Six best Step Two robots are selected for closer inspection

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Written by Forex Automaton   
Wednesday, 23 September 2009 09:05

Having identified the range of parameters where a Step Two trading system has the greatest advantage over Step One (in the course of a Step One vs Step Two performance comparison), I proceed by narrowing down the range of adjustable system parameters even further. I select six "best" algorithmic traders for a more thorough examination, by forming a set of tighter system parameter selections, complemented with cuts on the figures of merit such as skewness of return distribution, the annualized return and the fraction of months with a negative return.

 

Money management for the individual markets

separate

joint

Pattern analysis for the individual markets

separate

Step One

You are here: Step Two

joint

test-only

Step Three

Table 1. Various modes of the trading system operation. The present report deals with selecting the best Step Two algorithmic trader(s).

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.

In the scatter plots shown below, each point represents a virtual trader.

Risk vs return. Selected Step Two forex trading systems. Back-testing results.

Fig.1. Risk vs return view of the performance of selected Step two trading systems. 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. NTFM in the legend stands for New Trade Frequency Mean, and this quantity is expressed in inverse days.

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. The black points, selected by requiring new trade frequency statistic for the trader to be between 0.2 and 1, are seen as the most successful in that. Red and blue points represent higher trading frequency selections. (To avoid misunderstanding, trading frequency is an output figure, not an input to the trading system algorithm).

Fraction of negative monthly returns vs mean logarithmic annualized return.  Selected Step Two forex trading systems. Back-testing results.

Fig.2. Fraction of negative monthly returns vs mean logarithmic annualized return. NTFM in the legend stands for New Trade Frequency Mean, and this quantity is expressed in inverse days. Each point represents a virtual trader.

Fig.2 shows that the new trade frequency classification translates well into a classification according to the fraction of monthly negative returns, with the fraction being the higher, the higher is frequency. Part of the reason for this is trivial, since months with no trades are possible with these low levels of trading activity. Such months however do not create positive returns, while the progression toward positive returns (from blue to red and black) is obvious as the fraction of "negative" months goes down.

Skewness of monthly log return distribution vs new trade frequency.  Selected Step Two forex trading systems. Back-testing results.

Fig.3. Skewness of the distribution of trader's monthly logarithmic returns as a function of new trade frequency (NTFM) in inverse days. Each point represents a virtual trader. The colors correspond to those in Fig.2 but are not as informative here since the color-coded selection is along the horizontal axis.

Skewness, shown now for the first time, is a measure of asymmetry of the distribution. Positive skewness is a sign of "positive" asymmetry such as may be caused by a tail extending into the area of positive returns. In the case of Fig.3, the distribution is that of logarithmic returns recorded every month. Black points (the lowest trading frequency) show the highest skewness as a group. Since the system lowers trading frequency  by limiting the actionable forecasts to those with the highest magnitude of the anticipated movement, it can be understood that lower frequency results in an increase in the skewness of the profit distribution -- provided of course that those forecasts are valuable. The results imply that the forecasts at the core of the system are valuable.

Skewness of monthly log return distribution vs trade duration. Selected Step Two forex trading systems. Back-testing results.

Fig.4. Skewness of the distribution of trader's monthly logarithmic returns as a function of mean position duration, days. Each point represents a virtual trader. The colors correspond to those in Fig.2.

Skewness is seen to be somewhat correlated with position duration, which is natural. Skewness seems increasingly important as becomes increasingly evident that RMS and mean alone are insufficient to characterize the trading risk. (Had they been sufficient, Sharpe ratio would have sufficed). Positive skewness means that up-side risk outweighs the down-side risk, and the risk becomes a complex concept -- a lot of risk is not necessarily bad if it's all on the up-side.

