RISK AND REWARD

Proper money management should address two basic topics, risk andreward. A trader cannot address one without addressing the other andexpect to benefit from money management. This was one of the mainproblems with the Fixed Fractional methods. Any variation of themethod either addressed the growth without the overall risks (i.e., optimalf) or it addressed the risks (i.e., risking less than 3 percent oneach trade), which would inadvertently leave the potential reward falteringlike a bird with one wing. There were attempts to address bothof these topics somewhere in between the 3 percent or less variationand the optimal f variation. However, the efficiency of doing so wasflawed by the characteristics of the method itself. Therefore, no matterwhat fixed fractional method is applied, either the risk, the reward,or both are inadequately addressed.The goal behind developing a new money management methodwas to start by addressing both the risks and rewards of money managementin general. As stated earlier, for any situation with a positiveoutcome, the only type of money management that should beused is an antimartingale type method. This means that as equityincreases, the size of the investment or trade should also increase. Asequity decreases, the size of the investment or trade should also decrease.This is opposite of the martingale type where size increasesas equity decreases and vice versa. Therefore, the type of moneymanagement must stay the same as for the Fixed Fractional. Usingthat as a beginning point, I began to list the pros and cons of themethod. My list looked something like this:Pros1. Geometric growth was possible with higher percentages.2. Risk could be maintained with lower percentages.Cons1. Using higher percentages subjected the account to catastrophicrisks.2. Using lower percentages took too long to implement and thereforewas inefficient.3. Using a percentage in between did not properly proportion thereward potential with the risk potential.After contemplating these pros and cons for awhile, I decided thatthe root of the problem was that the method required unequalachievement. It was illogical for the Fixed Fractional method to requiremore profits from the system or strategy at the beginning andless and less profits as the equity increases. If anything, I concluded,80P82 FIXED RATIO TRADING RISK AND REWARD 83it should be the other way around. A money management methodshould require fewer profits at the beginning (hence be more efficient)and more profits as the equity increased (which would addressthe risk).At first, I tried different ideas for increasing the requiredamount to increase contracts, but I wasn’t completely satisfied. Thenit dawned on me that the answer is in the relationship of number ofcontracts being traded to the amount of profits required to increaseto an additional contract. And, that relationship should remain fixed.If the money management required $10,000 in profits trading onecontract to increase to two contracts, than it should require $20,000additional profits when trading two contracts to increase to three.Hence, this relationship was a fixed ratio of contracts to requiredprofits. This is how the Fixed Ratio method came to be and how itearned the name Fixed Ratio.The Fixed Ratio method has only one variable, the delta. Thisvariable simply fits into the mathematical formula of the method anddetermines how aggressively or conservatively to apply the moneymanagement. The lower the variable, the more aggressive the application.The higher the variable, the more conservative the application.There is no bell curve with the Fixed Ratio method.The following comparison of the Fixed Fractional and Fixed Ratiomethods shows where the increase levels are and how they relate toone another:Fixed Fractional Fixed RatioNumber ofContractsRequiredAccountBalanceNumber ofContractsRequiredAccountBalance$10,000 1 $10,00020,000 2 20,00030,00040,000 3 40,00050,00060,00070,000 4 70,000As the number of contracts increase with the Fixed Ratio method,the amount required for the next increase in contracts increases exactlyproportionally. As a result, the risk decreases far below that ofthe Fixed Fractional method. However, according to this scale, thegeometric growth is much quicker with the Fixed Fractional method.In fact, barring the effects of asymmetrical leverage, it will take$19,375 in profits based on a single contract to reach the $70,000 accountlevel