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Copyright 2002 Breakout Futures Trading the Risk Position Sizing and Exit Stops Michael R. Bryant, Ph.D. Breakout Futures

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Copyright 2002 Breakout Futures 2 Scope of Talk Short to intermediate-term trading Short to intermediate-term trading Rational methods of position sizing and stop selection; mostly quantitative Rational methods of position sizing and stop selection; mostly quantitative Oriented towards futures but also applicable to stocks Oriented towards futures but also applicable to stocks One market-system at a time One market-system at a time

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Copyright 2002 Breakout Futures 3 What is Position Sizing? Selecting the number of contracts or shares of stock for the next trade Selecting the number of contracts or shares of stock for the next trade A way to reinvest profits A way to reinvest profits The way traders compound their returns The way traders compound their returns

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Copyright 2002 Breakout Futures 4 Methods of Position Sizing Ad hoc: trade no larger than lets you sleep at night Ad hoc: trade no larger than lets you sleep at night Margin plus drawdown Margin plus drawdown Fixed Fractional Fixed Fractional Fixed Ratio Fixed Ratio Hybrid fixed fractional/fixed ratio Hybrid fixed fractional/fixed ratio

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Copyright 2002 Breakout Futures 5 Methods that Dont Work Martingale methods: increase position size after a loss; decrease it after a win. Martingale methods: increase position size after a loss; decrease it after a win. Equity curve methods: increase size when your equity curve falls below its moving average (reversion to mean), or increase size when you cross above the moving average (trade the trend in equity curve). Equity curve methods: increase size when your equity curve falls below its moving average (reversion to mean), or increase size when you cross above the moving average (trade the trend in equity curve).

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Copyright 2002 Breakout Futures 6 Why They Dont Work Martingale and equity curve methods assume dependency between trades. Martingale and equity curve methods assume dependency between trades. In most cases, trades are independent of each other. The odds of the next trade being a win are not related to whether the last trade was a win or a loss. In most cases, trades are independent of each other. The odds of the next trade being a win are not related to whether the last trade was a win or a loss. If trades are independent, you cant determine the likelihood of the next trade being a win or a loss based on the previous trade. If trades are independent, you cant determine the likelihood of the next trade being a win or a loss based on the previous trade.

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Copyright 2002 Breakout Futures 7 Margin Plus Drawdown Sizing The equity to trade one contract is the maximum historical drawdown multiplied by 1.5 plus the margin requirement. The equity to trade one contract is the maximum historical drawdown multiplied by 1.5 plus the margin requirement. Add another contract only when the closed profits are equal to drawdown * 1.5 plus margin. Add another contract only when the closed profits are equal to drawdown * 1.5 plus margin. Attributable to Larry Williams; see The Definitive Guide to Futures Trading, Volume II. Attributable to Larry Williams; see The Definitive Guide to Futures Trading, Volume II.

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Copyright 2002 Breakout Futures 8 Margin Plus Drawdown (cont.) You always have enough money to handle the worst historical drawdown plus 50%. You always have enough money to handle the worst historical drawdown plus 50%. Designed so you only increase the number of contracts, never reduce. Designed so you only increase the number of contracts, never reduce. Theoretically safe but doesnt reduce contracts in a drawdown, so drawdowns can be large. Theoretically safe but doesnt reduce contracts in a drawdown, so drawdowns can be large. Doesnt take the risk of each trade into account. Doesnt take the risk of each trade into account.

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Copyright 2002 Breakout Futures 9 Margin Plus Drawdown (cont.)

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Copyright 2002 Breakout Futures 10 Fixed Fractional Position Sizing Risk the same fraction (fixed fraction) of the account equity on each trade; e.g., 5%. Risk the same fraction (fixed fraction) of the account equity on each trade; e.g., 5%. Number of contracts: Number of contracts: N = ff * Equity/|Trade Risk| where ff = fixed fraction, Equity = account equity ($), Trade Risk = possible loss on trade ($)

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Copyright 2002 Breakout Futures 11 Fixed Fractional (cont.) Trade risk may come from: Trade risk may come from: –Estimate. Examples: n standard deviations of the trade distribution; largest historical loss. –Size of money management stop. Using a money management (mm) stop to define the trade risk may produce greater risk-adjusted returns than using the largest loss. Using a money management (mm) stop to define the trade risk may produce greater risk-adjusted returns than using the largest loss.

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Copyright 2002 Breakout Futures 12 Fixed Fractional (cont.)

