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itutestHow to DeveloppInWinning Trading SystemsTharThat Fit You021VanWorkshop(c)2Dr. Van K. Tharp, PhD&CopyrightRJ HixsonRecorded Video Handout

TharpObjectivesInstitutePosition Sizing Strategies1. To gain an overview of basic position sizing strategies,including CPR for traders.Van2. To learn some general guidelines for position sizing strategiesdepending on your objectives.Copyright(c)20213. To learn several strategies used by great traders to get maximumreturns.

itutePosition sizing strategies are the part of your trading system that answersthe question “how much” throughout the course of a trade.InstThe purpose of position sizing strategiesis to help you achieve your objectives.rpEffective position sizing strategies require two inputs -Tha1. Trading Objectives – Are they well defined? Have both components? Drawdown – avoid (plus your perceived probability) Returns – achieve (plus your perceived probability)(c)2021VanPossible Trading Objectives Make as much money as possible without worrying about drawdowns oreven ruin Maximize the probability of achieving your returns Maximize the probability of meeting returns objective while minimizingprobability of hitting your max drawdown (or some level of drawdown) Minimize the probability of ruin or even hitting a drawdown of X% Asset allocation for systems/asset classesrightBy assigning figures to these variations, you can see that a HUGEnumber of objectives (perhaps infinite) is possible. Each set ofobjectives would have a position sizing algorithm that wouldmaximize the likelihood of achieving those objectives.py2. System PerformanceCoSQN is easiest single measure for development of your position sizing strategy Higher SQN scoring trading systems makes it easier for position sizingstrategies to achieve your objectives Lower SQN scoring systems make it more challenging (for the positionsizing strategy and for trading) to achieve your objectives

021VanTharpInstituteUnderstanding CPR for Traders(c)2This figure shows the relationship between the Risk (R) per unit, the Position Size(P) for the trade, and the total equity or Cash (C) at risk in a trade. With any of thetwo variables the third can be calculated by following the “Y”.htP C / R Or P RT / RUPosition Sizerig(# of units) Cash (the equity you are willing to lose on the trade in or RT)Risk (difference between entry price and initial stop in per unit or RU)CopyWe’ve shown it this way so you don’t have to memorize the formulas. Just rememberthese simple mnemonics that you can use to remember the Y diagram:“I learned CPR at the Y.” or “Cash, Position Size, Risk.”

Martingale vs. Anti-Martingale SystemsWhen applying % of equity strategies - how do you define equity?stThere are three ways:ituteSome Position Sizing Strategy BasicsInTotal Equity: Equity is cash plus equity amounts in open positionsTharpReduced Total Equity: Equity is cash plus equity in open positions that stopsprotect.Core Equity: Equity is available cash only—no portion of open positions areincluded.VanSome Very General Equity Risk Percentage Guidelines0210.1% to 1% per trade when managing other people's money0.8% to 2% per trade when trading your own money3% or greater (according to Ed Seykota) is being a gunslingerAdditional Position Sizing Strategiespyright(c)2Percentage of VolatilityPercentage of MarginPercentage of LeverageOne Unit per So Much EquityScaling InScaling OutGroup RiskPortfolio Heat—Total Portfolio Heat should not exceed 20% to 25%Going for the Moon StrategiesCoRecommended - Market’s Money/Creative Position Sizing StrategiesNot Recommended - Kelly Criterion Percentage, Optimal f: (What fraction ofyour maximum loss should you bet?), Fixed Ratio Trading

