This section discusses how to formulate and test a simple, non optimized, trend-following system that makes as few assumptions as possible about price action. It arbitrarily uses a 65-day simple moving average of the daily close to measure the trend. Sixty-five days is simply the daily equivalent of a 13-week SMA (13×5= 65), representing one-quarter of the year. This is an intermediate length moving average that will consistently follow a market’s major trend.
As shown in Figure 4.1, when the market is trending up, prices are above the 65-day SMA, and vice versa. In sideways markets, this SMA flattens out and prices fluctuate on either side. Clearly, the trading system picks up and sticks with the prevailing trend (see Figure 4.2).
There are many ways to make the decision that the trend has turned up. The usual way is to use a shorter moving average of, say, 10 days, and decide that the trend has changed when the shorter average crosses over or under the longer moving average. If you decide to use a short moving average, its “length” will be crucial to your results. Another weakness is that often prices will move faster than the shorter moving average, so that the entries can seem rather slow.
Hence, the 65sma-3cc system will require three consecutive closes (3cc) above or below the 65-day SMA (65sma) to determine that the trend has changed. For example, the trend will be said to have turned up after three consecutive closes above the 65-day SMA. Similarly, the trend will have turned down after three consecutive closes below the 65sma. Once again, the requirement of three consecutive closes is arbitrary. It could be ten consecutive closes or any other number. Clearly, the results will vary with the number of confirming closes.
If you are afraid of false signals (see Figure 4.3), then the number of closes you use will act like a filter in reducing the number of trades. In a fast-moving market, requiring a large number of consecutive closes will give delayed entries (see Figure 4.4). Conversely, if a market is moving sluggishly, a small number of consecutive closes will give false signals. Thus, there is a trade-off here that determines how quickly you recognize a change in trend.
Once you recognize a change in trend, you still have to decide how to enter the trade. You should enter the trade on the next day’s open, to guarantee that you can execute the signal and get a fill. For example, if the three consecutive closes criterion is satisfied as of this evening’s close, you should buy at the market on the open of the next trading day. You will get a fill somewhere in the opening range the next day. It is likely that you will be filled near the top of the opening range for buy orders, and near the bottom of the opening range for sell orders. This slippage should be ignored, and just lumped into your $100 allowance for slippage and commissions. The main effect of this entry mechanism is that you are not filtering out any entry signals, and ensuring that you will put on this position the first time the entry conditions are satisfied.
There are a number of choices on how to actually enter the trade. For example, you could enter the trade on the close of the third consecutive close above or below the 65-sma. A second choice would be to enter the next day on a stop order beyond the previous, or a nearby, high or low. In effect, you would also filter out some entry signals, because you would not get a fill on every signal. This may be useful in situations where prices briefly spike beyond the 65-sma during prolonged trends.
A third entry choice would be to delay entry for x days after the signal, and then enter beyond a nearby n-day high or low. This is an-other way to filter down the entry signals in order to find more profit-able ones. Note that if you use a limit order for your entries, occasion-ally you may not be filled at all, missing the entry by just a few ticks. Hence, you should enter on the next day’s open to assure an entry into the new trend.
Before we proceed, let us put this entry signal through a critical test to check if the 65sma-3cc entries are better than random. Following the approach of Le Beau and Lucas (see bibliography for details), let us test the entry signal with exit on the close of the ra-th day, without any stops, and no deductions for slippage and commissions. For simplicity, only the effect of long entries are shown. The proportion of trades that are winners should consistently be more than 55 percent. The test in-cludes the long entry over 21 markets, stretching from January 1, 1975, through July 10, 1995, using a continuous contract. Because not all markets were trading back in 1975, all available data are used.
Table 4.1 shows that, on average, 55 percent of the long entries were profitable, suggesting that the 65sma-3cc model probably does better than random. The result for short trades is similar, and you can be reasonably confident that this model provides robust entry signals. Your task is now to combine this model with risk control and exit methods that match your trading mentality.
