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The wonders of a fixed fraction: how to never drain a deposit

Greetings, ladies and gentlemen, traders!

Today we will continue the theme of money management of your accounts and talk about the most common and most recommended method of money management for instruments that use leverage, that is, traded with margin - a fixed-fractional method. The fact is that small improvements to the classical method will allow you to almost never drain your accounts.

In fact, this is probably the only money management method known to us from various books and resources on the net. Moreover, in most books on trade, as a rule, only one chapter is given to the management of monetary resources with recommendations on what should be used. And at the same time, no explanation is given regarding the possible consequences, pluses and minuses of this or that approach.

Meanwhile, there is no ideal method of money management that would be perfectly suitable for use with a wide range of trading systems. Today we will continue to talk about methods of money management and get acquainted with the most common of them, and also consider the advantages, disadvantages and various variations of the fixed-fractional method of money management.

The classic version of the fixed-fractional method

The classic version tells us that for each transaction you can risk the amount not exceeding X% of the balance or of the equity of the account. This is the most widespread money management technique, both among professional financial managers and among ordinary private traders. Also, this method is often called the fixed share method, since it is the percentage of capital that is used.

According to this method, you simply risk X% of your money in each transaction. For example, you trade with the fixed-fractional method, using 2% of your deposit in each transaction. Your deposit is $ 1,200, and the stop loss (maximum loss) is 100 pips or 1000 pips. For simplicity, suppose that the price of an item with us is $ 1 for lot 1. Then our lot, with which we will enter the transaction, will be 1200 * 2% / (1000 * 1) = 0.024 or 0.02 lots.

Also, a modification is often found where, instead of the stop loss value, the maximum loss is taken into account. The fact is that many trading systems have rules for exiting transactions in the unprofitable zone and it often happens that getting a full stop loss is extremely unlikely. Therefore, in order not to underestimate the risks significantly and not artificially limit the capital growth in the system, they take the maximum loss according to the test results (for example, according to the results of 1000 transactions, the maximum loss for the transaction is 80 points) and it is used in calculations. And the real stop loss is either not used at all, or put it with a decent margin.

It is always worth remembering that the market is a market, and even when something seems extremely unlikely, it will certainly happen sooner or later. Therefore, even if you decide to use a similar option for calculating the lot, do not artificially increase the size of the stops and even more so do not remove them at all. At a critical moment, albeit with a big slippage, but your transaction will be closed and with adequate levels of risk you will not lose much.

Lot rounding rules for the fixed-fractional method

In the case analyzed above, as a result of rounding, we were not able to set the risk at exactly 2% and use the risk (0.02 * 1000/1200) * 100% = 1.67%. When the account increases to $ 1,500 with our given risk of 2%, we will be able to enter the market already with a lot of 0.03. In this case, the risk will be exactly 2%. But from a deposit level of $ 1300 we could round the resulting lot according to standard rounding rules (that is, at 0.025 we would round to 0.03), but in this case the actual risk would be 2.31%, which is decently more than the given 2 % Therefore, it’s more correct, in my opinion, to always round down to the same extent, so as not to risk extra money.

Classic fixed-fractional method and trade statistics

As you well understand, the risk calculation for the next transaction in this approach is built completely without reference to the account statistics. Whatever the market at the current moment, no matter how effective or ineffective your strategy is, the risks of the next transaction remain unchanged. This is the whole essence of this method and, despite the fact that almost every trader uses it in his trading, it is rather difficult to call such an approach effective.

One lot for every X units of currency in the account

This method is just a slightly modified variation of the classic method. It is he who is called the pure fixed fraction. The bottom line is that for every, for example, one hundred dollars on the balance sheet, you add the minimum unit of lottery. For example, your balance is $ 1,200, and you add 0.01 lots for every $ 500 in the account. Then you will enter each transaction with a lot of 0.02 until the account grows to $ 1,500. Next, you will work from 0.03 lots up to the mark of 2 000 $ balance.

Below you can see the chart of the trading system with 58% of profitable transactions and the ratio of profit to loss 1 to 1 (excluding trading costs):

The same system with a risk of 3% of the deposit per transaction:

The same system, but with the risk of one minimum lot for every $ 200 deposit:

Despite the slightly more modest profit margins of the latter option, its maximum drawdown is significantly lower, and the yield curve is smoother.