ituteSome Position Sizing GeneralExamples For Different ObjectivesstObjective 1: Make as much money as possible withoutworrying about drawdowns or ruin.rpInMethod 1: Risk the % Risk that Gives You the Highest MedianGainSystem Quality Number score above 5.0 – could do as much as 4%,but be careful of multiple correlated positions. System Quality Number score above 3.0 – could do as much as 2.5%,but again be careful of multiple correlated positions. System Quality Number score above 1.75 – could do as much as1.5%, but be careful of multiple correlated positions. System Quality Number score below 1.75 – with this objective,trading this kind of a system is probably a disaster021VanTha (c)2Method 2: Bill Eckhart PyramidingStart at ½-1% of equity and as the price goes up by a certain amount – whichyou define, scale in 3-4 times. Limit, however, your total exposure to themaximum amounts suggested in Method 1.rightObjective 2: Maximize probability of meeting goals.pyUse Percent Risk that Gives Highest Probability of Meeting YourObjectiveCo System Quality Number score above 5.0 – could do as much as 2.5%,but be careful of multiple correlated positions.

System Quality Number score above 3.0 – could do as much as 2.0%, butagain be careful of multiple correlated positions. System Quality Number above score 1.75 – could do as much as 1.25%,but be careful of multiple correlated positions. System Quality Number below score 1.75 – with this objective, tradingthis kind of a system is probably a disasterInstitute Method 1: Market’s MoneyTharpObjective 3: Maximize the probability of meeting your goal,while minimizing any loss to your initial equity.VanOn starting equity use % risk that has 0% chance of ruin. But on profits, userisk percent that is optimal for achieving goal or use median gain %.021Here are some examples for your starting risk (i.e., on your core equity beforemarket’s money):System Quality Number score above 5.0 – could do as much as 1%,but be careful of multiple correlated positions. System Quality Number score above 3.0 – could do as much as 0.8%,but again be careful of multiple correlated positions. System Quality Number score above 1.75 – could do as much as0.5%, but be careful of multiple correlated positions.right(c)2 py System Quality Number score below 1.75 – could probably trade thiswith 0.5%, but would not recommend using much more than 0.75%with Market’s Money.CoFor the Market’s Money portion of your position, use the examples listedabove for Objective 2.

ituteMethod 2: Use a Market’s Money strategy, but convert themarket’s money to equity every month.This is more conservative than Method 1. Scale-Out to maintain constant open riskScale-Out to maintain constant volatilityIn stMethod 3: Scaling-OutTharpThis method could require monitoring your position sizing on a periodicbasis—weekly, daily, or even hourly—to maintain a fairly constant exposure.What potential risk are you exposed to?(c)2021Van Here you need to calculate the difference between the current valueand the stops of each position you have. This is called the open risk ofyour portfolio. What if you controlled the total open risk or limited theopen risk of each open position by scaling-out of positions to limityour open risk? Think about the potential here. You could monitoreach position and make sure that your exposure was always 2% or lessper position. This means that, except in runaway markets, yourbiggest risk would always be about 2% per position. You must have aSystem Quality Number score of at least 2 to do this.right In addition, think about the potential volatility of each of yourpositions. What has the volatility been in the positions you hold overthe last few days? Is this volatility going up? What if you limited it byscaling-out of positions when a certain level of volatility has beenpassed?Copy Consider monitoring both ongoing risk and ongoing volatility with atotal equity calculation.

ituteObjective 4: Minimize probability of ruin or even adrawdown of X%.Method 1: Percent Equity Risked:System Quality Number score above 5.0 – could do as much as 1%,but be careful of multiple correlated positions. System Quality Number score above 3.0 – could do as much as 0.8%,but again be careful of multiple correlated positions. System Quality Number score above 1.75 – could do as much as0.5%, but be careful of multiple correlated positions. System Quality Number score below 1.75 – could probably trade thiswith 0.5%, but would not recommend using much more than 0.75%with Market’s Money.VanTharpInst 021Method 2: Calculate your average maximum R-drawdown and usethat to calculate position size.(c)2Let’s say your objective is to avoid a 25% drawdown at all costs. Andhere, we are talking about a drawdown at any time in the curve of 25%—not just a drawdown of 25% from the starting equity.CopyrightThe way we’ll do that is to calculate the maximum drawdowns of oursystem in terms of R. Let’s simulate a system making 100 trades 10,000times to see what is possible in terms of drawdowns expressed in termsof R.

itutestInrpThanVa(c)2021The median maximum drawdown was 38R. But in 1,000 of the simulations(i.e., the 10% level), we had a maximum drawdown of 62R. The table belowshows other probabilities from the simulator from this particular system.Probability of Maximum R-Drawdowns in Our SystempyrightMaximum y DD100%76.4%50%25%10%5%1%CoYour system, depending upon its R-multiple distribution, will have differentprobabilities.

