Chartwell/Books/Finance/PositionSizing - Unknown.txt

SUPER

TRADER

MAKE CONSISTENT PROFITS IN

GOOD AND BAD MARKETS



VAN K.THARP





PART4: Understanding the Importance of Position Sizing

System Quality and

Position Sizing

What is the purpose of position sizing? Position sizing is the

part of your system that you use to meet your objectives. You

could have the world's best system (e.g., one that makes money

95% of the time and in which the average winner is twice the

size of the average loser), but you still could go bankrupt if you

risked lOO% on one of the losing trades. This is a position

sizing problem.

The purpose of a system is to make sure that you can

achieve your objectives easily through position sizing. If you

look at the ratio of the expectancy and the standard deviation of

the R-multiple distribution that your system produces, you

generally can tell how easy it will be to meet your objectives by

using position sizing. Table 4-l provides a rough guideline.

With a poor system, you may be able to meet your

objectives, but the poorer the system, the harder your job will

be. However, with a Holy Grail system, you’ll find that it is

easy to meet even extreme objectives.

Of course, there is one other important variable in your

system: the number of trades it generates. A system with a ratio

of 0.75 that generates one trade each year is not a Holy Grail

system because it doesn’t give you enough opportunities.

However, a system with a ratio of 0.5 that generates 20 trades

per month is a Holy Grail system, partly because it gives you

more opportunities to make money.





System (luality and Position Sizing

I’ve developed a proprietary measure we call the System

Quality Number (SQNM) that takes into account the number of

trades. We’ve come up with a few important observations in

doing research on this concept:

I It’s very difficult to come up with a system with a

ratio of mean R to standard deviation of R as high

as 0.7. For example, if I take a system with a ratio of

0.4 and add a 30R winner to it, the net result is that the

standard deviation of R goes up more than the mean

does, and so the ratio declines. What you need for a

Holy Grail System is a huge number of winners and a

small variation in the amounts won and lost.

I If you con?ne a system to a certain market type,

then it isn’t that hard to develop something that’s in

the Holy Grail range, Keep in mind, though, that it is

in the Holy Grail range only for that market type (e.g.,

quiet bull).

I You need to understand how your system works in

various market types and use it only in the types of

markets for which it was designed. This says a lot

about developing systems and echoes whatl said

earlier. The common mistake most people make in

designing systems is to try to find a system that works

in all market conditions. That’s insane. Instead,

develop different systems that are close to the Holy

Grail level for each market type.

I received a report from one person who was trading

currencies from July 28 through October I2, 2008. Most people

were losing huge amounts of money during that period,

According to his calculations, the ratio between the expectancy

of his system and its standard deviation was 1.5, double what

I‘m calling Holy Grail. Once he realized how good his system

was, he started to position size at levels that are acceptable only

with a Holy Grail System.

Table 4-2 shows the unaudited results he reported to me.

I’ve seen people making l,OOO% per year before, but never

anything quite like this. However, I’m willing to believe it is

possible if he has found a system that provides a ratio of

expectancy of R to standard deviation of R of 1,53, as is





System Quality and Position Sizing

indicated by the data he sent me. However, his return was

possible only because he then realized what he could do with

position sizing with this system. His exposure per trade is huge

and would bankrupt most traders.

Again, I have no Way of knowing if the information sent

me was correct. I don’t audit trading accounts. My business is

to coach traders. This e-mail was sent to me as a thank-you

note for the insights he got from my advice‘

QUIET BULL MARKET





184 PART4: Understanding the Importance of Position Sizing

Position Sizing Is More Important

Than You Think

Most people think that the secret to great investing is to find

great companies and hold on for a long time. The model investor

for this, of course, is Warren Buffett. The model that mutual

funds work on is buying and holding great investments, and the

goal is simply to outperform some market index. If the market is

down 40% and they are down only 39%, they have done well.

If you pay attention to the academic world, you learn that

the most important topic for investors is asset allocation. There

was a research study by G. Brinson and his colleagues in the

Financial Analysts Journal in 19911 in which they reviewed the

performance of 82 portfolio managers over a 10-year period

and found that 91% of the performance variability of the

managers was determined by asset allocation, which they

defined as “how much the managers had in stocks, bonds, and

cash.” It wasn’t entry or what stocks they owned; it was this

mysterious variable that they called asset allocation, which was

defined in terms of “how much."

