## 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. 1%) 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.

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 expectatio**n). 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. 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. 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.

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 1%) 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. 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** . 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.

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.

Note: 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 . 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. 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. 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 risk **more** than 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 to **bypass** this trade and therefore **undermine 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.

## 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”.

This table 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 table above, 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.

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”.

**Note**: 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 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.

## 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.

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.

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.

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.

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. 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 . As you 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*.

*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.