InstituteLet’s use the 10% level of -62R to do our calculations. Thus, we can feel withcertainty that we have less than a 10% chance of reaching these levels. If wedivide 25% by 60R, we get a risk level of 0.4%. This is pretty similar to ourestimate of our initial risk size. However, if we want to only have a 10% chanceof a 25% peak-to-trough drawdown in our equity curve, then we must neverrisk more than 0.4% with this system. And if we wanted to guarantee a 1% orless chance of such a drawdown, we probably shouldn’t risk more than 0.2%(i.e., 25% drawdown/93R 0.00269).rpMaximumLosing g TradePercentageFrom The Definitive Guide to Position Sizing StrategiesExpected Losing Streaks in 100 Trades(or Losing Streaks as a Function of Winning Percentage of Trades)100%10%1% ProbabilityProbability forAverage LosingProbability forfor a Losinga Losing StreakStreak Lengtha Losing StreakStreak ThisThis LongThis LongLong2345 to 63356 to 7335 to 67 to 8346 to 78 to 94579 to 1045810 to 1156912671013 to 147811 to 1215 to 168913 to 1418 to 1991115 to 1622101318 to 1925 to 26121522 to 2332Method 2 Summary Steps-ht1. Determine the worst-case peak-to-trough equity drawdown you’d like toavoid.rig2. Simulate your system and determine the probability of various R-levelmaximum drawdowns.Copy3. Determine the maximum drawdown in terms of R at the probability levelyou are willing to accept.4. Divide this level into the value you selected at step one and the result shouldbe the position sizing level as a percent risk that you should use.

Objective 5:ituteBelief: Asset Allocation and Position Sizing are the same—they bothare designed to answer the question of “how much.”stMethod 1: Asset Allocation for Classes of Investments.TharpInSuppose you want to always hold some positions in the strongest markets ormarket sectors. You could do this by buying ETFs and staying in those positionsuntil they show themselves to be weaker than the S&P 500 or until they are out ofthe top relative strength positions. One good way to pursue this strategy is toallocate a percentage of your total capital to this strategy (i.e., such as 20%). Thisway you could invest in the five strongest sectors.nMethod 2: Asset Allocation between Systems.021VaTom Basso and Jack Schwager have shown that monthly or quarterly rebalancingworks to improve the performance of non-correlated traders, then it should alsowork with non-correlated systems.If you have 3 different systems, allocate money based on the following:The System Quality Number score of each system, with the best systemgetting the most money.(c)2 If the systems have similar SQN scores, allocate equally between them.rig 5.0 SQN 60%3.0 SQN 30%1.75 SQN 10%htoooCopyEach month (or quarter), rebalance your money between the systems basedupon the initial allocation.In Every Case of Calculating YourPosition Sizing Risk Amount -Remember that you also need to manage your total risk at the portfolio

stitutelevel. Numerous open positions in the market probably constitutemultiple correlated positions. Multiple correlated positions can act likeone big position when exogenous events happen – outside events whichaffect all positions in the market simultaneously. We refer to totalportfolio risk exposure as Portfolio Heat.rpup to 20%up to 15%up to 12%up to 6%up to 3%ThaSQN Score above 5SQN Score 3 - 5SQN Score 1.75 - 3SQN Score 1.75SQN Score 1.3 - 1.75InRough Guideline for Portfolio Heat Amounts021VanExample – You trade a system with a SQN score of 3 and based on yourobjectives, you intend to risk 1% of your equity on each position. You also knowthat you can have up to 24 positions open at any one time. Using the portfolio heatguidelines above you realize you would not want to have more than 12% open riskin the market at any one time. Therefore, you would then adjust your risk amountper position from a max of 1% down to a max of .5%.Copyright(c)212% portfolio heat / 24 open positions max .5% risk per position

