5. Money Management Models

Fixed Lot

Also called Fixed Value money management. this is the simplest of all the available money management models. With the Fixed Lot model, you set the number of lots you would like to trade per position. No matter how much your account balance or equity curve oscillates, you will still trade a fixed number of lots per position .

A basic example of this method is saying I have a 10,000 US Dollar account and I will trade one mini lot on every trade. It does not require a calculation, but still the fixed lot size should be determined by predetermined risk measures and not by the market behavior.

• Its easy to manage and understand because of the consistent lot size .

• It allows profits to grow arithmetically — that is, by a constant amount per time period. It is useful, for instance, if you withdraw your profits after each month of trading, starting anew with the same capital. Some traders perform poorly if their accounts start to grow exponentially — finding in this model an ally for their trading style. Others just prefer to trade with a large account and withdraw profits regularly — not aiming at growing the account.

• It does not provide an ability to maintain a constant leverage as account balance shrinks and rises. This can lead to big Drawdowns since during a string of losses the leverage increases with each new trade (please refer to the first part of this chapter and to Chapter A03 if the concept of leverage is still unclear to you).

• Another drawback of this model is that by trading the same position size on any given trade, you will soon find out that the trading results are very much dependent on whether the system continues to work or not — while the whole purpose of adopting a money management technique is to get rid of the burden of the systems profitability .

• Each withdrawal from the account puts the system a fixed number of profitable trades back in time. Therefore, this may not be the best model to trade if you pursuit an efficient growth in your trading account.

A trader that risks too much increases the chance of not surviving long enough to realize the long run benefits of a good trading strategy. Conversely, risking too little creates the possibility that a trading methodology may not realize its full potential. Therefore, while a positive expectation may be a minimal requirement to trade successfully, the way in which you are able to exploit that positive expectation will largely determine your success as a trader. Therefore, wisely choose which money management technique is better adapted to your system and to your trading profile.

Imagine a system with a Fixed Lot size of 1 mini lot averaging 10 pips per trade. After each 100 trades, the account grows by 1,000 USD. After the first 100 trades, this is a Return of 100% but after 1,000 trades the same result in pips accounts for a Return of 10% only.

1000 USD + 1000 pips @ 1USD/pip = 2000 USD

2000 USD + 1000 pips @ 1USD/pip = 3000 USD

4000 USD + 1000 pips @ 1USD/pip = 5,000 USD

5,000 USD + 1000 pips @ 1USD/pip = 6,000 USD

7,000 USD + 1000 pips @ 1USD/pip = 8,000 USD

8,000 USD + 1000 pips @ 1USD/pip = 9,000 USD

9,000 USD + 1000 pips @ 1USD/pip = 10,000 USD

Fixed Fractional

Fixed Fractional position sizing has been developed by Ralph Vince in his book Portfolio Management Formulas (John Wiley & Sons, New York, 1990) to remedy the problem of the equity drifting out of proportion in relation to the fixed lot size pointed in the prior model. The Fixed Fractional defines the trade (risk ) as a fraction of the equity. This is a model that directly incorporates the trade risk .

The idea behind the Fixed Fractional model is that the number of traded units is based on the risk of the trade. The risk is the same percentage or fraction of the account equity on each trade. By risking always the same percentage/position size, the risked fixed fraction stays proportional to the equity while the equity rises and falls.

The risk of a trade is defined as the capital amount that the trader would lose per trade 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 system doesnt use protective stops, the trade risk can be taken as the Maximum Drawdown or the Average Loss.

• One interesting artifact of the Fixed Fraction model is that, since the size of the trade stays proportional to the equity. it is theoretically impossible to go entirely broke so the official risk of total ruin is zero. As an anti-martingale technique, it is designed to accomplish the preservation of ones capital for as long as possible.

Note, that in the practice however, the abandonment of a trading methodology should come earlier than the accounts depletion.

• The compounding effect kicks in every time you have a winner. By using this method the position s size is gradually increased when winning and decreased when losing. Increasing the size of positions during a winning streak allows a geometric growth of the account (also known as profit compounding ); decreasing the size of the trades during a losing streak minimizes the damage to the traders equity .