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Copyright 2002 Breakout Futures 13 Observations on Fixed Fractional As a percentage of account equity, the risk of each trade is the same, regardless of the number of contracts. As a percentage of account equity, the risk of each trade is the same, regardless of the number of contracts. Takes advantage of trade risk. Takes advantage of trade risk. Responsive to changes in equity (unlike margin plus drawdown method). Responsive to changes in equity (unlike margin plus drawdown method). The trick is determining the best value of the fixed fraction; more on that later… The trick is determining the best value of the fixed fraction; more on that later…

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Copyright 2002 Breakout Futures 14 Fixed Fractional (cont.)

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Copyright 2002 Breakout Futures 15 Fixed Ratio Position Sizing Developed by Ryan Jones; see The Trading Game, John Wiley, Developed by Ryan Jones; see The Trading Game, John Wiley, Based on a fixed parameter called the delta: the profit per contract needed to increase the number of contracts by 1. Based on a fixed parameter called the delta: the profit per contract needed to increase the number of contracts by 1. Each contract contributes the same profit towards increasing the number of contracts, regardless of account equity. Each contract contributes the same profit towards increasing the number of contracts, regardless of account equity.

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Copyright 2002 Breakout Futures 16 Fixed Ratio (cont.) Number of contracts: Number of contracts: N = ½ *[ 1 + (1 + 8 * Profit/delta) 1/2 ] where Profit = total closed trade profit ($), delta = profit/contract to increase by 1 contract ($).

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Copyright 2002 Breakout Futures 17 Fixed Ratio (cont.)

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Copyright 2002 Breakout Futures 18 Fixed Ratio (cont.)

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Copyright 2002 Breakout Futures 19 Observations on Fixed Ratio Performance depends on total accumulated profits; i.e., account size. It becomes more conservative as the account size increases. Performance depends on total accumulated profits; i.e., account size. It becomes more conservative as the account size increases. Doesnt directly depend on trade risk. Doesnt directly depend on trade risk.

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Copyright 2002 Breakout Futures 20 A More Generalized Approach Consider the following equation for the number of contracts, N: Consider the following equation for the number of contracts, N: N = ½ *[ 1 + (1 + 8 * Profit/delta) m ] where Profit = total closed trade profit ($), delta = fixed ratio parameter ($), m >= 0. With m = ½, we get the fixed ratio equation. With m = ½, we get the fixed ratio equation.

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Copyright 2002 Breakout Futures 21 A Generalized Approach (cont.) Consider m = 0: Consider m = 0: N = ½ *[ 1 + (1 + 8 * Profit/delta) 0 ] = 1/2 * [1 + 1] = 1 i.e., we get fixed contract trading (N = 1).

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Copyright 2002 Breakout Futures 22 A Generalized Approach (cont.) Consider m = 1: Consider m = 1: N = ½ *[ 1 + (1 + 8 * Profit/delta) 1 ] = * Profit/delta Let delta = 4 * Risk/ff and Equity 0 = Risk/ff. Then, N = (Equity 0 + Profit) * ff/Risk (i.e., the equation for fixed fractional trading)

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Copyright 2002 Breakout Futures 23 A Generalized Approach (cont.) Rate of Change of N with Profit: Rate of Change of N with Profit: N/(Profit) = 4*m/delta * (1 + 8 * Profit/delta) m-1N/(Profit) = 4*m/delta * (1 + 8 * Profit/delta) m-1 m = 1 ROC of N independent of profit; e.g., fixed fraction. m > 1 N increases faster as equity grows. m < 1 N increases more slowly as equity grows; e.g., fixed ratio.

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Copyright 2002 Breakout Futures 24 A Generalized Approach (cont.)

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Copyright 2002 Breakout Futures 25 A Generalized Approach (cont.)

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Copyright 2002 Breakout Futures 26 Conclusions From Generalized Approach m < 1 works best when worst drawdowns come late. m < 1 works best when worst drawdowns come late. m >= 1 works best when biggest run-up comes late. m >= 1 works best when biggest run-up comes late. For any sequence of trades, there is probably an optimal value of m. However, the sequence of trades and drawdowns/run-ups is unknown. (Monte Carlo analysis to find the best m?) For any sequence of trades, there is probably an optimal value of m. However, the sequence of trades and drawdowns/run-ups is unknown. (Monte Carlo analysis to find the best m?)