I recently looked at a book on asset allocation by David

Darstf chief investment strategist for Morgan Stanley’s Global

Wealth Management Group. On the back cover there was a

quote from Jim Cramer of CNBC: “Leave it to David Darst to

use plain English so we can understand asset allocation, the

single most important aspect of successful performance." Thus,

you’d think the book would say a lot about position sizing,

wouldn’t you?

When I looked at the book, I asked myself these questions:

I Does he define asset allocation as position sizing?

I Does he explain (or even understand) why asset

allocation is so important‘?

I Is position sizing (how much) even referenced in

the book?

‘Gary Brinson, Brian Singer. and Gilbert Beebowen “Determinants of

Portfolio Performance: II. An Update." Financial Anuly.vt.v Journal 47: 40-49,

May—June 199].

1Da\/id Durst. Mastering the Art nfAs.\"erAllncari0n: Cumprehensii/1' Appruaz'I1c.r

to Managing Rixk and Optimizing Remrnx. New York: McGraw—Hill. 2007.





Position Sizing ls More Important Than You Think 185

I discovered that there was no definition of asset allocation

in the book, nor was there any explanation, related to the issue of

how much, or why asset allocation is so important. Finally, topics

such as position sizing, how much, and money management were

not even referenced in the book. Instead, the book was a

discussion of the various asset classes one could invest in, the

potential returns and risks of each asset class, and the variables

that could alter those factors, To me it proved that many top

professionals don’t understand the most important component of

investment success: position sizing. I'm not picking on one book

here, I can make the same comment about every book on the

topic of asset allocation l’ve ever looked through.

Right now, most of the retirement funds in the world are

tied up in mutual funds. Those funds are required to be 95% to

100% invested, even during horrendous down markets such as

the ones in 2000-2002 and 2008—present. Those fund managers

believe that the secret to success is asset allocation without

understanding that the real secret is the “how much” aspect of

asset allocation, This is why I expect that most mutual funds

will cease to exist by the end of the secular bear market, when

P/E ratios of the S&P 500 are well into the single-digit range.

Banks, which trade trillions of dollars of foreign currency

on a regular basis, don’t understand risk at all. Their traders

cannot practice position sizing because they don’t know how

much money they are trading. Most of them don‘t even know

how much money they could lose before they lost their jobs.

Banks make money as market makers in foreign currencies,

and they lose money because they allow or even expect their

traders also to trade these markets. Rogue traders have cost

banks about a billion dollars each year over the last decade,

yet I doubt that they could exist if each trader had his or her

own account,

I was surprised to hear Alan Greenspan3 say that his biggest

mistake as Federal Reserve chairman was to assume that big

banks would police themselves in terms of risk, They don‘t

understand risk and position sizing, yet they are all getting huge

bailouts from the government.

By now, you are probably wondering how I know for sure

that position sizing is so important.

3Alan Greenspan, The Age QfTllVl7Ml('!'l(‘£'.‘ Adventures in a New World. New York:

Penguin, 2007.





PART4: Understanding the Importance of Position Sizing

Let me present a simple trading system. Twenty percent of

the trades are 10R winners, and the rest of the trades are losers.

Among the losing trades, 70% are IR losers and the remaining

10% are 5R losers. Is this a good system? If you want a lot of

winners, it certainly isn’t because it has only 20% winners, but

if you look at the average R for the system, it is 0.8R. That

means that on average you‘d make O.8R per trade over many

trades. Thus, when it’s phrased in terms of expectancy, it’s a

winning system. Remember that this distribution represents the

R-multiples of a trading system with an expectancy of 0.8R.

It’s not the market; it’s the R-multiples of a trading system.

Let’s say you made 80 trades with this system in a year.

On average you‘d end up making 64R, which is excellent. If

you allowed R to represent 1% of your equity (Which is one

way to do position sizing), you’d be up about 64% at the end

of the year.

As was described earlier in this book, I frequently play a

marble game in my workshops with this R-multiple distribution

to teach people about trading. The R~multiple distribution is

represented by marbles in a bag. The marbles are drawn out

one at a time and replaced. The audience is given $100,000 to

play with, and they all get the same trades. Let’s say we do

30 trades and they come out as shown in Table 4-3.