• At lower percentages of equity risked, a winning or a losing streak simply does not have a spectacular impact on the equity curve. This results in smoother capital appreciation (and much less stress for the trader or 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 risked percent.

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. This is one of the advantages of the retail Forex industry and the allowed small trade sizes — without it, the growth of small accounts would be much more difficult. Depending on the Equity Model, the trader can accelerate or smoothen the account growth.

Remember that besides the equity model used, the pace at which the account grows is determined by the Average Profit and by the Win Rate. The speed (geometricity) and the smoothness of the accounts growth also depend on how much you risk per trade.

It is noteworthy to underline that only geometric capital growth allows making regular profit withdrawals from an account (as a certain percent of the equity ) without seriously affecting a trading systems money making ability.

• If you have a small account balance you are forced to work with a lot size which doesnt help in fine sizing the positions .

• This model will require unequal achievement at different size position levels. This means that every time you want to increase the position size it may require you to produce a high return before you can increase the trade size from one lot to two lots — otherwise you would be risking too much. So for smaller account sizes it will take a long time for this money management to actually kick in.

• For larger account sizes the number of traded lots will inversely jump wildly around.

• The reduction of the relative position size after every loss makes more difficult to recover from a severe Drawdown and makes of this model an anti martingale type of technique. It should be used if you have enough statistical data on the Drawdown series.

• If a large loss exceeds a certain amount and the risked percentage is now less than the smaller lot size, the trader is forced to break the risk rules just to trade the minimum allowed lot size.

• Once the account reaches a higher size, the growth of the position size accelerates to a degree which is unrealistic and highly risky.

Lets say youve got 1,000 US Dollars, you employ a Fixed Fractional methodology and a trading system that makes you about 10 pips per trade on average. You decide youre going to start by trading 1 mini lot, a sensible thing to do with an account of this size.

After your first 100 trades youve build up 1,000 US Dollars in profits. Since your account size has just doubled, you can now double your trade size according to the fixed fractional technique, so youre now trading 2 mini lots each time. Another 100 trades at 10 pips per trade on average, and youve doubled your account again to 4,000 US Dollars. Getting the idea? Each time you make 1000 pips. you double your account size. Following this logic, your trading progress would look like this:

1000 USD + 1000 pips @ 1USD/pip = 2000 USD

2000 USD + 1000 pips @ 2USD/pip = 4000 USD

4000 USD + 1000 pips @ 4USD/pip = 8000 USD

8000 USD + 1000 pips @ 8USD/pip = 16,000 USD

16,000 USD + 1000 pips @ 16USD/pip = 32,000 USD

32,000 USD + 1000 pips @ 32USD/pip = 64,000 USD

64,000 USD + 1000 pips @ 64USD/pip = 128,000 USD

128,000 USD + 1000 pips @ 128USD/pip = 256,000 USD

256,000 USD + 1000 pips @ 256USD/pip = 512,000 USD

The downside of the above fantasy is that each time you increase the trade size, you are also increasing the risked dollar amount and any violent Drawdown can severely damage your account.

Risking a high percentage of your account might indeed have dramatic effect on the geometric growth of your account balance in the very short-term. This happens because 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 .

But even if you keep the risked percentage the same, as in this model, the amount of capital risked increases as the available capital grows. Psychologically it may be hard to bear a risk of 2% in a 100k account- there fore other money management models have been designed to solve this problem.

Periodical Fixed Fractional

In this variant of the previous model we recalculate the risked percentage not in every single trade, but only if after a certain time the account equity has changed, lets say after one day, one week or one month.

• This will smooth the compounding mechanism during winning and loosing trades. If you win 10 trades in a row using the Fixed Fractional method you will significantly compound because after each trade you are taking the new balance into account to reevaluate the absolute risk amount. Using the Periodical Fixed Fractional you dont change the trade size even if you are having a winning or a losing streak. This breaks the geometricity of the equity curve.

