Trade Risk Talk

7/28/2019 Trade Risk Talk

1/57

Copyright2002 Breakout Futures

Trading the Risk

Position Sizing and Exit Stops

Michael R. Bryant, Ph.D.

Breakout Futures

www.BreakoutFutures.com


2/57

Copyright2002 Breakout Futures 2

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


3/57


What is Position Sizing?

Selecting the number of contracts orshares of stock for the next trade

A way to reinvest profits The way traders compound their returns


4/57


Methods of Position Sizing

Ad hoc: trade no larger than lets you sleepat night

Margin plus drawdown Fixed Fractional Fixed Ratio

Hybrid fixed fractional/fixed ratio


5/57


Methods that Dont Work

Martingale methods: increase position sizeafter a loss; decrease it after a win.

Equity curve methods: increase size whenyour equity curve falls below its movingaverage (reversion to mean), or increase

size when you cross above the movingaverage (trade the trend in equitycurve).


6/57


Why They Dont Work

Martingale and equity curve methods assumedependency between trades.

In most cases, trades are independent of eachother. The odds of the next trade being a winare not related to whether the last trade was awin or a loss.

If trades are independent, you cant determinethe likelihood of the next trade being a win or aloss based on the previous trade.


7/57


Margin Plus Drawdown Sizing

The equity to trade one contract is themaximum historical drawdown multiplied by 1.5

plus the margin requirement. Add another contract only when the closedprofits are equal to drawdown * 1.5 plus margin.

Attributable to Larry Williams; see The DefinitiveGuide to Futures Trading, Volume II.


8/57


Margin Plus Drawdown (cont.)

You always have enough money to handle theworst historical drawdown plus 50%.

Designed so you only increase the number ofcontracts, never reduce. Theoretically safe but doesnt reduce contracts

in a drawdown, so drawdowns can be large.

Doesnt take the risk of each trade into account.


9/57


Margin Plus Drawdown (cont.)

0

20000

40000

60000

80000

100000

120000

140000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity

1-Con

Marg+DD


10/57


Fixed Fractional Position Sizing

Risk the same fraction (fixed fraction) of theaccount equity on each trade; e.g., 5%.

Number of contracts:

N = ff * Equity/|Trade Risk|

where ff = fixed fraction,Equity = account equity ($),

Trade Risk = possible loss on trade ($)


11/57


Fixed Fractional (cont.)

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 greaterrisk-adjusted returns than using thelargest loss.


12/57



50000

100000

150000

200000

250000

300000

1/1/98 1/1/99 1/1/00 12/31/00 12/31/01

Equity

MM Stop

Max Loss


13/57


Observations on Fixed Fractional

As a percentage of account equity, therisk of each trade is the same, regardless

of the number of contracts. Takes advantage of trade risk. Responsive to changes in equity (unlike

margin plus drawdown method).

The trick is determining the best value ofthe fixed fraction; more on that later


14/57



0

20000

40000

60000

80000

100000

120000

140000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity 1-Con

Marg+DD

Fix Frac


15/57


Fixed Ratio Position Sizing

Developed by Ryan Jones; see TheTrading Game, John Wiley, 1999.

Based on a fixed parameter called thedelta: the profit per contract needed toincrease the number of contracts by 1.

Each contract contributes the same profittowards increasing the number ofcontracts, regardless of account equity.


16/57


Fixed Ratio (cont.)

Number of contracts:

N = *[ 1 + (1 + 8 * Profit/delta)1/2]

where Profit = total closed trade profit ($),

delta = profit/contract to increase by 1contract ($).


17/57


Fixed Ratio (cont.)

0

5

10

15

20

25

0 5 10 15 20 25 30

Trade

No.Contracts

Fix Frac

Fix Ratio


18/57


Fixed Ratio (cont.)

0

5

10

15

20

25

0 30,000 60,000 90,000 120,000

Profit

No.

Contracts

Fixed Frac

Fixed Ratio


19/57


Observations on Fixed Ratio

Performance depends on totalaccumulated profits; i.e., account size. It

becomes more conservative as theaccount size increases.

Doesnt directly depend on trade risk.


20/57


A More Generalized Approach

Consider the following equation for the numberof contracts, N:

N = *[ 1 + (1 + 8 * Profit/delta)m

]

where Profit = total closed trade profit ($),

delta = fixed ratio parameter ($),m >= 0.

With m = , we get the fixed ratio equation.


