TRADING A PORTFOLIO WITHOUTMONEY MANAGEMENT

Reinvestment strategies aside, portfolios are extremely beneficial forseveral reasons. As already mentioned, the first and most obvious isreduction in risk. A primary goal in creating a portfolio is to be ableto stay in the game should one or more of the trading vehicles not per-/ form as expected. Not putting all the available risk capital in onemarket automatically extends the staying power of any trader. Anothergoal and benefit of trading multiple markets and/or systems isithat it is likely to improve the risk/reward ratio.For our example for this statement, we will use the coin-flippingexample from Chapter 2. However, we will have slightly different1rules for one of the coins. The first coin is going to be the quartermarket. For the quarter market, every time the coin lands heads up,; the player will win $2. Every time the coin lands tails up will yield a; $1 loss. The next coin will be the half-dollar market. Every time theIcoin lands tails up will yield the player a win of $1.50 and every time!the coin lands heads up will yield a loss of $1. There will be 100 flipsof each coin. The first 100 flips will all be from the quarter market.1 ’The second 100 flips will all be from the half-dollar market.118120 PORTFOLIOSThen, there will be a separate time when each coin is flipped 100times except this time they will take turns being flipped one rightafter the other alternating in a 1: 1 even sequence. Just for the record,I am actually flipping the coins to represent real-life action. We willthen apply the same examples to the same system in two differentmarkets to show the remarkable resemblance between the effect ofcombining the actual system and market trades with the coin-flippingexamples.The first flips came from the quarter market. There were 52 tails(losing trades) and 48 heads (winning trades). The net profit was $44after 100 flips with a drawdown of $12.00. The second set of flipscame from the half-dollar market. This set of flips produced 47 tails(winning trades with the half-dollar) and 52 heads (losing trades).The net profit totaled $18.50 with a drawdown of $8.50. By adding thetwo together, the net profit is $62.50 and by adding the drawdown, theworst case possibility is both drawdowns occurred at the same timewould be a total drawdown of $20.50.Table 8.1 was taken from the Performance I money managementprogram. All quarter trades were on odd days and half-dollar tradeswere on even days to simulate trading markets alternately. As a resultof putting the two markets together, the total drawdown wasonly $15.00, not $20.50.The third illustration using these coin flips came from flipping thehalf-dollar first and then flipping the quarter. The wins and losses ofeach outcome are the same as the first two examples. Out of 200 flips,there were 50.5 percent winning trades for a total profit of $80.00.Meanwhile, the largest drawdown was only at $9.50. By separating thetwo markets through the Performance I program, the quarter marketalone generated 55 winning trades for $65.00 in profits with a drawdownof $8.00. The half-dollar market produced $15.00 in profits after46 percent winning trades and a drawdown of $7.50. The drawdownadded together totaled $15.50. In both instances, the drawdown wassmaller in the combined example.Now we will apply the same logic to actual markets. The firstmarket is the bond market. The second is the Swiss franc market.The same system is being applied to each market during the sametime period. The statistics for each market individually are shown inTable 8.2.The particular statistics that we need to pay close attention toare the total net profit of each market, winning percentage, andlargest drawdown. The total net profit for the bonds came in atTRADING A PORTFOLIO WITHOUT MONEY MANAGEMENT 121TABLE 8.1 Random Coin FlipDate Market W/LAccountBalancel/1/98l/2/98l/3/98l/4/98l/5/98l/6/98117198l/8/98l/9/98l/10/98l/l l/98l/12/98l/13/98l/14/98l/15/98l/16/98l/17/98l/18/98l/19/98l/20/98l/21/98I/22/98l/23/98l/24/981125l98l/26/98l/27/98I/28/98l/29/98l/30/9811311982121982131982141982/5/982161982161982171982181982191982/10/9850 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 150 cent 150 cent 1quarter 150 cent 1quarter 150 cent 1quarter 