

Revisiting the Day Range Strategy. Part 1. 
Written by Forex Automaton  
Wednesday, 16 June 2010 15:52  
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. One of conclusions of the previous strategy research report was that one has to find a way to benefit from the high stability of quality forecasts for daily extremes (high and low) while minimizing the exposure to the forecast of daily close. One way to do that is trading with the profit target on the basis of forecasts for daily extreme levels (high and low) alone. This report begins a series dedicated to just such a strategy. The research will culminate in a launch of a new model trading system (this time with a trade signal and a simulated portfolio of some sort!) which will complement Danica. A trading strategy relying on Danica's output and attempting to limit risk by placing a profit target on the previous day's extreme has been analyzed already in February 2010 soon after the Danica launch. Here are the key differences between that approach and the uptodate one:
Algorithmically speaking, the strategy under study (which may be referred to as Day Range, ClosetoLimit or OpentoLimit) consists in the following:
You exit the trade in one of the three ways:
Placing a trade with a very tight profit target and a generous stop loss is something that novice traders are tempted to do after they have discovered the disastrous effect of a tight stoploss. In terms of Fig.1, such trades would land close to zero along the axis labeled "dist. to profit" and farther away from zero along the axis labeled "dist. to stop". As you see, this area hosts a net loss (blue "water" in the landscape), and any hypothetic strategy combining low profit potential and high loss potential is to be avoided. On the contrary, the area of trades with a ratio of potential profit to potential loss above one is the "mountaineous area" in the landscape, resulting in net profit. The way to go therefore is to accept or reject trade setups on the basis of the balance between distance to profit and distance to loss, favoring situations with high profit potential relative to loss potential. In what follows, the following trigger condition was used to formalize this: the ratio of distance to profit to distance to loss (both positive quantities) was required to be above 11/9  a number found empirically after inspecting the histogram in Fig.1. Note that this is similar to the selection condition found and reported in the article Further analysis of the dayrange strategy... posted in February. The algebra of profit and loss in trading on a margin (follow the link for details) has been discussed before. The same notation is used here. If total trading capital is C, its increment per time step of the system (day for Danica system) is dC, then
where p is current price quote, dp is its increment during the time step, a is stoploss placement as a fraction of price quote p, and k is fraction of capital to be lost in the event a stoploss is triggered. Note that cost of capital is also ignored, and leverage does not appear in Eq.1 unless one becomes concerned with the cost of capital. Note that stoploss in this strategy is situational rather than fixed: it depends on the location of the previous day's low and high with respect to close, and takes advantage of the fact that one of the previous day's extremes will not be touched while the other will be. Therefore, the quantity a is not a fixed quantity, it s not exist as a system parameter. Instead,
where p_{s} denotes the price level of protective stop. Then,
Note that when the modulus sign around p  p_{s} is removed, the formula becomes valid for both long and short trades. Eq.1 ignores spread (assumes it is zero)  this does deserve a special discussion, but not in this post. With these two ingredients, 1) the selection condition (trigger) and 2) a choice of k, simulating the strategy performance becomes a matter of program execution. In this run, trading was simulated to begin on April 15, 2006 (after the initial learning of the system was over) and lasted till June 05, 2010. I emphasize that a significant fraction of the data is used in the learning and not in trading because the system must be and is limited to "past" data only. Of course, here "past" is past in the context of simulation, too, which is why I put quotes on it. In the course of the simulation, the time interval of backtest trading is split into five subintervals, nonoverlapping and of equal length. At the beginning of each such interval, the trading capital is set by hand to be 1. As trading days go by, it is incremented to reflect the ongoing gains and losses. At the end, the five intervals can be compared directly since their starting conditions are identical. That way, not only the performance itself but its stability in time becomes clearly visible. In the process, each forex pair is treated as having its own dedicated trading capital, set to unit at the beginning of the period, which evolves independently. Comparing the performances of these 14 independent evolutions is one way of arriving at an estimate of the overall reliability, sustainability of performance and risk level of the strategy. In Fig.2, the performance of the 14 independent forex pairs is aggregated in the usual way by using a profile histogram: the data plotted are the estimated mean and its precision after averaging the data for the forex pairs treated as independent. So you won't see trading system performance for the individual forex pairs. As for the amount to risk per trade, the k in the equations, it is currently a fixed proportion of the trading capital. Fig.2 presents data for k=1, 2 and 3%. 2.1 2.2 2.3 In Fig.2, logarithmic scale on the Fred axis has been applied to enable close inspection of the area of low Fred where the most attractive results are obtained  and where more data points have been measured. To put Fig.2 in context, the maximum of predictability would lie at or near Fred=33. (Which happens to be the number currently used in Danica, which is why Danica is not the best system for this strategy.) This value of Fred is clearly not the maximum of profitability. Naturally, higher allocation coefficients (consistent with higher leverage) result in higher profits. Stability of the results is remarkably good  indeed, based on the high stability of the forecasting quality for daily extremes, and given the fact that the strategy ignores the nottooreliable forecast for daily close, this outcome is not surprising. In the subsequent articles, the system will be elaborated, and the following, currently open, issues will be addressed:


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