Optimizing the forex trading system parameters: GBP/USD revisited

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Written by Forex Automaton   
Thursday, 11 June 2009 08:49

After important changes to the trading system optimization methodology, I am revisiting the case of GBP/USD on the day scale. In this study, the extended range of the entry threshold parameter, same as in the previous EUR/USD and USD/JPY studies, is used. The extended, more conservative threshold values are seen to increase the returns while reducing the risk. Unlike other cases, not one but two attractive ranges of the forecasting control parameter are seen.

The basic framework remains the same: a run of the program included simulations of trading histories of 12,789 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 GBP/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.

What is the best stop-loss to use in GBP/USD?

What is the best stop-loss parameter to use in GBP/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. GBP/USD.

Fig.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, comparing the trade entry parameter range from the previous reports (black) and the "extension" range (red).

The more conservative values of the trade-entry parameter, above 0.006, are seen to change magnitude of the average return for such a marginal distribution. Contrary to what was seen for EUR/USD, the shape of the curve remains similar for the black and red points. But the maximum of the return does move to the left as the entry requirement becomes more coservative, indicating, as was noted in the EUR/USD report just mentioned, that those more conservative values increase the relative weight of the situations where tighter stop-loss makes sense -- a welcome development, consistent with presence of intelligence in the forecast signal to which the entry threshold is applied.

Effect of stop-loss on the trading return volatility. Minimum bias. GBP/USD.

Fig.2. A profile histogram showing dependence of the RMS of the logarithmic annualized return distribution for a trader on the stop-loss placement. Compare the trade entry parameter range from the previous reports (black) and the "extension" range (red).

Fig.2, showing dependence of the RMS of the logarithmic annualized return distribution (a newly introduced quantity) on the stop-loss placement, demonstrates that tight stop-loss placement generally leads to bumpier rides in returns.

Trade entry and exit thresholds

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

Fig.3. Profile histograms showing dependence of the actual annualized return on the trade entry threshold parameter. No trader selection is applied.

The entry and exit threshold parameters have been explained elsewhere. In Figures 3 and 4 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 GBP/USD optimization study, the range of entry parameter has been extended from 0.006 to 0.009, 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. In the range considered, the data favor conservative entry (high threshold) and it looks like the optimum may still have not been reached. This is similar to conclusion of the USD/CAD and EUR/USD studies. The range for this parameter still needs to be extended further to the right, until the area is seen such that the returns begin to decline simply due to the lack of trading activity. We may not be there yet.

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

Fig.4. Profile histograms showing dependence of the actual annualized return on the trade exit threshold parameter. No trader selection is applied.

Speaking of the exit parameter, excluding the a few values on the left looks like the right thing to do. Below, I am excluding three such values, but I could exclude more.

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. The combined effect of the best stop-loss and entry parameters, shown in Fig.5, bottom (to compare with Fig.5, top with no such selection) is seen to enhance the returns considerably, especially for the higher values of Fred. The shape resembles USD/CHF and is different to what is seen for USD/CAD and EUR/USD.

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

Fig.5. A profile histogram showing the dependence of the annualized return on the forecasting control parameter Fred. Top: no selection on other parameters. Bottom: the best values of stop-loss, entry and exit parameters are used: stop-loss is 1.5 or 2, entry is 0.008 or 0.009, exit is 0.005 to 0.013.

Dependence of the log annualized return RMS on the forecasting control parameter. GBP/USD.

Fig.6. A profile histogram showing the dependence of the RMS of the series of the monthly annualized logarithmic returns on the forecasting control parameter Fred. RMS is the measure of risk. The "old" (black) and extended ranges of the entrance parameters are shown separately. The goal is to increase return and to reduce the RMS associated with its fluctuation.

As already noted, Sharpe ratio as used in the "old approach" reports like the one just linked, contains biased quantities and is avoided in the "new" approach. In this note, I keep experimenting with alternatives. One way to analyze information about riskiness of various trading strategies, executed by the robots, is to look at the RMS (measure of fluctuation) of the time series of returns. The essence of the "new" approach mentioned above is to replace the arithmetic average of the returns by the arithmetic average of the logarithms. The use of such an average calls for a corresponding change in the RMS, therefore it becomes the RMS of the logarithmic annualized returns. A dependence of such a quantity on the forecasting parameter is presented in Fig.6. The data clearly favor more conservative (higher) values of the entry threshold: for the red points, higher returns coexist with lower risk. Obviously, trades are executed rarely in the conservative entry strategies.

It is more difficult to make a choice between a moderate risk, moderate return strategy (values of the forecasting parameter in the range 14-23) and a high risk, high return (32-62 range).

Summary

With this input, the preferred ranges of the trading system parameters are given in the Table.

Forecasting parameter, Fred Two groups: 14, 17, 20, 23, and (less likely to be adopted) 32 to 62.
Stop-loss placement parameter, s 0.667, 1.13
Enter-the-trade threshold parameter, ten 0.007, 0.009
Exit-the-trade threshold parameter, tex 0.007, 0.009, 0.011, 0.013

Annualized return, comparison of three different choices of the forecasting parameter Annualized return, left range of the forecasting parameter Annualized return, right range of the forecasting parameter

Fig.7. Distributions of the actual annualized return in the course of the trading system parameter optimization. Top panel, black: all parameters except for Fred are as in Table 1, no selection on Fred. Blue: same as black, but with an extra condition on Fred (the first group of values in the table). Green: same as black, but with an extra condition on Fred (the second group of values in the table). Normalization is arbitrary. The unit of return is 100%. The other two panels show Gaussian fits to the blue and green distributions, the colors being the same as just explained.

Fig.7 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 12789 forex robots is reduced to two distinct groups of 96 and 264 winners by trading system parameter cuts. The two winning groups have identical selections of money management styles, but differ in the way the forecast is obtained.

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 top panel of Fig.7. The black-color data in this panel represent the options on the table in the absence of any Fred selection, and with the best selection of the money management style. Even in the absence of the Fred selection, except for the very basic one, the distribution is seen to be considerably shifted in the positive direction. Fred selection (blue or green) shifts in even more.

The choice between the blue and green groups has to be made now, and I am going to base it on the risk considerations. While the mean of the distribution in Fig.7 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). Unfortunataly, the chi-square statistic (also shown in the plots) rejects the Gaussian hypothesis for the blue distribution. The green distribution passes the chi-square test of Gaussianity.

Nevertheless, looking at the Mean/RMS ratios for the blue and green distributions, we obtain 4.2 vs 3.5 -- in favor of the blue. The fact that the blue choice also makes sense of USD/CHF, is a big additional argument in its favor.

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Last Updated ( Monday, 04 January 2010 12:33 )