The bottom row is the total R-multiple distribution after

each 1O trades. After the first 1O we were up +8R, and then

we had 12 losers in a row and were down 14R after the next

10 trades. Finally, we had a good run on the last 10 trades, with





Position Sizing ls More Important Than You Think

four winners, getting 30R for those lO trades. Over the 30 trades

we were up 24R, That number divided by 30 trades gives us a

sample expectancy of 0.8R.

Our sample expectancy was the same as the expectancy of

the marble bag. That doesn’t happen often, but it does happen.

About half the samples are above the expectancy, and another

half are below the expectancy, as illustrated in Figure 4-l.

The figure represents 10,000 samples of 30 trades drawn

randomly (with replacement) from our sample R-multiple

distribution. Note that both the expectancy (defined by the

average) and the median expectancy are 0.8R.

Let’s say you are playing the game and your only job is to

decide how much to risk on each trade or how to position size

the game, How much money do you think you’d make or lose?

Well, in a typical game like this, a third of the audience will

go bankrupt (i.e., they won't survive the first five losers or the

streak of 12 losses in a row), another third will lose money,

and the last third typically will make a huge amount of

money, sometimes over a million dollars. In an audience of

approximately [O0 people, except for the 33 or so who are at

zero, there probably will be 67 different equity levels.

That shows the power of position sizing, Everyone in

the audience got the same trades: those shown in the table.

Thus, the only variable was how much they risked (i.e., their

position sizing). Through that one variable we’ll typically have

final equities that range from zero to over a million dollars.





PART4: Understanding the Importance of Position Sizing

That's how important position sizing is. I've played this game

hundreds of times, getting similar results each time. Generally,

unless there are a lot nf bankruptcies, I get as many different

equities at the end of the game as there are people in the room.

Yet everyone gets the same trades.

Remember the academic study that said that 91% of the

performance variation of 82 retirement portfolios was due to

position sizing. Our results with the game show the same

results. Everyone gets the same trades, and the only variable

(besides psychology) is how much the players elect to risk on

each trade,

If the topic is ever accepted by academia or mainstream

finance, it probably will change both of those fields forever.

It is that significant.





Three Components of Position Sizing

Three Components

of Position Sizing

Performance variability produced by position sizing has three

components (see Figure 4-2).‘ They are all intertwined, and so

it is very difficult to separate thernt

The first component is the trader’s objectives. For

example, someone who thinks, “I'm not going to embarrass

myself by going bankrupt” will get far different results from

those of someone who wants to win no matter what the

potential costs may be. In fact, I’ve played marble games in

which I’ve divided the audience into three groups, each with a

different objective and a different “reward structure” to make

sure they have that objective. Although there is clearly sizable

variability in “within—group” ending equities, there is also a

distinct, statistically significant difference between the groups

with different objectives,

The second component, which clearly in?uences the first

component, is a person’s psychology. What beliefs are operating

to create that person’s reality? What emotions come up?





PART4: Understanding the Importance of Position Sizing

What is the person’s mental state? A person Whose primary

thought is not to embarrass herself by going bankrupt, for

example, isn’t going to go bankrupt even if her group is given

incentives to do so. Furthermore, a person with no objectives

and no position sizing guidelines will position size totally by

emotions.

The third component is the position sizing method,

Whether it is “intuitive” or a specific algorithm. Each model has

many possible varieties, including the method of calculating the

equity, which we’ll discuss later.





THE CPR Model for Position Sizing

THE CPR Model for

Position Sizing

A simple model for determining “how much?” involves risking a

percentage of your equity on every trade. We’ve alluded to the

importance of this decision throughout this book, but how exactly

do you do that’? You need to know tlircc distinct variables.

. How much of your equity are you going to risk?

This is your total risk, but we will call it cash (or C) for

short. Thus, we have the C in our CPR formula. For

example, if you were going to risk 1% of your equity,

C would be 1% of your equity. lf you had a $50,000

account. C would be 1% of that, or $500.

POSITION SIZING IS CPR FOR TRADERS

YT How many units do we buy (i.e., position sizing)? I

call this variable P for position sizing.

l r How much you are going to risk per unit that you

purchase? We will call this variable R, which stands

for risk. We’ve already talked about R in our discussion

of expectancy. For example. if you are going to buy a

$50 stock and risk $5 per sharc, your risk (R) is $5 per

share.