To summarize this nonopdmized system, the actual trade entry is at the market on the open of the next trading day after the close of the day the signal is received. You will notice that there are no specific exit signals at this point, which means that the short entry signal is also the long exit signal, and vice versa. In practice this means that if you are long one contract, you will sell two contracts to go net short one contract, and vice versa.
Note that for the tests below we will add a condition to prevent back-to-back entries of the same type. This will allow an apples-to-apples comparison when studying the effect of adding stops or exits. YOVL do not need this condition for actual trading.
To summarize what is not defined at this point: There are no specific risk-control rules in terms of an initial money management stop, nor any money-management rules to determine the number of contracts to trade. We will just trade one contract for simplicity without any risk-control stop. This is not a recommendation to trade without a risk control stop; the calculations are done without any stops here to illustrate a point. Later, we will examine how to add risk control and study the effect of money management.
The 65sma-3cc system should make all its profits during strong trends. It should lose money in sideways or nontrending markets. And it should have between 20 and 50 percent profitable trades. We tested this model over 23 markets using 20 years of continuous contract data. If a contract was not traded for 20 years, then we used all available data from the starting date. The usual allowance of $100 per trade for slippage and commissions was made. Thus, this is a rigorous test for a nonoptimized system over a long test period, and across a large number of markets. The results are summarized in Table 4.2.
The results for this simple, nonoptimized trend-following system are encouraging. You could have made a paper profit of $1,386,747 by trading just one contract for each market, and been profitable on 19 of 23 widely diverging markets. The test sample generated 2,400 trades, so this is a highly significant test. Approximately 34 percent of all trades were profitable, a number typical of trend-following systems.
The ratio of average winning to average losing trades was excellent, at 3.3 averaged over the 2,400 trades. This number is useful for calculating the risk of ruin; a number above 2.0 is desirable, and anything over 3 is welcome news. The average trade made a profit of $558, an attractive amount, considering transaction and slippage costs. It is customary to seek a number over $250 for the average trade. The average profit per market was $60,293, approximately 2.74 times the average maximum intraday drawdown, of-$22,014. This is a healthy recovery factor, or coverage of the worst losing streak of the system.
In summary, a simple trend-following approach worked on many markets over a long time period with few assumptions and no optimization. The results also point out some weaknesses of this system. The average profit per market is 90 percent of the standard deviation of the average profit. This means that profitability varied widely from market to market. The maximum intraday drawdown was 108 percent of its standard deviation, implying that the drawdowns also varied considerably among markets. The standard deviation of the average trade also implies that results can vary substantially over time or across markets. A further weakness is the relatively small number of profitable trades. Thus, we can summarize the principal weakness as a large variability in the results over time and across markets.
Combining the strengths and weaknesses, you would say that this is a sound trend-following system with good chance of being profitable over many markets over a long time period. But because of the large variability in results, you would have to trade this system relatively conservatively. You should allow a large equity cushion to absorb drawdowns.
A look under the hood of this trading system, so to speak, and a closer examination of the results of the analysis reveal further details of 65sma-3cc trades. A histogram of all 2,400 trades shows the distribution of trade profits and losses (see Figures 4.5 and 4.6). There are more large winners than large losers, and many small losers. Remember that these results were calculated without using an initial money management stop. Most of the trades are bunched between -$3,000 and $2,000, with the highest frequency near zero. There are few losing trades worse than -$5,000, balanced by even more trades with profits greater than $5,000. An initial money management stop will clean up the negative part of this histogram.
Thus, it should be obvious that most of the profits come from a relatively small number of trades. In Figure 4.6, 12.5 percent of the trades are seen to have closed-out profit greater than $3,000. Be aware that if you get out too soon, you are likely to miss one of 100 or so (4 percent) of the mega-trades that make trend-following worth the aggravation.
Figure 4.6 A histogram of the 65sma-3cc system over a narrower range of profits and losses. Notice that only a small number of trades show large profits.
Many measurements follow what is called a standard normal distribution. For example, if you measured the diameter of ball bearings, the measurements will follow a normal distribution. The normal distribution is a bell-shaped probability distribution of the relative frequency of events. The standard normal is a special case of the normal distribution with a mean of zero and standard deviation equal to one. To compare the distribution of the 65sma-3cc trades to the standard normal distribution, we first have to “normalize” the bin sizes. The comparison is shown in Figure 4.7.
