Trading the RiskPosition Sizing and Exit Stops Michael R. Bryant, Ph.D. Breakout Futures www.BreakoutFutures.com Copyright 2002 Breakout Futures Scope of Talk • Short to intermediate-term trading • Rational methods of position sizing and stop selection; mostly quantitative • Oriented towards futures but also applicable to stocks • One market-system at a time Copyright 2002 Breakout Futures 2 What is Position Sizing? • Selecting the number of contracts or shares of stock for the next trade • A way to reinvest profits • The way traders compound their returns Copyright 2002 Breakout Futures 3 Methods of Position Sizing • Ad hoc: trade no larger than lets you sleep at night • Margin plus drawdown • Fixed Fractional • Fixed Ratio • Hybrid fixed fractional/fixed ratio Copyright 2002 Breakout Futures 4 Methods that Don’t Work • 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”). Copyright 2002 Breakout Futures 5 you can’t determine the likelihood of the next trade being a win or a loss based on the previous trade. trades are independent of each other.Why They Don’t Work • Martingale and equity curve methods assume • dependency between trades. In most cases. 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. Copyright 2002 Breakout Futures 6 • . Volume II.5 plus the margin requirement. Copyright 2002 Breakout Futures 7 .5 plus margin.Margin Plus Drawdown Sizing • The equity to trade one contract is the • • maximum historical drawdown multiplied by 1. Add another contract only when the closed profits are equal to drawdown * 1. Attributable to Larry Williams. see The Definitive Guide to Futures Trading. Designed so you only increase the number of contracts. never reduce.) • You always have enough money to handle the • • worst historical drawdown plus 50%. Doesn’t take the risk of each trade into account. • Copyright 2002 Breakout Futures 8 . so drawdowns can be large.Margin Plus Drawdown (cont. Theoretically safe but doesn’t reduce contracts in a drawdown. Margin Plus Drawdown (cont.) 140000 120000 100000 Equity 80000 60000 40000 20000 0 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 1-Con Marg+DD Copyright 2002 Breakout Futures 9 . e.g. Number of contracts: N = ff * Equity/|Trade Risk| where ff = fixed fraction.. 5%. Equity = account equity ($).Fixed Fractional Position Sizing • Risk the same fraction (“fixed fraction”) of the • account equity on each trade. Trade Risk = possible loss on trade ($) Copyright 2002 Breakout Futures 10 . largest historical loss. – Size of money management stop. Copyright 2002 Breakout Futures 11 .) • Trade risk may come from: – Estimate. Examples: n standard deviations of the trade distribution. • Using a money management (mm) stop to define the trade risk may produce greater risk-adjusted returns than using the largest loss.Fixed Fractional (cont. Fixed Fractional (cont.) 300000 250000 Equity 200000 MM Stop 150000 Max Loss 100000 50000 1/1/98 1/1/99 1/1/00 12/31/00 12/31/01 12 Copyright 2002 Breakout Futures . • Responsive to changes in equity (unlike margin plus drawdown method). regardless of the number of contracts. the risk of each trade is the same.Observations on Fixed Fractional • As a percentage of account equity. more on that later… Copyright 2002 Breakout Futures 13 . • The trick is determining the best value of the fixed fraction. • Takes advantage of trade risk. ) 140000 120000 100000 Equity 80000 60000 40000 20000 0 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 1-Con Marg+DD Fix Frac Copyright 2002 Breakout Futures 14 .Fixed Fractional (cont. Copyright 2002 Breakout Futures 15 . • Each contract contributes the same profit towards increasing the number of