Comparing security market lines for the Step One and Step Two trading systems

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Written by Forex Automaton   
Wednesday, 16 September 2009 16:12
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Comparing security market lines for the Step One and Step Two trading systems
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I continue digesting results of the recent Step One and Step Two back-testing simulation runs. Today I am posting the risk vs return curves for the sets of virtual traders considered in the course of the optimization, comparing what might be called (by finance engineers) security market lines for the two modes of trading system operation. Then I zoom in on the range of trading system parameters where Step Two is seen to provide the greatest advantages.


Money management for the individual markets



Pattern analysis for the individual markets


Step One, .

Step Two, .



Step Three

Table 1. Various modes of the trading system operation. The present report presents a comparison of Step One with Step Two.

The basic framework remains the same: a run of the program included simulations of trading histories of about 5 thousand independent "virtual traders" (forex robots), each of them being an incarnation of the same algorithm, differing by the setting of the adjustable knobs. The algorithm learns continuously, but at any point in time, it may use only data from the past (and not the future) of the time series. For the forecasting parameter knob (so called Fred), the range of the settings is narrowed down to the best values on the basis of back-tested performance seen in the first set of Step One simulations, that range being 71 through 80.

As in all other studies posted here 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. This report uses the EUR/USD, USD/JPY, GBP/USD, USD/CAD, USD/CHF and AUD/USD day scale data covering the time interval from August 20, 2002 to August 21, 2009, with the actual trading starting in April 2006 (when the initial "training" of the system was completed). The trading system control parameters remain as previously defined.

The trading performance data are updated continuously and the mean annualized logarithmic return and its RMS are calculated on the monthly basis. These form the basis for the risk vs return approach to the trading system optimization. The rationale for using these measures of risk and return has been given before. Return vs risk analysis is done in the logarithmic variables, while the linear annualized return, an accountant's quantity you want to know, is used in parallel.

The simulations for this report have been performed with the most recent set of upgrades, documented separately and used in the most recent Step Two results. Step One and Step Two simulations cover exactly the same set of trading system parameters needed for an unbiased comparison.

Risk vs return. Step One/Two comparison. Back-testing results of a forex trading system shown as profile histograms.

Fig.1. Risk vs return view of Step One () and Step Two () modes of operation. RMS of the monthly series of logarithmic annualized returns serves as a risk measure, while the mean of the series serves as a measure of return.

Fig.1 is a variation on the security market line theme, using the Forex Automaton trading system back-testing data. Usually, they plot only one branch of the curve (the positive returns) and do it so that the vertical axis is that of return. In this profile histogram (a form of data presentation where the horizontal axis is split into bins and the statistical content is averaged within the bins) the axes are flipped so that positive and negative returns are separated and form different branches of the curve.

In Fig.1, the inverse slope of the curve, reflecting degree of return per unit of risk, is a measure of "portfolio management" quality. The ideal is to move points further to the right and at the same time down, and the predominant trends indicate that this is hard to do: one has to pay for an increase in return by the increase in risk. Among the losing traders, the big losers are also very risky traders, as Fig.1 indicates.

The overall advantage of Step two is seen very clearly in the positive branch of curve, which summarizes the performance of the winning parameter combinations on average. Not only do the yellow points advance further along the axis of returns, they do that while staying lower along the vertical axis. In other words, Step Two includes regimes which sport higher returns with reduced risks. Presumably this is paid for by the more sophisticated algorithm with the competitive trade idea selection from the multiple markets and dynamic rebalancing of the portfolio.

The above conclusion is true in an "integral" sense for the entire sets of parameters covered in the simulation. In practice, a trading algorithm operates with a single choice which needs to be made. A practical question therefore is to find the set of parameters which result in best returns with minimal risk. The next set of plots shows the Step One/Step Two comparisons for more narrow selections of parameters.

Last Updated ( Monday, 04 January 2010 12:28 )