Master Class Position Sizing

2011

Trevor Neil

BETA Financial Learning & Development

Limited

04/08/2011

Trevor Neil’s Master Class: Position Sizing

Trevor Neil’s Master Class

On the first Friday of each month at 2pm Singapore Time, 10am London time and at noon New

York time, Trevor Neil holds a 45 minute technical analysis surgery looking at a specific aspect of

technical analysis. These are more advanced sessions concentrating on trading techniques,

sometimes asset class specific. Trevor Neil will share with you his market timing skill and

experience. Here we take a small subject and cover it in detail. They are practical rather

than theoretical. They are given remotely and live via WebEx and you can interact. There is an

open question and answer session at the end. A full and detailed manual is subsequently provided

for attendees. There is a small charge for the Master Class manuals. The surgeries are aimed at

improving investor/trader skills and are not training in using Eikon, Metastock or 3000Xtra. Please

ask you Thomson Reuters Trainer for help with the terminal itself. They are for educational

purposes only. There are no investment recommendations implied in the examples.

Trevor Neil’s Friday Technical Analysis Surgery

On the third Friday of each month at 2pm Singapore Time, 10am London time and at noon New

York time, Trevor Neil holds a 45 minute technical analysis surgery looking at a specific aspect of

technical analysis. The purpose is to for you to gain a comprehensive understanding of

technical analysis and market timing. They are given remotely and live via WebEx and you can

interact. There is an open question and answer session at the end. A full and detailed manual is

subsequently provided for attendees. The surgeries are free and aimed at improving

investor/trader skills and are not training in using Eikon, Metastock or 3000Xtra. Please ask you

Thomson Reuters Trainer for help with the terminal itself. They are for educational purposes only.

There are no investment recommendations implied in the examples.

Charts and Data

All Charts and data are from Thomson Reuters and Eikon is used for analysis

Position Sizing

This session looks at the size of a trade that is appropriate. There is a small formula to use to

ensure capital preservation while exposing yourself to enough risk to make a profit. As well as the

usual manual, a small excel sheet will be supplied. If you do not understand this and have a grip on

it, you should not be trading.

As always, there are no recommendations implied or buy or sell signals generated. It is for

educational purposes only.

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www.betagroup.co.uk BETA Group©2011

3 Common ways to size trades

Trevor Neil

Trevor Neil has been a trader for over 30 years; starting at the age of 18 as a coffee floor trader for

Merrill Lynch. He moved into other „softs‟ and then became a broker. It was then he became

interested in technical analysis. At the time, the „70‟s, technical analysis was changing. It was

moving from the pencil, ruler and graph paper to the PC. He became very involved in the early

stages of the development of computerised technical analysis. When LIFFE opened, along with

many commodities traders‟ he moved into financial futures, then Forex and later equities. He

worked as a broker, fund manager, analyst but always in the area of technical analysis. He served

for many years on the board of The Society of Technical Analysts which awarded him MSTA. He

has written many articles and is a popular conference speaker all over the world. In 1999 he

became head of technical analysis at Bloomberg which he did for four years overseeing the

development of charting on that platform. He left to form a successful hedge fund based in South

Africa. He is now a director of BETA Group and works with traders at a large UK hedge fund

offering a timing overlay. As such, he remains and active trader in the equities, Forex and

derivatives markets. He is Consultant Editor of The Technical Analyst Magazine. He is an

International Advisor to the MTA Foundation which promotes the understanding and adoption of

technical analysis at universities. In 2010 he has started a small new hedge fund to trade his own

funds. This £15 million fund trades a diversified portfolio and is 100% technically driven.

BETA Group

The BETA Group consists of BETA Financial Learning and Development Limited and BETA

Educators Limited. BETA L&D Ltd offers institution skill enhancing seminars in the areas of

market timing and behavioural finance. There are open course and in-house tailored events for

many of the world‟s best dealing desks. They also offer market consultancy, including trading

system development and the production of „white label‟ technical analysis research.

Continuous Professional Development (CPD)

More and more regulators and professional bodies insist that members continually update their

skills to ensure that they remain at the top of their careers. Both also expect the individual to

manage their own CPD based on their own needs and the needs of the organisation they are part

of. BETA Group can facilitate this process by courses that are of benefit to the financial services

professional. This course counts as 60 minutes towards your required CPD Cycle and one CPD

point for securities reps in the US. If you require a certificate of attendance, please send an e-mail

to [email protected].