PART4: Understanding the Importance of Position Sizing

Essentially, you can use the following formula to determine

how much to buy:

P=C/R

Let’s look at some examples so that you can understand

how easy it is to apply this formula.

Example 1: You buy a $50 stock with a risk of $5 per share.

You want to risk 2% of your $30,000 portfolio. How many

shares should you buy?

Answer 1: R = $5/share; C = 2% of $30,000, or $600.

P = 600/5 = 120 shares. Thus, you would buy 120 shares of a

$50 stock. Those shares would cost you $6,000, but your total

risk would be only 10% of your cost (i.e., assuming you kept

your $5 stop), or $600.

Example 2: You are day trading a $30 stock and enter into

a position with a 30-cent stop. You want to risk only a half

percent of your $40,000 portfolio. How many shares should

you buy?

Answer 2: R = 30 cents/share. C = 0.005 X $40,000, or $200.

P = 200/0.3 = 666.67 shares. Thus, you‘d buy 666 shares that

cost you $30 each. Your total investment would be $19,980, or

nearly two-thirds of the value of your portfolio. However, your

total risk would be only 30 cents per share, or $199.80

(assuming you kept your 30-cent stop).

Example 3: You are trading soybeans with a stop of

20 cents. You are willing to risk $500 in this trade. What is

your position size? A soybean contract is 5,000 bushels. Say

soybeans are trading a $6.50. What size position should you

put on?

Answer 3: R = 20 cents X 5,000 bushels per contract = $1,000.

C = $500. P = $500/$|,000, which is equal to 0.5. However, you

cannot buy a half contact of soybeans. Thus, you would not be

able to take this position. This was a trick question, but you need

to know when your position has way too much risk.





THE CPR Model for Position Sizing 193

Example 4: You are trading a dollar-Swiss franc forex

trade. The Swiss franc is at 1.4627, and you want to put in

a stop at 1.4549. That means that if the bid reaches that

level, you’ll have a market order and be stopped out. You

have $200,000 on deposit with the bank and are willing to

risk 2%. How many contracts can you buy?

Answer 4: Your R value is 0.0078, but a regular forex

contract would be trading $100,000 worth, and so your stop

would cost you $780. Your cash at risk (C) would be 2% of

$200,000, or $4,000. Thus, your position size would be $4,000

divided by $780, or 5.128 contracts. You round down to the

nearest whole contract level and purchase five contracts.





PART4: Understanding the Importance oi Position Sizing

Position Sizing Basics

Until you know your system very well, I recommend that you

risk about 1% of your equity. This means that 1R is converted

to a position size that equals 1% of your equity. For example, if

you have $100,000, you should risk $1,000 per trade. If the risk

per share on trade 1 is $5, you’1l buy 200 shares. If the risk per

share on trade 2 is $25, you’ll buy only 40 shares. Thus, the

total risk of each position is now 1% of your account.

Let’s see how that translates into successive trades in an

account. On your first trade, with equity of $100,000, you

would risk $1,000. Since it is a loser (as shown in Table 4-4),

you’d now risk 1% of the balance, or $990. lt’s also a loser,

and so you'd risk about 1% of what’s left, or $980. Thus,

you'd always be risking about 1% of your equity. Table 4-4

shows how that would work out with the sample of trades

presented in Table 4-3.





Position Sizing Basics 195



Remember that in this sample of trades you were up 24R at

the end of the game. This suggests that you could be up about

24% at the end of the game. We’re up 22.99%, so We almost

made it. Equity peaks are shown in bold, and equity lows are

shown in italics.





PART4: Understanding the Importance of Position Sizing

Because of the drawdowns that came early, you would

survive. You have a low equity of about $91,130.99 after the

long losing streak, but you are still in the game. At the end you

would be up about 23%. Even though you risked 1% per trade

and were up 24R at the end of the game, that doesn’t mean

you’d actually be up 24% at the end of the game. That would

occur only if y0u‘d risked 1% of your starting equity on each

trade, which is a different position sizing algorithm,

You wouldn’t win the game with this strategy because

someone who does something incredibly risky, such as risking

it all on the sixth trade, usually wins the game‘ The important

point is that you’d survive and your drawdown wouldn‘t be

excessive.