for this Fixed Fractional method. Using the Fixed Ratiomethod of 1 contract per $10,000 in profits, it would take $40,000 toreach the $70,000 level. This is double the amount of the Fixed Fractionalmethod.Because the risk is so much less with the Fixed Ratio method, asmaller Fixed Ratio may be used. One of the problems with thefixed fractional method is that it takes too long to begin using themoney management in trading due to the large sum of money onecontract must generate. The Fixed Ratio method has decreased therisk on the long end of the trading and therefore may be utilizedquicker on the front end of trading. The comparison of the FixedRatio and the Fixed Fractional method can be made with a smallerdelta (or Fixed Ratio):Fixed Fractional Fixed RatioNumber ofContractsRequiredAccountBalanceNumber ofContractsRequiredAccountBalance1 $10,0002 20,0003 30,0004 40,0005 50,0006 60,0007 70,0001 $10,0002 15,0003 25,0004 40,0005 60,000With this example, the Fixed Fractional is using one contractfor every $10,000 in the account while the Fixed Ratio is using adelta of $5,000. As a result, it only took $20,000 to reach the$60,000 level instead of $40,000 to reach the $70,000 level. Further,another $5,000 in profits would take the account up to $85,000.Therefore, the geometric growth of the account is starting to reallykick in at this time.The formula for calculating the levels at which contracts (or optionsor shares of stock) will be increased is as follows:8 4 FIXED RATIO TRADING RISK AND REWARD 85Previous requiredequity + (No. of contracts x delta) = Next levelStarting balance = $10,000(first required level)No. of contracts = 1Delta = $5,000$10,000 + (1 x $5,000) = $15,000 to increase to 1contractsIf the account balance goes above $15,000, then $15,000 becomesthe previous required level in the equation:$15,000 + (2 x $5,000) = $25,000$25,000 + (3 x $5,000) = $40,000$40,000 + (4 x $5,000) = $60,000$60,000 + (5 x $5,000) = $85,000The word delta stands for change. It is the only variable in theequation that the user freely changes to fit a particular methodand/or trading style. It is also the variable that can change the dynamicsof the outcome. As a general rule, the smaller the delta, themore aggressive the money management, the larger the delta themore conservative the method.Fixed Ratio trading has a relationship of dollars required to numberof contracts being traded to achieve those dollars. This relationshipis a 1:l ratio. Multiply the number of contracts and the dollaramount required to achieve an additional contract must be multipliedby the same number. If the ratio is 1:$5,000, then you know that toincrease from 10 to 11 contracts, you will have to achieve $50,000 inprofits:1 x 10 = 10$5,000 x 10 = $50,000This number is not the same as the required account balance. It is theamount of additional profits required to increase to the next level.Because of this relationship, other relationships exist within themethod that allow us several additional benefits. First, because ofthis relationship, we can estimate the performance of any system orstrategy simply by plugging in a few statistics. If a particular tradingstrategy in the bond market produced $50,000 in profits over thecourse of 100 trades, the average trade is $500 ($50,000 + 100 =$500). Since the relationship of the Fixed Ratio method of dollars requiredto increase remains exactly proportionate to the number ofcontracts being traded, we also know that if we have an average tradeof $500 using a $5,000 delta, we will increase contracts on averageonce every 10 trades. If it takes 10 trades to increase from 1 to 2 contracts,it will take 10 trades to increase from 10 contracts to 11 (onaverage):$5,000 / $500 = 10 (trades on average)To increase from 10 contracts to 11 will require $50,000 in profits:10 contracts x $5,000 = $50,000Since we are trading 10 contracts we know our average trade alsoincreases by a factor of 10. Therefore, the equation is:$50,000 / $5,000 = 10 tradesThus, after 100 trades, we can estimate that we will be trading10 contracts. If you were to extend the $5,000 delta table to 10 contracts,you would know that the $50,000 in profits based on trading asingle contract should yield approximately $225,000:$85,000 + (6 x $5,000) = $115,000$115,000 + (7 x $5,000) = $150,000$150,000 + (8 x $5,000) = $190,000$190,000 + (9 x $5,000) = $235,000Subtract the starting balance of $10,000 and you come up with$225,000 