BETA Group’s Open Seminars

Trevor Neil gives frequent open seminars on market timing. He travels all over the world to give

them with the help of Reuters Academy. These are usually in the form of a two-day course,

Technical Analysis in the Dealing Room. The events are held in a local central hotel and, if

possible, the afternoon of the second day is held as a workshop in the local Thomson Reuters

office. This means attendees have a terminal each have a Reuters terminal to practice what they

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have been taught and to run through current case studies. The seminar numbers are limited to just

ten. This ensures near one-to-one attention from Trevor Neil during the two days. In this way the

course content can be totally personalised, ensuring that all attendees get the maximum benefit

from these mentoring sessions.

In 2009 we started offering our popular Technical Analysis in the Dealing Room in French. We

have run courses in local languages in France and West Africa.

Colleagues at BETA Group offer seminars in Risk related matters, options techniques and

strategies and trading psychology and profiting from behavioural biases. See

www.betagroup.co.uk for details.

Want a Seminar near you?

In the last 12 months BETA Group has run about 50 seminars with Thomson Reuters in Europe,

Middle-East, Africa and Asia. To see what we have planned in conjunction with Thomson Reuters

see www.betagroup.co.uk/courses or Knowledge Network. If you would like seminar run in your

city, please contact your local Thomson Reuters Knowledge Manager and ask them to contact us.

They book us to come if they see there is demand. If enough of you ask your Thomson Reuters

Knowledge Manager to book him, Trevor Neil will come. He will be visiting Scandinavia, Eastern

Europe, North America, Asia and Australia in the second half of the year. Make sure he comes to

your City.

BETA Group’s In-house Seminars

We run specialised seminars for firm tailored to your firm‟s needs. These vary in length and

content. We can run seminars for new starters to advanced subjects such as Ichimoku, Elliott

Wave, Market Profile and Short Term Trading Techniques for experienced professionals. Apart

from our open seminars in 2010 we have taught about 300 traders, analysts, portfolio managers

and others in small groups – often five to ten – at their offices. These seminars focus on your

securities, time-frame and learning objective. We can even run seminars for your clients as part of

your marketing effort too. We are flexible; we can work in the evenings, at the weekends; whatever

suits your desk. These in-house seminars can be surprisingly economical and certainly beneficial

in this environment. Ask [email protected] for details

e-Learning

We have developed an e-Learning course in technical analysis which you can do at your own

pace and convenience. It is designed to prepare you for Level I of the CFTe qualification if you

wish or to get you fully competent as a trader. See http://www.betagroup.co.uk/elearning for this

exciting new service and details of the IFTA qualification. Ask [email protected]

for details

Coaching and Mentoring

This is the ultimate option. These are totally individualised skill enhancement programs. It is not

cheap but you can benefit from decades of experience and skill in a short period in time. In this

http://www.betagroup.co.uk/elearning

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way, it is actually an incredible bargain. Ask [email protected] for details of our

coaching, and the less expensive alternative, our mentoring services. Mentoring is usually given

on a one-to-one basis via a WebEx call.

“White Label” Research

At BETA Group we have the skill and resource to write white label technical analysis research for

your firm. This is a cost effective solution for firms who would like to have this powerful marketing

tool but do not have the budget or ability to produce it. BETA Group can produce regular research

to your specification, with your branding, to the highest standard and at an economical price. Ask

[email protected] for details and a sample of our work.

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Trevor Neil MSTA MCSI

Trevor Neil personally runs seminars all over the world helping traders; analysts and portfolio

managers improve their market timing skills. His experience and his ability to bridge the gap

between the books and theory of technical analysis and

the practical difficulties of taking a trade confidently have

been recognised by those attending his seminars.

Go to www.betagroup.co.uk for details of his calendar

of seminars. You can also look for his seminars in your

area by going to Reuters Academy on your terminal. You

can request Reuters and BETA Group to run a seminar in

your City by sending a message to your Thomson

Reuters Training Manager. These seminars are

chargeable but, with Thomson Reuters marketing help,

they are able to keep the fee to well below the price of

many different investment courses.

Many firms ask him to give a tailored seminar in-house. These seminars are very popular. The

content is designed to meet your learning objective, covering your markets in your time frame.

They are economical too for just five or more people. Send a message to

[email protected] that can send you details of availability and cost structure.

