TABLE 22-2. Simulated Runs
Red Blacka
35 runs of | 35 runs of §12 runs of 2 14 cuns of 2
7 runs of 3 it runs of 3
7 runs of 4 3 runs of 4
2 runs of S 2 runs of S
2 runs of 6
[run of 8
 
138 cotal occurrences 118 toral occurrences
is a wi i ingle black coup,currence of black is a winner. Although $64 is actually won on a sicach sequence of runs nets only the initial bet because of the accumulated Josses duringi 22-2, there were a total of 65 distin
that sequence. For the 256 coups shown in Table 22-2, t unsresulting in a profit of $65 (or $455 based on a $7 initial bet), or about one-half at the initial capitalization ($128 or $1,000, respectively). Instead of using Martingales, if we haused the benchmark strategy of betting equal amounts on black to win on every coup, wewould have lost $20 ona $1 bet. The Martingales method, therefore, has a good chance o!
winning a reasonable amount.*
Anti-Martingales -
i-Martingales approach offers a smailer chance of winning a large amount, it isais the onpecie of apolying Martingales. Instead of doubling each losing bet, the wineners are doubled until a goal is reached. Because there isan excellent chance of 1 run fein 256 coups and a similar chance of a longer run, this method wins if the don mun occ <in the first half of the number of coups to be played (256 in this case). Onc
ust immediately stop playing.
ene Sready know that a mun ore returns $32 on a bet of $1, and a run of 8 ners $128.This method would have lost if it had been applied to black in the test sequence: ec sethere were 138 red coups with no black runs greater than 5, there would haye been a tossof $138. If the bet had been on red, looking for a run of 6, there would, have een reewins, each for $94, and a loss of $118 for that many appearances of black. Waiting for arinof 8 would have won $128 and lost $117 on black by stopping right alter the win, e suc:cess of anti-Martingales depends on how soon the long run appears. In 09 6 coups, anonof 11 will occur once, returning $1,024 on a bet of $1. In the same 4,096 spins, ther
2 The Martingales approach is likely to work if the player could withstand adverse runs of 11, but casinos tend tolimit bets to amounts significantly less than 2"? times the minimum bet.eRFIGURE 22-5 Betting pattern.
678910 111213 1415
   
7 oo: @ 24 ewe2 1@i24 @OO 23 +@i24 GOO: 24 OM1@: - Bi2485 28000 M1 B12
||
 
GAMBLING TECHNIQUE—THE THEORY OF RUNS. 569
be 2,048 losses, showing that if the long run happens in the middle of play, the methodbreaks even; if it occurs sooner, you win.
The Theory of Runs Applied to Trading
Before applying either Martingales or anti-Martingales to the markets, it must be deter-mined whether the movement of prices up or down is as uniform as in the case of roulette.A simple test was performed on a combined set of 21 diverse futures markets. The com-bined results of all up and down runs are shown in Table 22-3. The expected occurrencesof both up and down were twice the probability of either a red or black coup occurring.
Some differences between the random pattern previously used and actual results canbe seen in Table 22-3. These futures markets show fewer runs of 1 and more frequent runsof 2; their tendency to fluctuate in a narrowing pattern around the expected (random)length of a run (Figure 22-6) may be due to the smaller sample of longer runs. The proba-bilities found here might be used to decide the chances of the next trading day continuingin the direction of the prior day’s trend, noting that a 3- to 4-day run is as long as might beexpected. The most interesting applications are in the betting strategies of the Martingalesand anti-Martingales methods, applied to futures markets. The following sections showtwo possibilities.
Trading Daily Sequences
By combining the Theory of Runs with the direction of the trend, the chances of being onthe correct side of the longest run are increased; and, the size of the price move in thedirection of the trend may also tend to be larger. To give yourself the best chance of iden-tifying the trend, it should be long-term. Assuming that the trend is up as.determined froma chart or moving average, enter a long position on the close of a day in which the pricemoves lower.
If Martingales is used, double the position each day that prices move adversely. A sin-gle day in which prices move up should recoup all losses and net a reasonable profit. If thetrend is sustained, there should be fewer days down and more days up, thereby yielding abetter return to capitalization ratio. A variation on Martingales might include holding thetrade for 2 consecutive days in the profitable direction because of the bias shown in the dis-tribution of runs. Another variation would take profits while prices are moving in a favor-
TABLE 22-3 Expected Occurrences of Ups and Downsfor a Diverse Set of Markets
 
