## 16.1. What is Money Management System?

**Money management system** is the subsystem of the forex trading plan which **controls how much** you risk when you get an entry signal from your forex trading system. One of the best money management methods used by many professional forex traders is to **always risk a fixed percentage of your equity** (e.g. 3%) per position. By using this method a trader gradually increases the size of his trades while he is winning and decreases the size of his trades when he is losing. Increasing the size of bets during a winning streak **allows for a geometric growth of the trader's account** (also known as profit compounding). Decreasing the size of bets during a losing streak **minimizes the damage** to the trader's equity. You can view interactive demonstration of this technique by opening the forex trading simulator (Please note: The size of this page is 0,6 Mbs and it requires that you have Flash installed and Javascript enabled in your browser).

Trading on forex allows to multiply your account over time - or to make it grow geometrically. Geometric capital growth is produced when the profits are reinvested into the trading which leads to progressively larger positions being taken and, consequently, to bigger profits and losses. The pace at which the account grows is controlled by the **size of the profits and by their frequency** (which should always be remembered by forex trading system developers). While the geometric equity growth can and should be smooth (i.e. consistent), some traders try to accelerate it by artificially inflating the size of their profits by risking very high percentages of their account. Because the actual sequence of the winning and the losing trades can never be predicted in advance, such practice results in very erratic trading performance (i.e. sharp equity fluctuations). Among other things this practice betrays the trader's lack of confidence in his or her trading system's long-term profit potential. As long as the trader is confident about his trading system he can risk small percentages (%1 to 3%) of his account on every trade and simply watch the system realize its potential. It should be noted that only the geometric capital growth allows to make regular profit withdrawals from an account (as a certain percent of the equity) without seriously affecting a trading system's money making ability. This contrasts sharply with the fixed-dollar-bet money management system (e.g. always risk $500 per trade) whose profits grow arithmetically and where each withdrawal from the account puts the system a fixed number of profitable trades back in time.

**Both** proper money management and sound trading system are required for a **smooth geometric capital growth**. The speed (i.e. "geometricity") and the smoothness of the account's growth depend on how much you risk per trade (as set by the money management system) and on the trading system's **accuracy and the payoff rati**o parameters (trading system's mathematical expectation). Apart from the controlling equity fluctuations by setting a fixed percentage of the capital to be risked on any trade, money management system can also reduce equity swings through diversification (splitting your risk capital among unrelated currency pairs/trading systems).

Quote:"..analysis is the door to fabulous riches, while money management is the key that opens that door.", Robert Balan, in his book, "Elliott wave principle applied to the foreign exchange markets".

## 16.2. How Much to Risk?

Quote:"There is no return without risk", the 1st rule of the 9 Rules of Risk Management, by RiskMetrics.

Trading on the forex market can be a very profitable business. Armed with this fact some traders start determined to make huge sums of money in as little time as possible - by risking too much. In other words, they are aiming for fast geometric growth of their accounts with no regard for the smoothness of the equity curve. Doing so **invariably results in severe drawdowns or complete wipe-outs **as can be easily seen if you enter values larger than 10 as the “Percent Risked” in the forex trading simulator (Please note: The size of this page is 0,6 Mbs and it requires that you have Flash installed and Javascript enabled in your browser) and model a few equity scenarios with this setting. Risking high percentage of your account might indeed have dramatic effect on the geometric growth of your account balance** in the very short-term**. However, winning streaks (however long) are always followed by losing streaks (however short) and **much of what was “given” by the high percentages is very likely to be “taken away” by the same percentages. **

For example, if you risk 25% of your account balance per trade with the system accuracy of 50% and the payoff ratio of 2 you can expect to double your account in 6 trades (as you can see from the "Exp # of trades to TR" cell on the forex trading simulator when you use such settings). You can also expect to give away most or all of these profits in the next few traders – as the same percentages will now cut deep into your profits when your trading system generates losing signals. Now try to imagine how you would feel if your car accelerates to a 500 miles per hour in a few seconds then suddenly reverses and flies back at the same speed. You would achieve similar effect on your feelings or your investors' if you got your account up to 100% in a few trades and then lost all of the profits in the very next few trades.