1($1.00)(1.00)1.502.00(1.00)(1.00)(1.00)2.00(1.00)(1.00)(1.00)(1.00)1.50(1.00)1.50(1.00)(1.00)(1.00)1.502.00(1.00)(1.00)(1.00)(1.00)(1.00)(1.00)1.50(1.00)(1.00)(1.001(1.00)(1.00)(1.00)(1.00)1.50(1.00)(1.00)1.50(1.00)(1.00)2.00(2.00)(0.50)1.500.50(0.50)(1.50)0.50(0.50)(1.50)(2.50)(3.50)(2.00)(3.00)(1.50)(2.50)(3.50)(4.50)(3.00)(1.00)(2.00)(3.00)(4.00)(5.00)(6.00)(7.00)(5.50)(6.50)(7.50)(8.50)(9.50)10.50)11.50)12.50)11.00)12.00)13.00)(11.50)(12.50)(13.50)(11.50)(Continued)126 PORTFOLIOSTABLE 8.2 System 1 BondsBondsTotal net profitNo. of tradesNo. of winnersNo. of losersWinning %Gross profitGross lossSwiss FrancTotal net profitNo. of TradesNo. of winnersNo. of losersWinning %Gross profitGross loss$ 41,7181278 24565%$ 95,750$ 54,031$ 58,4252101416967%$114,625$ 56,200TRADING A PORTFOLIO WITHOUT MONEY MANAGEMENT 127TABLE 8.3 Bonds and SF Single Contract Combined StatisticsAverage winnerAverage loserRatio average tradeAverage trade W/L/DMaximum DDProfit factor$1,167$1,200.97$ 328$5,9681.77Total net profit $100,413 Average winner $ 9 4 3Number trades 337 Average loser $ 966Number winners 223 Ratio average trade .98Number losers 114 Average trade W/LID $ 297Winning % 66% Maximum DD $7,025Gross profit $210,375 Profit factor 1.90Gross loss $110,231Average winnerAverage loserRatio average tradeAverage trade W/L/DMaximum DDProfit factor$ 813$ 8141.00$ 278$8,1252.04$41,718 and at $58,425 for the Swiss franc. Add the two net profitstogether and we come up with $100,143. The winning percentage forthe bonds came in at 65 percent, while the winning percentage forthe Swiss franc was 67 percent. Finally, the drawdowns for each totaled$5,968 for the bonds and $8,125 for the Swiss franc. Add thetwo together and the combined total drawdown is $14,093.The risk/reward ratio of net profit to drawdown for the bond marketis computed at 6.99. The risk/reward ratio for the Swiss franc iscomputed at 7.19. Add the two net profits and drawdowns togetherand we come up with a risk/reward ratio of 7.09. The same number iscalculated if you add the 6.99 and the 7.19 and then divide by 2:(6.99 + 7.19) I2 = 7.09The two market performance records will now be combinedchronologically and new statistics formed. This simply means that ifthe bond system traded every Monday and the Swiss franc systemtraded every Tuesday, that each bond trade would be followed by aSwiss franc trade and every Swiss franc traded followed by a bondtrade. Table 8.3 shows the combined statistics.Notice that the total net profit remains the same as the two singleperformance totals being added together. The winning percentageis the average of the two single performance statistics. The drawdownon the other hand is not the two added together, nor is it the twoaveraged together, but is its own, completely independent statistic.(Although in this case, it is very close to the average of the twosingle-performance drawdowns. However, there is still no relationship.)This makes the risk/reward ratio increase all the way to 14.26.This is the greatest benefit of creating portfolios.The reason the drawdown is so much lower than the sum of thetwo drawdowns added together is because the two single largest drawdownsoccurred two years from one another. They did not occur at thesame time. The sum of the drawdowns represents the largest possibledrawdown between the two and can only occur if they happen simultaneously.Even if they are overlapping, the drawdown will not cometo $14,093. It has to be something less than that number.As a result of this necessity, the more markets and/or systemsthat are being traded in a portfolio, the less likely that the sum of allthe added drawdowns will be suffered. To examine the probability,we will use two coins for our illustration. We will flip each coin twicewith the tails up representing the drawdown. Each coin will beflipped at the same time. There are four possible outcomes from thefirst flip:1. Coin1 = heads Coin2 = heads2. Coin1 = heads Coin2 = tails3. Coin1 = tails Coin2 = heads4. Coin1 = tails Coin2 = tails128 PORTFOLIOS TRADING A PORTFOLIO WITHOUT MONEY MANAGEMENT 129These are the only four possibilities and each has an equalchance at occurring. Therefore, each has a 25 percent chance of happening.If the tails represent the drawdown, then there is only a 25percent chance of both drawdowns occurring at the same time. If anothercoin is added to the scenario (i.e., another market), the probabilityof all three drawdowns occurring at the same time are only12.5 percent. If all