21 Markets Combined
 
Length Expected Probability ——e—veveeeeeof Run of Occurrence Expected Actual-1 12 1,225 1214
2 14 — 612 62003 8 306 314 Ine 153 1678 1732 7 676 M64 38 47 W128 19 16a 1/256 10 59 11512 . 5 3paid 11,024 4007 5Total tested 449
  
 
 
PRACTICAL CONSIDERATIONS570
FIGURE 22-6 Actual futures movement compared with random movement.
 
 
 
 
 
 
 
 
 
 
 
 
 
coprER1970-753™1621 COMBINEDCATTLE: 1936 CONTRACTS# 'Sesgs82 | Expected: esulte¢ ° Bameary Res& 73.75g££Zé22s5 S*SOYBEANS7378X16MEAL73.952 —+cotton -1970-75 -2POTATOES50.7340
 
 
 
 
  
3 4 3 6 7 8{MBER OF CONSECUTIVE OCCURRENCES (RUNS)
 
|
  
GAMBLING TECHNiQUE—THE THEORY OF RUNS s7t
able direction and set new trend positions after 1 or even 2 days of price reversal. Eithervariation might improve the return ratio after a random occurrence of runs.
For the anti-Martingales approach, double the position after each profitable day, takeprofits after runs of 3, and begin again after a reversal day. By trading with the trend, profitsequences may be increased to 4 days; it may also be expected that, on average, the pricechange will be smaller on days that move counter to the trend.
‘System Trading
A standard trend-following system can expect 30% to 40% successful trades (called its re/i-ability) of varying profitability, which can be defined in terms of a profit/loss ratio. In con-sidering the Martingales or anti-Martingales methods, it should be noted that the lowerprobability of profitable trades would make the wait for a long run of profits less attractive.If a system has a profile of 35% successful trades and a profit/loss ratio of 3 : 1, chen trad-ing equal amounts on each signal results in the following, assuming $750 each profit and$250 each loss:
Total trades 100 x $25 (commission) = $-2,500Profitable trades , 35 x $750 = $26,250Losing trades 65 x $250 = $-16,250Net ($75 per trade) $7,500
‘Taking these same figures and applying Martingales to a uniform sequence of twolosses and one profit gives $275 as the first loss ($250 plus a $25 commission), $550 forthe second loss, then $2,175 for the profit, netting $1,375 for three trades, which wouldreturn $229 per contract traded.
‘The disadvantage of applying Martingales to the irregular returns of high-leverage mar-kets is that a long run of losing trades requires a large amount of capital. If it is necessaryto keep a large reserve in the event of a long run of losses, why not simply trade equalamounts of a larger position on each signal, without using Martingales? A sound tradingstrategy should differ from a pure gambling situation because a specific system will win inthe long term, while you will lose at roulette, The results show that trading the same larger
_position on each signal will return a higher profit than an application of Martingales, which
requires the same available capital; however, a less aggressive betting method that assumesfavorable odds can improve the return on investment.
In another study of applying Martingales, an actual trading system based on Wilder'sRSI was used to create buy and sell signals.? During the test, a total of 277 contracts wereheld at one point, which is far beyond the realm of the normal speculator. That means aninvestment of 277 times the initial margin, plus any accumulated loss, just to recover oneunit of your initial margin! It should not be surprising that the risk-to-reward ratio of thisbetting method was found to be unacceptably large.
Complex Martingales
The-simple Martingales discussed do not present an attractive way of managing risk; how-ever, a slightly more complex form is far more practical and has very different results.Instead of doubling the bet each time there is a loss, as in thé case of simple Martingales,increase the bet by a smaller amount, for example, 40%.‘ This slows down the process andavoids the risk of ruin, or table limits. You may even choose to divide one bet into more than
3 Roger Altman, “Tactical Trading Revisited,” Technical Analysis of Stocks & Commodities (September 1993).
“James William Furguson, “Martingales," Technical Analysis of Stocks & Commodities (February 1990); and“Reverse Martingales,” Technical Analysis of Stocks & Commodities (March 1990). 
 
