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However, there are two main drawbacks to this technique:

1.This money management technique/approach filters the trades in a system to keep them below a certain risk value. As described above, this approach may change the percent of winners and other statistics about a system. This in turn can effect the results of the system. Traders should have a good idea of what kinds of risk to expect, before employing their systems. If the threshold for risk is very low, this money management technique/approach could effectively screen out most, or all of the trades. This is undesirable for several reasons. Firstly, it is assumed you have developed a reliable trading system otherwise you wouldn't be worried about money management. If this is the case, it is generally not a good idea to introduce any additional filters to a good system. The less curve fitting the better. On the other hand, a little filtering of the most volatile trades can help stabilize the equity growth of an account.

2.The second drawback of this money management technique/method is the fact it is not responsive to the size of the trading account. If the trading account doubles or halves in size, the amount of money to risk, which was determined at the beginning of trading, may not be appropriate or commensurate with the new account size. In these situations, it will be necessary to decide on a new amount of money to risk on each trade. But, if this is done, it may effect the percentage of winners and losers. Therefore, it will be necessary to re-characterize the trading system/money management combination to insure it is still acceptable and working properly. It is very possible to have a trading system that performs poorly for trades that have a risk of less than $1000, performs well for trades that have a risk between $1000 to $2000 and again does poorly on trades with a risk above $2000. In this case, if the system iswere not doing well, it would do more harm than good to filter the trades for the reduced risk of $1000. On the other hand, if the account is doing well, increasing the risk may not be beneficial either.

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The following is a table showing the profit and drawdown for different values that are used for this system:

SYSTEM A



System A, as previously mentioned, is a high probability system designed to limit the risk to $500. (This system was actually developed using TradeStation . A trailing stop of $500 dollars was used to insure the risk was not above $500.) With this in mind, it is clear why the profit over drawdown numbers level out after more than $500 is risked per trade, at a value of 3.32. An interesting fact about this system is that although the risk was locked at $500, there were many trades that experienced a loss greater than $500. The reason for this is that the particular market used for the development of this system was not particularly liquid. As a result, there were several trades that were exited when the market gapped on the open and the trade was exited with a larger loss than expected. Steps can be taken to minimize these types of problems, but this will be addressed in a later section of this book.

It is also important to note that the drawdown to the account creeps up, as more money is risked.


SYSTEM B



This system made $5,315 using no money management with a drawdown of 20%. Assuming traders risked $750 per trade, applying this approach would allow them to increase the profitability of the system by about 50%, while only increasing the drawdown by 10%, overall. This is a substantial improvement.
System B illustrates what is typical of most systems, schizophrenia. If traders want the best profit to drawdown ratio (1.24 profit/drawdown), they should decided to risk $750 per trading signal. On the other hand, if the traders want to achieve a higher profit ($21,075), the most reasonable choice is to risk $2,500 per trading signal, assuming they only want to keep the drawdown under a whopping 70%. (Alternatively, traders could risk $1,500 per trade, since the percent of drawdown to the account is equally bad for the values achieved at both a $2,500 and $1,500 risk.)


SYSTEM C



System C is the trending system with a low percentage of winners. This system made $6,847 when using no money management, on a drawdown of 20%. Assuming traders risked $750 per trade, applying this approach will allow them to increase the profitability of the system by approximately 50%, while only increasing the drawdown by 20%. This is another substantial improvement.
This example is similar to System B in its schizophrenic nature. To achieve the best profit to drawdown ratio, traders should only risk $750 per trade. However, to achieve the best profit, one needs to drop to the bottom of the table and risk $4,500 per trade to make $50,963.


Risking a Fixed Percentage of Equity on Each Opportunity Technique

The main disadvantage of the previously described techniques/approach, is that it will not allow traders to compound the winnings and/or decrease the risk in bad times. A way to compensate for this is to only risk a certain percentage of the account value for each opportunity. This technique allows traders to increase or reduce the risk as the account grows or shrinks.

With this technique/method, traders decide on a fixed percentage of the account to risk on each trading signal. For example, they may decide to risk exactly 10% on each opportunity. Once this is established, they would take that percentage of the current account value and only risk up to that amount on the trade. For example, if traders have a $25,000 account, on the first trade they would risk only $2,500 on this opportunity. On the next trading signal, the traders would recalculate the total equity for their account and then risk exactly 10% of the new account value, and so on.

