Summary of the trading system optimization results. Step One. - Stop-loss

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Written by Forex Automaton   
Tuesday, 21 July 2009 14:28
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Summary of the trading system optimization results. Step One.
Stop-loss
How often to place new trades?
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2. Stop-loss

Average position duration vs the stop-loss parameter.

Fig.2.1. A profile histogram showing dependence of the position duration (in days) on the placement of the stop-loss on average for the set of algorithmic traders entering the simulation (minimum bias sample). A caveat: unlike the rest of simulations in this report, the trades were allowed to roll over the week-ends.

The distribution of returns is known to get broader with time scale; in the classic random walk problem, your expected root-mean-square departure from the origin grows with time as a square root of time. 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. By expressing it in the units of the market volatility, I can have apple-to-apple comparisons between different markets and different time frames. Fig.2.1 allows a model-independent discussion of the stop-loss, as it maps this parameter onto the average position duration which is an observed quantity, rather than a model one. (When computing the position duration, every trading lot entering a "trade idea" is counted with the same weight. Multiple trading lots can enter and exit the same "trade idea" at various times, for example when carrying out a pyramid strategy. Therefore the position duration, synonymous with the trading lot's life time, should not be confused with the life time of a "trade idea", nor can it be longer than the latter).

Annualized return vs stop-loss sum over markets RMS of log annualized return vs stop-loss sum over markets

Fig.2.2. Top: profile histograms showing dependence of the annualized return (measured directly for each algo trader by comparing equity at the beginning and end of trading history) on the stop-loss placement. Different symbols represent different trade entry parameter ranges. The unit of return is 100% (100%=1, 10%=0.1 etc). Bottom: a similar set profile histograms showing a measure of fluctuation in the profit ( RMS of the logarithmic  month-to-month return time series) as a function of the stop-loss placement. Here, no zero-suppression is applied when calculating the RMS: if no trades are placed in a month and the return is zero, that zero still enters the calculation. Being non-fluctuating repetitive constants, such zeros can reduce the RMS dramatically. This explains the sharp drop in the RMS for the very conservative values of the trade-entry parameter.

The stop-loss studies show the main problem to be avoiding needlessly tight stop-loss -- those are able to ruin otherwise solid trading strategies. The exact position of the stop-loss curve depends on the entry parameter, the "excitement threshold" a trade idea needs to pass before being accepted by the robot. In the figures, the different sets of point painted in different color, depending on the value of this treshold: from black (very low, when even trades that do not promise too much are placed) to magenta, when only the most promising trades are accepted.

Curves corresponding to the more conservative trade-entry policy generally have a maximum of return corresponding to stop-loss parameter in the vicinity of 1.2. Either the shifting of the maximum (towards lower stop-loss) or its growth with the increase in the entry parameter (non-monotonic, taking place in the lower range of the trade-entry parameter) or both have been seen in the six forex markets researched so far. Apparently 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. A reader remarked that an automated trading system should not use a stop-loss other than a "catastrophic world event" backstop. Such a view corresponds to the trading regime reflected in the behaviour of the curve to the right of the maximum -- the return (Fig.2.1, top) is practically unaffected while the chosen measure of risk (the RMS fluctuation of return, Fig.2.1, bottom) keeps dropping. The generous stop-losses get triggered rarely if ever and from a practical point of view the respective trading style is not much different from the one with no stop-loss at all. Of course this does not mean that the algorithm keeps unprofitable trades until they turn into winning ones: they may never do. The decision making is based on a forecast filtered by the the discriminating threshold (in this case, since we are talking about existing positions, this is the exit threshold). As soon as the direction-change signal is above the threshold, the trade which goes agains the newly predicted market direction will be closed.

Annualized return vs stop-loss, AUD/USD Annualized return vs stop-loss, EUR/USD
Annualized return vs stop-loss, GBP/USD Annualized return vs stop-loss, USD/CAD
Annualized return vs stop-loss, USD/CHF Annualized return vs stop-loss, USD/JPY

Fig.2.3. Collection of profile histogram fragments following the same format as Fig.2.1 (return vs stop-loss), but for the individual markets. Compare the trends in the distributions of the points. Click on any panel to get to the report with the full information.

Fig.2.2 is effectively an average of the individual currency pair data presented as separate panels in Fig.2.3. Those latter ones show considerable similarity in shapes. AUD/USD and EUR/USD however are seen to break out of the pack the most, AUD/USD due to its different location of the entry optimum (urging one to be extra-conservative, as discussed in the next section) and EUR/USD due to existence of a local sweet spot of a trading strategy combining tight stop-loss with a very conservative trade entry policy -- not seen with this algorithm in other exchange rates.



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