in profits! Obviously, trades do not carry the same averageP86 FIXED RATIO TRADINGin uniformity throughout the entire sequence of trades. The first 50trades may have produced $35,000 of the profits (which makes the averagetrade $700), whereas the second 50 trades only produced$15,000 of the profits (which brings the average trade to $300 for thesecond 50 trades). It makes no difference in our estimate where theaverage is at any given point. For the method will simply increasecontracts faster during the period when the average is at $700 than itwill when the average is at $300.However, this is only an estimate, and it is a liberal estimate atthat. The reason it is not set in stone is asymmetrical leverage, whichthe estimate does not take into consideration. A conservative estimatethat includes asymmetrical leverage is about 90 percent of theestimated profits. There is no possible mathematical formula for includingasymmetrical leverage simply because it is solely determinedon the sequence of trades, as discussed in Chapter 2.After having acquired $100,000 in profits using the $5,000 asthe delta for the Fixed Ratio method, we would be trading 20 contracts.The minimum level of profits to trade 20 contracts is$l,OOO,OOO. Therefore, what took 4 years to generate $225,000 estimatedprofits, generated $750,000 more in profits during the next 4years. Notice that the rate of compounding remained relatively cosnistent.$225,000 is 450 percent more than trading a single contractin four years. $l,OOO,OOO is 400 percent of $225,000 by continuingthe method the following four years. The overall increase from tradingone contract is 1,000 percent or 10 times greater!We have talked about the profit potential, let’s now take a look atthe risk factors. With an account size of $240,000 and trading 10contracts, if a drawdown of $5,000 per contract were to occur, the accountwould draw down to approximately $194,000 or 19 percent:$240,000 trading 10 contracts with a $1,000 loss= ($10,000)$240,000 - $10,000 = $230,000 trading 9 contracts9 x ($1,000) = ($9,000)$230,000 - ($9,000) = $221,000 trading 9 contracts9 x ($1,000) = ($9,000)$221,000 - ($9,000) = $212,000 trading 9 contracts9 x ($1,000) = ($9,000)RISK AND REWARD 87$212,000 - ($9,000) = $203,000 trading 9 contracts9 x ($1,000) = ($9,000)$203,000 - ($9,000) = $194,000 trading 9 contracts and thedrawdown is overIf the same drawdown was suffered trading a single contract, thedrawdown would be 8.3 percent of the account. Therefore, profits increased450 percent while the risk only increased 11 percent! Whencomparing account sizes, would you rather risk 10 percent of $60,000or 20 percent of $240,000? After the drawdown you would be at$55,000 trading a single contract and at $190,000 after trading withthe Fixed Ratio method. This is still a 350 percent increase.The ultimate comparison though is with the Fixed Fractionalmethod. This comparison uses the one contract for every $10,000scenario. With that scenario, after $50,000 in profits based on onecontract, the method would have increased to $830,000 trading 83contracts. After only the first loss of $1,000, the account would dropback by $83,000 to $747,000. After the full $5,000 drawdown, theaccount will be down to $490,000. This is still quite a bit higherthan the conservative Fixed Fractional method but it would havebeen a 41 percent drop. Further, a $10,000 drawdown would dropthe account to $291,000. Can you imagine going from $830,000 inprofits to only $291,000 in profits from just a $10,000 drawdown?The account would be 52 percent higher, but the risk would be at 65percent of the account. Nothing was gained on the risk-to-rewardrelationship.Further, at $40,000 in profits (instead of $50,000), the accountwould be trading 30 contracts with only $300,000 in the account.This means that 64 percent of the profits came from just the last 20percent of the performance record. If the drawdown were to occur atthat point instead of the $50,000 profit level, the account would decreaseto $180,000 and nothing would be gained.You might be saying that the $800,000 is worth using the FixedFractional method and that you are willing to suffer a 41 percentrisk with just $5,000 worth of drawdown. Or, even increase thatdrawdown to $10,000 with a drop in the account of 65 percent for thepotential reward. It is true, you can trade a Fixed Fractional methodand reach larger profits faster. If that is your goal, trade optimal