Logarithmic annualized return vs new trade frequency. Selections on the stop-loss parameter. Selected Step Two forex trading systems. Back-testing results. 5.1 Logarithmic annualized return vs new trade frequency. Selections on the trade entry parameter. Selected Step Two forex trading systems. Back-testing results. 5.2 Logarithmic annualized return vs new trade frequency. Selections on the trade exit parameter. Selected Step Two forex trading systems. Back-testing results. 5.3

Fig.5. Mean of the distribution of trader's monthly logarithmic returns as a function of new trade frequency, inverse days, 5.1: with stop-loss selections; 5.2: with trade entry selections; 5.3: with trade exit selections. Each point represents a virtual trader.

Fig.5 shows that while stop-loss (5.1) is fairly irrelevant this late in the optimization game, the exit parameter (5.3) gives a good control of return -- the more conservative it is, the better. The way to accomplish a low new trade frequency, desirable on the basis of Figs.1,2, and 3, is to set a higher entry threshold (5.2). Thus, the range of the entry parameters of 0.018-0.02, and exit parameters of above 0.008 are chosen for the final product. (By the way, there is no evidence that higher values of the exit parameter are worse -- this has not been investigated as all previous studies showed this parameter to be of very little relevance.)

Risk vs return.  36 Step Two forex trading systems selected by system parameter cuts alone. Back-testing results.

Fig.6. Risk vs return view of the performance of selected 36 Step Two trading systems. 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.

The above-mentioned selection alone, combined with others implicitly present in the sample of traders under study, leaves 36 virtual traders "in". This number has to be reduced to a more manageable one for the more detailed studies, including inspections of the actual trading histories and charts. Fig.6 marks a major mile-stone: all the trader selections made so far (including those made in the earlier reports before entering the home-stetch phase) have been obtained by applying only system parameter cuts -- and not cuts on the performance figures of merit.

Now I am going to reduce the number of chosen robots down to 6, by cutting on the "things we want" rather than "things we control". To do that, I require the fraction of negative monthly returns to be below 0.13 (which leaves 12 robots), the mean logarithmic annualized return -- to be above 0.2 (which leaves 10), and the return skewness parameter -- to be above 1.3. I understand very well that these are random numbers, and any choice on their basis is very different in nature from a choice of trading system parameters, the latter being optimizable on a cause-and-effect basis. Yet, I need to narrow down the variety of possible systems to a manageable number for a closer inspection of those few.

Trader # 510552 553 584 588 622

Stop-loss

2.5 2 2.5 2 2 2

Entry, ten

0.020.02 0.02 0.020.02 0.02

Exit, tex

0.0090.0110.009 0.009 0.013 0.013

Fred

80 80 71 80 77 80
New trade freq, 1/day0.097 0.083 0.095 0.093 0.085 0.082
Position duration, day3.9 4.1 4.5 3.8 4.4 4.4
ann. return, 1=100% 0.23 0.30 0.30 0.37 0.38 0.46
Sharpe 0.30 0.31 0.23 0.37 0.30 0.39
log. ann. return mean 0.24 0.30 0.30 0.36 0.36 0.42
log. ann. return RMS0.81 0.96 1.32 0.96 1.20 1.09
log. ann. return min. -1.38 -1.42 -2.36 -1.4 -2.11 -1.27
log. ann. return max. 2.89 3.01 6.11 3.71 4.42 3.88
log. ann. return skewness1.63 1.63 2.29 1.96 1.39 1.51
neg. return fraction 0.10 0.13 0.13 0.05 0.10 0.13

Table 2. Performance of the six selected winning traders.

Table 2 presents a considerable variation of performance figures of merit for a fairly similar set of controlled parameters of the trading system. On the surface, #510 and #622 look the most attractive. The immediate plan is to look at the simulated trading records of the traders in the table on a decision-by-decision basis, with the charts. Should it reveal loop-holes in the "quality harness" used so far, the quality harness will have to be improved by creating and adding new figures of merit -- and repeating the process.

The final caveat: as may or may not be already clear to the reader, there is currently no strict definition of "the best" when it comes to the trading system performance, not to mention the parameter selection for which a definition of "the best" is only the starting point. The current process was driven by the desire to maximize Step Two advantage over Step One, as opposed to looking at Step Two on a stand-alone basis. This is just one possible approach.

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