Principles of Trading System Design : Robust Trading Rules

Robust trading rules can handle a variety of market conditions. The performance of such systems is not sensitive to small changes in parameter values. Usually, these rules are profitable over multi period testing, as well as over many different markets. Robust rules avoid curve-fitting, and are likely to work in the future.


Figure 2.5 Adding more rules delayed entries and exits, increasing maximum intraday drawdown. Note that the horizontal scale is not linear.

An example of a system with delayed long entries illustrates the use of non robust parameters. The entry rule is as follows: if the crossover between 3- and 12-day simple moving averages (SMAs) occurred x days ago, and the low is greater than the parabolic, then buy tomorrow at the today’s high + 1 point on a buy stop. A $1,500 initial stop was used and $100 was charged for slippage and commissions.
The results above are for an IMM (International Monetary Mar-ket) Japanese yen futures continuous contract, from August 2, 1976 through June 30, 1995. The dollar profits are sensitive to the number of days of delay, and can vary widely due to small changes in parameter values. It also does not seem reasonable to wait 12 days after a crossover for such short-term moving averages. Hence, the flattening out of the curve after a 9-day delay is of little practical relevance. The delay parameter is not robust because a small change in the value of this parameter can make system performance vary widely with markets and time frames.
Next consider the effect of nonrobust, curve-fitted rules, illustrated by the August 1995 N.Y. light crude oil futures contract (Figure 2.8, page 26). The market was in a narrow trading range during February and March, and then broke out above the $18.00 per barrel price level. The market moved up quickly, reaching the $20 level by May. A volatile consolidation period ensued through June, before prices broke down toward the $17 per barrel level by July.


Figure 2.6 Increasing the number of rules decreased profits in the U.S. bond market from January 1, 1975 through June 30, 1995. Note that the horizontal scale is not linear.

The following trading rules were derived simply by visual inspec-tion of the price chart in an attempt to develop a curve-fitted system that picked up specific patterns in this contract.
Rule 1: Buy tomorrow at highest 50-day high + 5 points on a buy stop (breakout rule).
Rule 2: Sell tomorrow at low -2 x (h-1) – 5 points on a sell stop (downside range-expansion rule).
Rule 3: If this is the twenty-first day in the trade, then exit short trades on the close (time-based exit rule).
Rule 4: If Rule 3 is triggered, then buy two contracts on the close (countertrend entry rule).
Rule 5: If short, then sell tomorrow at the highest high of last 3 days +1 point limit (sell rallies rule).

forex trading system

Figure 2.7 The effect on profits of changing the number of days of delay in accepting a crossover signal of a 3-day SMA by 12-day SMA system is highly dependent on the delay.

The first rule is a typical breakout system entry rule, albeit for a breakout over prior 50-bar trading range. The second rule is a volatility-inspired sell rule. The idea was to sell at a point five ticks below twice the previous day’s trading range subtracted from the previous low. This will typically be triggered after a narrow-range day, if the daily range expands on die downside due to selling near an intermediate high. The third rule is a time-dependent exit rule, optimized by visual inspection over the August contract. The idea behind time-based exits is that one expects a reaction opposite the intermediate trend after x days of trending prices. Rule 4 merely reinforces rule 3 by not only exiting the short position but putting on a two-contract long position at the close. Rule 5 is a conscious attempt to sell rallies during downtrends. In this case, limit orders were used to sell, to avoid slippage. These rules assumed diat as many as nine contracts could be traded at one time, using a $1,000 initial money-management stop.

The results of the testing are summarized in Table 2.3, page 27. The first clue that this may be a curve-fitted system is the number of profitable trades. As many as 87 percent of all trades (20 out of 23) were profitable. A second clue was in the 14 consecutive profitable trades. A third clue was in a suspiciously large profit factor (= gross profit/gross loss) of 13.49. These results are what you might see in curve-fitted systems tested over a relatively short time period. The computer-generated buy and sell signals are shown in Figure 2.8.
This curve-fitted system was tested by using a continuous contract of crude oil futures data from January 3, 1989, through June 30, 1995. Not surprisingly, this system would have lost $107,870 on paper, as shown in Table 2.4. Note how only 32 percent of the trades would have been profitable. There would have been as many as 48 consecutive losing trades, requiring quite an act of faith to continue trading this system. Also, the profit factor was a less impressive 0.61, a sharp drop from the 13.49 value in Table 2.3. These calculations show that curve-fitted systems may not work over long periods of time.


Table 2.3 Results of testing August 1995 crude oil curve-fitted system N.Y. Light Crude Oil 08/95-Daily

Interestingly, this system has its merits. When tested over 12 other markets to check if these rules were robust enough to use across many markets (Table 2.5), the results were better than expected; on some markets the system tested very well. This result was surprising because (1) this particular combination of rules had never been tested on these markets and were derived by inspection of just one chart; and (2) the long entries and short entries are asymmetric. A symmetrical trading system uses identical rules for entries and exits, except that the signs of the required changes are reversed. For example, a moving average system would require an upside crossover or a downside cross under for signals.

Table 2.5 A check for robustness: crude oil curve-fitted system over 12 markets (test period: 1 /3/89-6/30/95, using continuous contracts, $100 slippage, and commission charge)

A closer look at the rules shows that they do follow some sound principles. For example, during an uptrend, each successive 50-bar breakout adds a contract until nine contracts are acquired. Thus, market exposure is increased during strong up trends. The sell rule tends to lock in profits close to intermediate highs. As we sell rallies in downtrends, we are increasing exposure in the direction of the intermediate term trend. Also, a relatively tight $1,000 initial money management stop was used. Thus, even though these rules were derived by inspection, they followed sound principles of following the trend, adding to with-the-trend positions, letting profits run, and cutting losses quickly.

In summary, it is easy to develop a curve-fitted system over a short test sample. If these rules are not robust, they will not be profitable over many different market conditions. Hence, they will not be profitable over long time periods and many markets. Such rules are unlikely to be consistently profitable in the future. Hence, you should try to develop robust trading systems.

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