Types of Equity Models 197

Types of Equity Models

All the models you’ll learn about in this book relate to the

amount of equity in your account. These models suddenly can

become much more complicated when you realize that there are

three methods of determining equity. Each method can have a

different impact on your exposure in the market and your

returns. These methods include the core equity method. the

total equity method, and the reduced total equity method.

SO MANY WAYS TO CALCULATE EQUITY

The core equity method is simple. When you open a new

position, you simply determine how much you would allocate

to that position in accordance with your position sizing

method. Thus, if you had four open positions, your core equity

would be your starting equity minus the amount allocated for

each of thc open positions.

Let’s assume you start with an account of $50,000 and

allocate 10% per trade. You open a position with a $5,000

position sizing allocation, using one of thc methods described

later in the book. You now have a core equity of $45,000. You

open another position with a $4,500 position sizing allocation,





PART4: Understanding the Importance of Position Sizing

and so you have a core equity of $40,500. You open a third

position with an allocation of $4,050, and so your core equity is

now $36,450. Thus, you have a core equity position of $36,450

plus three open positions. In other words, the core equity

method subtracts the initial allocation of each position and

then makes adjustments when you close that position out.

New positions always are allocated as a function of your

current core equity.

I first learned about the term care equity from a trader who

was famous for his use of the market’s money. This trader

would risk a minimum amount of his own money when he first

started trading. However, when he had profits, he’d call that

market’s money and would be willing to risk a much larger

proportion of his profits. This trader always used a core equity

mode] in his position sizing.

The total equity method is also very simple. The value of

your account equity is determined by the amount of cash in

your account plus the value of any open positions. For example,

suppose you have $40,000 in cash plus one open position with

a value of $15,000, one open position worth $7,000, and a third

open position that has a value of minus $2,000. Your total

equity is the sum of the value of your cash plus the value all

your open positions. Thus, your total equity is $60,000.

Tom Basso, who taught me methods for maintaining a

constant risk and a constant volatility, always used the total

equity model. It makes sense! If you want to keep your risk

constant, you want to keep the risk a constant percentage of

your total portfolio value.

The reduced total equity method is a combination of the

first two methods. It is like the core equity method in that the

exposure allocated when you open a position is subtracted from

the starting equity. However, it is different in that you also add

back in any profit or reduced risk that you will receive when

you move a stop in your favor. Thus, reduced total equity is

equivalent to your core equity plus the pro?t of any open

positions that are locked in with a stop or the reduction in

risk that occurs when you raise your stop.-‘

5This sometimes is called the reduced core equity method. However, that title

doesn’l make any sense tome. so I’ve renamed it.





Types of Equity Models 199

Here’s an example of reduced total equity. Suppose you

have a $50,000 investment account‘ You open a position with a

$5,000 position sizing allocation. Thus, your core equity (and

reduced total equity) is now $45,000. Now suppose the

underlying position moves up in value and you have a trailing

stop. Soon you only have $3,000 in risk because of your new

stop. As a result, your reduced total equity today is $50,000

minus your new risk exposure of $3,000, or $47,000.

The next day, the value drops by $1,000. Your reduced

total equity is still $47,000 since the risk to which you are

exposed if you get stopped out is still $47,000. It changes only

when your stop changes to reduce your risk, lock in more

profit, or close out a position.

The models briefly listed in the next section generally size

positions in accordance with your equity. Thus, each model

of calculating equity will lead to different position sizing

calculations with each model.





200 PART4: UnderstandingtheImportanceotPositionSizing

Different Position Sizing Models

In most of my books, I talk about the percent risk position

sizing model. lt’s easy to use, and most people can be safe

trading at 1% risk,

However, in the De?nitive Guide to Position Sizing“, I list

numerous position sizing methods, all of which can be used to

achieve your objectives. My goal here is to list a few of the

methods so that you can see how extensive your thinking about

position sizing can be.