three are flipped at the same time, there are eightpossible outcomes:1. Coin1 = heads Coin2 = heads Coin3 = heads2. Coin1 = heads Coin2 = tails Coin3 = heads3. Coin1 = tails Coin2 = heads Coin3 = heads4. Coin1 = tails Coin2 = tails Coin3 = heads5. Coin1 = heads Coin2 = heads Coin3 = tails6. Coin1 = heads Coin2 = tails Coin3 = tails7. Coin1 = tails Coin2 = heads Coin3 = tails8. Coin1 = tails Coin2 = tails Coin3 = tailsThese are the only eight possibilities and each has an equalchance at occurring. Therefore, each have a 12.5 percent chance ofhappening. If the tails represent the drawdown, there is only a 12.5percent chance that all of them will land tails up at the same time.Every coin that is added will cut the percentage probability in half sothat by the time you are trading 10 markets, there is less than a %O of1 percent chance of all landing tails up at the same time. That is betterthan 1 in 1,000 odds! Even though the probability that the addedsum of the drawdown occurring will continue to diminish, 100 percentof the profits from each market will be added. This means thatthe risk/reward ratio over the long haul continues to improve.The previous example was with coins and limited to the drawdownseither happening now or not happening now. In trading, theprobability is fractionally smaller with just two markets. When weflipped the coins, we flipped them at the same time and either thedrawdown was going to occur or it wasn’t. Trading drawdowns are different.Each time the coin is flipped, the coin landing heads up is consideredthe largest drawdown. With trading, however, the largestdrawdown occurs only once (in hypothetical testing). In other words,the test results given for the bonds and the Swiss franc were over afive-year period. If the longest drawdown in each market were to lastfor three months apiece, then the five-year period would need to bedivided into 20 equal divisions of three months per division. Sincethe largest drawdown will only occur once, there is a 1 in 20 chance,or 5 percent chance, that it will occur at any given three-month timeperiod. This means that with just two markets over a five-year timeperiod, there are two chances in 40 that they will occur but 1 chancein 400 that they will occur at the same time. The probability is 1/4 of 1percent that in any given three-month period, one market will sufferits largest drawdown during the same three-month period as theother market. Add another market to that scenario and the odds areonly 1 in 8,000 that all three will occur simultaneously. With fourmarkets, the odds are %O,OOO, and that factor is a multiple of 20 everytime you bring another market into the picture. Meanwhile, 100 percentof the profits are added to the net profit total.These statistics look pretty promising for portfolio trading. Althoughthis information is all accurate, one other statistic needs to bediscussed further to shed more light on the subject. Up to this point,we have only discussed the largest drawdown and that was based onhypothetical back testing. However, one little known statistic that isnot revealed by most system vendors is that most systems are in adrawdown of some sort between 60 and 75 percent of the time. Thismeans that only 25 percent to 40 percent of the time is the equitymaking new equity highs. If we take the adjective “largest” off theword drawdown, it becomes an entirely different scenario.In the coin-flipping example with three coins, the probability ofat least one of them being in a drawdown (or tails) on any given flipis 88.5 percent. The probability of any two of them landing tails up(drawdown) is 50 percent:1. Coin1 = heads Coin2 = heads2. Coin1 = heads Coin2 = tails3. Coin1 = tails Coin2 = heads4. Coin1 = tails Coin2 = tails5. Coin1 = heads Coin2 = heads6. Coin1 = heads Coin2 = tails7. Coin1 = tails Coin2 = heads8. Coin1 = tails Coin2 = tailsCoin3 = headsCoin3 = headsCoin3 = headsCoin3 = headsCoin3 = tailsCoin3 = tailsCoin3 = tailsCoin3 = tailsAdd another market and the percentage goes higher at the samerate it went lower for all of them being in a drawdown at the sametime. A fourth market would increase one of the markets being in a130 PORTFOLIOS PORTFOLIOS AND THE FIXED RATIO MONEY MANAGEMENT METHOD 131drawdown at any given time to 93.75 percent. The probability of anytwo of the markets being in a drawdown at the same time is 68.75percent. The probability