This can be more clearly assessed when transactions bring a different amount of profit or loss:


If you study these two graphs more closely, you will see the benefits of the second method. This is especially evident in the drawdown in the area of ​​transactions 900-950 - it is really decently smaller than with the classical fixed-fractional method.

However, the method of one lot for every X units of currency in the account also has several disadvantages. He also does not take into account trading statistics at all and prescribes to always calculate the lot based only on the size of the account. Also, this method does not at all take into account the fact that the amount of profit and loss can be different from transaction to transaction.

Also, this method of calculating the lot does not take into account the real value of the possible maximum loss. That is, if during the selection of lottery according to the test results it did not include cases of closing by stop loss, you still have a chance in the future to get this same stop loss and it will be sad if it is four times the average loss.

Such a situation is quite real when your average loss is, for example, 2%, because you usually close by the signal of the system, without waiting for a complete stop, but there comes a moment when, due to, for example, the market reacts too quickly to foundation, the deal is closed exactly at a complete stop and you get a loss of 10%.

Well, the last, but very important drawback is that you need to get 100% profit in order to switch from one to two minimum lots at the initial stage. For example, you need to have $ 500 to trade a lot of 0.01 to keep the maximum drawdown in the region of 20%. Then, to trade in a lot of 0.02, you need to make $ 500 or 100% of the initial deposit. The next transition will happen already at 50% profit. Then by 33%. As a result, after each transaction you will have to increase the lottery by a few minimum lot units. But the very first transition requires 100% profit.

A big problem will arise if you try to reduce the huge period of time that is required to switch from trading lot 0.01 to lot 0.02. The only way to increase the speed here is to increase the percentage of risk (which is especially dangerous with a small account size).

The disadvantages of both methods

The main drawback is the need for a very long time to work with the same lot until the transition "to the next level". This drawback applies to both methods, but it is more clearly visible in the latter. For example, when trading 0.01 lots for every $ 500 on a deposit, you can trade a lot of 0.01 for a whole year until the deposit is equal to $ 1,000. All this period between transitions to new levels, you essentially work as a fixed lot and deprive your account of the effect of "geometric growth", well, or at least stretch this effect very much.

With an increase in the risk level, this drawback can be mitigated a little, but here one more significant drawback comes out. If you think that the growth rate of the account with the geometric model corresponds to the rate of decline, then you are mistaken. It is regrettable, but the rate of decline exceeds the growth rate.

For example, in order to increase your account as quickly as possible, you decided to use the optimal f method, which involves trading with a high percentage of risk, usually from 10 to 20% per trade. Suppose that your system will always give either a profit of 10% of the deposit, or the same loss. Then, with a deposit of $ 1,000 and a risk of 10%, you will win $ 100 in the first transaction and get $ 1,100 on the deposit. If the next transaction is unprofitable, you will risk $ 110 and get $ 990 in the account as a result.

Thus, in both transactions, you risked ten percent of the account and received a loss of $ 10, but not $ 0. Moreover, the higher the risk, the stronger this effect. This is called the asymmetry of the lever, which is common to all instruments traded with margin. All this sadness can be clearly demonstrated with such a table:

As you can see, already at a risk of 5%, the effect of this effect begins to affect your score. That is why you need to immediately decide what is more important for you - to strengthen the effect of the geometric growth effect (and at the same time the drawdowns will decently increase), or to preserve and maximize your initial capital security.

Unfortunately, there is so far no way that would reliably realize both of these goals, but there are some tricks that will still allow you to bite a small piece of these two pies. But about them a little lower, and now we will analyze these two basic approaches - increasing the effect of geometric growth and protecting profits.

Profit Protection

The ability to reduce risk faster than it increases, allows you to protect your profits in the period of losses. What is a reduction rate? This is quite simple - the more unprofitable deals we get through the system at the moment, the more we reduce the lottery. The simplest example is that after each losing trade we decrease the lot by 20%, that is, multiply the lot by a factor, for example, 0.8. Suppose that our profit is equal to loss and we are trading a fixed 1 lot in an account of $ 10,000. Then after 9 losing trade we will have nothing to trade:

Now let's try to risk 10% of the account:

After 10 unprofitable transactions in a row, we lost almost 65% of our capital and, based on the table above, we need a profit of about 200% to restore the account.