Strategies of the MastersituteEd Seykota’s Market’s Money StrategyrpInstWhen you size to make the optimal rates of return, you risk big drawdowns, whichis usually not acceptable. However, if you only position size for optimal rates ofreturns on the equity you’ve earned from the market (i.e., the market’s money),then it’s possible to still have huge returns without risking a large drawdown toyour starting equity.ThaFor example, you might determine that the optimal risk size for returns is about5%, but that anything over 1% risks unacceptable drawdown. Thus, you might risk1% of your starting equity and 5% of the market’s money.VanFor example, if you started with 100,000, then the starting position size would bebased on 1% of 100,000 or 1000.021However, two months later your total equity might be 120,000. Now you can risk1% of 100,000 (i.e., 1000) plus 5% of 20,000 (i.e., the markets money), whichis also 1000. Thus, your new position size would be 2000. Your equity has onlygone up by 20%, but your position size has doubled.(c)2It’s possible to make huge rates of returns using a market’s money philosophy.The only question you need to answer is “WHEN DOES THE MARKET’SMONEY BECOME MY MONEY?”htAt the end of the year when you get taxed on it.At the end of the month when you must report to your investors.At any other time period.After your account has increased by a desired percentage.After your account has increased by a desired amount of money.Copyrig

Tom Basso - Scaling OutituteRisk Control1. New Position RiskInstFirst, use a decision making model to decide the price at which you will enter themarket. Make sure you have a plan to get out of the trade if you are wrong. Thisplan should include some sort of stop loss point to protect you from catastrophicloss. Convert the distance from the stop into dollars per contract.TharpExample: Buy gold at 400, with a stop price of 390, and the objective being ashigh as it wants to go. Let's trail it with a 10-day moving average of the closingprice and use an account size of 200,000. RISK (400 - 390) 100/point 1,000 risk per contractVanNext we decide how many contracts to buy. I trade for clients and I prefer to limitmy risk to 1% of equity. Lower risk levels will reduce your exposure even more.High risk requires more stomach lining and psychological control.021Allowable risk 1% of 200,000 2,000 per positionContracts 2,000/ 1,000 risk per contract 2 contracts2. Ongoing Risk Exposure in an Existing Trade(c)2Some investors/traders limit the risk of a new trade, but forget the psychologicalimpact of higher risk associated with an existing trade. To control existing risk, Ilimit my risk in existing positions to 2.5% of equity.htContinuing with the same example: Gold jumps to 450 overnight and our stopmoves to 405. Our new equity is now 210,000. Where is our current risk andhow do we maintain risk control?rigRisk per contract ( 450 - 405) 100 per point 4500. Since we have twocontracts we have 9,000 risk.Copy2.5% of 210,000 5,250 risk that we can allow. 5,250/ 4,500 risk percontract (see above) 1.167 contracts. Round this down to one contract.Therefore, it's necessary to sell one contract and keep the other one. Thus, everyday the risk of your position is within a fixed range. Thus you are focused on theprocess of good trading, letting profits run and keeping risk to acceptable levels.

Volatility ControlstituteVolatility is the dollar value of the true range of price movement for the day. The higher theamount of volatility, the more it will tend to distract you from your purpose of concentrating ongood trading. Thus, I like to limit the amount of movement in any position to no more than 1%of equity on new and existing positions. This seems comfortable to my clients as well as me.More is a wilder ride, and less volatility is even more stable.InExample: Gold is at 400 and the previous few sessions have averaged 3.00 range for anaverage day. Our equity is still 200,000. How many contracts would volatility allow us to do?rp 3.00 100 per point 300/contractTha1% allowable volatility 1% of 200,000 2,000 per positionContracts 2,000/ 300 6.67 contracts. I'd round this down to 6 contracts.nRisk and Volatility ControlVaLimit your position to the smaller of either risk or volatility. In the two examples shown, riskcontrol yielded 2 contracts and volatility yielded 6, so I'd open the trade with 2 contracts.021Volatility in an Existing TradeCopyright(c)2I limit volatility in an existing trade to 1%, exactly like I calculate it for a new position. Then Ijust peel off the number of contracts necessary to get me back to an acceptable level of 1%equity.

