Learning from simulations
Dr. Bruce Vanstone
This material is presented for educational
purposes only.
I am not a financial advisor, and this material is
not advice.
In many cases, the material represents ongoing
research findings.
Bruce Vanstone
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Part 1 – What are we trying to achieve?
◦ Purpose
 What this part is (and isn’t!) about
 Examples are specific to equity trading
◦ 3 parts to developing a system
◦ Importance of Position Sizing
◦ Types of techniques in common use
 ‘Standard’ approaches
 ‘Advanced’ approaches
◦ Requirements of a good position sizing approach
Dr. Bruce Vanstone
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Part 2 – What we can learn from simulations
◦ An ‘example’ system: Trending 101
◦ Standard Techniques
 Percent of Equity approach
 Equity Risk Percent approach
◦ Advanced Techniques
 Martingale / Anti-Martingale
 Equity Curve approach
 Monte-Carlo
Dr. Bruce Vanstone
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Part 3 – Drawing conclusions from the results
◦ Overall summary
◦ General conclusions
Dr. Bruce Vanstone
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What this part is (and isn’t!) about
Position Sizing is also often referred to as
Money Management – these are the same
thing
This part is about the best ways to determine
the size of your positions – in other words,
how much of your portfolio gets allocated to
each stock selected
Dr. Bruce Vanstone
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Interestingly, this is mainly a problem that
concerns traders!
◦ From a finance perspective, many investors are
interested in self-financing portfolios
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This is because in academia, it is understood
that the market is efficient. As price
movements are thought to be random, there
is no reason for preferring (in a position
sizing sense) one position over another
Dr. Bruce Vanstone
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A strategy must have an ‘edge’ for you to be
‘successful’ at trading
How ‘successful’ ($ vs risk) you are is
determined by how well you can size your
positions
The dollar return from a strategy is a factor of
the dollar amount traded
◦ Casino blackjack makes a good analogy here
Dr. Bruce Vanstone
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3 parts to developing a system (Chande)
◦ Rules to enter and exit trades
◦ Risk control
◦ Money Management (Position Sizing)
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Important:
No Position Sizing strategy can turn a ‘bad’
system ‘good’
A good Position Sizing strategy can make a
‘good’ system ‘better’
Dr. Bruce Vanstone
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Importance of position sizing
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Many traders spend a great deal of time backtesting their entries and exits…
◦ Which appears to be of very limited value!
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…and almost no time at all on Position Sizing
In terms of ‘Contribution to Success’, the entry
and exit rules appear to have only (at best) a
minor influence
◦ Likely related to when in the cycle they are applied, not
what they are!
Dr. Bruce Vanstone
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As we shall see, the Position Sizing rules can
have a major influence
Research regarding time spent in parts of
trading system design shows that Money
Management contributes more benefit than
entry/exit research (3 Laws of Successful
Trading)
Dr. Bruce Vanstone
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Types of techniques in common use
◦ ‘Standard’ Approaches
◦ ‘Advanced’ Approaches
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Most traders seem content to stop at
standard techniques
They normally run a few simulations, change
a few position sizing parameters, pick the
best one, then get busy…
◦ ... Or use that ridiculous 2% risk rule
Dr. Bruce Vanstone
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This is a ‘poor’ strategy for selecting the
most significant determinant of your
‘success’!
We should all be spending a lot more time
thinking about position sizing, and a lot less
worrying about ‘the market’ and our ‘rules’
◦ Focus on things we can control
◦ Focus on things with the biggest effect
Dr. Bruce Vanstone
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Requirements of a ‘good’ position sizing
technique
A good position sizing technique relates to
◦ 1. Quality of your signal
◦ 2. State of the market
◦ 3. Amount of your equity
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‘Standard’ techniques normally react only to
number 3, and occasionally, (in a much lesser
way), number 1
Dr. Bruce Vanstone
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In the next part of this seminar, we will take a simple
system, and examine the effect of different position sizing
techniques on it
Look, whether at this stage of your trading
knowledge you are willing to accept it or not,
the rules you use to enter and exit the market
are almost inconsequential – they just provide
you with a slight edge and help you engage
with the market at the right time
Having gone through this process many times, with many,
many systems and traders, these results are quite
‘generalizable’
Dr. Bruce Vanstone
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An example system: ‘Trending 101’
To see the results of different position sizing
techniques, we need a ‘system’ to work with
◦ I typically use a system I call ‘Trending 101’ – its
about as simple a trending system as you can
imagine, and clearly shows the ‘generalizable’
effect of this work on trend trading strategies
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For this system, we are interested in the
question ‘What is in the DNA of a ‘longerterm trade?’
Dr. Bruce Vanstone
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Rules for ‘Trending 101’
Buy: if closing price today is higher than the
last 21 days
Sell: if closing price today is lower than the
last 21 days
THIS IS AN EXAMPLE ONLY! It is not a
recommendation to trade this way!