In the percent risk model, which we have described as CPR

for traders and investors, you simply allocate your risk to be a

percentage of your equity, depending on how you want to

measure it. In some of the other methods, you use a different

way to allocate how much to trade,

Here are some examples of ways you could allocate assets

as u form of position sizing:

1 . Units per ?xed amount of money: buying 100 shares

per $10,000 of equity or one contract per $10,000

2. Equal units/equal leverage: buying $100,000 worth of

product (shares or values of the contract) per unit

3. Percent margin: using a percent of equity based on the

margin on a contract rather than the risk

4. Percent volatility: using a percent of equity based on

the volatility of the underlying asset rather than the risk

as determined by R

5. Group risk: limiting the total risk per asset class.

6. Portfolio heat: limiting the total exposure of the

portfolio regardless of the individual risk

7. Long versus short positions: allowing long and short

positions to offset in terms of the allocated risk,

8. Equity crossover model: allocating only when the

equity crosses over some threshold

9. Asset allocation When investing in only one class of

asset: investing a certain percentage of one’s assets,

say, 10%, in some asset class

“Van Tharp. The Definitive Guide to Position Sizing: l-low to Evaluate Your

System and Use Position Sizing to Meet Your Obiectives. Cary, NC. IITM. 2008.





Different Position Sizing Models

10. Over- and underweighting one’s benchmark: buying

the benchmark and considering an asset as being long

when you overweight it and short when you underweight it

1 1 . Fixed-ratio position sizing: a complex form of position

sizing developed by Ryan Jones; requires a lengthy

explanation

12. Two-tier position sizing: risking 1% until one’s equity

reaches a certain level and then risking another

percentage at the second level

1 3. Multiple-tier approach: having more than two tiers.

14. Sealing out: scaling out of a position when certain

criteria are met

15. Scaling in: adding to a position based on certain

criteria

16. Optimal f: a form of position sizing designed to

maximize gains and drawdowns

17. Kelly criterion: another form of position sizing

maximization, but only when one has two probabilities

1 8. Basso-Schwager asset allocation: periodic reallocation

to a set of noncorrelated advisors

1 9. Market’s money techniques (thousands of

variations): risking a certain percentage of one’s

starting equity and a different percentage of one’s

profits

20. Using maximum drawdown to determine position

sizing: position sizing to make sure that you do not

exceed a certain drawdown that would be too dangerous

for your account,

Are you beginning to understand why position sizing is

much more important and much more complex than you have

conceived of in your trading plans to date?





202 PART4: UnderstandingtheImportanceoiPositionSizing

The Purpose of Position Sizing

Remember that position sizing is the part of your trading

system that helps you meet your objectives. Everyone probably

has a different objective in trading, and there are probably an

infinite number of ways to approach position sizing. Even the

few people who have written about position sizing get this point

Wrong. They typically say that position sizing is designed to

help you make as much money as you can Without experiencing

ruin. Actually, they are giving you a general statement about

their objectives and thinking that that’s what position sizing is.

Let’s play our game again with the O.8R expectancy‘ Say

I give the following instructions to the people playing the game

(100 people are playing): First, it costs $2 to play the game.

Second, if after 30 trades your account is down from $100,000

to $50,000, it will cost you another $5. Third, if you go bankrupt,

you will have to pay another $13, for a total loss of $20.

If at the end of 30 trades you have the most equity. you will

win $200. Furthermore, the top five equities at the end of the

game will split the amount of money collected from those who

lose money.

Your job is to strategize about how you want to play the

game. I recommend that you use the following procedure; it is

also an excellent procedure to follow in real~life trading to

develop a position sizing strategy to fit your objectives.

First, decide who you are. Possible answers might be

(1) someone who is determined to win the game, (2) someone

who wants to learn as much as possible from playing the game,

(3) a speculator, or (4) a very conservative person who doesn’t

want to lose money‘

The next step is to decide on your objectives. In light of the

various payoff scenarios, here are possible objectives:

1 . Win the game at all costs, including going bankrupt

(the person winning the game usually has this as the

objective).

2. Try to win the game but make sure I don’t lose more

than $2.

3. Try to win the game but make sure I don’t lose more

than $7.





The Purpose of Position Sizing

4. Be in the top five and don’t lose more than $7.

5. Be in the top five and don’t lose more than $2.

6. Be in the top five at all costs.

7. Do as well as I can without losing $7.

8. Do as well as I can without losing $2.

9. Do as well as I can without going bankrupt.

Note that even the few rules I gave for payoffs translate into

nine different objectives that one might have. Creative people

might come up with even more. You then need to develop a

position sizing strategy to meet your objectives.

The last step is to decide when to change the rules. At the

end of every IO trades, I assess the room to determine who has

the highest equity. If at the end of 10 trades you are not one of

the top five people, you might want to change your strategy.

