here for those with graphical and quantitative inclinations.

Probability distribution of net profit/loss as a fraction of quote price. Tails are included. 2.1 Probability distribution of net profit/loss as a fraction of quote price. Central part of the distribution. 2.2


Fig.2. Probability distribution of net profit/loss as a fraction of the amount placed at risk. 2.1: tails are included. 2.2: central part of the distribution.

A realized profit/loss in a trade, relative to the amount at risk on a trade is more interesting. In the perfect world, when you hit the stop-loss, you loss a unit in terms of the variable plotted. That corresponds to the peak at -1. (In this simulation, every day is an entry and the histogram is filled with then-current profit/loss on the position, including spread, even if in the real life you would continue with the position for another day). There is a tail of larger losses due to the way spread is accounted for in the simulation code. A fairly fat real-life spread from a certain non-ECN broker is used. In these series of articles on the patterns of spread variation there a paragraph explaining how their tick data are used to infer spread. (Note that data in Table 1 ignore spread).

Importantly, in Fig.2 you see why Fred=10 gives better results: it has a better risk/reward profile, dominating the area of positive returns.

Table 1. Key statistics of the strategy for three values of the forecasting parameter Fred. The numbers in the table count "events" (an event being any forecast for any of the 14 forex pairs). 14 "events" happen every day the system has enough accumulated data to make predictions, in other words they happen continuously after the training time is over. The total number of events in this sample is 18,102 (1,293 days times 14 pairs), same for all three Fred values.

"Simulated growth of unit equity" is represents equity at the end of the simulated 1,293-day long trading period, taking one unit in the quote currency money for every pair to be the beginning equity. This estimate ignores slippage, commissions, spread and taxes. Precision of the mean is estimated by taking the RMS variation of results among the markets and dividing it by the square root of the number of markets, thus treating results for every market as independent measurements. All three versions of the strategy are executed with 1% of capital at risk per trade.

Fred passed L0 passed L0 and risk/reward cut passed L0 and risk/reward cut and made profit simulated growth of unit equity with estimated precision average and RMS profit or loss per trade as a fraction of price
10 15495 5029 1629 6.75+-2.09 0.000255, 0.00450
34 14165 2451 878 1.255+-0.0847 0.000194, 0.00527
90 13216 2766 1032 1.505+-0.115 0.000245, 0.00468

In table 1, key statistics for three versions of Day Range strategy, differing by an algorithmic parameter responsible for forecasting, are presented. Note that the difference in profitability is accomplished despite the similarity of risk: all three versions risk 1% of trading capital per trade. Since the location of the stop loss is set by the previous day's extreme (low or high for the long or short trade respectively) and varies, the position amount also has to vary to ensure fixed degree of risk.

From Table 1, I conclude that the main factor responsible for the higher profitability of Fred=10 is the following: among the events that have passed the L0 trigger, Fred=10 delivers a higher percentage of trade ideas passing the risk/reward quality cut. This percentage is roughly twice as high as in two other cases. This is consistent with the message of Fig.2.

A disturbing aspect of these data is the relatively thin margin by which the system would be able to beat the spreads: the 0.00025 number (average profit per trade as a fraction of quote) has to be compared with spread which in the same units would, for the 10 most liquid pairs with a broker such as Oanda, vary from 0.00008 (EUR/USD) to 0.00017 (EUR/AUD, EUR/CHF, USD/CHF) with EUR/GBP, EUR/JPY, GBP/USD, USD/JPY in between. In other words, a retail trader operating the system would have to share roughly half the profit with her broker.

For a large scale (institutional) operator, the spread may be lower but slippage would have to be taken into account and the picture could be comparable at the end of the day.

Nevertheless, the time stability of this strategy (analyzed in Part 1 of this report) is impressive and this is for now the main factor making it attractive. The potential of making the strategy more profitable by assigning more intelligent weights (capital allocation) to the trades (as was demonstrated for example in this report) remains completely untapped.

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Last Updated ( Tuesday, 17 August 2010 14:36 )