of any three of the four being in a drawdowncomes to 31.25 percent. That is the rest of the story. You have to remember,though, that the probabilities of one or more of the marketsnot being in a drawdown at any given time is the same as the probabilitiesstated for markets that are in drawdowns.Once again, trading is not coin flipping. As stated earlier, mostsystems are in drawdowns between 60 and 75 percent of the time(they are not making new equity highs). And lest you think that goodsystems can’t possibly be in drawdowns that much of the time, here isan example of a system in crude oil that was optimized:Total net profit = $60,690Number wins/losses = 29154Winning percentage = 53.70Largest drawdown = $3,750Average trade = $1,173Win/loss ratio = 3.25Numbers don’t get any better than that. However, the system wasmaking new highs in this market only 35 percent of the time. Thatmeans it was in drawdown 65 percent of the time! You say how canthat be? A new equity high must come from a winning trade; however,a winning trade does not necessarily have to make a new equity high.Therefore, the maximum amount of time even possible for making newequity highs is equal to the percentage of winning trades. Since a winningtrade is not, by definition a new equity high, some winning tradesare not going to make new equity highs. There were only 53 percentwinning trades meaning that unless every single winning trade alsomade a new equity high, the maximum time period that the systemwas making new equity highs could not have exceeded this percentage.Further, having a higher winning percentage system does notmean that you will have a higher percentage of the trades makingnew equity highs. As a general rule, the winning percentage is relatedto the win/loss ratio. The higher the winning percentage, thesmaller the average win to average loss will be (there are exceptionsto this and there are no set numbers-it is just a general rule). Thereasoning behind the rule is that having a higher winning percentagetrading method means that profits are taken often while the risk ona per trade basis remains relatively high. I have an end-of-day systemin the S&P that targets a $650 profit but will let the trade moveagainst me by as much as $1,250. Although the winning percentageis 85 percent, it only makes new equity highs 33 percent of the time.The system still makes money; it just takes more winning trades tomake up a single loss.As a result of this single statistic, there are even higher probabilitiesthat one or more markets in any given portfolio are sufferingthrough a drawdown. This information is certainly not placed withinthis book to discourage you from trading portfolios. It is simply includedto give you a full picture of the dynamics of trading with portfolios.The bottom line is that trading with portfolios will increasethe long-term risk/reward ratio by a significant sum. Further, moneymanagement is not based on the number of drawdowns, but ratherthe largest drawdown. Therefore, the smaller the largest drawdown,the more efficiently the money management can be applied.One last caution before moving on. The largest drawdown withina hypothetical testing situation does not mean in any way, shape, orform that this drawdown cannot be exceeded in the future. Further,it is completely impossible for hypothetical results, no matter howprofitable, to ensure that the method will generate any amount of netprofit over time. Systems are not mathematical certainties. As a generalrule, they are math formulas applied to price action trying tocapture potential profitable trades in the future. Price action doesnot have to conform to whatever mathematical parameters were appliedto it. Markets change as do the way they move and are traded.Therefore, you cannot rely on these statistics and probabilities to determineabsolutes from a performance standpoint.PORTFOLIOS AND THE FIXED RATIOMONEY MANAGEMENT METHODThe more you understand the Fixed Ratio money managementmethod, the more you will understand how much drawdowns can affectthe final outcome of trading. Potential drawdowns determinehow much capital is needed to start as well as how aggressively orconservatively the trader should apply money management to thestrategy. The lower the largest expected drawdown, the higher thepotential returns after applying money management. The higherthe drawdown, the lower