contracts. regardless of account equity. see The • Based on a fixed parameter called the Trading Game. 1999. John Wiley.Fixed Ratio Position Sizing • Developed by Ryan Jones. delta: the profit per contract needed to increase the number of contracts by 1. ) • Number of contracts: N = ½ *[ 1 + (1 + 8 * Profit/delta) ] where Profit = total closed trade profit ($).Fixed Ratio (cont. 1/2 Copyright 2002 Breakout Futures 16 . delta = profit/contract to increase by 1 contract ($). Fixed Ratio (cont.) 25 20 No. Contracts 15 Fix Frac Fix Ratio 10 5 0 0 5 10 15 Trade 20 25 30 Copyright 2002 Breakout Futures 17 . Contracts 15 Fixed Frac Fixed Ratio 10 5 0 0 30.) 25 20 No.Fixed Ratio (cont.000 Profit Copyright 2002 Breakout Futures 18 90.000 120.000 .000 60. • Doesn’t directly depend on trade risk. i.Observations on Fixed Ratio • Performance depends on total accumulated profits. account size. Copyright 2002 Breakout Futures 19 .e.. It becomes more conservative as the account size increases. we get the fixed ratio equation.A More Generalized Approach • Consider the following equation for the number of contracts. Copyright 2002 Breakout Futures 20 . N: N = ½ *[ 1 + (1 + 8 * Profit/delta) ] where Profit = total closed trade profit ($). delta = fixed ratio parameter ($). m >= 0. m • With m = ½. ) • Consider m = 0: N = ½ *[ 1 + (1 + 8 * Profit/delta) ] = 1/2 * [1 + 1] =1 0 i.A Generalized Approach (cont. Copyright 2002 Breakout Futures 21 .e. we get fixed contract trading (N = 1).. e.. N = (Equity0 + Profit) * ff/Risk (i.) • Consider m = 1: N = ½ *[ 1 + (1 + 8 * Profit/delta) ] = 1 + 4 * Profit/delta Let delta = 4 * Risk/ff and Equity0 = Risk/ff. the equation for fixed fractional trading) Copyright 2002 Breakout Futures 22 1 .A Generalized Approach (cont. Then. m > 1 N increases faster as equity grows.. m < 1 N increases more slowly as equity grows. Copyright 2002 Breakout Futures 23 .A Generalized Approach (cont. fixed fraction. e. fixed ratio..g.) • Rate of Change of N with Profit: ∂N/∂(Profit) = 4*m/delta * (1 + 8 * Profit/delta)m-1 m = 1 ROC of N independent of profit. e.g. 0 m=1.5 Copyright 2002 Breakout Futures 24 .A Generalized Approach (cont.5 m=1.) 450000 400000 350000 300000 Equity 250000 200000 150000 100000 50000 0 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 m=0. 0 m=1.5 Copyright 2002 Breakout Futures 25 .A Generalized Approach (cont.) 500000 425000 350000 Equity m=0.5 275000 200000 125000 50000 12/31/98 12/31/99 12/30/00 12/30/01 m=1. the sequence of trades and drawdowns/run-ups is unknown.Conclusions From Generalized Approach • m < 1 works best when worst drawdowns come • • late. (Monte Carlo analysis to find the best m?) Copyright 2002 Breakout Futures 26 . there is probably an optimal value of m. m >= 1 works best when biggest run-up comes late. However. For any sequence of trades. • “Secure f”: Leo Zamansky & David Stendahl. Copyright 2002 Breakout Futures 27 . 2001.g.Finding the Best Fixed Fraction • Ad hoc. • “Optimal f”: Ralph Vince.. February. TASC. • Monte Carlo simulation: Bryant. TASC. 1990. Portfolio Management Formulas. 1998. July. 2% rule. e. • Doesn’t take the drawdown into account.Best Fixed Fraction (cont.) Optimal f: • f value that mathematically maximizes the compounded rate of return. Copyright 2002 Breakout Futures 28 . • Typically results in very large – and dangerous – f values. • Theoretically sound but not practical to trade. Best Fixed Fraction (cont.g. e. • Only problem: the drawdown calculated from the historical sequence of trades is not very reliable. “what f value gives the greatest rate of return without exceeding 30% drawdown?” • Improvement on optimal f.) Secure f: • f value that maximizes the compounded rate of return subject to a limit on the maximum drawdown.. Copyright 2002 Breakout Futures 29 . 