William Eckhardt’s Scaling In with Limited RiskInstituteFor example, suppose you have a 100,000 account and you want to make your money grow asrapidly as possible. You are using a 3 times volatility stop as I did in the random entry tradingsystem (reference Course Update #23a). You’ve also decided that your system is optimal risking24% of equity at a time, using a reduced total equity model. You plan to have as many as sixopen positions at one time, so you are willing to risk up to 4% per position—but not all at once.You’ll build up to a position as big as 4% as your profits increase. Your initial risk will only be2%.TharpLet’s see how such a position sizing strategy system might work. You buy corn at 3.025. Theten day average true range (which we’ll call “V”) is 3.5 cents. Therefore, a 3 times volatility stopis 10.5 cents (i.e., at 2.92), which amounts to a total risk of 525. You can risk 2% of your 100,000, which amounts to 3 contracts (rounded down to the nearest contract).VanYour pyramiding scheme is to add one contract every time your profit increases by one dailyvolatility or V (which is currently 3.5 cents). When this occurs, (i.e., corn moves to 3.06) yourisk another 2% with a 3 times V stop at 2.955. However, your stop on the original positionmoves up by 3.5 cents to 2.955. Thus, you now have six contracts all with stops at 2.955.However, notice that your total exposure of your original equity is now only 3% (actually lessdue to rounding) because you raised your initial stop.(c)2021Let’s say that your daily volatility now increases to 4 cents. Thus, a new stop would now be 12cents or 600. Corn moves up to 3.10, so you can now risk another 2%. (Actually, you couldhave done so at 3.095—when the price had increase by the old V-value of 3.5 cents.) Yourreduced total equity is now 97,000 and 2% of that is 1,940. As a result, you can still purchase3 contracts at 3.10—with a stop at 2.98. You also get to raise your stop on both of your otherunits by their respective V-values. Therefore you now have six contracts with stops at 2.99 andthree contracts with a stop at 2.98.htYou might be saying, “How can you do that? Your risk is over the 3% limit with the reducedtotal equity model.” No, it isn’t because you raised your other stops enough so that yourexposure is still about 3% of your reduced total equity.CurrentRemaining Risk inTotal Risk toStopOriginal EquityOriginal Equity3 at 3.025 2.993.5 cents10.5 cents 5253 at 3.06 2.997 cents21 cents 1,0503 at 3.10 2.9812 cents36 cents 1,800pyrigContractsCoLet’s say that volatility stays at 4 cents and corn now goes to 3.14. It’s time to risk another 2%.Your reduced total equity is now 96,625. You can risk 2% of that or 1932.50. Your 12 centstop is a 600 risk, so you can again purchase another 3 contracts. You must also raise your stopson the existing contracts. The stop on the first six contracts rises to 3.025 (i.e., it was raised 3.5cents, the original V). The stop on the last three contracts rises to 3.02.