It certainly pays to keep the speed (percent risked) of your car (forex trading system) within reason so that you can reach your destination (e.g. doubling you account balance) without submitting your emotional and financial well-being to excessive risks - as both your financial and emotional strength tends to be limited. At lower percentages of equity risked a winning or a losing streak simply does not have as spectacular impact on the equity curve which results in smoother capital appreciation (and much less stress for the trader or for the investor). This is because when you risk small fractions of your equity (up to 3%) each trade is given **less "power" to affect the shape of your equity curve** which leads to smaller drawdowns and consequently greater ability to capitalize on the winning signals in the future. In other words, the size of drawdowns is directly proportional to the percent risked. You can see this if you enter progressively larger values in the "Percent Risked" filed in the forex trading simulator and then compare the resultant maximum drawdowns (in "Max DrawDown in %" field) for each of percent values that you entered. In addition to being directly proportional to the % risked, drawdowns are** inversely proportional to both the accuracy and the payoff ratio (average win/average loss) of a trading system** (as you can see if you enter different accuracy and payoff ratio values in the forex trading simulator). This relationship can be clearly seen with the help of the three 3D charts shown below which plot the combined effect of the payoff ratio and the accuracy of a trading system on the maximum percent drawdown, as seen during 15,000 trading scenarios modelled on the forex trading simulator (5,000 for each of the three different "perecent risked" settings which were tested - 1%, 3% and 5%).

Click to Enlarge.

Quote:"..the final return is only a function of how well you would like to sleep at night", Thomas Stridsman, in his book "Trading Systems That Work: Building and Evaluating Effective Trading Systems".

A drawdown is the **distance** from the **lowest** point between **two consecutive equity highs** to the **first** of these highs. For example, if your account increases from $10,000 to $15,000 (first equity high) then drops to 12,000 (lowest point between equity highs) and then rises again to $20,000 (second equity high) your drawdown will be $3,000 ($15,000-$12,000) or 20% ($3,000/$15,000). When deciding on the percent to be risked on each trade you should keep in mind that as the drawdown grows **arithmetically**, the profits (and psychological fortitude to stick to the system) required to get out of it increase **geometrically** (as you can see from the chart below). You can also use the following calculator to model the effect of a losing streak on the equity and the profit required to recoup the loss. The "%" stands for the percent of the equity risked per trade. The "#" stands for the number of consecutive losses. The "loss" column calculates the cumulative damage to the equity in percentage terms. The "recoup" column shows how much profit is required to return to the breakeven. Alternatively, you can just enter the value of loss into the cell below the "Loss" heading to calculate the size of the profit necessary to recoup it.

Click to Enlarge.

As can be readily seen from the above calculator it takes only a few trades to severely damage your prospects as a currency trader - if you risk too much in your trading. With this information in mind it is **best to always risk a ma**ximum of 1% of the equity if you are managing other people's money and a maximum of 3% of the equity if you are trading with your own funds. As a general rule the higher the accuracy of a trading system AND the higher its payoff ratio the safer it is to risk more per trade. This principle is the basis for the money management calculator (Please note: This calculator requires that Javascript is enabled in your browser) located in the forex tools section of the site.

