Optimizing the forex trading system: AUD/USD revisited

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Written by Forex Automaton   
Tuesday, 23 June 2009 10:58

The recent changes to the trading system optimization technique do show an effect on the AUD/USD optimization, shifting the preferred value of the forecasting quality parameter. This study covers an extended range of the trade-entry threshold parameter, the one that controls the "patience" of a trading system or the amount of "excitement" about a trade idea needed to enter the trade. The new optimum takes advantage of that as well.

1. The basics

The basic framework remains the same: a run of the program included simulations of trading histories of 26999 independent "virtual traders" (forex robots), each of them being an incarnation of the same algorithm, differing by the setting of the adjustable knobs. This report uses the AUD/USD 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.

2. Stop-loss optimization

What is the best stop-loss parameter to use in AUD/USD? The answer depends on the time scale of trading, since so does the distribution of returns. The distribution of returns gets broader with time scale; in the random walk problem, your expected root-mean-square departure from the origin grows with time as a square root. For this reason, my stop-loss parameter is not expressed in pips or dollars. Instead, it is a fraction of the root-mean-square of the series of linear returns (price differences) in the nearest subset of the price series.

Effect of stop-loss on the trading returns. Comparing trade entry ranges. AUD/USD.

Fig.2.1. A profile histogram showing dependence of the annualized return (measured directly by comparing equity at the beginning and end points of trading) on the stop-loss placement. Different symbols represent different trade entry parameter ranges. The unit of return is 100% (100%=1).

The more conservative values of the trade-entry parameter are seen to change magnitude of the average return for such a marginal distribution, in particular, for the lower stop-loss settings. Contrary to what was seen for EUR/USD, the shape of the curve remains similar for the various symbol types as the entry threshold is varied. 

Fig.2.1 shows that the importance of the trade entry parameter grows as the stop-loss gets tighter (up to a certain point, until everything seems to become a losing strategy with a very tight stop loss). Somewhat counter-intuitively, it is the traders using tight stop-loss who need to be particularly conservative about when to enter a trade. The tight stop-loss is not a replacement for being critical and selective!

3. Trade entry and exit thresholds

Dependence of the annualized return on the trade entry parameter. AUD/USD

Fig.3.1. Profile histograms showing dependence of the actual annualized return on the trade entry threshold parameter. Traders are grouped according to the trade entry threshold parameter, as in the previous figures. The unit of return is 100% (100%=1).

The entry and exit threshold parameters have been explained elsewhere. In Figures 3.1 and 3.2 I present minimum-bias (no particular selection applied to the set of traders) data for the trade entry and trade exit parameters, respectively. Compared to the previous AUD/USD optimization study, the range of entry parameter has been extended from 0.006 to 0.016, and the range of the exit parameter was extended up to 0.013. In this latter case, the step of the optimization grid has also been changed since it was concluded that the dependence is weak and featureless. The dynamics of the annualized return in Fig.2 is understandable: lack of selectiveness in the trade ideas leads to decreased returns. The extreme conservatism, on the other hand, leads to the situation when trades are made so seldom that it is hard to expect returns. Thus, a maximum is to be expected; it seems like we reach it with the ENTRY values in the 0.012-0.016 range, but we do not get to see the right-side tail of falling returns with extremely conservative ENTRY values. It is worrysome that the location of the maximum is in a different place here, as compared to what was seen in the case of USD/CAD.

Dependence of the annualized return on the trade exit parameter. AUD/USD

Fig.3.2. Profile histograms showing dependence of the actual annualized return on the trade exit threshold parameter. The unit of return is 100% (100%=1).

Speaking of the exit parameter, a very weak and featureless dependence is seen, as usual with the minimum bias data (minimum selection on other parameters).

4. Optimizing the forecasting parameter

We optimize the forecasting quality parameter, the least trivial of all, with the combined (simultaneous) cut on the parameters inspected so far. The parameter is euphemistically called Fred to avoid disclosing its nature.

Optimizing the forecasting control parameter. All entry ranges. AUD/USD. Optimizing the forecasting control parameter. Best values of other parameters. AUD/USD.

Fig.4.1 Profile histograms showing the dependence of the annualized return on the forecasting control parameter Fred. The unit of return is 100% (100%=1), with minimum selection on the other parameters (top), and with a strong selection (bottom).

The two panels of Fig.4.1 correspond to the different parameter selection regimes, explained in the legends and the caption. The bottom panel is a sub-set of the magenta set of the top panel, split additionally according to the stop-loss placement. The maxima look a lot more convincing in the bottom panel, while the overall shape in that panel looks familiar from the USD/JPY, USD/CAD, EUR/USD. Since part of the rationale for these studies is to see how consistent the performance-driven selection results for the different currency combinations are, existence of shared optima among such different currency pairs is a good news.

