More Step Three back-testing results. Trade entry threshold range is extended.

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Written by Forex Automaton   
Monday, 17 August 2009 13:18

In the previous back-testing report featuring the "ultimate" scenario of multi-market analysis coupled with multi-market competitive portfolio management system, I noticed that one of the key optimization variables, the trade-entry threshold, does not reach the optimum value at what used to be the optimum in the single-market analyses. In this report, the range of entry-threshold parameters has been extended to reach the expected optimum, but there is still no hard evidence that the optimum has been capped within the range.

The basic framework remains the same: a run of the program included simulations of trading histories of 5184 independent "virtual traders" (forex robots), each of them being an incarnation of the same algorithm, differing by the setting of the adjustable knobs. As in all other published studies so far, the trading is performed on one-decision-a-day time scale, with 1:100 leverage, risking no more than 10% of the trading capital at any point in time. The robots simulateneously analyze and simultaneously trade the six major currency pairs, EUR/USD, USD/JPY, GBP/USD, USD/CHF, USD/CAD and AUD/USD. This report uses the day scale data covering the time interval from August 20, 2002 to March 23, 2009, with the actual trading starting in March 2006 (when the initial "training" of the system was completed). The key concepts of conditional projection distributions and profile histograms have been explained before. The trading system control parameters remain as previously defined.


Money management for the individual markets



Pattern analysis for the individual markets


Step One

Step Two



You are here: Step Three.

Table 1. Various modes of the trading system operation. The present report deals with the configuration denoted as Step Three, which is supposed to be the best.

Table 1 helps explain where Step Three stands among the various test modes used in the simulated back-testing studies performed so far.

Annualized return vs stop-loss parameter. Back-testing results shown as a profile histogram.

Fig.1. Mean annualized return vs stop-loss parameter. Back-testing results in Step Three mode are shown as a profile histogram.

Considerable differences with Step One, the best studied option so far, begin with the very basic plots such as Fig.1, dependence of the mean annualized return on the stop-loss parameter. The dependence is much simpler than what was typically seen in similar dependencies in Step One. Unlike Step One, the relative performance of tighter stop-losses is much worse. No sweet spot is seen with tight stop-loss and conservative entry, unlike Step One, despite the fact that we are looking at the same (and in case of the entry parameter, even wider) parameter range. It is possible that the sweet spot migrated towards even more conservative entry threshold values in this regime. The fact that the average profitablity is negative in Fig.1 is normal, since we already know that the profitable regimes occupy a compact but tiny fraction of the overall volume in the parameter space.

Mean position duration vs stop-loss parameter. Back-testing results shown as a profile histogram. Annualized return vs entry-threshold parameter.  Back-testing results shown as a profile histogram.

Fig.2. Top: mean position duration (days) vs stop-loss parameter. Bottom: mean position duration (days) vs entry-threshold parameter. Back-testing results shown as a profile histogram.

One of the main features of the Step Three mode, as compared to Step One, is the competition between trade ideas in different market for the portfolio capital. Fig.2 illustrates the effect of the stop-loss and entry threshold parameter on the mean life time of a trading position. Note that a trade idea may include multiple trading positions of different life time as the risk is being continually managed and the up-coming trade ideas compete for the capital. Obviously a high entry threshold makes it more difficult for a trade idea to even get considered, let alone become accepted. High competition with other trade ideas (low values of entry threshold) reduces the life time of a position, as seen in the figure. The effect of stop-loss parameter is obvious. The typical values of the position duration are much lower than seen for the same values of stop-loss in Fig.2.1 of the Step One report. This fact has to be attributed almost entirely to the availability of multiple markets for trading and competitive capital allocation among them.

Annualized return vs entry-threshold parameter.  Back-testing results shown as a profile histogram. Annualized return vs the forecasting parameter.  Back-testing results shown as a profile histogram.

Fig.3. Top: Mean annualized return (1=100%) vs entry-threshold parameter, for the selected ranges of the forecasting parameter. Back-testing results shown as a profile histogram. Bottom: Dependence of the mean annualized return (1=100%) on the forecasting parameter for the selected ranges of the entry threshold. Back-testing results shown as a profile histogram.

As usual in these reports, the nature of the forecasting parameter, called Fred, will not be disclosed. As compared to the first Step Three report, the extension of the entry threshold range does not seem to have improved the returns much so far. Typically, the plots like Fig.3, top, have an asymmetric bell-like shape: both lack of selectiveness in the trade ideas and extreme conservatism lead to decreased profits, the top of the bell being the spot where the threshold of conservatism is high enough so that no nonsese ideas are accepted while at the same time this threshold is low enough so that trades are still placed at all. There is no indication that we have reached the top: only the left side of the bell is currently visible.

Another very interesting development (especially if you knew what Fred really is) is the fact that with the entry threshold being high enough, a secondary maximum at very low values of Fred becomes more and more pronounced. To see that, compare different colors in the bottom panel of Fig.3. In the top panel, the same effect is seen in the difference of curves formed by the magenta and green data points. The overall improvement brought about by the more conservative entry thresholds is spread over a wide range of Fred values -- of course, a welcome development, since this makes it harder to end up with a wrong one when the ultimate choice is made.

In summary, this is a work-in-progress state of affairs in the most CPU-intense operating mode under study so far. The subsequent reports will aim to finalize the optimization, compare and understand the relative return/risk benefits and disadvantages of the three modes listed in Table 1 and clarify the choices for our first live day-scale forex trading system.

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Last Updated ( Monday, 04 January 2010 12:30 )