It is best not to rely too much on the **theoretical** probability of a large number of losing trades happening in a row. In other words, because the probability of a few losses happening in a row is very low it doesn't mean this cannot happen in your trading. Suppose you trade a system which generates 60 winning trades out of 100 on average. The probability of a profitable trade is always 60%, while the probability of a losing trade is always 40% with such a system. The chances of 5 consecutive losses can be calculated by multiplying 0,4 five times by itself or 0,4*0,4*0,4*0,4*0,4 which results in 1,02%. Even if the probability of roughly one percent does look very remote this is** not a zero probability** and quite likely to happen in real trading - as you will quickly see if you model just a few equity scenarios in the forex trading simulator with system accuracy set to 60% (be sure to check the "Max. Consec.Losses" cell). Moreover, given that the outcome of any single trade **can be considered random** there is nothing in the world that can guarantee that your system's next five trades will not be all losses or all profits, for that matter. Therefore, it is best to be prepared for such an outcome in advance by risking less of your account per each trade. Closely related to this is the idea of luck in trading, which can be defined as the clustering of large number of profitable trades in narrow periods of time. For example, you can easily generate a string of 12 winning trades on the forex trading simulator with the system accuracy set to 60%. The probability of such an event is equal to 0,6 raised to the 12'th power or 0,2% or 1 in 500. Despite such a low probability you can expect to see 12 or more successive winners in your trading (be sure to check the "Max. Consec.Wins" cell on the forex trading simulator as you perform the above simulation) when you trade long enough with a system that has success rate equal to %60. Even if the short-term effect on the equity (and trader morale) of such a long series of successful trades can be quite dramatic, it plays little role in the long-term success as a currency trader. In other words, the fact that your trading system has just generated a long run of profitable trades doesn't say very much about its long-term profit potential, which should instead be measured by its mathematical expectation.

Money management system is similar to the forex trading system in that sticking to it is vital to the long-term success in currency trading. Once you decide on the percentage of equity that you will risk per position you should **never** deviate from this number and try to stay as close to it as possible - **no matter how bad or good your system performance is.** This question becomes especially important when you decide on the type of account that you open - if it will be a mini or a standard trading account. As you can see from the allocation efficiency calculator (Please note: This calculator requires that Javascript is enabled in your browser) mini accounts are vastly superior to the standard accounts (especially with account balances less than $50,000) when it comes to meeting the constraints of both your money management system (% risked) and your trading system (size of the stop-loss).

Note:When you select the account type you should pay close attention to the level of the leverage offered by your forex broker. Even if high leverage (from 1:100 and up) allows to trade multiple lots with very little money of your own, it can be dangerous when it forces you to overtrade - to assume positions which riskmorethan the percentage value set by your money management system. For example, you might be compelled to risk $400 (40 pip stop-loss) on a very attractive EUR/USD trade while on a standard account with the maximum allowable risk per trade set at 3% of $10,000 or $300. The only way to stick to your money management system would be tobypassthis trade and thereforeundermine your system's profitability(and your morale). You wouldn't need to avoid this signal or use smaller stop-loss than the one suggested by your system if you traded at half the leverage (which would mean only $200 risk per trade) or if you traded on a mini account altogether - as is shown by the allocation efficiency calculator.

## 16.3. Mathematical Expectation of a Forex Trading System

Mathematical expectation of a forex trading system is **how much of the risked capital you can expect to earn per trade on average**. You can calculate the mathematical expectation of a system by the following formula:

Mathematical Exectation= (1+average win/average loss)*(system accuracy) -1

This formula requires that you take into account **both** the success rate (percent of winning signals) and the payoff ratio (average win/average loss) of any trading system when estimating its long-term profit potential. For example, a system with 50% accuracy and the 2 to 1 payoff ratio has the expectancy equal to +0,5. This means you can expect to earn 50% of the amount that you risk per trade on average. If you risk 2% of your capital per trade you can expect to earn 1% per trade (50% of 2%) on average with such a system. Negative mathematical expectation (e.g. casino roulette) means you will lose your money over the long-term no matter how small or big your positions are. Zero expectation means you can expect your account to fluctuate around breakeven for ever.

Quote:"The difference between a negative expectation and a positive one is the difference between life and death. It doesn't matter so much how positive or how negative your expectation is; what matters is whether it is positive or negative." Ralph Vince in his book "The Mathematics of Money Management: Risk Analysis Techniques for Traders".

