Further analysis of the day-range strategy. Selecting the forecasts to trade.

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Written by Forex Automaton   
Tuesday, 09 February 2010 12:45
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Further analysis of the day-range strategy. Selecting the forecasts to trade.
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In the January performance review for the Danica trading system, an idea of a day-range trading strategy capitalizing on the high quality forecasts for the direction of daily high and low was expressed and a set of what-if charts for the forex pairs tracked was provided and discussed. This post is a deeper and more quantitative discussion of the strategy. Which forecasts should be acted upon? What is the expected profit per trade? How are profits/losses distributed statistically? -- these are the questions addressed.

As a brief introduction for those new to this, Danica is an algorithmic forecasting system launched in December 2009. The system is trained and optimized using historical forex data beginning in August 2002. The system's output is a forecast of the next day's low-high-close "candle". This report is based on version 0.5 of the system and daily data from August 21, 2002 to January 23, 2010.

The trick is to formulate selection criteria entirely on the basis of information known before the trade is placed, such as to bias the outcome in our favor. Fig.1 represents one way of looking at the data with such a goal in mind. As the zero level of trade selection, the forecasts with same direction of expected change for low, high and close ("level 0 trigger word=3") are selected in the daily output of the system. The day-range system then calls for a trade in the direction of the forecast (long or short) with the profit target at the level of the previous day's high (low for a short trade) and the protective stop at the level of the previous day's low (high for a short trade). It can be assumed with good accuracy that the trade will be entered at the previous day's close. At least, that's a number known before the trade is placed, and the trick is to build the selection criterion entirely on the basis of information known before the trade is placed.

The potential trades differ considerably in the distance between the entry price and the profit target on the one hand, and between the entry price and the protective stop, on the other. To some extent, these determine the profit/loss potential of a trade. The quantity labeled as "potential profit-loss to volatility" in the figures is, for long trades,

[(High-Close) - (Close-Low)]/volatility = [High + Low - 2×Close]/volatility,

while for short trades, it is

[(Close-Low) - (High-Close)]/volatility = [2×Close - High - Low]/volatility,

where volatility is defined to be the root-mean-square of the recent 10 linear returns (price differences) in the time series of daily close. The potential profit-loss is defined to be positive for trades with "more room" on the profit side of the trade, regardless of the direction of the trade.

Relative profit of a selected trade vs the difference of potential profit and potential loss divided by volatility

Fig.1. Landscape-map view of a two-dimensional histogram of relative profit of a selected trade vs the difference of potential profit and potential loss divided by volatility. Landscape "elevation" is the number of events falling in a particular bin. Cross-hair lines mark position of zero. The only selection applied is "trigger word=3" explained before. The lighter background band represents the current best trade selection as explained in text.

The quantity plotted along the vertical axis of Fig.1 becomes known only after the trade is closed. As discussed in detail in the context of specific examples in January issue of performance review, four outcomes are possible.

  1. During the day, the profit target is hit while the protective stop is not hit. The trade is closed with a profit.

  2. During the day, the stop is hit while the profit target is not hit. The trade is closed with a loss.

  3. During the day, both the stop and profit target could be hit. In reality or in a more detailed simulation, this situation would resolve itself into either (1) or (2) above. In this study, I assume that the distribution of outcomes is 10 to 6 (10 cases of (1) for every 6 cases of (2)). This proportion of outcomes is what took place in January and is currently my best guess.

  4. Neither limit is hit. The trade is assumed to be closed at day's close. Of course, an actual trade does not need to be closed, this is just the way of book-keeping for this simple study.

In Fig.1, the distribution's center of gravity is seen to be shifted to the left with respect to 0; understandably, a typical candle has more room to go from its close against its trend than in the direction of the latter.

Relative profit of a selected trade vs the difference of potential profit and potential loss divided by volatility. Profile histogram.

Fig.2. Profile histogram view of the data in Fig.1. The two-dimensional histogram of Fig.1 is represented as a set of vertical slices advancing along the horizontal axis, each with a mean and RMS of the value along the vertical axis, shown by the marker and the vertical bars, respectively. Highlighted area is the same as in Fig.1 and represents the current best trade selection approach.

One may argue that trades with a small distance to a profit target and a long distance to the protective stop have a better chance of turning into profits than into a loss; on the other hand, the size of the possible profit is smaller than the size of the possible loss. What is the interplay of the two effects?

Fig.1 and particularly Fig.2 make it clear that the interplay is generally in favor of the trades that have a longer distance to the profit target than they do to the protective stop, as measured in the volatility units (the horizontal axis). To the left of zero on the horizontal axis, the cases when the possible loss by protective stop exceeds the possible profit by profit target result, on average, in negative profits. The extreme right of the horizontal axis represents the rare exceptions when the distance to the profit target is very much longer than the distance to the protective stop. In those cases, one may argue there is a trend for the expected profit to drop. By the same token, one may argue that there are similar but "opposite" exceptions, where the profit target is so close to the price when the trade is entered that the frequent but small profit outweighs the less frequent but very large possible loss. The curve cetainly does bend upward for extreme negative values of potential profit-loss, but it's harder to make a convincing case that there is an area where one benefits from accepting trades -- possibly due to the lack of data.

Distribution of relative potential profit-loss difference of a hypothetic trade.

Fig.3. Distribution of the relative (to the previous day's close) potential profit-loss difference of a hypothetic trade. The inset shows the subset of data corresponding to the highlighted area of best trades according to Figs.1 and 2. The 2365 trades that pass the criterion represented by the inset here and by the highlighted bands in Figs.1 and 2, constitute 21% of trades that pass the trigger word=3 condition.

On the basis of these arguments, the rest of the analysis is done only for trades with potential profit-loss relative to volatility  between 0 and 2. Fig.3 illustrates that these situations constitute about 21% (2365/11234) of all trades which pass the level zero criterion of same direction for high, low and close.



Last Updated ( Wednesday, 08 September 2010 16:00 )