Now, after the first losing trade, we will reduce the lot by 30% each time:

As you can see, we are in a drawdown of 33% and for recovery we need about 45% of the profit.

The trader is interested in reducing risk outstripping growth for several reasons.

First, a trader can limit the amount of losses. If the strategy or trading system used by him brings big losses, then the possibility of faster risk reduction will provide the following effect: the larger the possible losses, the less capital will have to be risked, which will seriously reduce the depth of maximum drawdown.

Secondly, this allows a conservative trader to act more aggressively while increasing the volume of reinvestment. Traders do not use aggressive money management because they are worried that this will affect the amount of potential losses. Faster risk reduction compared to previous rates leads to less significant costs.

Let's compare the results of the same system with and without a reduction rate:


Risk in% of deposit:


One lot for every X units of currency in the account:


Drawdowns, although not too much, but still decreased. In addition, we are now protected from a large number of losing trades in a row.

Modifications to the rate reduction method

But, again, you need to understand that such an approach works best with a large number of losing trades in a row, otherwise the effect of using this method is almost invisible. Therefore, its modifications are often used.

One of these modifications is the system balance curve. A moving average of the deposit balance is built, and with the current balance below the moving average, a reduction rate is applied until the balance is above the curve. When the balance crosses its moving average, you can again switch to the standard calculation of lottery. Here, too, there is one drawback - the farther we managed to deviate from the moving one, the more difficult it will be if the lot is reduced to return back. Therefore, it is worth adding an oscillator in balance to the moving average in balance, thus obtaining a trend system:

At point 1, when the balance line (green line) crosses the moving average line (red line), we begin to apply the reduction rate until we reach point 2. At point 2, the oscillator calculated from the balance line readings leaves oversold, and we gradually begin to increase the lot until we find ourselves at point 3. At point 3, the balance chart is again above the moving average and we again calculate the lot based on the usual logic adopted in the system.

This approach already allows you to reduce drawdowns during periods of lowering the balance sheet (unfavorable market conditions for our system), as well as quickly return to the initial lot. With this approach, a high reduction rate is not only not harmful for reaching the initial lot, but even turns out to be useful - we can set a reduction rate, for example, 0.7, and increase the rate (increase lottery with an increase in the oscillator) to set it at 1.5.

Thus, we will rather rapidly reduce losses on the balance sheet and even more rapidly move out of drawdowns. This is true in the case when the oscillator continues to grow from the oversold level, but if the breakdown of the level was false and the next trade turns out to be unprofitable, we will be in even greater drawdown, as we entered an increased lot. Therefore, you should carefully use the betting method and carefully test the system on the history.

Faster growth geometric progression

In the previous example, we reduced lottery faster than it would have been with the usual method of money management, for example, using 2% of the deposit in each transaction. But who will stop us from increasing the lot when finding the line of balance above our moving average and the growth of the oscillator? That is, for example, according to our system, we must risk 2% in each transaction. Moreover, under suitable conditions (growth of the moving average and the oscillator, for example), we can say that at the moment our system is in "good shape" and works in accordance with market conditions. Then why not increase the lot after each profitable transaction in such conditions? All this will increase the effect of geometric progression on the account without a significant increase in drawdowns, because we will act in this way only at market phases favorable for the trading system:

That is, while the balance line is above its moving average and the oscillator is growing (segments 1-2 and 3-4), we can increase the lot above the inherent in the system.During periods of recession, the oscillator can be traded in the base lot, which is laid down in the classical rules of the system. Thus, in the most favorable periods, we will risk a little more.

Profit Trading

As you know, the very first task of proper money management is to protect the initial capital. Trade is not a sprint, but a marathon, and the most important thing here is not to leave the race.

I perfectly understand people who are first trying to disperse the deposit, and then trade more calmly. Not every trader is able to afford a deposit, trading on which would fully cover his living expenses. Therefore, many people want to reach this level as soon as possible and try to take big risks at the very beginning. This seems like the right decision, because it’s really really faster to start making full money only from the market, and it’s not a pity to lose a small deposit. But, unfortunately, not everyone succeeds in sustaining this sprint with increased risks, and such a decision, as a rule, leads to the opening of a new account. This technique is especially dangerous when a trader opens an account for a new strategy, for which he does not have statistics or very little.