CurrentRemaining Risk inTotal Risk toOriginal Equity0Original Equity3 at 3.025Stop 3.033 at 3.06 3.033.5 cents10.5 cents 5503 at 3.10 3.028 cents24 cents 1,2003 at 3.14 3.0212 cents36 cents 1,800InstContractsituteConsider where you are with respect to the reduced total equity model in terms of risk. You nowhave risked 2% four times, but have you exceeded your 4% limit?TharpThe total risk to your original equity is now only 3,550 or 3.55%—still under our 4% limit. Solet’s say corn starts to really get volatile now and V goes to 6 cents. And you get a chance to buymore corn as it goes up to 3.20 (actually you could buy at 3.18, when it increased by the lastvalue of V). But we’ll say that you buy at 3.20.VanYour total reduced equity is now 96,450 and 2% of that is 1,929. Your new stop, at 3 V, isnow 18 cents or 900. Thus, you can now only purchase two contracts, but you also get to raiseyour other stops. Let’s say that we make a decision to leave the break-even stop alone, giving itplenty of room to move. However, you can now move the stop on the second 3 contractspurchased to break-even, move the stop on the contracts purchased at 3.10 to 3.06, and movethe stop on the contracts purchased at 3.14 to 3.06.ContractsCurrentRemaining Risk inTotal Risk toStop 3.03Original Equity0Original Equity0(c)23 at 3.025021Thus, the current risk picture is shown below. Notice that by the reduced total equity model, yourrisk has changed very little. The risk to your original equity is now 3,600 or 3.6%. 3.06003 at 3.10 3.064 cents12 cents 6003 at 3.14 3.068 cents24 cents 1,2002 at 3.20 3.0218 cents36 cents 1,800ht3 at 3.06CopyrigLet’s now say that corn goes as high as 3.50. Your exit gets you out at 3.40. Your profit is asfollows.Contracts3 at 3.0253 at 3.063 at 3.103 at 3.142 at 3.20Profit on Contract37.5 cents34 cents30 cents26 cents20 centsTotal ProfitProfit in Dollars 5,600 5,100 4,500 3,900 3,000 22,100

Your total profit was 22,100 and your maximum risk to your core equity was 3,600.Does that seem like a reasonable rate of return?ituteSome of you might be saying “. but you ended up with 14 contracts! It might have beendisastrous if you’d had some limit moves against you.” That’s true, but my point was toshow you creative a position sizing strategy. In addition, there are other ways to protectagainst such limit moves (i.e., options) that make the risk well worthwhile.TharpInstIn fact, it is quite ironic that at the time I developed this example I was looking at a realcorn trade. Corn actually went above 4.80 in that particular move. Had you reallypressed this particular trade (as this position sizing strategy will allow) that trade wouldhave been a trade of a lifetime. I haven’t figured it out, but you probably could havemade as much as a million dollars without risking over 3,600 in your core equity.However, your risk to your total equity would have been considerable before the tradewas over.VanThere are any number of variables that you can vary in creative money management—your initial stop, your maximum risk per commodity, moving your stops in your favor,your equity model, your money management model, etc. For example, you could evenuse the idea of increasing your “reduced total equity” by raising your stop to justifyopening up positions in other commodities. This could really help the small trader whodoes not have a large enough account to trade using most of these models.021Contest Winning StrategiesCopyright(c)2Using “Go for It Strategies” that produce the highest returns if you are lucky and survivethe drawdowns: For example, one trade supposedly turned 10,000 into 2 million (lostsome of it down to 1.1 million at the end of the contest). This trader was trading bondswith a volatility breakout system using optimal f.

Kelly CriterionstituteOnce you have a trading system and have tested it out, you need to calculate threeprimary statistics to determine the amount of risk that will produce the maximum rate ofreturn for you. The maximum rate of return will also tend to produce the largestdrawdowns. These statistics include the reliability of the system, the size of the averagegain, and the size of the average loss.rpKelly % A – [(1 – A)/B]InGambling has worked out a formula that you can use to determine your maximum risksize as a percentage of equity.ThaWhere A is the % of winning trades in decimal form (reliability of system),And B is the average profitable trade in divided by the average losing trade in .VanFor example, suppose I flip a fair coin. Thus, the reliability of the system (whether itcomes up heads or tails) is 0.5. The rules of the game are you make twice the amount yourisk when you win and you lose the amount you risk when you lose. Thus, B 2. Thequestion is "What percentage of my remaining equity should I risk on each run toproduce the maximum rate of return?"Maximum % 0.5 – [(1 – 0.5)/2] 0.5 – (0.5/2) 0.5 – 0.25 0.25021Thus, a maximum risk of 25% would yield the largest returns in this game. However, aKelly criterion only works when you have two possibilities, not a bag full.(c)2Expectancy Divided by Worst-Case LossExpectancy/ Worst possible risk against yourightNote that the Kelly or the Expectancy criteria gives you a maximum ceiling for your bet.In reality, your maximum risk size should be nowhere near either level. It should be waybelow them!!!! Both could overshoot the optimal risk size as determined by thespreadsheet you were shown.CopyNeither of these calculations is safe—both result in a high probability of ruin!