Please note that traders will only risk up to, but not over this amount on any trading opportunity. (If a trade has a potential $2,500 risk then they would only take a one unit/contract position. If a trade only has a $1,250 dollar risk then they would take two units/contracts. If the trade has a potential $2000 risk then the traders would only take a one unit/contract position. If the trade has a potential $3,000 dollar risk then the trade would be skipped.)

This approach can do wonderful things for an account by compounding the profits of the account. Other methods often need to be reworked when the account size grows, but this method automatically readjusts with each trade. This can be a real administrative advantage to traders.

On the other hand, during down periods, it will slowly reduce the dollar value of the trades. This feature automatically protects traders from being wiped out after a long series of losses. The following table shows how an account would react after a given number of losses, using this method:




The following represents an example on how to use this table. Assume that traders using a specific system lose seven trades in a row. If the traders always risked 10% of their account, after seven losing trades in a row, they could expect to have 48% of the original account size. After fourteen losses in a row, these traders would still have 23% of the original account size. This is a pretty good example of how this method can help save traders when they are experiencing a long string of losses.

But this is only half of the story. Although it takes seven losing trades to move the account down to 48% of it's original size, it takes nine winning trades to get it back up to it's original size. This is a well-known phenomena in many sales and marketing circles. Good sales and marketing executives are aware that if they cut prices on their products by 25%, then they must increase sales by 33%, just to get back to even again. This can create an uphill battle for some systems that will have to win more times than they lose, to recoup the money that was lost. On the other hand, this may not be an issue. If you are using a statistically winning system, sooner or later you should get back to where you were before the string of losses.

The following table shows how many trades it would take to lose 50% of the account and the number of trades necessary to build the account back up again to where it was, before the losses.



As you can see from the table, it will always take more wins than losses to get the account back to the original size, after losing a portion of the account.

Another disadvantage of this approach is that it can be hard for traders to calculate. This is especially true for day traders. It is often inconvenient for traders to figure out the results of the last trade, adjust the account value and figure out what the correct amount is for the next trade. Of course, if the traders are fairly automated, it may be possible to keep all this data in a spreadsheet and quickly and easily calculate it out.

Since this technique allows traders to risk up to, but not over the allotted percentage, this money management approach may have the effect of filtering out some high-risk trades. This may or may not be favorable to traders. However, for the most part, it should be considered an advantage for the same reasons discussed in the "Risking A Fixed Dollar Value for Each Opportunity" section.

An important result of the "risk up to, but not over" condition is that the growth to the account will not always be linear in regards to the percent of the account risked. In the following examples you will see that the growth of the account is linear in one example and non-linear in the other two. This highlights the necessity for traders to look over the different scenarios to find the best fit.

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SYSTEM A -



System A is the system with the highest percentage of winners. This system made $9,490 when using no money management on a drawdown of 8%. If traders are willing to accept a drawdown of 22%, they could almost double the profitability of the system from $9,490 to $17,145.

Once again we see that you can't have your cake and eat it too. If profitability is the traders' goal, they will need to risk 12% of the account on each signal. If this is the case, they could make $60,470 using this approach but with a 63% draw- down. On the other hand, some traders may prefer to maximize their profit to drawdown ratio. If that is the case, the traders will need to risk only 4% of the account to make $17,145, with a 22% maximum drawdown.

SYSTEM B - 53% Winning Average System



System B is the "normal" system, with about 50% winners. It made $5,315 when using no money management, on a drawdown of 20%. Applying this technique of money management to this trading system did very little to improve it. The profitability of the trading system was doubled but the drawdown also increased substantially.
It is also interesting to point out that using this money management technique with this particular system, had a very distinct peak, with low values to either side. This kind of formation can suggest that there is some instability for this combination. Generally, traders should steer away from systems that act in a similar way, since the results may not be predictable.


SYSTEM C - 35% Winning Trend Following System



System C is the trending system with a low percentage of winners. This system made $6,847 when using no money management, on a drawdown of 20%. As you can see from the table above, there was no combination that would be worth taking. It would be better to trade this system using no money management, rather trying this technique/approach.