You can model various equity development scenarios under the positive, the negative or the zero mathematical expectations by entering the following accuracy and the payoff values in the system controls on the forex trading simulator:

This calculator demonstrates the value of letting your profits run and cutting your losses short when you start to trade and don’t yet have a reliable currency trading system to follow. When you begin to trade your accuracy tends to be low. To compensate for the larger number of losses you absolutely have to let your profits run and keep you losses small. This will ensure that the profits from the few winners that you are able to capture will more than cover the total loss from all the losses that you take. Not allowing your profits to run at the start of your trading career would simply be "suicidal". This boils down to selecting the trades only with high reward/risk ratios. This will help to improve your payoff ratio and, therefore, your profit potential.

As you can also see from the initiital values of the above calculator, systems with different accuracy and payoff ratios can have identical mathematical expectations. This means, for example, that in the long run the profit that you can achieve with the system that is the first in the table will be equal to the profit that you will make using the second system - even if the second system is twice as accurate as the first one. You can compare how the equities develop for both of these systems by using the currency diversification simulator (Please note: The size of this page is 0,7 Mbs and it requires that you have Flash installed and Javascript enabled in your browser). Enter 40 in "past accuracy" field for system A and 80 for system B. Payoff ratio should be set to 3 for A and to 1 for B and set the "Percent Risked" to 1. If you wish to compare B with a more dissimilar trading system you can enter 20 as the accuracy and 7 as the payoff ratio on the A's control panel.

The closer the simulated equity performance (shown in the "Actual Accuracy" field) is to the past accuracy of each of the systems the clearer you will see that both systems tend to converge at the same final equity level. Because geometric capital growth is highly dependent on the frequency of the profits - when you increase the Percent Risked - a system with substantially higher accuracy will outperform a less accurate system even if both of them have identical mathematical expectations. This is one of the reasons to strive for the highest possible rate of accuracy in your trading. The other reason is that drawdown duration and size (in both absolute and percentage terms) tend to be much larger with the lower accuracy systems which leads to lower reward-to-risk ratios - as you can quickly see if you check the ""Drawdown time", the "Max Drawdown" and the "Max % Drawdown" fields in the diversification simulator when you do the simulation described above. As a third reason, it is always necessary to give a trading system some "room for error" in real-life trading - or excpect it to trade with accuracy lower than the past accuracy. Very low accuracy and high payoff ratio systems simply do not offer this - which means you should be prepared to sit through very long losing streaks before you see any profit. In contrast, higher accuracy forex trading systems make the currency trading less stressful by ensuring that you take smaller yet much more regular profits.

It stands to reason that the higher the mathematical expectation of a trading system the faster your account will grow. Very good trading systems have mathematical expectation close to 0,8. Common definition of an excellent trading system is that its payoff ratio is one point better than the payoff ratio of a breakeven system with the accuracy of 10 percent less. For example, the payoff ratio for a breakeven system with 40% success rate is 1,5, therefore an optimal system with 50% accuracy will have 1,5+1 = 2,5 payoff ratio. The following calculator allows you to compute the payoff ratio for a breakeven system and an optimal system:

Quote:"The first part of your system design should focus on building the highest possible expectancy into your system" by Van K. Tharp in his "Special Report on Money Management".

You can get the most reliable measure of mechanical expectation of a trading system when you can translate it into computer code. One example of a simple trading system which can be readily backtested to calculate its expectancy is the moving average crossover system. Most of the advanced forex charting packages (e.g. FXtrek IntelliChartâ„¢ Copyright 2001-2007 FXtrek.com, Inc.) allow to construct wholly mechanical trading systems and to backtest them over historical price data. If you are using interpretive technical analysis tools in your trading (like price patterns, trendlines) you can only generate the statistics required for the calculation of your system's expectation by using the information from your trading log (where you enter individual trade results when you test-trade your trading system on a demo account). However, since these statistics are generated using interpretive analysis methods their validity will stay the same **only if** you continue to interpret price formations in **exactly the same manner** as you did before. Because signals of mechanical trading systems are never open to conflicting interpretation, their mathematical expectation is **more** reliable measure of future system performance than the expectation of interpretive trading systems.