the potential returns by applying the Fixed132 PORTFOLIOS PORTFOLIOS AND THE FIXED RATIO MONEY MANAGEMENT METHOD 133Ratio money management method. The reason is the lower the drawdown,the smaller the delta variable can-be in the Fixed Ratio formula.The smaller the delta variable, the faster the Fixed Ratiomethod will affect trading. The larger the delta variable, the slowerthe Fixed Ratio method will affect trading.This has nothing to do with changing the risk factor of themethod. If the largest expected drawdown is $5,000, a 2: 1 ratio ofdrawdown to delta is $2,500. If the largest expected drawdown is$10,000, a 2 : 1 ratio of drawdown to delta is $5,000. The relationship ofthe increase levels to the drawdown potential remains the same inboth. However, if each make the same amount of net profits, the strategywith the lower delta will make considerably more profits than themethod with the larger delta variable.Also, the more you understand money management and geometricgrowth in general, the more you will understand that the benefits ofapplying money management are more visible on the back end thanthey are on the front end. It is exactly the opposite of the law of diminishingreturns. If you had gone without food for days and days andthen walked into a burger joint and bought their largest, thickest,everything on it including the kitchen sink, burger for $5.00, the firstburger would return the greatest benefit and be the most satisfying.If you were still a little hungry after the first and decided to buy asecond, you might not finish the second. Therefore, the second burgerwas less satisfying and returned a smaller benefit than the first. Ofwhat value would be a third burger? None. With money management,it is exactly the opposite. The first increase will yield the least benefitbecause it will yield smaller profits. The more risk increases that areexperienced, the greater the profits.Using the math for figuring out levels at which to increase risk,we can determine what the account size will be when the methodreaches the 5-contract level using a $5,000 delta:5 x 5 = 25 / 2 = 12.512.5 x $5,000 = $62,500 + Starting account balance of $20,000= $82,500.Now calculate the minimum account size to trade 10 contracts:10 x 10 - 10 I 2 = 4545 x $5,000 = $225,000 + $20,000 = $245,000.Now calculate the minimum account size to trade 15 contracts:15 x 15 - 15 I 2 = 105105 x $5,000 = $525,000 + $20,000 = $545,000.Now calculate the minimum account size to trade 20 contracts:20 x 20 - 20 / 2 = 200190 x $5,000 = $950,000 + $20,000 = $970,000.Therefore, 5 contracts to 10 contracts yields $162,500 in profits.The yield for 10 to 15 contracts is $300,000 in additional profits. Finally,15 to 20 yields $425,000 in additional profits.If it took exactly the same number of trades and profits based ona single unit to achieve each level, the last set of trades yielded$262,500 more profits than the first set of trades that made the exactsame amount on a single-unit basis.The Three Phases of Money ManagementBecause of this effect, I have divided the application of money managementprinciples into three phases. The first is the sowing phase.This is when the account is at the minimal level needed to begin tradingand apply money management. The account is trading a singleunit. During this time, the trader will receive the least benefit fromthe money management and suffer the greatest effects of asymmetricalleverage. The second phase is the growing phase. This is thephase where the account starts to see significant growth from theapplication of money management, the effects of asymmetrical leverageare diminishing, and the trader is close to a point of no return. Inother words, by applying proper money management, even if the systemor method that is being traded goes down the toilet, the traderwill still show profits.The final phase, the harvest phase, is where the trader reapsgreat rewards from applying proper money management. Asymmetricalleverage is almost nonexistent and not only is the trader to thepoint of no return, but even if the system being traded fails, significantprofits will have been preserved.Trading the Fixed Ratio method on portfolios tackles two majorobstacles. First, since the risk/reward ratio has been vastly improved,134 PORTFOLIOS PORTFOLIOS AND THE FIXED RATIO MONEY MANAGEMENT METHOD 135it allows the trader to benefit from the money