The 65sma-3cc curve is more sharply peaked than the standard normal curve. To generate a normal distribution that would fit our data, I used a Microsoft Excel 5.0 spreadsheet and employed an iterative process of manually tweaking the values. The fitted normal curve, with a mean of-0.16 and standard deviation of 0.18 is shown in Figure 4.8. The fitted normal distribution shows that the actual 65sma-3cc distribution has “fat” tails. This simply means that there is a larger probability for the “big” trades than would be expected from the normal distribution. This chart shows that unusually large profits or losses are more likely than might normally be expected.
The modified normal distribution fits the observed curve nicely on the losing side, but the small positive trades fall off sharply. This implies that you will not get very many small positive trades with a trend-following model. Small trades will occur during broad consolidations, and these are not very common. Small losing trades are more likely during consolidations, as shown by the good fit on the left side of the peak.
The huge spike at the right-hand edge of the Figure 4.6 represents the 4 percent or so of mega-trades that make trend following worth-while. The distribution shows you it is easy to miss these trades, and if you do, your portfolio performance will drop off quickly. You should try to develop such a frequency distribution curve for your own systems to get a better feel for model performance.
A closer look at losing trades reveals another weakness of the 65sma-3cc system. Figure 4.9 is a distribution of the maximum profit of each of the 1,565 trades that were closed out at a loss, called the maximum favorable excursion (MFE). The glaring weakness is that because there is no specific exit strategy, many trades with profits greater than $3,000 were eventually closed out at a loss. However, we have to be careful with our exit strategy, since only 4 percent of the trades were mega-winners. If we are not careful, we may lock in some profits from losing trades, but lose out on the truly big winners. Another way to use the information from the maximum favorable excursion plot is to select the profit point at which to move your trailing stop to break-even. For example, you can move your stop to break-even after a $2,000 profit and capture a significant proportion of losing trades.
You can also use the maximum adverse excursion plot to set profit targets for scaling out of large positions. For example, if you were trading ten contracts, you could sell some at each of the profit targets
Figure 4.9 A histogram of maximum profit in 1,565 losing trades over 20 years and 23 markets from the 65sma-3cc system. This is a maximum favorable excursion plot.
of $500, $1,000, $2,000 and $3,000. We continue our analysis by examining the maximum drawdown in 777 winning trades following John Sweeney (see bibliography for details). This drawdown is on an intraday basis. These trades show some loss, but were eventually closed out at a profit. The histogram (Figure 4.10) reveals several interesting insights.
Figure 4.10 Analysis of 777 winning trades: maximum loss in trades that were closed out at a profit. This is also known as the maximum adverse excursion plot.
About 500 (64 percent) of the trades were immediately profitable, with a loss during the trade of less than -$250. Another 100 trades showed drawdowns of less than -$500.
Thus, almost 77 percent of the trades showed a loss of -$500 or less during their evolution. There were very few trades that showed losses greater than -$1,750 and then closed out at a profit. This suggests that we could set an initial stop at $1,000 and capture almost 88 percent of the winning trades. This is a realistic way to pick the point at which a mechanical initial money management stop could be placed.
The same information can be viewed as a cumulative frequency chart to see how many trades achieved a certain profit target (see Figure 4.11). This type of chart shows what proportion of trades had a maximum favorable excursion of, say, $500. It shows, for example, that 50 percent of trades had reached a $1,000 profit target, and so on.
In summary, the 65sma-3cc system test over 20 years of data and 23 markets showed it is a robust and profitable system that makes money in trending periods. Since we tested the system without any initial money management stop, there were several trades with losses greater than -$3,000. We can try to clean this up by placing a stop at $1,000, as shown by the MAE plot. The detailed analysis showed several profitable trades that were closed out at a loss. We would like to minimize such trades. There were about 4 percent truly huge trades with profits in excess of $5,000. We must find an exit strategy that does not miss out on such mega-profits.