Notice how this changes what could happen in the game.

Chances are that l’ll still have as many as 100 distinct equities,

but chances are also that there will be a strong correlation

between the objectives people select and their final equity.

Those who want to win the game probably will have huge

equity swings ranging from $lmillion or more to bankruptcy.

However, those who want to do as well as they can without

going banknipt probably will trade quite conservatively and

have their final equities distributed within a narrow range.

The game makes it clear that the purpose of position sizing is

to meet your objectives. As I said earlier, few people understand

this concept.





204 PART4: Understanding the Importance of Position Sizing

One Way to Use Position Sizing to

Meet Your Objectives: Simulation

One way to use position sizing to meet your objectives is to use

a simulator. We will assume that there is only one position

sizing method: the percentage of your equity you are willing to

risk per trade.

Here is how we can set up a trading simulator by using the

system that was described earlier. Its expectancy is 0.8R, and it

has only 20% winners.

We know the expectancy will allow us to make 40R over 50

trades on the average. Our objective is to make 100% over 50

trades without having a drawdown of more than 35%. Let’s see

how we can do that with an R-multiple simulator. Figure 4-3

shows a position sizing optimizer.

I’ve set the optimizer up to run 10,000 simulations of 50

trades for our system. It will start risking 0.1% for 50 trades

10,000 times, then it will move up to 0.2%, then to 0.3%, and

so on, in 0.1% increments until it reaches 19% risk per trade.

FIGURE 4-3. Using a position-sizing optimizer





One Way to Use Position Sizing to Meet Your Obiectives 205

We have a 5R loss, and so a 20% risk automatically results in

bankruptcy when that is hit. Thus, we are stopping at a 19%

risk per position.

The simulator will run 10,000 fifty-trade simulations at

each risk level unless it reaches our criteria of ruin (i.e., down

35%), in which case it will say that was ruin and move on to

the next one in the sequence of 10,000 simulations. That‘s a

lot of computing to be done, but today’s computers can handle

it easily.

The results of this simulation are shown Table 4-5.

The top row gives the risk percentage that delivers the

highest mean ending equity. Typically, this is the largest risk

amount simulated because there will be a few samples that may

have many, many 10R winners. That run would produce a huge

number and boost the average result even if most nins resulted

in a drop of 35% or more. Note that at 19% risk, the average

gain is 1,070%. However, we have only a 1.1% chance of

making 100% and a 98.7% chance of ruin. This is why going

for the highest possible returns, as some people suggest, is

suicidal with a system that is at best average.

The median ending equity is probably a better goal. This

gives an average gain of 175% and a median gain of 80.3%.

You have a 46.3% chance of meeting your goal and a 27.5%

chance of ruin.

What if your objective is to have the largest percent chance

of reaching the goal of making 100%? This is shown in the

Opt. Retire row. It says that if we risk 2.9%, we have a 46.6%

chance of reaching our goal. However, our median gain actually

drops to 77.9% because we now have a 31% chance of ruin.





PART4: Understanding the Importance of Position Sizing

What if our objective is just under a 1% chance of ruin

(being down 35%)? The simulator now suggests that we should

risk 0.9% per trade. This gives us a 10.5% chance of reaching

our goal but only a 0.8% chance of ruin.

You could have your objective be just above a 0% chance

of ruin. Here the simulator says you could risk 0.6%. The risk

is just above 0%, but the probability of reaching your objective

of making 100% is now down to 1.7%.

Finally, you might want to use the risk percentage that gives

you the largest probability difference between making 100%

and losing 35%. That turns out to be risking 1.7%. Here we

have a 37.9% chance of reaching our objective and only an

ll.l% chance of ruin. That‘s a difference of 26.8%. At the

other risk levels given it was l5% or less.

Just by using two different numbers—a goal of 100% and a

ruin level of 35%—l came up with five legitimate position

sizing strategies that just used a percent risk position sizing

model.

I could set the goal to be anything from up 1% to up

l,OOO% or more. l could set the ruin level from anything from

being down 1% to being down 100%. How many different

objectives could you have‘? The answer is probably as many as

there are traders/investors. How many different position sizing

strategies might there be to meet those objectives? The answer

is a huge, huge number.

We used only one position sizing strategy: percent risk.