• By compounding per day, the result will be similar to the Fixed fractional if the trade frequency is close to one trade per day — the more it varies the greater will be the difference.

• By compounding per month, you cant expect huge compounding returns but on the other hand you are also locking in the risk. The maximum profit potential will be not dependent of the alternation of Profit and Loss trades.

• Regardless of the alternation of winning and losing trades, by compounding per month, your result will be always the same- means the systems performance is less impacted by winning and losing streaks.

• The problem with this technique is when you have strings of losing trades. These strings hurt because now you have to take the account back up and you are trading smaller sizes as your account decreases. Typically this will bring an account balance lower and lower.

Using the classical Fixed Fractional model, you will always have a potential lowest return, a potential highest return and a potential average return. The higher the period chosen to size the positions. the narrower will be the potential lowest and highest returns.

This means that the less impact has the alternation of wining and losing traders on the systems performance and the closer the end result will be to the potential average return.

Profit Fixed Fractional

The profit risk position sizing method is another variant of the Fixed Fractional position sizing.

In Fixed Fractional position sizing, the dollar amount risked on a trade is a percentage of the current account equity or balance. In the Profit Fixed Fractional method, the dollar amount risked on a trade is a percentage of the starting account equity plus a percentage of the total closed trade profit. Once the risk amount is determined, the number of units is calculated the same way as in Fixed fractional, namely: the amount to be risked is divided by the trade risk per unit.

Compared to the Fixed Fractional model, the Profit Fixed Fractional method is sometimes more convenient because it separates the account equity into initial equity and closed trade profit. The percentage applied to the initial equity provides a baseline level of position sizing independent of the trading profits. Note that if both percentages are the same, the Profit Fixed Fractional method will produce the same result as the Fixed Fractional model.

• This strategy is for traders looking for higher return and still preserving their starting balance.

• The increased risks in the buffer fraction of your account: if a Drawdown occurs when trading with the first accumulated buffer, it may force the trader to start anew if the buffer is depleted by a string of losses.

As an example, consider a start balance of 10,000 US Dollars and after 1 year, this amount might be 15.000 where the risk was kept to 1% of your balance. Now you have your initial balance + 5.000 US Dollars in profit. You can now increase your potential profit by risking more from the profit while restricting your initial balance risk to 1%. For example, you can calculate your trade through the following pattern :

1% risk of the 10.000 USD (initial balance) + 5% risk of 5.000 USD (profit)

In this way, you will have more potential for higher returns and at the same time you are still risking 1% of your initial deposit.

In the recorded webinar Position sizing and money management , John Jagerson points those contingencies that usually happen down the road and explains money management techniques beyond the Fixed Fractional model as being the most common method. He also treats diversification as a function of risk control, a subject which falls out of the scope of this chapter.

Optimal Fixed Fractional Trading

The concept of Optimal F is that a Fixed Fraction of a trading account will grow it at the most efficient rate. In other words, it gives us the optimal fraction that we place in each trade for maximum net return.

It is a variant of the Fixed Fraction model that Ralph Vince developed to enhance a model based on fixed odds, that is, where winners and losers were of consistent amounts. Since any trading performance may have strong deviations after a loss of 2.5% on one trade, a gain of 6.18% may happen on the next trade, and so on — Vince created a model for variable returns. But in order to measure the results of variable returns its helpful to understand the concept of the so called geometric mean .

Geometric mean is simply the effect of compounding. An example might be this: two trades increase our portfolio by 10% each one. At the end of the second trade, how big is my portfolio. If you said 120%, you missed the effect of compounding that geometric mean will yield. The right answer is: 110% * 110% = 121%.

A Return of 120% would be an arithmetic mean .

Vince explained that Optimal F is that fixed fraction which grows the portfolio at that highest geometric mean . Determining Optimal F consists of trying different values of F and determining which one provides the best geometric returns. This is done using software, or you can simply use the GEOMEAN() function in excel.