Based on this, I like Fred in the range 50-75. This is quite different from the previous study, where a similar peak in Fred was also seen but rejected for reasons that are believed to be wrong: the use of biased quantities.

5. Further iterations

My frequent strategy of parameter optimization is to take the parameter values that I am relatively sure about and apply them to re-examine the other ones, thus narrowing the scope of study. In this case I am fixing ENTRY and FRED, and look at STOPLOSS and EXITT.

Optimizing the trade exit parameter. Best ranges of other parameters. AUD/USD.

Fig.5.1 A profile histogram showing the dependence of the annualized return on the trade exit control parameter for the best ranges of other parameters. The unit of return is 100% (100%=1).

Optimizing the stop-loss parameter. Best ranges of other parameters. AUD/USD.

Fig.5.2. A profile histogram showing the dependence of the annualized return on the stop-loss control parameter for the best ranges of other parameters. The unit of return is 100% (100%=1).

Optimizing stop-loss -- second iteration. Best ranges of other parameters. AUD/USD.

Fig.5.3. A profile histogram showing the dependence of the logarithmic annualized return RMS  (a measure of the risk) on the stop-loss parameter for the best ranges of other parameters.

Which stop-loss should be preferred? Fig.5.2 shows the local maximum of stop-loss around 1.2. By moving there from the stable area of stop-loss parameters 2 to 3, one can hope to gain about factor 2 in the return. But Fig. 5.3 shows that this factor 2 or so increase in the return comes at a price of factor 2 increase in the RMS of the logarithmic RMS variable measuring fluctuations of return, and thus quantifying the risk. In my opinion, this is not worth the trouble, and one has to stay with the more generous stop-loss placement.

6. The winners

With this input, the preferred ranges of the trading system parameters are given in the Table. Still to be discussed is the risk associated with making a wrong choice of a robot, and how much value is added to the system by the selection of the forecasting parameter, the most problematic of all.

Table 6.1. Preferred values for the AUD/USD forex trading system parameters.

Forecasting parameter, Fred 50, 53, 56, 59, 62, 65, 68, 71, 74
Stop-loss placement parameter, s 2.06667, 2.53333, 3.
Enter-the-trade threshold parameter, ten 0.012, 0.013, 0.014, 0.015, 0.016
Exit-the-trade threshold parameter, tex 0.009, 0.011, 0.013

Annualized return, Green forecasting parameter selection on and off Annualized return, Green forecasting parameter selection only

Fig.6.1. Distributions of the annualized return in the course of the trading system parameter optimization. Black histograms: all parameters except for Fred are as in Table 6.1, no selection on Fred. Green: same, with an extra condition on Fred. Normalization is arbitrary. The unit of return is 100%.

Fig.6.1 presents the summary of progress accomplished so far, using the annualized return statistic. Entries in the histogram are the forex robots (algorithmic traders) and the statistic refers to their trading performance. In the course of the optimization, the initial sample of 26999 forex robots is reduced to 405 winners by trading system parameter cuts.

From the analysis of various foreign exchange rates so far, it's evident that forecasting is the most tricky aspect of the trading system to optimize. We may end up with a single, compromise approach for all exchange rate or be forced to class exchange rates according to the similarity of the Fred optimization solutions. In either case, we must be prepared to face the worst-case scenario when we will have to admit that the Fred selection adds no value to the algorithm. That's why I am showing the black histograms in Fig.6.1. The black-color data represent the options on the table in the absence of any Fred selection, and show the effect of the money management style selection alone. Fred selection shifts the return distribution in the positive direction considerably.

While the mean of the distributions in Fig.6.1 is the measure of return, its RMS is the measure of risk associated with choosing a particular robot, or a particular version of the trading system, and its importance is hard to overestimate. One has to minimize the probability of ending up with a "lemon", a robot which belongs to the parent distribution and lands in the negative area of returns. For Gaussian distributions, a good measure of the probability that this happens is the ratio of mean to the RMS (or Sigma). The higher it is, the lower is the chance of a bad choice. This is, essentially, the rationale behind the Sharpe ratio (when different trading strategies, rather than different periods, are used to obtain the return estimate).

Looking at the Mean/RMS ratio for the green distribution, we obtain 0.18/0.076=2.4, which feels comfortable. To compare with the previous AUD/USD optimization report, based on the flawed arithmetic mean of annualized monthly return approach, the new study moved the Fred selection away from the lower values into the 50-75 range, closer to the currently preferred Fred range for USD/JPY, USD/CAD, EUR/USD.

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Last Updated ( Monday, 04 January 2010 12:32 )