There are many different position sizing models and many

different varieties of each model.





The Problems of the R-Multiple Simulator 207

The Problems of the

R-Multiple Simulator

Obviously, there are some huge advantages to simulating your

system‘s R-multiple distribution to help you learn about that

system easily. However, there are also some serious problems

with R-multiples. Unfortunately, nothing in the trading world is

perfect. The problems, in my opinion, are as follows:

I R-multiples measure performance on the basis of

single trades but won’t tell you what to expect when

you have multiple trades on simultaneously.

I R—rnultiples do not capture many of the temporal

dependencies (correlations) among the markets (in fact,

only the start date and stop date of a trade are

extracted). Thus, you cannot see drawdowns that occur

while a trade is still on and you are not stopped out

(i.e., by IR).

I As with all simulations, R—multiple simulations are

only as good as your sample distribution is accurate.

You may have a good sample of your system’s

performance, but you never will have the “true”

population. You may not have seen your worst loss or

your best gain.

I R-multiples are a superb way to compare systems when

the initial risk is similar. However, they present some

problems when one or more of the systems have a

position sizing built into the strategy, such as scale in

and scale out models. In fact, in these conditions, you

would have trouble determining the absolute

performance of two different systems. As an example,

compare two systems. The first system opens the whole

position at the initial entry point. The second system

opens only half the position at the initial entry point

and the other half after the market moves in favor of

the system by one volatility. If one gets an excellent

trade (say, a 20R move), the R~multiple of system 1

will be better (bigger) than that of system 2 (larger

profit and smaller total initial risk). However, if we get





208 PART4: Understanding the Importance of Position Sizing

a bad trade that goes immediately against us and hits

the initial exit stop, the R-multiple is the same for both

systems, namely, -l. The fact that system 2 loses only

half of the money system l loses is completely missed.

The impact of position sizing techniques (like

pyramids) that change the total initial risk of a trade are

difficult to test with the concept of R~multiples, since

the R-multiple distributions of the trading systems (with

and without the position sizing technique) cannot be

compared directly. One way to evaluate the money

management technique is to divide the trading system

into subsystems so that the subsystems are defined by

the entry points and evaluate each subsystem separately.

For instance, each pyramid could be treated as a

subsystem.

Since R-multiples capture only a few of the temporal

dependencies between markets, simulations using

R-multiples must be based on the assumption that the

R-multiples are statistically independent, which is

not the case in reality. However, one can cluster

trades according to their start date or stop date and

thus try to introduce a time aspect into simulations.

When you do this, the volatility and the drawdowns

become considerably larger when the R-multiples are

blocked. In other words, simulations based on one

trade at a time clearly produce results that are too

optimistic (1) when you are trying to determine the

performance of systems that generate multiple trades

at the same time and (2) when you are trading

multiple systems simultaneously.





Getting Around the Problems of Simulation 209

Getting Around the Problems

of Simulation

To get around the problems with a simulator, I developed the

System Quality Numberm (SQNTM). Generally, the higher the

SQN, the more liberties you can take with position sizing to

meet your objectives. In other words, the higher the SQN is, the

easier it is to meet your objectives. For example, I commented

earlier on a trader who claimed to have a 1.5 ratio between

expectancy and the standard deviation of R in a currency

trading system that generated nearly one trade each day.

Although I don’t know if it is possible to develop such an

incredible system, if he does have one, I have no doubt about

his results: turning $1,300 into $2 million in a little over four

months during a period when most of the world was having a

terrible economic crisis.

In The Definitive Guide to Position Sizing I was able to

show how, with 31 different position sizing models (93 total

since each can use any of the three equity models), it was

possible to achieve your objectives easily from the SQN. There

are still precautions you must take because of the following:

1 . You never know if your R-multiple distribution is

accurate.

2. You never know exactly when the market type will

change, which usually changes the SQN.

3. You have to account for multiple correlated trades. I did

this with the SQN by assuming that the maximum risk

was for the entire portfolio rather than for a single

position.

Thus, in our example, with an average (at best) system and

a ratio of the mean to the standard deviation of about 0.16, our

best risk percentage was 1.7%. However, if we were to trade

five positions at the same time, our risk per position probably

would have to be reduced to about 0.35%, However, a Holy

Grail system might allow us to risk 5% or more per position.