S72 PRACTICAL CONSIDERATIONSation in which you would trade 8 contracts may be traded in two trades of4 each. You must simply remember to stop the sequence and begin again when your profits have exceeded your losses. In the following example, each loss is followed by increasingthe bet by an equal amount. When a profit occurs, the bet size is reduced by one unit andthe sequence ends when there is a net profit. Profits and losses are equal to the bet size.
one, so that a situ:
—_—_—<—_EXAMPLE | Equal-Size Bets with Equal Payoff
Bet Amount Result Net Profit or Loss#1 $500 Loss —$500#2 $1,000 Loss $1,500#8 $1,500 Loss $3,000#4 $2,000 Profit -$1,000#S $1,500 Profit $500
0 win twice to realize a profit the size of the original invest-
Example 1, it was necessary tm weve Id be achieved with 40% winning trades and 60% losing
ment; however, that profit coultrades. .
‘Applying this strategy to a more realistic trading profile, consider a system with an
average loss of $1,000, an average profit of $2,000, and a win to loss ratio of 1 to 3. Thismeans that there are 2 losses and 1 profit in every 3 trades; a net system result of zero,equivalent to a gambling situation. Example 2 shows another sequence of trades. Eventhough there are 3 losses to start, a single win nets a profit for the sequence.
EaEXAMPLE 2 Equal-Size Bets with a Trading System ProfileEXAMPLE 2 Equa
. No. ofBet Units Bet Result Net Profit or Loss#l 1 Loss ~$1,000#2 2 Loss $3,000 S#3 3 Loss $6,000#4 4 Profit $2,000
EN
When applying a more complex form to reverse Martingales, it is best to targetsequences of profitable runs that are likely to occur with reasonable frequency. Instead ofbetting the entire accumulated profit on the next trade, bet a fixed percentage of thoseprofits. Alternatively, if you are looking for profitable runs of 4, remove the amount of theinitial bet from the total bet after the system has returned two profits in sequence. This
tends to conserve capital but slows down the process. —
SELECTIVE TRADING
realistic to think that you can always follow a technical, fully automatic system
veutheut manval intervention. Overriding system signals may occur for reasons of soundrisk management during a crisis period when you feel that the system is not programme
to deal with the current volatility and that a conservative action is the best business policyThe beginning system trader often has concerns that the impersonal buy and se
orders will not react properly to the underlying forces that are driving prices. This can
 
 
 
SELECTIVETRADING 373
 
cause the trader to override the system signals. For example, if the program is geared totake profits after a move of 2%, the trader might judge that the current price move is goingto continue; therefore, he will hold the trade rather than take profits. The application ofthis special intuitive filter generally favors holding a position through ups and downs untilit shows a profit, rather than applying consistently good risk management. Judgment tendsto interpret ali news in favor of the position being held until it shows a profit. A trader whowill survive must learn not to take a loss personally, to keep losses small, to establish andstay with a trading plan, and to filter out unsupported opinions. Trading is a business, andbusiness principles must apply.
Technical systems can be taken to extremes in an effort to automatically select onlyprofitable trades. Two approaches to this are most common. The use of more than onetrend indicator, such as two moving averages, is one method of isolating the best trend. Itis intended to find a smaller piece of a trend that is more reliable or one that performs bet-ter than a single, longer trend. In principle, it is no different from using three, four, ormore trends of different periods to isolate the one point of a price move that always gen-erates profits. As you become more and more selective, you will find that your opportuni-ties have disappeared, you have used your capital poorly, and the performance profile hasactually deteriorated. Using multiple trends, just as any system with many rules, is anotherattempt at perfection, but only succeeds at overfitting the problem.
There are many systems that can be bought that promise profits. Trying to incorporatea black-box approach, a method that does not disclose its exact rules, to improve the per-formance of your own program is not a good idea. Without knowing everything about theother system, there may be inadvertent dup! ion of a faster trend, a 3-day cycle, or someother feature. You may think that an analysis of the correlation of results between theblack-box system and your own method will show if the methods work well together, butthere are stil] too many uncertainties. The unknown system may have been overfitted andwill not show its real risk, or it may havé a particular weakness to a market pattern that hasnot occurred during your testing period. You must understand every method that youtrade. It’s your risk.
The best way to create a successful trading system is to look for unique elements, eachwith a sound basis, and combine them one at a time, testing each to be sure they success-fully stand on their own. The selection of the speed of a moving average will be moreimportant than either the smoothing technique or the number of moving averages to beused. There may be an advantage to the double moving average approach, but a third,fourth, and so on, lose their significance. A momentum indicator bears a close resem-blance to a moving average when its rules are to buy or sell in the direction of the pricemove, especially when it crosses the zero line. Both have great similarities and will notoffer much diversification when applied to the same data. Each system building blockshould be fundamentally different. A technique, such as a breakout method, that does notdepend on time would be a sensible complement to a moving average, which is driven bytime. The more complicated cycle and wave theories, contrary opinion, and other methodsall view price movement in a completely different way than a moving average, even whenapplied to the same data. The same moving averages may make the most sense when youapply the same period to different types of data, such as volume and-open interest, or com-pare two related series, such as the Swiss franc and German bund exchange rates.
Filtering is a tool not restricted to price analysis, but applicable to money management,reliability, risk, portfolio selection, and other aspects ofa trading program. Selection of whichmarkets to trade and position size is as important as the buy and sell signals. If the systemitself corrects for high-volatility markets by decreasing the distance of the stap-loss point(Keeping the risk constand), it would be redundant to trade fewer positions of that market,thereby reducing the effects of any profits or losses relative to other items in a portfolio.
 