21/57


A Generalized Approach (cont.)

Consider m = 0:

N = *[ 1 + (1 + 8 * Profit/delta)0 ]= 1/2 * [1 + 1]

= 1

i.e., we get fixed contract trading (N = 1).


22/57



Consider m = 1:

N = *[ 1 + (1 + 8 * Profit/delta)

1

]= 1 + 4 * Profit/delta

Let delta = 4 * Risk/ff and Equity0 = Risk/ff.

Then, N = (Equity0 + Profit) * ff/Risk

(i.e., the equation for fixed fractional trading)


23/57



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., fixedfraction.

m > 1 N increases faster as equity grows.m < 1 N increases more slowly as equity grows; e.g.,

fixed ratio.


24/57



0

50000

100000

150000

200000

250000

300000

350000

400000

450000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity m=0.5

m=1.0

m=1.5


25/57



50000

125000

200000

275000

350000

425000

500000

12/31/98 12/31/99 12/30/00 12/30/01

Equity m=0.5

m=1.0

m=1.5


26/57


Conclusions From Generalized Approach

m < 1 works best when worst drawdowns comelate.

m >= 1 works best when biggest run-up comeslate. 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?)


27/57


Finding the Best Fixed Fraction

Ad hoc; e.g., 2% rule.Optimal f: Ralph Vince, Portfolio

Management Formulas, 1990.Secure f: Leo Zamansky & David

Stendahl, TASC, July, 1998.

Monte Carlo simulation: Bryant, TASC,February, 2001.


28/57


Best Fixed Fraction (cont.)

Optimal f:

f value that mathematically maximizes the

compounded rate of return. Doesnt take the drawdown into account. Typically results in very large and

dangerous f values. Theoretically sound but not practical totrade.


29/57



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 greatestrate of return without exceeding 30%drawdown?

Improvement on optimal f.

Only problem: the drawdown calculated fromthe historical sequence of trades is not veryreliable.


30/57



15000

25000

35000

45000

55000

65000

75000

85000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity

DD=9.3%


31/57



15000

25000

35000

45000

55000

65000

75000

85000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity

DD=16.7%


32/57



15000

25000

35000

45000

55000

65000

75000

85000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity

DD=25.6%


33/57



15000

25000

35000

45000

55000

65000

75000

85000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity

DD=37.6%


34/57



15000

25000

35000

45000

55000

65000

75000

85000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity

DD=46.2%


35/57



15000

25000

35000

45000

55000

65000

75000

85000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity

DD=9.3%DD=16.7%

DD=25.6%

DD=37.6%

DD=46.2%


36/57



Historical sequence: 14% max drawdownon 2 contracts, starting with $50k.

Find the fixed fraction that maximizes theRoR of the historical sequence with nomore than 30% drawdown f = 8.2%

Try f=8.2% on some randomizedsequences of the original trades. Oneresult: max drawdown = 76%!


37/57



0

100000

200000

300000

400000

500000

600000

700000

800000

12/31/97 12/31/98 12/31/99 12/30/00 12/30/01

Equity Original

Optimized

Randomized


38/57



Monte Carlo Simulation:

Replaces random variables in a simulation with

their probability distributions. Distributions are randomly sampled many times. Output of simulation is a distribution. Can be used to find the best fixed fraction by

replacing the tradewith the distribution oftrades.


39/57



Distribution of Profit/Loss

0

5

10

15

20

25

-300

0

-200

0

-100

0 0

1000

2000

3000

4000

5000

6000

Trade P/L


40/57



Applying Monte Carlo to Fixed Fractional Trading:

Randomize the sequence of trades, and, for eachsequence, calculate the return and max drawdown using

a given value of f. The drawdown at 95% confidence is the drawdown suchthat 95% of sequences have drawdowns less than that.

The return at 95% confidence is the return such that95% 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.


41/57



0

20

40

60

80

100

120

0 0.02 0.04 0.06 0.08 0.1 0.12

Fixed Fraction

P(40%D

D

)

0200

400

600

800

1000

1200

1400

1600

AveRoR(%

)


42/57



-500

0

500

1000

1500

2000

2500

3000

3500

4000

0 0.1 0.2 0.3 0.4

Fixed Fraction

RoRatP=95

%

0

20

40

60

80

100

120

DDatP=95%


43/57


Money Management Stops

Lesson from fixed fractional trading: amoney management stop defines the

trade risk, which enables more preciseposition sizing.