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Copyright 2002 Breakout Futures 27 Finding the Best Fixed Fraction Ad hoc; e.g., 2% rule. Ad hoc; e.g., 2% rule. Optimal f: Ralph Vince, Portfolio Management Formulas, Optimal f: Ralph Vince, Portfolio Management Formulas, Secure f: Leo Zamansky & David Stendahl, TASC, July, Secure f: Leo Zamansky & David Stendahl, TASC, July, Monte Carlo simulation: Bryant, TASC, February, Monte Carlo simulation: Bryant, TASC, February, 2001.

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Copyright 2002 Breakout Futures 28 Best Fixed Fraction (cont.) Optimal f: f value that mathematically maximizes the compounded rate of return. f value that mathematically maximizes the compounded rate of return. Doesnt take the drawdown into account. Doesnt take the drawdown into account. Typically results in very large – and dangerous – f values. Typically results in very large – and dangerous – f values. Theoretically sound but not practical to trade. Theoretically sound but not practical to trade.

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Copyright 2002 Breakout Futures 29 Best Fixed Fraction (cont.) Secure f: f value that maximizes the compounded rate of return subject to a limit on the maximum drawdown; e.g., what f value gives the greatest rate of return without exceeding 30% drawdown? f value that maximizes the compounded rate of return subject to a limit on the maximum drawdown; e.g., what f value gives the greatest rate of return without exceeding 30% drawdown? Improvement on optimal f. Improvement on optimal f. Only problem: the drawdown calculated from the historical sequence of trades is not very reliable. Only problem: the drawdown calculated from the historical sequence of trades is not very reliable.

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Copyright 2002 Breakout Futures 30 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 31 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 32 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 33 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 34 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 35 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 36 Best Fixed Fraction (cont.) Historical sequence: 14% max drawdown on 2 contracts, starting with $50k. Historical sequence: 14% max drawdown on 2 contracts, starting with $50k. Find the fixed fraction that maximizes the RoR of the historical sequence with no more than 30% drawdown f = 8.2% Find the fixed fraction that maximizes the RoR of the historical sequence with no more than 30% drawdown f = 8.2% Try f=8.2% on some randomized sequences of the original trades. One result: max drawdown = 76%! Try f=8.2% on some randomized sequences of the original trades. One result: max drawdown = 76%!

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Copyright 2002 Breakout Futures 37 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 38 Best Fixed Fraction (cont.) Monte Carlo Simulation: Replaces random variables in a simulation with their probability distributions. Replaces random variables in a simulation with their probability distributions. Distributions are randomly sampled many times. Distributions are randomly sampled many times. Output of simulation is a distribution. Output of simulation is a distribution. Can be used to find the best fixed fraction by replacing the trade with the distribution of trades. Can be used to find the best fixed fraction by replacing the trade with the distribution of trades.

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Copyright 2002 Breakout Futures 39 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 40 Best Fixed Fraction (cont.) Applying Monte Carlo to Fixed Fractional Trading: Randomize the sequence of trades, and, for each sequence, calculate the return and max drawdown using a given value of f. Randomize the sequence of trades, and, for each sequence, calculate the return and max drawdown using a given value of f. The drawdown at 95% confidence is the drawdown such that 95% of sequences have drawdowns less than that. The drawdown at 95% confidence is the drawdown such that 95% of sequences have drawdowns less than that. The return at 95% confidence is the return such that 95% of sequences return at least that much. The return at 95% confidence is the return such that 95% of sequences return at least that much. Find the f value that maximizes the return at 95% confidence while keeping the drawdown at 95% confidence below your drawdown limit. Find the f value that maximizes the return at 95% confidence while keeping the drawdown at 95% confidence below your drawdown limit.

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Copyright 2002 Breakout Futures 41 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 42 Best Fixed Fraction (cont.)

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Copyright 2002 Breakout Futures 43 Money Management Stops Lesson from fixed fractional trading: a money management stop defines the trade risk, which enables more precise position sizing. Lesson from fixed fractional trading: a money management stop defines the trade risk, which enables more precise position sizing. How do we choose the size of the money management stop? One approach: volatility. How do we choose the size of the money management stop? One approach: volatility.

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Copyright 2002 Breakout Futures 44 Money Management Stops (cont.)

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Copyright 2002 Breakout Futures 45 Money Management Stops (cont.)

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Copyright 2002 Breakout Futures 46 Money Management Stops (cont.)

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Copyright 2002 Breakout Futures 47 Money Management Stops (cont.)

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Copyright 2002 Breakout Futures 48 Money Management Stops (cont.)