• The resulting value, whatever the Fraction is, is supposed to achieve the larger amount of profits. So if your Optimal F is 15%, you place 15% of your account at risk on each and every trade. Then, at the end of a given amount of trades, you will have built up your account to a larger amount than if you had you risked 14% or 16% of your account.

• While this might be mathematically the best way to grow a portfolio. it will be psychologically challenging for most to execute it faithfully, as it is usually very aggressive.

• If we use a fraction above the Optimal F we will ruin the account by over aggressiveness, whereas if the Fraction is below the Optimum F the growth of our account will be too slow.

• Clearly this is not a method that shows a ratio with which to operate since the Optimal Fraction will provide the greatest net return, but with a risk level measured by the Drawdown that very few traders can bear .

• Note that the Optimal F is based on the past trade results — if the F number was 15% for the last hundred trades, it doesnt mean that it will be the same for the next hundred trades. This means you can be over trading and turning a winning situation into a losing one. And conversely it can lead you to under trading, and youre obviously not going to get maximum growth.

• Note as well that the Optimal F is still a fixed fraction. The problem with a fixed fraction is that if you go too low, youre never going to see growth. And if you go too high with the Optimal F youre going to be very aggressive and probably face huge Drawdowns.

We know that if we are using optimal F when we are fixed fractional trading, we can expect substantial drawdowns in terms of percentage equity retracements. Optimal F is like plutonium. It gives you a tremendous amount of power, yet it is dreadfully dangerous. These substantial drawdowns are the problem, particularly for novices, in that trading at the optimal F level gives them the chance to experience a cataclysmic loss sooner than they ordinarily might have.

Source: The mathematics of Money Management by Ralph Vince, Wiley and Sons, 1992.

Secure Fixed Fractional

This model is another variation of the Fixed Fraction and was introduced by Ryna Systems. The Secure F is similar to the Optimal F except for the introduction of a restriction on the Maximum Drawdown the trader is willing to tolerate.

Leo Zamansky and David Stendahl in their article Secure fractional money management (Stocks & Commodities magazine, June 1998), observed that this strategy had to be made more operational. The reason was the inability of most traders to withstand large losses and the high risks inherent to the Optimal F model.

If the Maximum Drawdown is a very small value, we are facing a very conservative strategy. so the Secure F can be adjusted to the risk tolerance (or appetite) of each trader.

This is a question out of the Practice Chapter:

If a trader was wrong 20 times in a row and still has 80% of his or her equity left, what is the model is he/she trading?

• The Optimal F
• The Fixed Percentage based on Total Core Equity
• The Reduced Total Core Equity Model

The practice Chapter contains more than 250 questions, based on different trade scenarios. Test your knowledge and become an expert!

Measured Fixed Fractional Model

Many traders have passed through the experience of giving profits back to the market after a winning period. This happens usually when the adopted money management model is not adequate to the kind of trading methodology used, or when there is no money management regime at all. Yet there is another variant of the Fixed Fractional which aims to protect the traders gains: the Measured Fixed Fractional model.

Like other methods, this one also increases and decreases the trade size on a regular basis, and for doing this, it scales the equity s (or account balance) growth in fractions. Instead of increasing the position size after each trade, or after a certain time, it does it after a predefined amount of capital growth.

• It smoothes the equity curve more than in the traditional Fixed Fractional model.

• It simplifies calculations as the position size has only to be changed once the account has grown of a certain amount.

• It helps traders to recover faster from losses because the position size is not reduced immediately after the loss is produced. After a loss you are still trading with the same size, and although your leverage might increase, it does it only slightly.

• Although leverage doesnt swing so wildly as in the Fixed Lot model, it is not constant.

• For more aggressive traders it may represent an impediment to profit from the compounding effect during a winning streak.

Here below we take the example of risking 1% of the account balance. Remember that instead of account balance you can use any of the equity models explained in the third section of this chapter. The Measured Fraction is calculated simply by rounding down the available capital to a lower fraction. Depending on your trading style, you can increase the measured fraction each 1,000 units of accumulated profit as in the below example — or set any other amount.