## 16.4. Diversification in Currency Trading

Diversification is the distribution of the risk capital across unrelated currency pairs and/or trading systems for the purpose of** increasing the consistency** of trading performance. For example, if you trade one system on two unrelated currency pairs you can protect yourself against long losing streaks that any of these pairs can go through on its own. When you get a losing signal on the first pair, the second pair might generate a winning trade which will cover the loss of the first pair or vice versa. By splitting the risk capital (% of your equity) among two pairs you can be sure that when both pairs generate losing trades at the same time your total risk will not exceed the maximum value set by your money management system. This way you can achieve smoother capital appreciation than you would be able to do if you traded only one pair. For an interactive demonstration this concept please visit the currency diversification simulator. It should be noted that this calculator assumes **zero** correlation between the pairs or systems (more on correlation below).

Be sure to compare the values in the "Consistency" cells for each of the pairs when they are traded separately with the value of consistency achieved when trading them together (in the "Trading A&B" column). The combined consistency will almost always exceed the consistency of either of the pairs when they are traded individually.

The more unrelated pairs or systems you add to your portfolio the better protection you can have against the risk. For example, when trading one trading system on two absolutely uncorrelated currency pairs you decrease the probability of a losing trade (two pairs generating a losing trade simultaneously) by the **percentage value equal to the system's accuracy**. Suppose your system has the success rate of %60, therefore the probability of a losing trade for each pair is %40. The probability that both pairs will generate a losing signal is calculated by multiplying %40 by itself - which results in %16. This is the %60 decrease (24/40=0,6) in the probability of a losing trade achieved when you trade both pairs simultaneously. If your system has %70 success rate you can reduce the probability of a loss by %70 if you trade two unrelated pairs instead of one. The probability of a losing trade occurring for both pairs at the same time is %9 (%30*%30) which is a %70 decrease in the likelihood of a loss if you traded only one pair (21/30=0,7). I will note that even if you diversify into two or more weakly correlated currencies/trading systems, this won't eliminate the drawdowns completely. However weak is the correlation between the pairs or trading systems, they are likely to go through the losing streak all at once, at some point in the trading. You can see this by modelling the performance of two similar trading systems with the help of the currency diversification simulator (e.g. set accuracy to 40 and payoff ratio to 2 for both A and B) and checking if the yellow curve on the DRADOWN chart is moving in sync with the other two curves.

There is a weak relationship between two pairs if the absolute value of their correlation coefficient (usually denoted by r) doesn't exceed 0,3 (i.e. it can be anything from -0,3 to +0,3). A medium strength relationship exists when the absolute value of the coefficient is greater than 0,3 but less than 0,5. There is a strong relationship between two pairs if r is greater than 0.5 in absolute terms (i.e. bigger than 0.5 or less than –0.5). Currencies are said to be highly correlated if the absolute value of their correlation coefficient is equal to or bigger than 0,8. You can visualize these concepts with the help of the interactive correlation simulator. (Please note: This calculator requires that you have Flash installed and Javascript enabled in your browser)

Suppose you trade two currency pairs which are highly positively correlated like the EUR/USD and the GBP/USD (daily r is equal to 0,8 on average). When you get a sell signal for EUR/USD your system is likely to generate the same signal for the GBP/USD. If the first signal results in a loss this increases the probability that the second signal will not be profitable either. The same holds if you are trading very negatively correlated pairs with the same system - like EUR/USD and USD/CHF (daily r is equal to -0,9 on average). Selling one lot of EUR/USD and buying one lot of USD/CHF at the same time (e.g. on the break of a trendline which usually is simply a mirror image of the trendline visible on the other pair's chart - e.g. set "Target Correlation" to -0,9 on the correlation simulator and notice how similar are the imaginary trendlines for A and B) amounts roughly to selling 2 lots of EUR/USD or buying 2 lots of USD/CHF individually - with no reduction in risk whatsoever.

Quote:"Through bitter experience, I have learned that a mistake in position correlation is the root of some of the most serious problems in trading. If you have eight highly correlated positions, then you are really trading one position that is eight times as large." Bruce Kovner in Jack D. Schwager's book "Market Wizards: Interviews with Top Traders ".

