System trading: Kroll's Method

(from Dragons and Bulls, Stanley Kroll)

As discussed earner, out or all the diverse technical methods utilized in trading systems, I have opted for the KIS approach, primarily using moving averages crossover methods. As trading systems go, the moving averages approach is the oldest and most basic of all analysis methods. In its simplest form, a moving average (MA) is the sum of ‘x‘ consecutive closes divided by ‘x'. For example, you would obtain a ten day simple moving averages (SMA) by adding the closing prices for the previous ten days and dividing the sum by ten. Perhaps the most popular SMA combinations are the 5 versus 20 day, and the 4 versus 9 versus 18 day. The ‘versus’ comes into the picture because systems traders have discovered through years of trial and error and testing, that a ‘ctossover' technique captures the maximum advantage of a MA trading system. 

There are, essentially, two ways to play MA systems, and they can amaze traders by frequently outperforming much more complicated and elaborate systems. In a simple, basic system, where you use, for example, a 12 day SMA, you would buy when the closing price goes above the 12 day SMA, and would sell when the closing price goes below the 12 day SMA. This simple system, however, offers less flexibility and probably inferior performance than the second approach, which uses a dual (or even a triple) crossover, for instance a 5 versus 20 day crossover system. You would buy when the short term line (the 5 day SMA) crosses above the long term line (the 20 day SMA), and liquidate long and possibly go short as well, when the opposite occurs. 

Serious systems traders tend to get considerably more involved with moving averages. Some use so called weighted moving averages which give greater weight to recent than to older price action, while other operators use exponentially smoothed moving averages, which may incorporate a potentially infinitely smoothed time span via more complex calculations Such approaches clearly require the use of a personal computer with customized software, where all calculations can be done at lightning speed. 

For any moving averages strategy, regardless of its complexity, the critical question concerns the number of days of the analysis and Whether it should be optimized (tailored) for each distinct commodity. In this regard, some of the best technical research has been by American analysts Frank Hochheimer and Dave Barker. I should point out that, notwithstanding their excellent research, these studies were done many years ago and should not be depended on today, as markets and overall volatility have changed. Nevertheless, I include this research to indicate how the studies can be done, and as a starting point for modern research. 

Hochheimer tested a broad array of moving averages, from 3 to 70 days, on each of 13 different futures for the 1970 1976 period. His results showed that there was not one ‘best' universal combination. His best combinations (closing price going through a SMA) Which projected best overall profits were: If 

           Best       Cumulative                                                                           Ratio
           average  Profit Loss     Number of      Number of      Number of      profits/
           (days)     (US$)             trades               profits            losses             Totalt trades/

Silver      19         42,920 +       1,393                429                 964                 .308 

Pork        19         97,925 +        774                  281                 493                  .363 

bellies
Com        43         24,646 +        565                  126                 439                  .223 

Cocoa      54         87,957 +        600                  157                 443                  .262 

Soybeans 55         222,195 +      728                  151                 577                  .207 

Copper     59        165.143 +       432                  158                 274                  .366 

Sugar        60        270,402 +       492                  99                  393                   .201 

Figure 15.1 Frank Hochheimer's testing of "best combination" moving average calculations. 

It should be noted that these are purely hypothetical trades done on the basis of an after the fact calculation. Clearly, real time results are unlikely to show such profxts. Also, note the low ratio of profits to total trades, from .201 to .366; quite typical of systems and formula trading. 

For those traders interested in going beyond the simple closing price versus a single moving average, the dual moving average crossover would be the next step. With this technique, you calculate both a short term and a long term moving average, for example an 8 versus 35 day average. You buy when the 8 day crosses above the 35 day, 

and you sell when the reverse occurs. Here again, Hochheimer did some excellent research in the testing of optimum crossover periods, using 20 different combinations for the years 1970 1979. Some of his optimum combinations are: 

C Silver 13 versus 26 days

Pork bellies 25 versus 46 days

Com 12 versus 48 days

Cocoa 14 versus 47 days

Soybeans 20 versus 45 days

Coppper 17 versus 32 days

Sugar 6 versus 50 days 

Dave Barker also did some fine work in systems testing. He tested the 5 versus 20 day dual MA crossover system (without optimization) versus an optimized dual MA crossover system for the 1975 1980 period. Not surprisingly, the optimized version consistently outper formed the straight 5 versus 20 day version. Here is a partial list of Barker's best combinations: 

0 Silver 16 versus 25 days

Pork bellies 13 versus 55 days

Com 14 versus 67 days

Cocoa 14 versus 38 days

Soybeans 23 versus 41 days

Copper 4 versus 20 days

Sugar 14 versus 64 days 

It is particularly interesting to note the close correlation between some of Hochheimer’s and Barker’s optimized crossover combinations. 

For those operators who wish to pursue moving averages crossover trading further, here is a description of two trading systems, one long term and the other short term, that have been shown to work well in 1992 and 1993. 

Long term system Either of the following combinations: 

0 Close versus 5 day EMA versus 8 day EMA. 0 Close versus 7 days SMA versus 50 day SMA. 

Where: SMA Simple Moving Averages and EMA Exponential Moving Average 

0 Buy signal: the first time that the close plus both MA's line up positive, Buy tomorrow on stop at high of today plus 3 ticks. 

0 Sell signal: the first time that the close plus both MA's line up negative, Sell tomorrow on stop at low of today minus 3 ticks. O Exiting a market: use money management stop of US$1,500. 

It should be noted that this is a long term system which utilizes loose stops. 

Short term System 

Use 60 minute (hourly) bat charts. (For this analysis, you will require an on line inttaday technical analysis system.) Trades are made on the close or next day's opening. Avoid taking trades based on intraday signals. Watch the following indicators: close price, 7 day SMA and 50 day SMA. 

0 Long entry: if you get a bullish close versus 7 SMA versus 50 SMA line up on 60 minute chart, buy tomorrow on stop at high of today plus 3 ticks. 

0 Short entry: if (you get a bearish close versus 7 SMA versus 50 SMA line-up on 60 minute chart, sell tomorrow on stop at low of today minus 3 ticks. 

0 Exiting a market: initial stop: US$600.00. Advance stop by US$300 when you have a US$400 profit. Move stop to break even after US$800 profit. Do not change this stop. 

As you can readily see, one of the virtues of a computerized trading system is that it is quite specific and exact. Another significant feature is that it suffers no bias for the long side of each market, as the majority of speculators do. All signals are derived from the mathematics within the system. 

In essence, it boils down to this. A trading system is a tool, and like most tools, there are quality ones and mediocre ones. No system can be the ‘ultimate answer' to consistent profits and at best must be combined with good market strategy, money management and viable risk control. There are still plenty of successful traders who wouldn't know the difference between a data disk and a slipped disk. However, in the hands of an objective and distiplined operator, the ‘right’ system can be a significant aid for successful trading. But, and here comes the big ‘but' again, its benefit will be proportional to the patience and discipline with which the operator applies the system. 

Chapters 14 and 15 should have provided you with a realistic, understandable introduction to systems trading. For a more detailed study, which is outside the scope of this book, refer to other works completely devoted to computer systems trading.