 FOCUS
on the DNA idea!
Dr. Bruce Vanstone
Dr. Bruce Vanstone
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What we will now do is look at the return,
exposure, and maximum drawdowns of
‘Trending 101’ over prior 10 years in the
Australian Stockmarket (ASX200), subject to a
variety of position sizing techniques
Our goal is to see the effects of different
position sizing techniques on this system,
with the aim of understanding how to
generalize these effects
Dr. Bruce Vanstone
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This should enable us to draw sensible
conclusions about better ways to size our
positions
For simulation purposes, we will assume a
starting capital of $100K, and include the
effects of transaction costs
Dr. Bruce Vanstone
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Data
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ASX200
◦ includes effect of delistings, name changes etc
◦ doesn’t need controlling for liquidity
Dr. Bruce Vanstone
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I have divided position sizing up into two
main camps
◦ Standard techniques (used by the vast majority of
traders)
◦ Advanced techniques (not very common, but
potentially much more powerful)
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I will explain each approach within each
technique, and assess it according to the
three requirements for a good Position sizing
strategy.
Then we will see its effect on ‘Trending 101’s
DNA
Dr. Bruce Vanstone
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Remember, we are not focused on the actual
values for return, exposure and maximum
drawdowns
We are focused on how much as a percentage
(and in which directions) these values change, as
we examine some different position sizing
techniques
Remember that all we are doing is changing the
way we bet our money. We are still using the
same trades every time.
Dr. Bruce Vanstone
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Recap!
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A good position sizing techniques reacts to
◦ 1. Quality of your signal
◦ 2. State of the market
◦ 3. Amount of your equity
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We will monitor changes in
◦ Returns (APR%)
◦ Exposure (% of time money is in the market)
◦ Maximum drawdown (%)
Dr. Bruce Vanstone
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Standard Techniques
◦ Fixed Dollar approach
◦ Percent of Equity approach
◦ Risk Stop percentage – I won’t even bother!
Dr. Bruce Vanstone
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Standard Technique: Fixed Dollar sizing
◦ We will use this first technique as our ‘baseline’ to
compare different techniques to
Fixed Dollar Sizing
Description
Allocates the same amount of capital to every trade
Reacts to…
Quality of your signal - NO
State of the market - NO
Amount of your equity - NO
Simulation
100K, $2K per trade
Return
7.93%
Exposure
95.73%
Max. Drawdown -39.34%
Dr. Bruce Vanstone
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Standard Technique: Percent of equity
Percent of equity
Description
The amount of capital allocated to each trade is 2% of
the value of open equity
Reacts to…
Quality of your signal - NO
State of the market - NO
Amount of your equity - YES
Simulation
100K, 2% per trade
Return
10.78%
(Change from baseline: 35.93%)
Exposure
96.27%
(Change from baseline: 0.56%)
Max. Drawdown -40.91% (Change from baseline: 3.99% )
Dr. Bruce Vanstone
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Advanced techniques
◦ Martingale / Anti-Martingale approach
◦ Market driven
◦ Equity Curve approach
Dr. Bruce Vanstone
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To understand where these techniques come
from its necessary to revisit basic probability,
statistics and a little game theory (sorry!)
Consider the following ‘game’:
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Toss a fair coin 10 times
I can bet $1 on the outcome of each toss
If the result is a Head, I get an extra $1
If it’s a Tail, I lose my $1
Easy Question: Can I make any money at this
game?
Dr. Bruce Vanstone
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To be honest, we should say NO… but the
reason why is important.
Harder question: Why not?
Dr. Bruce Vanstone
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Its not because the probability of winning is
50:50
We must say NO because the outcome of the
next coin toss is not dependant on the last
coin toss (coin tosses are statistically
independent events)
Dr. Bruce Vanstone
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Game 1:
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HTHHTHTTHTTHHTHT
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Game 2:
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HHHHHHHHTTTTTTTT
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50:50? What about a sequence?
Dr. Bruce Vanstone
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In academic finance, this is why there is so
much debate about Random Walks and
Efficient Markets
Its really a debate about whether price
changes are statistically independent from
each other
◦ Which means random!
Dr. Bruce Vanstone
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Advanced techniques rely on the fact that the
trades you generate from your trading system
may not all be independent of each other
(even though the prices could be)
Or, put differently, the success of your next
trade may (in some way?) be determined by
your last trade, and/or the state of the
market, and/or something else
Dr. Bruce Vanstone
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This is really important, because many
traders treat each individual trade as if it was
independent of the last (or of the market),
but it is extremely unlikely that this is true.
It is important to understand that in trading,
you believe that the probability of winning a
given trade is most likely not a statistically
independent event
◦ unless your trading rules are actually random, in
which case, you have a bigger problem!