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Copyright 2002 Breakout Futures 49 Trailing Stops Some ideas for trailing stops: Try basing the size of the stop on volatility, as suggested for money management stops, but use a smaller value. Try basing the size of the stop on volatility, as suggested for money management stops, but use a smaller value. Try tightening the stop sharply after a big move in your favor (but not before). Try tightening the stop sharply after a big move in your favor (but not before). If the trailing stop is tighter than the mm stop, wait until the market has moved in your favor by some multiple of the ATR before applying the trailing stop. If the trailing stop is tighter than the mm stop, wait until the market has moved in your favor by some multiple of the ATR before applying the trailing stop.

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Copyright 2002 Breakout Futures 50 Performance Measures Problem: If you simulate trading with position sizing, how does this affect performance measurements? Problem: If you simulate trading with position sizing, how does this affect performance measurements? Short answer: Dont rely on the TradeStation performance summary. Short answer: Dont rely on the TradeStation performance summary.

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Copyright 2002 Breakout Futures 51 Performance Measures (cont.) If given in dollars, some performance statistics could be skewed by the higher equity and larger number of contracts at the end of the equity curve: Average Trade Largest Win Largest Loss Win/Loss ratio Max Drawdown

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Copyright 2002 Breakout Futures 52 Performance Measures (cont.) Solution: Calculate equity-dependent performance statistics by recording the trade profit/loss as a percentage of the equity at the time the trade is entered. Solution: Calculate equity-dependent performance statistics by recording the trade profit/loss as a percentage of the equity at the time the trade is entered. Consider my FixedRisk and MonteCarlo EasyLanguage user functions… Consider my FixedRisk and MonteCarlo EasyLanguage user functions…

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Copyright 2002 Breakout Futures 53 Performance Measures (cont.) * MM ANALYSIS: PERFORMANCE OF HISTORICAL SEQUENCE * NQ_0_V0B.CSV (Daily Data), 4/19/2002 NQ_0_V0B.CSV (Daily Data), 4/19/2002 TRADING PARAMETERS: Initial Account Equity: $ Position Sizing Method: Fixed Fractional Risk Percentage (fixed fraction): 4.00% PERFORMANCE RESULTS: Error Code: 0 Total Net Profit: $ Gross Profit: $ Gross Profit: $ Gross Loss: $ Gross Loss: $ Profit Factor: 1.60 Profit Factor: 1.60 Final Account Equity: $

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Copyright 2002 Breakout Futures 54 Performance Measures (cont.) Number of Trades: 103 Number Winning Trades: 51 Number Winning Trades: 51 Number Losing Trades: 52 Number Losing Trades: 52 Number Skipped Trades (# contracts=0): 0 Number Skipped Trades (# contracts=0): 0 Percent Profitable: 49.51% Percent Profitable: 49.51% Largest Winning Trade (%): 16.02% ($ ) Largest Winning Trade ($): $ (14.54%) Average Winning Trade (%): 5.85% Average Winning Trade ($): $ Max # Consecutive Wins: 5 Largest Losing Trade (%): -6.77% ($ ) Largest Losing Trade ($): $ (-6.77%) Average Losing Trade (%): -3.10% Average Losing Trade ($): $ Max # Consecutive Losses: 5

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Copyright 2002 Breakout Futures 55 Performance Measures (cont.) Ratio Avg Win(%)/Avg Loss(%): 1.89 Ratio Avg Win($)/Avg Loss($): 1.63 Average % Trade: 1.33% Average $ Trade: $ Max # Contracts: 18 Avg # Contracts: 5 Max Closed Trade % Drawdown: 21.13% ($ ) Date of Max % Drawdown: 4/1/2002 Max Closed Trade $ Drawdown: $ (21.13%) Date of Max $ Drawdown: 4/1/2002 Return on Starting Equity: %

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Copyright 2002 Breakout Futures 56 Performance Measures (cont.) * MM ANALYSIS: MONTE CARLO ANALYSIS * INPUT DATA: Initial Account Equity: $ Risk Percentage (fixed fraction): 4.00% Number of Trades: 103 Rate of Return Goal: % Drawdown Goal: 30.00% Probability Goal: 95.00% Number of Random Sequences: 1000

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Copyright 2002 Breakout Futures 57 Performance Measures (cont.) OUTPUT/RESULTS: Error Code: 0 Average Rate of Return: % Average Final Account Equity: $ Probability of Reaching Return Goal: % Probability of Reaching Drawdown Goal: 85.10% Probability of Reaching Return and Drawdown Together: 85.10% Rate of Return at 95.00% Probability: % Drawdown at 95.00% Probability: 35.16%

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