  
 
574 PRACTICAL CONSIDERATIONS
SYSTEM TRADE-OFFS
Although traders are continually searching for a system that has no losses,'they are realis-tic enough to know that most profit, loss, and risk decisions are dependent on oneanother. Just as in Gambling Theory, a system can be structured to have frequent smalllosses and occasional large profits—or frequent small profits with some large losses. It issimply not possible to create a system with such small losses that these losses are essen-tially zero without increasing the frequency of the losses to the point at which profits rarelyoccur. In short-term or high-leveraged trading, the cost of doing business prevents such anapproach from working.
The basic principles of systematic wading require that the trader choose between thefrequency of profits to losses, the relative size of those profits and losses, and the numberof opportunities that will be available to trade. These interrelationships will be different for
various types of systems.
Trend-Following SystemsThe relative risks and rewards of a trend-following system are based primarily on the selec-tion of the trend speed. As an example, using a simple moving average system applied toclosing prices, Figure 22-7 shows that a faster moving average (smaller number of days)will stay closer to the current price than a moving average that uses a larger number ofdays. The maximum risk is equal to the largest lag, as measured from the current price tothe corresponding moving average value. This lag is limited by:
M=P-(LXN)/2where Pig the current closing price, Z is the limit move or 3 standard deviations of the aver-age daily true range, and Nis the number of days in the moving average.
The smaller losses of the faster trend system are kept in proportion to the profitsbecause of the relative system sensitivity. The price changes of smaller magnitude, whichcause the moving average to change direction and hold losses to a minimum, also breakthe sustained trends into shorter movements. The net results are more frequent tradeswith relatively small losses and modest profits. Longer-term trends cause fewer trades by
ns
FIGURE 22-7 _ Relative risk of a moving average system.
Faster
moving7 averageSlowermovingaverage
           
Maximumrisk forfaster
movingaverage
Maximumrisk forslower‘movingaverage
—_—F;
=— Commodity
yee
 
 
 