In conclusion, different systems seem to respond differently to this money management technique/approach. It is wise to do testing on your system before implementing this type of money management. For the right system it can increase the profitability of the system and protect the trader from losing periods. On the other hand, with the wrong system, it can be worse than no money management at all.


Adjust Trading on a Win or Loss Technique

This type of trading goes by several different names: Pyramiding (up and down) and Martingale (normal and reverse). Basically it consist of varying the number of units/contracts taken, based upon the results of the last trade. For example, traders can choose to double up on a position after a losing trade in hopes of recouping losses or doubling up only after a winning trade to maximize the system's potential. This can be a very effective money management technique/strategy. However, it will only work correctly for some systems. Many traders try this approach in testing and get very successful results, only to have their systems fall apart in real time. In order to effectively employ this technique, it is necessary to know the Z-score of the trading system. (The Z-score is discussed later in this book, with specific applications to this form of money management.) Basically, the Z-score will tell traders if there is a dependence or relationship between winning and losing trades. For example, what is the statistical evidence that winning trades follow losing trades and vice a versa. Knowing the dependency between subsequent trades, (Z-score), gives traders the information on how to exploit their trading systems correctly. Without this information, traders are unable to accurately gauge the appropriate risk for the next trade, using this money management technique. It is very important to understand the Z-score and the Confidence limit of a system before applying this technique/approach. Please read the sections on Z-scores and Confidence limits, before using this approach.

This technique of money management can do wonders for a system that meets the Z-score requirements. The main strength of this technique is that it allows traders to maximize the risk reward ratio on high probability opportunities, while reducing the risk on low probability situations. The result is that a trading account can grow substantially faster, without increasing the over all risk to it.

There are two ways the trades in a system can be dependent on each other:

1.There are trading systems that tend to have wins and losses in runs. Under these circumstances, traders would want to implement strategies where after a wining trade; they would double up on the next trade and decrease the exposure after a loss.

2.On the other hand, there are trading systems that tend to flip flop between wins and losses and thus have fewer runs than one would expect. Under these circumstances, traders would want to double up after losing trades and cut back after wins.

Another advantage of this type of money management technique/approach is that it is relatively easy to implement in real time. Once traders are aware of the desired pyramiding technique to use, it is easy for them to know exactly how many positions to take on the next trade, based on the results of the last trade.

The major disadvantage of this money management technique/approach is that it is very sensitive to optimization, especially if the Z-score and Confidence limits are not high enough. Traders must be very careful not to over optimize the system/technique. Consider the following results:

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Pyramiding Schemes Applied to System B



The table above shows wide variability of the results. With strict application of the Z-score and Confidence limits, traders can easily achieve very reliable results, plus large increases in profit and low drawdowns, using this money management technique/ approach. See the section on Z-scores and Confidence limits for more details on how to use this money management technique.

The table above shows some common pyramiding techniques, such as pyramiding up or down on wins or loses. Example A has no pyramiding and is shown just as the base number. Example B is pyramiding up on losses, while example C is pyramiding down on losses. The rest of the table goes over other different possibilities for pyramiding.
Example H looks particularly interesting for this trading system. In example H, the applied technique has traders reducing their exposure after successive wins. Applying this method allows traders to triple the profit for their account, while reducing the drawdown. Other methods didn't work as well, but still allowed them to make additional profit.

As one can see, the particular scheme that traders take can have significant effects on the profitability of their accounts. In fact, this technique has the ability to transform a losing system into a winning system. However, just as easily, it can change a winning system into a losing one. It is the wide variability in the results that makes this money management technique/approach very sensitive to optimization. Traders can easily select values that seem to make good profit only to find that their systems lose money in real time. The reason for the loss is that often the real time wins and losses come in a slightly different order. Since this new order (win/loss sequence) is different than the order in the historical results tested, the money management technique used is not well prepared for the future. This is the major reason why it is important to know the Z-score for any trading system used. The Z-score will give you the statistical basis to justify using this method and, as a result, the future performance of the system will be more consistent with the historical results.

A drawback to this approach is that traders will periodically have to re-evaluate the money management technique, as the account grows. The number of units/contracts taken on past trades would not be appropriate if the size of the account had doubled in size. For this reason traders will have to set profit goals and then re-evaluate the money management technique/approach once these goals are reached.