3% 45000 35000 25000 15000 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 30 Copyright 2002 Breakout Futures .) 85000 75000 65000 Equity 55000 DD=9.Best Fixed Fraction (cont. Best Fixed Fraction (cont.7% 45000 35000 25000 15000 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 31 Copyright 2002 Breakout Futures .) 85000 75000 65000 Equity 55000 DD=16. Best Fixed Fraction (cont.) 85000 75000 65000 Equity 55000 DD=25.6% 45000 35000 25000 15000 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 32 Copyright 2002 Breakout Futures . Best Fixed Fraction (cont.) 85000 75000 65000 Equity 55000 DD=37.6% 45000 35000 25000 15000 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 33 Copyright 2002 Breakout Futures . Best Fixed Fraction (cont.) 85000 75000 65000 Equity 55000 DD=46.2% 45000 35000 25000 15000 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 34 Copyright 2002 Breakout Futures . 3% Equity 55000 45000 35000 25000 15000 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 DD=16.6% DD=37.) 85000 75000 65000 DD=9.Best Fixed Fraction (cont.7% DD=25.6% DD=46.2% Copyright 2002 Breakout Futures 35 . 2% • Try f=8.) • Historical sequence: 14% max drawdown on 2 contracts.2% on some randomized sequences of the original trades.Best Fixed Fraction (cont. One result: max drawdown = 76%! Copyright 2002 Breakout Futures 36 . • Find the fixed fraction that maximizes the RoR of the historical sequence with no more than 30% drawdown f = 8. starting with $50k. ) 800000 700000 600000 500000 Equity Original Optimized Randomized 400000 300000 200000 100000 0 12/31/97 12/31/98 12/31/99 12/30/00 12/30/01 Copyright 2002 Breakout Futures 37 .Best Fixed Fraction (cont. • Output of simulation is a distribution.) Monte Carlo Simulation: • Replaces random variables in a simulation with their probability distributions. • Can be used to find the “best” fixed fraction by replacing the trade with the distribution of trades. • Distributions are randomly sampled many times. Copyright 2002 Breakout Futures 38 .Best Fixed Fraction (cont. ) Distribution of Profit/Loss 25 20 15 10 5 0 0 10 00 20 00 30 00 40 00 50 00 -3 00 0 -2 00 0 -1 00 0 Trade P/L Copyright 2002 Breakout Futures 39 60 00 .Best Fixed Fraction (cont. • 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. Copyright 2002 Breakout Futures 40 . for each sequence. • Find the f value that maximizes the return at 95% confidence while keeping the drawdown at 95% confidence below your drawdown limit.Best Fixed Fraction (cont. and.) Applying Monte Carlo to Fixed Fractional Trading: • Randomize the sequence of trades. calculate the return and max drawdown using a given value of f. 12 60 40 Fixed Fraction Copyright 2002 Breakout Futures Ave RoR (%) P (40% DD) 80 41 .Best Fixed Fraction (cont.08 0.04 0.02 0.) 120 100 1600 1400 1200 1000 800 600 400 20 0 0 0.1 200 0 0.06 0. 4 DD at P=95% 2500 80 42 .Best Fixed Fraction (cont.) 4000 3500 100 3000 120 RoR at P=95% 2000 60 1500 1000 500 20 0 -500 0 0.2 Fixed Fraction Copyright 2002 Breakout Futures 40 0 0.3 0.1 0. which enables more precise position sizing. • How do we choose the size of the money management stop? One approach: volatility. Copyright 2002 Breakout Futures 43 .Money Management Stops • Lesson from fixed fractional trading: a money management stop defines the trade risk. Money Management Stops (cont.) ATR Volatility .E-mini S&P 500 60 50 40 30 20 10 0 9/1/97 9/1/98 9/1/99 8/31/00 8/31/01 44 Copyright 2002 Breakout Futures 10-day ATR . Money Management Stops (cont. E-mini S&P 200 180 160 