In contrast, when you trade two **uncorrelated** or loosely correlated pairs you can expect your system to perform differently on each pair which should result in smoother overall trading performance. As an example you can buy a touch of a uptrendline on one pair (e.g. USD/JPY) and sell the top of the range on another unrelated pair (e.g. GBP/CHF, which has an average r of 0,3 with USD/JPY) without having to worry that price developments in USD/JPY might "spill over" into GBP/CHF (or the other way round) and by doing so spoil your whole trading setup. As the next best alternative, you can reduce the risk by opening opposing trades in the positively correlated pairs or same direction trades in the negatively correlated pairs - by using a different system for each of the pairs, as is described below. Yet another way you can use correlation is to select among highly correlated pairs that pair which offers the highest reward potential under the current market conditions and trade only it.

You can monitor the correlations between the currency pairs that you trade by using the information on the currency correlations page (which contains most up-to-date correlation data for the commonly traded currency pairs). I will note that it is best to keep the number of the currency pairs in your portfolio to a minimum because the number of the correlations to be tracked and the time required for this rises geometrically with the addition of each new pair. The formula for calculating the number of correlations between n number of pairs is [n*(n-1)]/2. You can start with one currency pair and gradually increase to a maximum of four pairs (with 6 correlations to monitor) as your experience grows.

When you diversify into **different trading systems** you should look for a combination of systems which results in the lowest possible correlation between their returns. Ideally you would trade only two systems which are **perfectly negatively correlated** (r=-1). This means that whenever one system generated a losing signal the other would produce a winning signal and vice versa. Examples of this possible combination are a mean-reversion system (e.g. RSI) and a trending system (e.g. Moving average) - for more examples please consult Richard L. Weissman's book "Mechanical Trading Systems: Pairing Trader Psychology with Technical Analysis". If you could find such a perfect combination of systems you would not see a single loss (as their net result) because the loss of one system would always be covered by the profit of the other. You can see how this works if you enter minus one into "Target Correlation" cell on the system correlation simulator (Please note: The size of this page is 0,7 Mbs and it requires that you have Flash installed and Javascript enabled in your browser). In practice, it is extremely hard to find perfectly negatively correlated systems. Nevertheless, even if systems traded are only mildly negatively correlated the trader can expect to benefit from the risk reduction offered by the diversification.

Quote:"The correlations of the different market systems can have a profound effect on a portfolio. It is important that you realize that a portfolio can be greater than the sum of its parts (if the correlations of its component parts are low enough). It is also possible that a portfolio may be less than the sum of its parts (if the correlations are too high)." Ralph Vince in his book "The Mathematics of Money Management: Risk Analysis Techniques for Traders".

## 16.5. Mastering Money Management in Forex Trading

The key to mastering money management is **shifting your attention from the dollar value** of your profits and losses to their **percentage value of your account balance**. Once you have trained yourself to think of your profits and losses exclusively in percentage terms it will be a simple mathematical task to stick to your money management system (e.g. just enter your constraints into the money management calculator and it will give you the number of lots to trade). As your account grows this practice will help you to avoid the hesitation in placing the trades when the absolute value of the dollars risked becomes very large - since you will know at that moment that you are still risking **no more** than amount dictated by your money management system (which will have played a major role in getting your account to that level in the first place).

You should also remember that the outcome of any single trade is** almost always random. **It is, therefore, **not practical to attach yourself too strongly - either emotionally or financially** (by risking too much)- to the result of any one trade or a series of trades. This concept of randomness is incorporated into all the trading simulators on this site which use random number generators to determine if any single trade is profitable or not.

As with the forex trading system, you can receive **protection** from your own destructive tendencies by **closely** following your money management system. It will protect you from greed and pride (which always demand that you overtrade) when your system generates unusually large number of winning signals in a row. It will also protect you from trader paralysis (inability to open new positions) when your system goes through a losing streak because you will know that, as long as you risk a small fraction of your equity per each trade (as is set by your money management system) and use a currency trading system with positive mathematical expectation, no string of losses can wipe out your trading account.