SYSTEM TRADE-OFFS 575
 
holding to the market direction for a longer time. This results in larger profits and corre-spondingly larger losses.
The risk of a single trade being small or large is not a complete measure of trading risk.Because there are more losses than profits in normal trend-following systems, it is impor-tant to consider the sequence of losses as part of the ultimate risk of trading. It is theaggregation of these losses that provides a reasonable comparison in determining whethera slow or fast moving average system has the best profit to loss ratio.
‘The feature of a trend system that is most appealing is the small losses relative to largeprofits. This feature also causes frequent small losses during sideways markets, and thenumber of these false signals cannot be significantly reduced simply by using a longer-termtrend. Testing will show that there is always some sideways price movement that coincideswith the trendline, resulting in a high percentage of whipsaw losses. It is unrealistic toexpect a smoothing technique to produce more than 40% to 45% profitable trades.
Countertrend Systems
The risk and reward structure of a countertrend method is different from that of a trend-following approach. Although the size of your profits and losses relates to the time periodof analysis in a manner similar to trend following, positions must be set in advance of anexpected price reversal. This clearly introduces more risk and makes the success of themethod dependent upon good timing. When countertrend methods are discussed here,those techniques that require a confirmation (ie., they wait until prices reverse their direc-tion) are not included as countertrend systems.
Due to the greater risk of a countertrend system, its objectives are generally welldefined. In a trend system you let the profits run until prices reverse; however, most coun-tertrend methods rely on an oscillator, contrary opinion, or an overbought/oversold analy-sis, and set goals for exiting when the overbought or oversold condition disappears. Thisresults in a profile that limits profits; therefore, it should not also limit losses.
Trade-Offs
The selection of a performance profile goes together with particular trading styles. Somecombinations are entirely incompatible. Ideally, you would want very large profits, highreliability, and small losses. Unfortunately, these combinations are not possible. The trade-offs that are readily available are:
1. A few large profits and frequent small losses
2. Many small profits and a few large losses
3. More opportunities with greater risk _4, Fewer opportunities with less risk
It is easy to identify the first combination with trend following. To have fewer lossesyou must allow greater risk. Keeping losses small means being stopped out because of mar-~ket noise rather than underlying trend; therefore, you can expect many more losses thanprofits. In the case of a countertrend system you might profit from market noise, whichaccounts for a large percentage of the price variability. The moves caused by market noiseace also much smaller and more frequent than trend moves. To profit from noise you mustenter the market while prices are going in the opposite direction, as in a countertrendtechnique, and allow more risk. This causes the profile in option 2, many small profits anda few large losses.
The last two choices are-the result of a random distribution of price moves..If you lookback at the study of runs, you will remember that price changes exhibit a patiern very simi-lar to random movement. For every 100 days of prices, there will be 50 days in which pricesseem et soanemangal
 
een
 
 
576 PRACTICAL CONSIDERATIONS
 
reversed after only 1 day of up or down movement, 25 days of price movement in the samedirection for 2 consecutive days, 12.5 days for 3 consecutive days, and so on. Although realprice patterns may vary slightly from that distribution, they are very close. For any fixed timeperiod, these patterns remain the same; that is, there are always more opportunities forSmaller moves than larger ones. To hold a trade for the long term, you must be able to with-stand all of the market noise that might occur during that period. The longer you hold atrade, the greater chance you will see jarger market noise, or adverse price moves.
You can see how this applies to a countertrend trading using a typical price oscillator.Figure 22-8 shows the fluctuations ofa sideways market, one that has no trend bias. Assum-ing that there is a normal distribution of prices, there is a clustering near the center andless frequent peaks and valleys as prices move further away from the ‘middle. Construct anoverboughvoversold indicator, which can be categorized as slightly (S), moderately (M),or extremely (E) overbought or oversold, by drawing lines on Figure 22-8.
Tt can be seen that there are more opportunities to buy a slightly oversold market andsell a slightly overbought market; all prices must pass through the area closest to the cen-ter before reaching a more overbought or oversold condition. Therefore, the opportunt-ties must increase as profit goals decrease. But what about the risk? If profits are limited,tisk must be restricted to a small past of the potential profits, or not limited by a dollarAmount but by a patterned condition. In this countertrend system example, an attempt tomake losses small relative to profits entered during the slightly oversold zone would causethe number of losses to increase dramatically, overwhelming the potential profits (seen inFigure 22-8). If losses are not restricted, they will be larger when there are more opportu-nities with smaller price objectives, and smaller for the fewer cases when prices are in theextreme zone. The minimum risk occurs on a single trade taken at the absolute extremepoints. Figure 22-9 shows the relationships that exist in a standard countertrend system.
‘All systems have trade-offs. To reduce the losses, either the profits or the frequency ofopportunities must be reduced whether the trading approach favors the trend or coun-tecteend. A trend follower looking for the big move must also take a big risk. In the devel-opment of a system or trading philosophy, personal preference determines thecombination of risk, reward, and opportunity.
The Commodex Method of Combining Elements\
‘The Commodex system was first presented in 1959 and is still active, published daily byCommodity Futures Forecast in New York. Commodex combines the components mostacceptable to the experienced trader in a unique weighting method. It includes movingaverages, price momentum, and open interest to calculate a trend index.
‘The most interesting aspect of the Commodex system is its ranking process, intendedto produce a relative strength value for each trend. Using a 10- and 20-day double moving
FIGURE 22-8 Countertrend alternatives using detrended price series.
    