140 120 100 80 60 40 20 0 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 10-day ATR Copyright 2002 Breakout Futures 45 .) Distribution of ATR. ES 100 90 80 70 % of Total 60 50 40 30 20 10 0 12 16 20 24 28 32 36 40 44 48 10-day ATR Copyright 2002 Breakout Futures 52 46 .) Cumulative ATR Distr .Money Management Stops (cont. E-mini Nasdaq 400 350 300 10-day ATR 250 200 150 100 50 0 6/30/99 12/30/99 6/30/00 12/30/00 7/1/01 12/31/01 47 Copyright 2002 Breakout Futures .Money Management Stops (cont.) ATR Volatility . E-mini Nasdaq 60 50 40 30 20 10 0 5 5 5 5 5 5 0 0 28 35 55 75 95 11 13 15 17 19 21 24 Average True Range Copyright 2002 Breakout Futures 48 32 0 .) Distribution of ATR.Money Management Stops (cont. • Try tightening the stop sharply after a big move in your favor (but not before). Copyright 2002 Breakout Futures 49 . • 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.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. how does this affect performance measurements? • Short answer: Don’t rely on the TradeStation performance summary.Performance Measures • Problem: If you simulate trading with position sizing. Copyright 2002 Breakout Futures 50 . 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 • Win/Loss ratio • Largest Win • Largest Loss • Max Drawdown Copyright 2002 Breakout Futures 51 . 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. • Consider my FixedRisk and MonteCarlo EasyLanguage user functions… Copyright 2002 Breakout Futures 52 . 00 Gross Profit: $319002.) * MM ANALYSIS: PERFORMANCE OF HISTORICAL SEQUENCE * NQ_0_V0B.00 Copyright 2002 Breakout Futures 53 .00 Gross Loss: $-199430.60 Final Account Equity: $169572. 4/19/2002 TRADING PARAMETERS: Initial Account Equity: $50000.CSV (Daily Data).00 Profit Factor: 1.00 Position Sizing Method: Fixed Fractional Risk Percentage (fixed fraction): 4.Performance Measures (cont.00% PERFORMANCE RESULTS: Error Code: 0 Total Net Profit: $119572. 00 (-6.00) Largest Winning Trade ($): $24400.) Number of Trades: 103 Number Winning Trades: 51 Number Losing Trades: 52 Number Skipped Trades (# contracts=0): 0 Percent Profitable: 49.77% ($-12805.00 (14.54%) Average Winning Trade (%): 5.85% Average Winning Trade ($): $6254.51% Largest Winning Trade (%): 16.94 Max # Consecutive Wins: 5 Largest Losing Trade (%): -6.19 Max # Consecutive Losses: 5 Copyright 2002 Breakout Futures 54 .77%) Average Losing Trade (%): -3.02% ($9400.10% Average Losing Trade ($): $-3835.00) Largest Losing Trade ($): $-12805.Performance Measures (cont. ) Ratio Avg Win(%)/Avg Loss(%): 1.40 (21.14% Copyright 2002 Breakout Futures 55 .13%) Date of Max $ Drawdown: 4/1/2002 Return on Starting Equity: 239.89 Ratio Avg Win($)/Avg Loss($): 1.Performance Measures (cont.13% ($43351.63 Average % Trade: 1.90 Max # Contracts: 18 Avg # Contracts: 5 Max Closed Trade % Drawdown: 21.40) Date of Max % Drawdown: 4/1/2002 Max Closed Trade $ Drawdown: $43351.33% Average $ Trade: $1160. 00% Probability Goal: 95.) * MM ANALYSIS: MONTE CARLO ANALYSIS * INPUT DATA: Initial Account Equity: $50000.00% Drawdown Goal: 30.00% Number of Trades: 103 Rate of Return Goal: 100.00% Number of Random Sequences: 1000 Copyright 2002 Breakout Futures 56 .00 Risk Percentage (fixed fraction): 4.Performance Measures (cont. 16% Copyright 2002 Breakout Futures 57 .00% Probability of Reaching Drawdown Goal: 85.00% Probability: 195.48% Average Final Account Equity: $174741.10% Rate of Return at 95.) OUTPUT/RESULTS: Error Code: 0 Average Rate of Return: 249.Performance Measures (cont.00% Probability: 35.10% Probability of Reaching Return and Drawdown Together: 85.31% Drawdown at 95.00 Probability of Reaching Return Goal: 100.