Crossing Equity Curves Technique

Using crossing equity curves for money management can be an excellent technique/method to trade an account. Often this technique can minimize the drawdown periods better than any other methodology. Additionally, when properly applied, this technique can actually improve the percentage of winning trades taken.

Many traders are familiar with using moving averages to decide when to enter the market. Almost every charting software package has this feature. Usually, traders will use two moving averages and enter the market when the short moving average crosses the larger moving average. Traders would enter a long position when the short average crosses from below to above the longer moving average, and vice a versa for a short position.

This form of money management technique/approach is similar to the trading technique of using moving averages. First, you decide on a long and short moving average. This is an average of the profit of all the trades. The shorter average is an average of the profit (or loss) of the most recent trades. The longer average is an average of a lager block of the most recent trades. When the short average is greater than the long average, it means the trading system is doing better per trade than it has done in the immediate past. If the short average is less than the long average, it means the trading system is doing worse now than it did in the immediate past, on a per trade basis.
Consider the following example. Note how the shorter average is sometimes above or below the longer average:

Trade # Profit
1 $ 500
2 $1,200
3 ($1,000)
4 ($ -500)
5 ($ -500)
6 $ 500
7 $ 500
8 ($ -350)
9 ($ -500)
10 $ 25
11 ($ -200)
12 $ 200
13 $ 560
14 $2,135
15 $ 750

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When using this form of money management, traders would only enter a position in the market when the short average is above the long average. This is noted in the graph by the arrows. If traders got a trading signal and the short average was below the long average, they would skip that particular trade. However, for the purpose of calculations, all the trading signals and their results will need to be tracked. The averages are for all of the signals generated, not just the trades that where taken.

It is reasoned that this strategy will help keep traders out of long drawdown periods. Additionally, traders will only be trading the system when it is "in sync" with the markets. Numerous results show this to be true. Often, traders can achieve equal or greater profit, with less drawdown, on fewer trades. The fact that a higher profit is achieved on fewer trades is an especially attractive bonus. Fewer trades result in fewer fixed costs and less exposure to the market.

The basic assumption is that there are "phases" when a trading system does better or worse. This is true in many cases. However in other cases, what traders perceive as phases, are simply statistical consequences of the percentage of wins or losses of a system. As mentioned repeatedly though out this book, a 50% system has a very high chance of getting several wins or losses in a row. These runs may be perceived by traders as being "phases", when in actuality they are not. They are just the statistical consequences of a particular system.

In order for this type of money management technique to work effectively, it is necessary that there really are "phases" in the trading system. (Otherwise its just luck, that will probably run out.) Lets clarify the term "phases" to mean that wins and losses are grouped more together than would be expected, according to a normal statistical distribution. For example, the wins and losses tend to come in runs. The best tool for determining if a trading system has phases is to consult the Z-score and Confidence limits for that system. (Z-scores and Confidence limits are dealt with extensively in following sections of this book. These sections will also deal with specific applications for this from of money management.)

Although this money management technique has several substantial advantages over other methods, there are also disadvantages to this approach:
· This technique/approach can be hard to implement in real time. This can be especially tiresome for day traders. This is not an insurmountable problem, if the traders have a fairly automated approach to trading.
· Since it is necessary to track all the trading signals given, whether or not a position was taken in the market, traders may find themselves spending a fair amount of time tracking trades that provide no real equity for the them.
· Many trades are necessary for both historical testing and real-time trading. Since a fair number of the trading signals will be filtered out, traders will need additional trades in order to trade as frequently. The real-time aspect may not be necessary for some traders since they may be making more money with fewer trades. However, from a testing perspective, more trades are necessary since some of the sample set will not be taken. It is only the trades that are taken that a money manager can base the statistical reliability of their trading system/money management approach on.

One last concern about this technique/approach is that this method of money management can be sensitive to optimization, especially if the system does not have a high enough Z-score. Traders may find that a 3 short and 6 long moving average combination works wonders for their account. On the other hand a 4 short and 7 long combination loses money. To get an understanding of how sensitive to optimization a system can be, consider the following combinations tried on System C, the low probability trending system:




The table above shows the wide variability of the results. With strict application of the Z-score and Confidence limits, traders can easily achieve very reliable and favorable results, large increases in profit and low drawdowns using this money management technique/approach. Please see the sections on Z-scores and Confidence limits for more details on how to use this money management technique.