management sooner.The sooner the money management can increase the risks, the soonerthe trader will get past the first sowing phase of trading. Second,profits do not diminish by combining markets and systems and thereforethe trader can use the profit potential of several markets or systemsto reach the growing and harvest phase of trading.As a result, the goal with applying the Fixed Ratio method is toapply it to as small a risk/reward ratio as possible. Often, more thanone market or system is traded at the same time. The question oftenarises as to whether the money management should be applied toeach individual market or to the markets combined as a portfolio. Wehave already given the answer but the proof is in the pudding, or resultsin this case. Since smaller drawdowns allow for more efficientmoney management results and higher single unit profits bring enhancedmoney management results in the long run, it is only logicalthat combining the markets and systems and applying the moneymanagement to the combined portfolio as a single entity, is the mostefficient application of the money management.We will begin with the single contract result for the bond andSwiss franc example used earlier (see Table 8.2).Next, the money management will be applied to the bond marketindividually and then to the Swiss franc market individually. Thedelta will be determined by using 1/z of the largest drawdown roundedup or down to the nearest $500. This means that for the bond market,a delta of $3,000 will be applied and to the Swiss franc market, adelta of $4,000 will be applied. The results are shown in Table 8.4.These numbers are based on profits only. There is no starting accountbalance to these numbers and therefore the risks are based onprofits at risk only. The total net profit between the two markets is$636,636 with a total possible $ drawdown of $130,219, which is stillonly 20 percent of the profits.TABLE 8.4 Individual Results for Bonds and Swiss FrancsBonds Swiss FrancTotal ending equity $271,544 $365,092Total number contracts 1 4 14Maximum current percent risk 20% 20%Maximum current dollar risk $ 55,144 $ 75,075TABLE 8.5 Fixed Ratio to Combined Bonds and Swiss FrancsCombined ResultsTotal ending equity $1,327,536Total number contracts 28Maximum current percent risk 13.5%Maximum current dollar risk $ 129,822Look again at the previous single contract results for both thebonds and Swiss franc. Notice that the combined drawdown is $7,025,which means the delta is calculated at $3,500 for Fixed Ratio moneymanagement purposes. Meanwhile, the total net profits remain thesum of the single market profits added together at $100,143.The results in Table 8.5 are from applying the Fixed Ratio moneymanagement to the combined portfolio.These results are almost unbelievable. However, the numbersand trades prove that this is the effect of money management whenapplied to portfolio situations compared with application to singlemarkets and/or systems. Notice that the net profit is more than double,while the dollars being risked are lower than the dollars beingrisked on the individual market application results. This is the resultof reaching the harvest phase of applying money management. Further,these are only two markets in the five-year results.The number of contracts being traded is listed at 28. This meansthat 28 contracts are being traded on both markets. If the next signalis a bond trade, 28 contracts are traded. If it is a Swiss franc trade, 28contracts are traded. If a signal is generated in both markets, then 28contracts are traded in both markets. Many traders have a difficulttime with this concept. The reasoning is that the logical thing to do isto trade 14 contracts in each market. However, that is what each marketwas trading when the money management was being applied tothe single performance records. Further, contracts are increased accordingto profits in the markets and have already taken into considerationthe largest expected drawdown of the combination.The percentage of profits being risked on the single market applicationwas 20 percent with each market. The percentage being riskedeven with trading 28 contracts on each market is only 13.5 percent. Ifthe total number of contracts were 14 per market, the risk would be6.75 percent. Portfolios can be a huge tool to increase dramaticallythe efficiency of the Fixed Ratio trading method.