If you would like to attend one of BETA‟s seminars go to www.betabroup.co.uk and click on

Calendar. If you would like Trevor Neil to come to your institution to give a seminar in person,

please contact [email protected]. These sessions can be economical and requires

a low minimum number of people. Subjects covered are technical analysis at all levels, tailored for

spot trader, equity trader, fixed income analyst (or whatever) and specialised subjects like Profiting

from Behavioural Finance, DeMark Studies, Short Term Trading Techniques, Ichimoku Charting,

Algorithmic trading.

BETA Learning & Development Ltd

Pantiles Chambers

85 High Street

Royal Tunbridge Wells

Kent TN1 1XP, United Kingdom

www.betagroup.co.uk

Tel: +44 189250 6864

Fax: +44 870 622 1624

http://www.betabroup.co.uk/

mailto:[email protected]

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Contents

Trevor Neil‟s Master Class ....................................................................................................... 2

Trevor Neil‟s Friday Technical Analysis Surgery ...................................................................... 2

Charts and Data ....................................................................................................................... 2

Position Sizing ......................................................................................................................... 2

Trevor Neil ............................................................................................................................... 3

BETA Group ............................................................................................................................ 3

Continuous Professional Development (CPD) .......................................................................... 3

BETA Group‟s Open Seminars ................................................................................................ 3

Want a Seminar near you? ...................................................................................................... 4

BETA Group‟s In-house Seminars ........................................................................................... 4

e-Learning ............................................................................................................................... 4

Coaching and Mentoring .......................................................................................................... 4

“White Label” Research ........................................................................................................... 5

Trevor Neil MSTA MCSI........................................................................................................... 6 Common ways to size trades ........................................................................................... 8

Martingale and anti-Martingale ......................................................................................... 8

Trade size based on risk .......................................................................................................... 9

Optimal f ................................................................................................................................ 11 Monte Carlo .................................................................................................................... 12

Draw-down ............................................................................................................................ 12

Generating a Monte Carlo sequence ..................................................................................... 13 Robustness .................................................................................................................... 14 References ..................................................................................................................... 14

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Most trading experts agree that money management is one of the most critical aspects of trading. Position sizing is one of the key elements of money management. It is the process of determining how much to trade. If you trade stocks, it‟s the number of shares to trade. If you trade futures or options, it‟s the number of contracts. If you trade forex it is the amount in dollars or yen. Position sizing can be used to increase returns, reduce risk, improve the risk/return ratio, and smooth the equity curve, among other goals. Position sixing can be used to ruin you.

Position sizing is particularly important when leverage is involved, as with futures and forex trading. If you trade too many futures contracts, a string of losses could force you to stop trading. On the other hand, if you trade too few contracts, much of your account equity will sit idle, which will hurt your performance. Finding the right balance is a key element of risk management.

Common ways to size trades

There are many different ways to vary the number of contracts or shares when trading. Some of the most commonly used methods are listed below.

Fixed size. The same number of contracts or shares is applied to each trade; e.g., two contracts per trade.

Fixed dollar amount of equity. A fixed dollar amount of account equity is needed for each contract or share; e.g., $5000 of account equity per contract.

Fixed fractional (also known as fixed risk). The number of contracts or shares is determined so that each trade risks a specified fraction of the account equity; e.g., 2% of account equity is risked on each trade. Fixed fractional position sizing has been written about extensively by Ralph Vince. See, for example, his book “Portfolio Management Formulas,” John Wiley & Sons, New York, 1990.

Fixed Ratio. The number of contracts or shares increases by one for each “delta” amount of profit earned per contract. For example, if the delta is $3000, and the current number of contracts is two, you‟ll need $6000 of profit before increasing the number of contracts to three.

Margin Target. Margin target position sizing sets the size of each position so that the chosen percentage of account equity will be allocated to margin. For example, if you choose a margin target of 30%, then 30% of the account equity will be allocated to margin.

Leverage Target. This method sets the position size so that the leverage of the resulting position matches the selected target. Leverage is defined as the ratio of the value of the position to the account equity. For example, if 1000 shares of a $30 stock are purchased with a $25,000 account, the leverage would be $30,000/$25,000 or 1.2.

Percent Volatility. The per cent volatility method sizes each trade so that the value of the volatility, as represented by the average true range (ATR), is a specified percentage of account equity.

Martingale and anti-Martingale

With each of these methods, except for fixed contract position sizing, the number of contracts or shares increases as profits accrue and decreases as the equity drops during a drawdown. Position sizing methods that use this approach are known as anti-martingale methods. Anti-martingale

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9 Martingale and anti-Martingale

methods take advantage of the positive expectancy of a winning trading system or method. If you have an “edge” with your trading (i.e., your trading method is inherently profitable), you should use an anti-martingale method, such as one of those listed above.