 
 
 
 
 
versold , Overbought
 
Ov
 
i13ii
 
SYSTEM TRADE-OFFS 577
 
FIGURE 22-9 Relationship of profits to risk per trade based on opportunities.
             
‘Overbought-oversold
Extremely Moderately Slightly
   
Profits per trade
Risk per trade
o 12 3
OpportunitiesEEE
average, the system scores the current market performance to establish the value of the‘trending component. Bullish and bearish values are calculated by looking at three situa-tions independently: the simple moving average signals derived from both the long- andshort-term trends, and the double moving average signal generated by combining the twotrends. The two techniques of single and double moving averages are exactly as treated inChapter 5. The most important of the three factors is the long-term trend; second is theshort-term trend, and last the relative position of the fast to the slow moving average. Thestrongest upward-moving trend is generated when current prices are above both the faster-and slower-moving averages and the faster average is below the slower. The opposite posi-tions would result in the strongest downward-trending component. Trends are consideredneutral if the most important element, the long-term moving average, conflicts with theother two factors. .
‘The rate of change in open interest is considered a secondary reinforcement of thetrend. Using a concept different from the usual charting techniques, Commodex considersit a bullish sign if there is an increasing growth momentum in open interest combined withrising prices. The growth momentum is the difference between the rate of increase of theopen interest and the 20-day moving average of the open interest. Continuing a bull movewith rising prices and rising open interest is a classic concept of charting. The bear moveis confirmed with rising open interest and falling prices. Conimodex also considers a dropin open interest along with falling prices to be a bullish factor. The movement of volume istreated in the same manner as open interest and can confirm a bull or bear trend. Anincreasing volume momentum with rising prices is support of an upward move; othercombinations indicate bear trends. -
‘Added together, the signals are ranked from a strong buy to a strong sell with lesserdegrees in between. The system must be given credit for the quantification and balancingOf these elements, which are generally treated as highly interpretive charting techniques.The rules for applying the daily signals to trading combine both the individual strength ofthe signal with the movement of the Commodex trend index. The trend index itself acts asan overbought-oversold indicator, encouraging profits at specified leyels and consideringa position reversal in more extreme situacions; stops are placed using the 20-day movingaverage with predetermined band penetrations. Additional objectives are based on the 
 
 
s78 PRACTICAL CONSIDERATIONS
 
profits accrued from a trade, with a 50% return justifying a protective stop On part of thepositions, and a 100% profit requiring the liquidation of half the position. These moneymanagement concepts are an important aspect of any system and tend to round out Com-modex.
The Commodex system has been used as an example of combining techniques thathave been studied individually in previous sections. It is important to see that each ele-ment is simple to understand and avoids duplication; it has single and double moving aver-ages (with and without bands), momentum indicators derived from yolume and openinterest, an overbought-oversold indicator formed from a combination of all elements,trading stops, and liquidation based on money management and inverse pyramiding.
Combining Trends and Trading Ranges
‘Trends and trading ranges account for most price movement; a small percentage cannot beidentified. Most traders must decide whether they intend to profit from trend moves orsideways markets and then develop techniques that target that objective. A trend is con-cerned with the periodic tendency of prices to move in one direction without a limitingobjective, and a trading range is a definition of price containment. The role of time is different for the two approaches. The trend is expected to advance with some regularity overtime, while prices within a trading range can move in any direction with varying speed,providing the upper and lower bounds are not violated.
"Trading ranges and trends take turns dominating price movement, with the tradingrange most common. Long-term trends are easy to see, as for example, represented in thebuying power of the U.S. dollar and the Consumer Price Index. When there is no actual oranticipated change in fundamental factors, prices fluctuate in a restricted range, boundedby support and resistance levels. The top of a trading range is often wider than the bottombecause of the inherently greater volatility at higher prices; but even with the broader for-mation, there is a clear point at which prices have gone higher and are no longer withinthe trading range.
It often happens that the two techniques of price trend and trading ranges are in con-flict: The trend is up and a resistance level is encountered, or the downtrend is stopped bya support level. Established