The table above shows how subtle changes in the two moving averages can dramatically effect the profitability of a system. System C, when traded with no money management made $6,847 on a 20% drawdown. If you consider examples D and E, you can see how changing from a 5 period to a 6 period moving average made the profitability of the trading system range from almost double the profit, down to almost half of the profit, of the trading system with no money management. Examples A, B and C also illustrate the dangers of optimizing this approach. As the subtext under the graph states, if the Z-score is high enough, the danger of optimizing is negligible, since you then have mathematical justification for applying this technique/approach.



On the other hand, example D shows how valuable this method can be when employed correctly. Under these circumstances, traders can almost double the profit from a system while reducing the drawdown in half. Frequently you will find that this method of money management can increase the profit and reduce the drawdown at the same time. In the section on Z-scores, you will see how when it is properly applied to this technique/approach it quadruples the profit of the trading system. Because of it's enormous utility, this money management technique should definitely be considered by all serious traders.



Optimal f Technique

For any particular system, it is possible to find the optimal amount to risk on each trading opportunity. Trading with this optimal amount of capital will result in the greatest gain to the account. If traders risk either a higher or lower dollar amount, they will make less money. (This is because a greater risk does not necessarily result in more gain. This is a good example of a non-linear force in money management.) For this reason, it is important to know what the Optimal f is for your system. If traders do not trade at the Optimal f value, they are essentially curbing the potential return on their trading system. However, some traders may have a desire and/or reason to do this, others may not. The Optimal f was popularized by Ralph Vince in his book "Portfolio Management Formulas" (Wiley 1989). Although, it was originally developed by a Mr. Kelly to solve problems in the Communications Industry.

(This section deals with the money management aspects of applying the Optimal f technique. In the section of this book on "How to Compare Money Management Approaches", there is another discussion about the Optimal f. That section will go into detail on the mechanics of what the Optimal f is, how the Optimal f is calculated and what it will tell traders when comparing systems.)

The Optimal f is not hard to work with. Some of the math can be confusing and the application of it is a bit obtuse, but the kNOW Software will do most of the work for you. When one usually sees a graph for the Optimal f, it looks like the following:

System B - Optimal f Graph

The Optimal f is a value that is between 0 and 1. The kNOW Software displays it as a percentage. This graph shows an optimal value of about 30% or 0.30. When the account is traded at this level, the account will grow most quickly.
Different points along the graph represent different amounts of profit or loss. At the peak of the graph, traders will make the most money. If traders move equally to either side of the peak, they will make roughly the same amount of money on either side. To illustrate this point, consider the following table for different values of f.

System B Traded With Different Values For f



As you can see from the table, 30% is the optimal value. (Actually it is more like 31%, but the example still shows the point.) Likewise, traders can see how risking more or less than this optimal value results in a lower return on the account. However, it is important to note that any time traders are risking more than the optimal value, they are getting less return on their money with a greater risk to their account. This can be seen from the growing drawdown number as you proceed down the table. It is because of this drawdown value that traders may not want to trade their accounts at the optimal level. If you remember, System B made $5,315 with an 18% drawdown. It is true that if traders are trading at the optimal level, they can double their profit, however the drawdown is 53%! This is a very high drawdown and may be unacceptable for most traders. To combat this problem, traders may want to limit the drawdown of an account to underless than 30%. In this case, if traders were going to use the Optimal f technique, they would have to use 15% for the f value. In this scenario, traders are limiting the profit in order to bring the drawdown into a more reasonable number. Please keep in mind this is only an example. Some trading systems may respond much better to the Optimal f technique while others will respond worse.

If you reference the table again, you will see that it also shows another anomaly that can appear in this type of money management technique/trading. In a statistically perfect world, since we know that 31% is the optimal value, we would expect the values closest to 31% to have more profit than values that are farther away from 31%. In the real world, this is not always the case. If you look closely at the profit, when traders risk either 20% or 25%, you find that 20% made more money than the 25% value. This is caused by the fact that often, for a given value of f, this method of money management can suggest taking something like 3.2456 contracts. Since this is not feasible, it is necessary to round down. The reason we round down rather than up, is because, if we round up, then we are trading at a value for f that is greater than what was selected. And, when we trade with greater values of f we increase the risk, but not necessarily the return. Since the reality of trading forces us to round down, there are cases when the effects of the rounding are not equal. As a result of this situation, it is not uncommon to find that 31% is the optimal value for f, but using 30% the trading system actually makes more money historically. Moving into the future, it would be best to use 31% for actual trading, because the more trades there are in a sample, the more likely the highest profit value will converge with the optimal value for f.