The alternatives, known as martingale methods, decrease the amount at risk after a win and

increase the amount at risk after a loss. A commonly used example is “doubling down” after a loss

in gambling. Martingale methods are most often used by gamblers, who trade against the house‟s

advantage.

Provided you have a profitable trading method, anti-martingale methods are always preferable

over the long run because they‟re capable of growing your trading account geometrically.

However, it‟s sometimes possible to lower your risk by taking advantage of patterns of wins and

losses, similar to martingale methods. Two ways to do this are via dependency rules and

using equity curve trading. Both of these methods can be used in addition to whichever position

sizing method you choose.

While martingale methods are not recommended by themselves, these adjustments to the anti-

martingale methods listed above can sometimes prove beneficial. For example, if your trading

system or method tends to have long winning and losing streaks, it might be beneficial to skip

trading after a loss until the first skipped trade would have been a winner. Resume taking the

signals until a loss is encountered. This is an example of a dependency rule for systems with

positive dependency. Alternatively, you might try trading the equity curve. For example, you could

stop taking the trading signals when the moving average of the equity curve crosses below the

equity curve line. Resume trading when the moving average crosses back above the equity curve.

Trade size based on risk

It‟s a common axiom of investing that the greater the risk the greater the reward. One method of

sizing short-term trades based on this principle is fixed fractional position sizing. The idea behind

the fixed fractional method is that you base the number of contracts or shares on the risk of the

trade. Fixed fractional position sizing is also known as fixed risk position sizing because it risks the

same percentage or fraction of account equity on each trade. For example, you might risk 2% of

your account equity on each trade (the 2% rule). Fixed fractional position sizing has been written

about extensively by Ralph Vince. See references below.

The risk of a trade is defined as the dollar amount that the trade would lose per contract or share if

it were a loss. Commonly, the trade risk is taken as the size of the money management stop

applied, if any, to each trade. If your trading strategy doesn‟t use protective (money management)

stops, the risk can be taken as the largest historical loss. This was the approach Vince adopted in

his book Portfolio Management Formulas.

The equation for the number of contracts or shares in fixed fractional position sizing is as follows:

N = f * Equity/| Trade Risk |

where N is the number of contracts or shares, f is the fixed fraction (a number between 0 and 1),

Equity is the current value of account equity (i.e., the value of account equity just prior to the trade

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for which you‟re calculating N), and Trade Risk is the risk of the trade per contract or share for

which the number of contracts or shares is being computed. The vertical bars (|) mean that we

take the absolute value of the trade risk (risk is usually given as a negative number, so we make it

positive).

Why is Fixed Fractional trade sizing superior to Fixed dollar or Fixed sizing?

Let me demonstrate with a betting example. Firstly, for our experimental betting system we must

define the bet. In each case we will always bet $20 on Heads and we have a 2:1 profit loss ratio-

i.e we win $20 and lose $10 when we lose. This is a simulation of a good trading system and the

effect trade size has on it in the long run. The first way to define the bet is to make it a constant

fixed amount, say $10 each time, no matter how much we win or lose. This is a Fixed Size system.

In this case, as in fixed-betting systems in general, our $1,000 equity might increase or decrease

to the point where the $10 fixed bet becomes proportionately too large or small to be a good be

We also run the same experimental betting system where we define the bet as Fixed Fraction of

our equity. A 1% fixed-fraction bet would, on our original $1,000, also lead to a $10 bet. The result

of the first trade (bet) is the same. But it changes over time. With a Fixed Fractional trade size

(bet), as our equity rises and falls, our fixed-fraction bet stays in proportion to our equity. In the

table below we compare the effects of these two position sizing systems.

One interesting artefact of fixed-fraction betting is that, since the bet stays proportional to

the equity, it is theoretically impossible to go entirely broke so the official risk of total ruin

is zero

Simulation

Let‟s start trading (betting):

Fixed Bet $10 Fixed-Fraction Bet 1%

Start 1000 1000

Heads 1020 1020

Tails 1010 1009.80

Heads 1030 1030

Tails 1020 1019.70

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Heads 1040 1040.09

Tails 1030 1029.69

Heads 1050 1050.28

Tails 1040 1039.78

Heads 1060 1060.58

Tails 1050 1049.97

Both systems make $20.00 (twice the bet) on the first toss that comes up heads. On the second

toss, the fixed bet system loses $10.00 while the fixed-fraction system loses 1% of $1,020.00 or

$10.20, leaving $1,009.80.