The rule follows from here - in order not to open a new account every new month, when an advance drops on your card, it is worth trading a minimum lot on new accounts for a while. And it doesn’t matter how many zeros your balance contains - it is always worth trading one or three months with a minimum lot. Firstly, it will make it clear how good your system is and not drive you into a big drawdown. Secondly, if the system is capable of generating profit in principle, this will be understandable after this period, as it will create some growth, which can still be useful to you if, after increasing the risks, your TS suddenly falls into a drawdown period. So you will squander the accumulated profit, not the initial deposit, which psychologically will be a little easier - you have already seen how the system works and you know that this is just a drawdown and the system works.

The second task of money management is to make a profit. From this moment, the fun begins. If you have correctly defended your initial capital, you have a very good chance to stay in the game long enough to finally extract some income from your trading. I assume that you read everything that was written above and understood how to properly increase your risk. If the risk increase is performed correctly, there is a chance that the amount of income that will be received during a favorable trading period will surprise you. However, you must protect this income, as there is always a chance of a drawdown that can drive you into a corner.

Therefore, if protecting your profit is more important to you than continuing to build up your account at the fastest pace, then the most important step at the time of drawdown is to reduce your risk per trade at a faster pace than the rate at which the risk increased period. And we have already examined this technique in detail above when we used the moving average balance.

There is such a thing as a critical point. This is such a balance value, the achievement of which practically guarantees that no matter what happens, you can no longer lose your initial deposit. Naturally, this point is reached only if the rate of decrease in lottery is applied. As you remember, in one example, applying a reduction rate of 0.7 for 10 losing trades, we dropped from 1 lot to 0.04. Let's say for our trade 1 lot corresponds to a risk level of 2% and we have $ 10,000 in our account:

Even with such a rather conservative risk level of 2% with 30 losing trades in a row, we will lose almost half of the account. What happens if the same thing happens with a system that uses a reduction rate of 0.7:

We will literally lose a cent and get a drawdown of 7% after a full 30 losses. That is, with such a risk of 2%, with such a deposit of $ 10,000 and at such a reduction rate of 0.7, it is enough for us to get 10% of the profit in order to assume that we are almost guaranteed not to deposit our deposit. Let's extend the system’s results plate with a reduction rate of up to one hundred losing trades in a row:

Agree, it is unlikely, but still. Well, for those who have not yet felt the full power of this approach:

A thousand losing trades in a row and a drawdown of 20%.

After what level of profit to consider your deposit indestructible - decide for yourself. Of course, you can reproduce 10,000 losing trades in a row, and they really will merge your deposit. But will you in reality look for years at how your system is slowly losing money? Most likely, after a maximum of 500 transactions, you will change your mind and remove the system from the account:

And you lose about 13% on this, which is not too sad. Of course, real systems do not merge in this way and you will have much more time to think. But I do not know of any more powerful method for protecting the initial deposit than this.

But, as I already said, for its successful application it is important to find a moment to return to the initial lot and there can be many different strategies - after the first profitable transaction, after the account reaches the level after which the balance begins to decline (count after exiting the drawdown) guided by the whole system on top of the balance chart. There are a lot of options, as many different trading systems, and their balance charts. Some systems give smooth graphs with almost no significant deviations, in which case the moving average with the oscillator will not be particularly effective. Some systems involve serious and prolonged deviations of the balance line from the moving average. In each case, an individual approach is required, confirmed by the test results.

Conclusion

Today we have examined in more detail such a popular method of money management as fixed-fractional. I hope that knowing the advantages and bottlenecks in using a fixed fraction will help you avoid many mistakes when managing your money. Such tools as the reduction rate and the reduction rate allow you to level out the shortcomings of the fixed-fractional method, as well as, as you have seen, reliably protect your initial capital and profit received during the trading process.

Nevertheless, it is worth remembering that there is no ideal method of money management and that the trading system is not selected according to the "ideal" method of money management, in your opinion, but on the contrary, a method is selected for a specific trading system that will most effectively hide all the shortcomings of the strategy and best distinguishes its virtues. The money management system is primarily a system and it is quite normal that the money management system will not be any easier than the trading strategy itself.

Good luck and see you soon!

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