f.However, I have spoken to many, many traders in the past and not oneof them use optimal f because of the drawdowns. Most are not willing88 FIXED RATIO TRADING RISK AND REWARD 89to come so close to $l,OOO,OOO only to give 65 percent of it back on ahit-up. Besides, the delta is an extremely conservative one to be applyingwhen taking into consideration a small $5,000 possible drawdown.By decreasing the delta size to $2,500, that same $50,000would turn into $485,000 trading 20 contracts while risking only 20percent of that. After $30,000 in profits, the Fixed Fractionalmethod would only be at $100,000 while the Fixed Ratio methodusing a $2,500 delta would be at $175,000. The $5,000 drawdownwould take the Fixed Fractional method down to $60,000 while theFixed Ratio method would take the account to $122,500, more thandouble that of the Fixed Fractional!As you can see, there are a few trade-offs; however, when takinginto consideration both risk and reward, the Fixed Ratio method offersa balance between the two. Drawdowns will happen and theyoften determine whether a trader continues to trade. The trader whocannot tolerate the drawdown will not be able to see it through tohigher profits. The strategy will be dumped and replaced with anotheronly to go into another drawdown. This is the cycle of mosttraders. You must take into consideration both the risk and the rewardsof any money management method.This brings us to another relationship that exists within theFixed Ratio method. That relationship is with the drawdown. Similarto the relationship between the average trade and delta, there is alsoa relationship of the drawdown to the delta. For example, if the deltais $5,000 and the expected drawdown of the method is $10,000, theratio of delta to drawdown is 1:2. Whatever is done on the side ofthe delta must also be done on the side of the drawdown. If you takethe drawdown and divide it by the delta (in this case it is 2) you willhave this relationship no matter where the drawdown occurs in relationto the number of contracts being traded. Should a drawdownoccur, the account would suffer a loss that is equal to two deltas (ortwo contracts). If I reach the lo-contract level using the $5,000 deltaand then suffer a drawdown of $10,000 per contract, I cannot decreasemore than two contract levels. Therefore, I will be trading 8contracts at the end of that drawdown. If I am trading 10 contractswith a $2,500 delta and suffer a $10,000 drawdown, I will not dropbelow trading 6 contracts at the end of the drawdown:$10,000 drawdown / $2,500 delta = 4 delta levels (contracts)lo-4=6The great thing about this relationship is that you not only knowwhere you are at all times but what your risk is at any level of drawdowncompared with the delta you are using. The following formulawill yield each level of contract change without having to go througha tedious table process:[(No. of contracts x No. of contracts - No. of contracts) i 21 x delta= minimum profit levelIf the number of contracts I am trading is 10 with a delta of$5,000, then the minimum profit level required would be $225,000:10 x 10 = 100100 - 10 = 9090 I 2 = 4545 x $5,000 = $225,000At $225,000 in profits, I will change from 9 to 10 contracts andfrom 10 to 9 contracts depending on whether I go above or below thatnumber.By simply changing the “- No. of contracts” to a “+ No. of contracts,”I can calculate the upper level of trading 10 contracts. Atthis level, I would increase from 10 to 11 and from 11 to 10 dependingon whether I go above or below it:10 x 10 = 100100 + 10 = 110110 I2 = 5555 x $5,000 = $275,000I have now calculated the lower ($225,000), and upper ($275,000)profit levels for trading 10 contracts. These levels also serve as theupper level for 9 contracts and the lower level for 11 contracts. SinceI am able to calculate these levels as well as calculate the maximumlevels that any drawdown will decrease the account, I know the exactdollar risk at any given time. If my account is trading at $250,000 inprofits, I know that should a $10,000 drawdown occur, I would notdrop below the lower level of 8 contracts:90 FIXED RATIO TRADING APPLYING THE FIXED RATIO METHOD TO STOCK TRADING 918 x 8 = 6 464-8=56 ’56 / 2 = 2828 x $5,000 = $140,000This is the minimum profits I will have if there is a $10,000 drawdown.However, if I wanted to be more exact, I could go a step furtherand calculate the distance between the 10 and 11 contract levels andthat