The results from both these systems are approximately identical at the start. Over time, however,

the fixed-fraction system grows exponentially and surpasses the fixed-bet system that grows

linearly. Also note that the results depend on the numbers of heads and tails and do not at all

depend on the order of heads and tails.

In fixed fractional position sizing, the number of contracts or shares per trade increases over time

as profits accumulate, which allows the trader to more fully utilise the available account equity.

Likewise, the number of contracts or shares per trade drops when account equity declines after a

series of losses, reducing the impact of subsequent losses.

Optimal f

Fixed risk position sizing can be used to implement another one of Vince‟s methods, called optimal

f position sizing. This is a generalized version of a classic formula called Kelly‟s formula, which

provides the fixed fraction that maximizes the geometric growth rate for a series of trades where all

the losses are one size and all the wins are another size. In this case, the optimal fixed fraction is

given by the following equation:

f = ((B + 1) * P – 1)/B

where B is the ratio of a winning trade to a losing trade, and P is the percentage of winning trades.

Optimal f position sizing extends the Kelly formula so that the wins and losses can all be different

sizes. Optimal f calculates the fixed fraction that maximizes the rate of return for a given series of

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12 Monte Carlo

trades. While this sounds like a good idea, in practice the optimal f value (or the f value from the

Kelly formula) often results in drawdowns that are too large for most traders to tolerate.

Also, relying on the historical sequence of trades is risky in that the sequence of profits and losses

in the future may be less favourable than what was encountered historically. As a result, the

drawdowns in the future could be much larger than predicted by the historical sequence of trades.

Performing a Monte Carlo analysis on the trade sequence is one way to generate a more

conservative estimate of the future worst-case drawdown.

Monte Carlo

A less risky alternative to optimal f is to optimize using Monte Carlo analysis and with a specified

limit on the maximum allowable drawdown. This will generally yield a much smaller and therefore

less risky fixed fraction than Optimal f.

Before trading the markets with real money, it‟s essential to understand the risk of the trading

strategy or method you intend to use. One way to assess risk is by testing your strategy over

historical market data to see how well the strategy would have done in the past. While this so-

called back testing approach is very helpful, one of the drawbacks is that the future is never

exactly the same as the past. Employing Monte Carlo analysis can help to address this problem.

Monte Carlo analysis is a computational technique that makes it possible to include the statistical

properties of a model‟s parameters in a simulation. In Monte Carlo analysis, the random variables

of a model are represented by statistical distributions, which are randomly sampled to produce the

model‟s output. The output is therefore also a statistical distribution. Compared to a simulation

method that doesn‟t include random sampling, the Monte Carlo method produces more meaningful

results, which are more conservative and also tend to be more accurate when used as predictions.

When using use Monte Carlo analysis to simulate trading, the trade distribution, as represented by

the list of trades, is sampled to generate a trade sequence. Each such sequence is analysed, and

the results are sorted to determine the probability of each result. In this way, a probability or

confidence level is assigned to each result.

Without Monte Carlo analysis, the standard approach for calculating the historical rate of return, for

example, would be to analyse the current sequence of trades using, say, fixed fractional position

sizing. It might be found that the rate of return over the sequence was 114%. With Monte Carlo

analysis, on the other hand, hundreds or thousands of different sequences of trades are analysed,

and the rate of return is expressed with a probability qualifier. For example, the rate of return as

determined by Monte Carlo analysis might be 83% with 95% confidence. This means that of all the

thousands of sequences considered, 95% had rates of return greater than or equal to 83%.

Draw-down

Monte Carlo analysis is particularly helpful in estimating the maximum peak-to-valley drawdown.

Drawdown is often used as a proxy for the risk of a trading strategy. Consequently, improving the

calculation of the drawdown enables a better estimate of the risk of a trading system or method.

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13 Monte Carlo

Although we can‟t predict how the market will differ tomorrow from what we‟ve seen in the past, we

do know it will be different. If we calculate the maximum drawdown based on the historical

sequence of trades, we‟re basing our calculations on a sequence of trades we know won‟t be

repeated exactly. Even if the distribution of trades (in the statistical sense) is the same in the

future, the sequence of those trades is largely a matter of chance.