Dr. Bruce Vanstone
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Consider two of our ‘Coin Toss’ games
The probability of a win in both games is 50%
Game 1: H,H,T,H,T,T,H,H,T,H,T,T,…
Game 2: H,H,T,T,H,H,T,T,H,H,T,T,…
I cannot win Game 1
I cannot lose Game 2 (if I recognize the fact
that the outcome of a toss is not independent
of the previous toss)
◦ This would mean a ‘crooked’ coin of course!
Dr. Bruce Vanstone
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So the key to ‘Advanced’ methods relates to
finding something which relates to your trade
sequence probability
Fortunately, that may not be as hard as it
sounds
In statistical terms, this is called finding
‘streaks’, and can be implemented via a ‘runs
test’
Dr. Bruce Vanstone
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However, for many traders, logic also
suggests the answer could be related to:
◦ The previous trade (or trades)
 Most systems go through periods of winning and
losing – not random wins/losses
◦ The market
 For many systems based on trends, the overall market
may help dictate sequences of wins and losses
◦ Unknown
 Just because we are not sure what it is, doesn’t mean
we can’t use it!
 Because…. It shows itself in our equity curve
Dr. Bruce Vanstone
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The previous trade?
If the probability of winning is influenced by
the success or failure of the previous trade(s),
then this is exploitable
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Technique: martingale/anti-martingale
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Dr. Bruce Vanstone
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Martingale betting: increasing bet size after a
loss
Anti-Martingale betting: increasing bet size
after a win
Martingale strategies for betting were popular
in 18th century France, when playing games
of chance
Dr. Bruce Vanstone
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Advanced Technique: Anti-Martingale
Anti-Martingale
Description
Increase bet size after a win
Reacts to…
Quality of your signal - Yes
State of the market - NO
Amount of your equity - YES
Simulation
100K, 2% per trade, doubled after each win (once only)
Return
14.40% (Change from baseline: 81.59%)
Exposure
96.28% (Change from baseline: 0.57%)
Max. Drawdown
-47.34% (Change from baseline: 20.34% )
Dr. Bruce Vanstone
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Advanced Technique: Equity Curve driven
Equity Curve Driven
Description
Decrease bet size when equity curve below 20day sma
Reacts to…
Quality of your signal - Yes
State of the market - Yes
Amount of your equity - YES
Simulation
100K, 2% per trade, reduced if equity curve below sma
Return
11.16% (Change from baseline: 40.73%)
Exposure
74.8%
Max. Drawdown
-31.33% (Change from baseline: -20.36% )
(Change from baseline: -21.86%)
Dr. Bruce Vanstone
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Advanced Technique: Equity Curve driven (2)
Equity Curve Driven (2)
Description
Double trade size when equity is going up, skip trades
when in drawdown by 10% or more
Reacts to…
Quality of your signal - Yes
State of the market - Yes
Amount of your equity - YES
Simulation
100K, 2% per trade, adjusted as above
Return
15.5%
(Change from baseline: 95.46%)
Exposure
83.29%
(Change from baseline: -12.99%)
Max. Drawdown
-26.23% (Change from baseline: -33.32% )
Dr. Bruce Vanstone
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Overall Summary
Technique
Fixed Dollar (Baseline)
Return (APR%)
Exposure (%)
Max. DD (%)
7.93%
95.73%
-39.34%
Percent of Equity
10.78%
96.27%
-40.91%
Anti-Martingale
14.40%
96.28%
-47.34%
Equity Curve (1)
11.16%
74.80%
-31.33%
Equity Curve (2)
15.50%
83.29%
-26.23%
Dr. Bruce Vanstone
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General Conclusions
Significant improvement can be made to a
strategy by changing the way it sizes positions
Overall, the largest improvements in increasing
return and decreasing risk appear to come not
from your trading signals, but from knowing
when to act on your signals…
… and stopping trading as soon as you enter a
drawdown period
Dr. Bruce Vanstone
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The really hard question for tonight: Why?
Dr. Bruce Vanstone
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Turns out it appears to be a bit of a slap in the
face for most traders
Returns increase and drawdown decreases
because of when you aren’t trading, NOT because
of when you are!
Which relates back to what I was getting at in an
earlier slide:
◦ (from prior slide) Look, whether at this stage of your
trading knowledge you are willing to accept it or not, the
rules you use to enter and exit the market are almost
inconsequential – they just provide you with a slight
edge and help you engage with the market at the right
time
Dr. Bruce Vanstone
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Returns increase and drawdown decreases
because of when you aren’t trading, NOT
because of when you are!
The curse of Technical Analysis and back
testing software:
◦ Makes you wonder why people spend so much time
playing with their entry signals
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 Probably because even though its almost pointless, its
easy and can be fun!
 Seriously, though... The better the ‘edge’ the more
robust/reliable the systems can be… the better the
position sizing, the more lucrative the systems can be
Dr. Bruce Vanstone