is where I would be between the 8 and 9 contract levels.The amount of $250,000 is exactly halfway between the $225,000lower level and the $275,000 upper level. The halfway mark betweenthe upper level and lower level of 8 contracts is $160,000. This iswhere the $10,000 drawdown would drop the account:10 x 10 / 2 x $5,000 = $250,0008 x 8 / 2 x $5,000 = $160,000The “-No. of contracts” portion of the equation calculates thelower level. The “+ No. of contracts” portion of the equation calculatesthe upper level. Therefore, leaving the plus or minus out of theequation will calculate the exact middle between the two equations.With these three as a reference, it is easy to calculate exactly wherethe account is in the level of contracts being traded to compare to anotherlevel. For example, if the account were at $230,000, then it is 20percent of the way to the exact middle. Therefore, 80 percent of thenumber of contracts being traded would be subtracted in the equation.It is as follows:10 x .80 = 8[(lo x 10 - 8) / 21 x $5,000 =46 x $5,000 = $230,000The compared drop after the drawdown would be as follows:8 x .8 = 6.4[(B x 8 - 6.4) / 21 x $5,000 =28.8 x $5,000 = $144,000This method allows you to know exactly what to expect duringdrawdown periods at any given time. Knowing what to expect is halfthe battle in preparing for what may come along.APPLYING THE FIXED RATIOMETHOD TO STOCK TRADINGThere are some differences in applying the Fixed Ratio method, orany money management method for that matter, to stock trading. Thedifference, however, is not that the markets are inherently dissimilar.The most important fact to understand about money management,and specifically the Fixed Ratio method, is that this is a numbersgame. We are not playing the markets or any aspect of the markets.Nor are we necessarily applying money management to the method orsystem that we are trading. We are applying money management tothe net sum of the profits and losses generated by the markets, methods,or systems producing those profits or losses. Therefore, it doesn’tmatter whether the $500 profit came from IBM stock or the soybeanmarket-$500 has the same value in any market.Since we are playing a numbers game, we can completely ignorethe markets and/or methods being applied and concentrate on thenumbers being produced. With the stock market, however, applyingthe Fixed Ratio method is slightly different for two basic reasons.First, there is a large disparity in margin allowances and betweenstocks and commodities. Margin in commodities can sometimes beless than 10 percent of the value of the underlying market. One S&P500 index contract (which is a futures contract in the stock market)is currently worth $318,000, but to trade one contract in that marketrequires less than $20,000. Margin is only about 6 percent of thevalue of the contract. Stocks, on the other hand, only allow a 50 percentmargin rate. Therefore, if you buy $50,000 worth of IBM stock,you must have $25,000 in the account. Later, we discuss how thismargin difference affects the application of money management.The second major reason for the difference in application is theability to trade odd lots. It used to be very hard to find a broker whowould actively trade 103 shares of a stock or 17 shares of a stock;now you can find them all day long. Odd lots are exactly what theysound like, a position size other than a nice round number. The mostcommon size was 100 shares, which is also the value of one option in92 FIXED RATIO TRADINGstocks. One option is on the value of 100 shares. Nonetheless, thisability to trade odd lots allows for highly efficient money managementapplication.These are the two major differences when applying the FixedRatio to trading stocks, but before continuing, I need to stress thatthis type of money management is not for buy-and-hold strategies.Buying and holding is a method of investment. You might consider atrading account to be an investment; however, the trades themselvesare normally based on active buying and selling. Wal-Mart stockbought back in the 1970s and held today is definitely an investment.Money management requires increasing and decreasing the size ofthe trade as the equity increases and decreases. Buying and holdingusually does not use margin, and increasing an existing positionwould actually fall under the category of pyramiding. So, if you areonly buying and holding stocks, this section generally will not applyto you.