Optimal fituteSince the Kelly Criterion is really based on a fixed bet size (as in gambling), Ralph Vincehas come up with the idea of Optimal f, which is applied to a string of wins and losses inwhich the bet size varies.TharpInstRalph Vince: "For any given independent trial situation, where you havean edge (i.e., a positive mathematical expectation), there exists an optimalfixed fraction (f) between 0 and 1 as a divisor of your biggest loss to beton each and every event to maximize your winnings. Most people thinkthat the optimal fixed fraction is the percentage of your total stake to bet.This is absolutely false. Optimal f is the divisor of our biggest loss, theresult of which we divide our total stake by to know how many bets tomake or contracts to have on." Portfolio Management Formulas, p. 80.Tharp: Optimal f gives you a larger bet size, so the Kelly Criterion is actually a moreconservative number. Even though it is more conservative, it still results in a highprobability of ruin and huge drawdowns.VanOptimal f is based on the largest sized loss you have had in your historical testing of yoursystem. Thus, if you use optimal f and you have not yet had your largest loss (a likelypossibility since the variable of price change may be infinite), you might be in for atremendous loss trading at optimal f.021You must calculate optimal f for each market and each market system pair.(c)2There is no easy formula for calculating optimal f. You must use a computer and test allpossible values between 0.01 and 1.00 in 0.01 increments or use some form of iteration.This amounts to finding the f that produces the largest Terminal Wealth Relative (TWR)in the following formula:TWR Σi from 1N trades of [1 (– trade i/biggest loss)]CopyrightRalph Vince’s definition of optimal f means he uses the highest average ending equity todefine this.

Strategies to AvoidituteJoe Ross SystemstTrade 5 contract units, but get out of 3 contracts when you are slightly ahead ofall costs.Raise stops on remaining contracts to break-even.InLarry Williams’ Martingale Strategies (Definitive Guide to Trading, Part 2)TharpSystem Expectations Are Low: When the actual results of the system areout-of-whack with the expectations of the system, then you can startincreasing your commitment. For example, if you have a 65% system,when you’ve had 13 losers out of the last 20 trades (i.e., 65% losses), thenincrease your commitment by stepping up one unit. If you normally trade1 unit, you now trade 2 units and continue to trade 2 units until you havewinners in 13 out of 20 trades.021VanMinimal Martingale: If you have a system that is only right about 30% ofthe time, you might do the following. After every losing trade, increaseyour commitment on the next trade by 1 unit. If you normally trade 1 unit,then you’d move up to 2 units after a loss. If you have another loss, youadd another unit so that you’re trading 3 contracts. If that trade wins, thenyou’d move back to 2 units. If the next trade wins, you’d go back to 1 unitand stay at that level until you had a loss.(c)2Fixed Ratio Trading (as defined by Ryan Jones)rightWhile fixed ratio trading may have some merits, the way Ryan Jones presents it has somehuge holes Risk of

From The Definitive Guide to Position Sizing Strategies Expected Losing Streaks in 100 Trades (or Losing Streaks as a Function of Winning Percentage of Trades) System Winning Trade Percentage . 100% Probability for a Losing Streak This Long Average Losing Streak Length . 10% Probability for a Losing Streak

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