Summary of Money Management Techniques

As previously outlined, usually there is more than one way to improve a trading system with money management techniques. It is important to note that often it is initially very hard to tell which money management technique will work the best, with any specific type of trading system. There are only a few clues to tell traders what works the best, such as the Z-sore and related methods. However, even these methods need to be thoroughly tested by traders. The only way traders can possibly know what works best for their trading system and their personal goals/needs is to test out the system with all of the different money management techniques and scenarios.
Any one of the techniques can dramatically improve the profitability and reduce the drawdown for the right trading system. For the wrong trading system, it can have the opposite effect. At the time of this writing, little research has been done to correlate the different types of trading systems with particular money management techniques/approaches. The authors are planning on doing more research into this subject area but in the meantime it is up to the users of the kNOW Program to thoroughly test their own trading systems to determine what works best. This is a good example of how much more knowledge is needed to be acquired about using our money

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wisely and the arcane subject of money management.


Using Optimizations

This section will be brief, since most experienced traders either know or ignore the
facts about optimization.

For most of the different money management techniques discussed, it is possible to find the optimal values. For example, X% is the perfect percentage of the account to risk on each trading opportunity or X and Y are the perfect values for using a crossing equity curve approach to money management. Knowing these different values is important to traders. However, far too many traders expect their systems to perform the same in the future as they do in the "optimal" past. This just isn't the case.

Optimal values are important because they give traders an idea of about where they need to be, but they are poor indicators of the future. The best way to determine the success of a particular technique/approach is to try it out on several different data sets.
When traders are looking to pick the best value for a particular money management technique, it is best to look at all the values around the optimal value and select the one that is most in the middle, of the good values. Consider the following table:

Value Profit
1 $ 100
2 $ 150
3 $ 200
4 $ 300
5 $ 500
6 $1,700
7 $1,200
8 $1,500
9 $1,300
10 $2,000
11 $ 400
12 $ 600

In the table above, it is clear that the optimal value is 10 ($2000). However, if one considers the other good values in this area, values 6 through 9 are also worthwhile. Under these circumstances, traders will have more reliable results if they use 8 as the value in real-time trading. It is not the optimal value, but it will offer the most security in terms of the variably of the results.

This method of selecting an optimal value should not be used in lieu of doing testing on additional data sets, but it can direct traders to the most secure value to use.
(The only exception to this is probably the Optimal f value. Please consult that section of this book in order to determine how to pick the optimal value for f.)


Before Comparing Management Approaches, Know What You Want

Many of us have heard the joke, "You want to lose 10 pounds of ugly fat? Cut your head off." In a strange way, this kind of thought process applies to money management. There is an aspect to money management that is not something you can think about, it is something that you feel about. This section has a lot to say about values, but nothing about numbers, trades or statistics. Additionally, we will only discuss profits in terms of happiness and peace of mind.

Before a person can really dive into selecting the correct money management approach, there are a couple of steps that need to be completed.

· Establish your investment goals and limits.
· Develop realistic expectations for your trading system and money management combination.
· Reconcile the two.

The vast majority of this book and software deal with steps two and three. This is the only chapter that deals with step one. It seems reasonable to expect most traders to read through this chapter academically and never take the ten minutes that are necessary to evaluate what they really want in a system. The exercises below are designed to move this chapter from an academic curiosity into reality.
Far too many traders use money management methods they are barely familiar with. Far fewer traders use money management methods they are comfortable with. Fewer still are the people who are happy about the money management choices they have made. This is because most traders very seldom or never, make choices about money management or what they want. Knowing your own personal limits is the first step in picking what is right for you. It is also the most powerful tool for doing what is right for both you and your trading account.