How do we choose the size of the money

management stop? One approach:volatility.


44/57


Money Management Stops (cont.)

ATR Volatility - E-mini S&P 500

0

10

20

30

40

50

60

9/1/97 9/1/98 9/1/99 8/31/00 8/31/01

10-dayATR


45/57



Distribution of ATR, E-mini S&P

0

20

40

60

80

100

120140

160

180

200

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


46/57



Cumulative ATR Distr - ES

0

10

20

30

40

50

60

70

80

90

100

12 16 20 24 28 32 36 40 44 48 52

10-day ATR

%o

fTotal


47/57



ATR Volatility - E-mini Nasdaq

0

50

100

150

200

250

300

350

400

6/30/99 12/30/99 6/30/00 12/30/00 7/1/01 12/31/01

10-dayATR


48/57



Distribution of ATR, E-mini Nasdaq

0

10

20

30

40

50

60

35 55 75 95 115

135

155

175

195

215

240

280

320

Average True Range


49/57


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 tightening the stop sharply after a big movein your favor (but not before).

If the trailing stop is tighter than the mm stop,

wait until the market has moved in your favor bysome multiple of the ATR before applying thetrailing stop.


50/57


Performance Measures

Problem: If you simulate trading withposition sizing, how does this affect

performance measurements? Short answer:Dont rely on the

TradeStation performance summary.


51/57


Performance Measures (cont.)

If given in dollars, some performancestatistics could be skewed by the higher

equity and larger number of contracts at theend of the equity curve:

Average Trade

Largest Win

Largest Loss

Win/Loss ratio

Max Drawdown


52/57



Solution: Calculate equity-dependentperformance statistics by recording the

trade profit/loss as a percentage of theequity at the time the trade is entered.

Consider my FixedRiskand MonteCarlo

EasyLanguage user functions


53/57



* MM ANALYSIS: PERFORMANCE OF HISTORICAL SEQUENCE *NQ_0_V0B.CSV (Daily Data), 4/19/2002

TRADING PARAMETERS:Initial Account Equity: $50000.00Position Sizing Method: Fixed FractionalRisk Percentage (fixed fraction): 4.00%

PERFORMANCE RESULTS:Error Code: 0Total Net Profit: $119572.00

Gross Profit: $319002.00Gross Loss: $-199430.00Profit Factor: 1.60

Final Account Equity: $169572.00


54/57


Performance Measures (cont.)Number of Trades: 103

Number Winning Trades: 51Number Losing Trades: 52Number Skipped Trades (# contracts=0): 0Percent Profitable: 49.51%

Largest Winning Trade (%): 16.02% ($9400.00)Largest Winning Trade ($): $24400.00 (14.54%)Average Winning Trade (%): 5.85%Average Winning Trade ($): $6254.94Max # Consecutive Wins: 5

Largest Losing Trade (%): -6.77% ($-12805.00)Largest Losing Trade ($): $-12805.00 (-6.77%)Average Losing Trade (%): -3.10%Average Losing Trade ($): $-3835.19Max # Consecutive Losses: 5


55/57



Ratio Avg Win(%)/Avg Loss(%): 1.89Ratio Avg Win($)/Avg Loss($): 1.63Average % Trade: 1.33%Average $ Trade: $1160.90

Max # Contracts: 18Avg # Contracts: 5

Max Closed Trade % Drawdown: 21.13% ($43351.40)Date of Max % Drawdown: 4/1/2002Max Closed Trade $ Drawdown: $43351.40 (21.13%)

Date of Max $ Drawdown: 4/1/2002Return on Starting Equity: 239.14%


56/57



* MM ANALYSIS: MONTE CARLO ANALYSIS *

INPUT DATA:Initial Account Equity: $50000.00

Risk Percentage (fixed fraction): 4.00%Number of Trades: 103Rate of Return Goal: 100.00%Drawdown Goal: 30.00%Probability Goal: 95.00%Number of Random Sequences: 1000


57/57


OUTPUT/RESULTS:Error Code: 0Average Rate of Return: 249.48%Average Final Account Equity: $174741.00

Probability of Reaching Return Goal: 100.00%Probability of Reaching Drawdown Goal: 85.10%Probability of Reaching Return and Drawdown Together: 85.10%Rate of Return at 95.00% Probability: 195.31%Drawdown at 95.00% Probability: 35.16%

Documents

Trade Risk Talk