Calculating the drawdown based on one particular sequence is somewhat arbitrary. Moreover, the

sequence of trades has a very large effect on the calculated drawdown. If you choose a sequence

of trades where five losses occur in a row, you could get a very large drawdown. The same trades

arranged in a different order, such that the losses are evenly dispersed, might have a negligible

drawdown.

In using a Monte Carlo approach to calculate the drawdown, the historical sequence of trades is

randomized, and the rate of return and drawdown are calculated for the randomized sequence.

The process is then repeated several hundred or thousand times. Looking at the results in

aggregate, we might find, for example, that in 95% of the sequences, the drawdown was less than

30% when 4% of the equity was risked on each trade. We would interpret this to mean that there‟s

a 95% chance that the drawdown will be less than 30% when 4% is risked on each trade.

Generating a Monte Carlo sequence

In general, there are two ways to generate the sequence of trades in a Monte Carlo simulation.

One option is to construct each sequence of trades by random sampling of the same trades as in

the current sequence, with each trade included once. This method of sampling the trade

distribution is known as random selection without replacement. Another possible sampling method

is random selection with replacement. If this method were used, trades would be selected at

random from the original list of trades without regard to whether or not the trade had already been

selected. In selection with replacement, a trade could occur more than once in the new sequence.

The benefit of selection without replacement is that it exactly duplicates the probability distribution

of the input sequence, whereas selection with replacement may not. The drawback to selection

without replacement is that the randomly sampled sequences are limited to the number of trades

in the input sequence. If you have a short sequence of trades (say, less than 30 trades), this may

limit the accuracy of certain calculations, such as the drawdown.

Pyramiding

In the case of a random process, such as coin tosses, streaks of heads or tails do occur, since it

would be quite improbable to have a regular alternation of heads and tails. There is, however, no

way to exploit this phenomenon, which is in itself random. In non-random processes, such as

secular trends in security prices, pyramiding and other trend-trading techniques can be effective.

Pyramiding is a method for increasing a position, as it becomes profitable. While this technique

might be useful as a way for a trader to pyramid up to his optimal position, pyramiding on top of an

already-optimal position is to invite the disasters of over-trading. In general, such micro-tinkering

with executions is far less important than sticking to the system. To the extent that tinkering allows

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14 Robustness

a window for further interpreting trading signals, it can invite hunch trading and weaken the fabric

that supports sticking to the system.

The Martingale system is a method for doubling-up on losing bets. In case the doubled bet loses,

the method re-doubles and so on. This method is like trying to catch a falling sword, one day

a losing streak will stab you.

Robustness

The problem with all this and often missed by our Quant friends is that the worse is always ahead

of us and not behind us. All this work is on past events. Certainly these methods increase our

confidence in a method of trading and position sizing will be effective in the future. However, there

is no certainty. The markets are always changing. Gold is in a strong trend now. I‟ve known it to be

flat and lifeless for years as it moved to being an asset to protect against fear and uncertainty into

a conductor of electricity in over-supply. You have no idea whether the worse loss you have ever

seen is anything like as large as one you will suffer in the future. The worse run of bad trades you

ever saw is only the worse run you have seen. You can be confident a worse run lays ahead. The

worse you have had may not have been a particularly bad one, although you may rely on it being

so for your future trading survival. It may have been the worse so far but the worse is certainly

ahead of you and not behind you – remember this. This is often underappreciated.

How do you cope with this? How do you use your experience up until now to judge how to position

size and money manage in the future? Here is Trevor Tip: The solution is to multiply the historic

„worse‟ of all your data by a factor which you find acceptable. Take the worse drawdown, the

worse string of losses, the worse period „under water‟ the worse anything and multiply it by a

safety fact. I double it. It‟s a guess but it does make some allowance for the worse being ahead of

you and hopefully it does so sufficiently to give you a long trading life.

References

Fixed ratio position sizing was developed by Ryan Jones in his book “The Trading Game,” John Wiley & Sons, New York, 1999.

Optimal f is covered in Ralph Vince’s book “Portfolio Management Formulas,” John Wiley & Sons, New York, 1990.

Kelly‟s formula, as provided by Ralph Vince, Portfolio Management Formulas, John Wiley & Sons, New York, 1990

For details of the Per Cent Volatility technique see Van K. Tharp’s book “Trade Your Way to Financial Freedom,” 2nd ed., McGraw-Hill, New York, 2007, pp. 426-8.

All books are available from www.betagroup.co.uk

Master Class Position Sizing

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