Let's take a little different approach to explaining why it is important to identify your limits in advance. Have you ever seen a friend lose all their money trading, all of it, including their house? It has to be one of the most sobering and scary things to watch. The main reason people fall into these traps is because they have not set up the boundaries necessary to effectively manage their money. (Of course, there are other reasons also.) The reason traders puts in stop loss orders is to protect the capital in their accounts. Why not have the same mechanisms for the total account. For example, "If I lose $XXX, then I quit."

On the positive side, "When I make "$XXX, then I will take $XXX out of the account to buy a new sports car." The horror story above was meant to scare casual traders, but fear of the negative repercussions is only one reason to go through this exercise. On the other hand, there are many very positive reasons to make these kinds of decisions in advance. Making these kinds of decisions in advance can relieve the anxiety for traders. Additionally, these kinds of goals can keep traders focused on the markets and their accounts in a positive way.

As final thoughts, keep in mind two things:

You will probably never find a perfect system. (A system that is more reliable than the US post office, makes a fantastic profit and is easy to trade.) You probably will find a good system, or at least, an OK system. Many very successful money mangers are successful because they know how to effectively use a couple of OK systems. In short, try to have realistic expectations.
The best traders in the world are the ones having the most fun. The best money management technique/system is the one that gives traders the greatest peace of mind. It is important to make money, but you are only on this planet once.

Please give some thought to the following questions and please take the time to enter your responses. This is a simple but very important exercise.

What is your profit goal for your trading account?

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How quickly do you want to achieve this goal?

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How much are you comfortable losing on one trade?

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How much of your trading account are you comfortable losing, before you stop?

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Do you ever intend to be a professional money manger?

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If so, what professional risk/reward goals do you have?

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It would be wise to revisit this chapter after you have had an opportunity to look at the effects of the different money management techniques/methods on your trading account.

With clear and stated goals, you are ready to Compare Money Management Approaches.


How to Compare Money Management Approaches

The previous sections have spoken about different kinds of money management techniques and approaches and how they can effect the results of a trading account.
This section discusses some of the ways for analyzing these results, with the aim of giving traders the methods to select the best approach. It also discusses some of the hazards of using a particular type of analysis, so traders may avoid common mistakes when deciding on a particular system.

In addition to helping traders pick the best money management technique(s), these methods work equally well in helping traders decided on which trading system to use. These methods include comparing results on the basis of:

1.The total profit
2.The drawdown
3.The profit / margin ratio
4.The profit / drawdown ratio
5.The profit / time ratio
6.The percentage of winners
7.Z-score and Confidence limits
8.The Optimal f
9.The probability of ruin

Each of these methods can give the user a little different perspective on the results of a trading system and/or money management technique. On the flip side, each of these methods also has limitations. In all likelihood, traders will find it necessary to use several of these methods to find the technique that works best.

It is probably important at this stage to define the word "best." The problem is that "best" has two definitions:

1.It is the highest reward to risk ratio. The optimal asset allocation where capital grows the fastest with the smallest amount of risk.

2.It is the method that maximizes profit within levels of risk that are acceptable to traders.

These two definitions are not always compatible with each other. The optimal risk/reward ratio may have too much risk involved for small traders/investors. For example, traders may find by doing the Optimal f analysis, they should risk 25% of their account for the fastest equity growth. However, this may put them in a position where the probability of ruin is high enough to warrant concern. In cases like this, traders would have to choose a non-optimal value that corresponds to an acceptable amount of risk.
With this in mind, definition number two becomes our working definition. It is the seconddefinition of how the word "best" is used through out this section.


Comparing Results on the Basis of Total Profit:

Total profit is often the most intuitive way to compare results. If you were offered either a ten-dollar bill or a twenty-dollar bill, you would probably pick the twenty. The same applies to systems. Knowing that trading system X made $10,000 profit and trading system Y made $20,000, most traders would choose system Y.

Profit data is the easiest data to get on a system. It is important to remember to add commissions and slippage to your calculations. Many novice system developers will omit or underestimate commissions and slippage. For example, if a system trades 100 times and earns a $5,000 profit, if commission and slippage ($75 per trade) are added to the equation, the system actually loses $2,500. It is also important to note that while commissions may be similar for different commodities, the chance of getting a bad fill is not. Traders should account for larger slippage in markets that have a low volume or are fast moving markets. This is particularly true for traders that do spreads. They can get caught in the low volume period of the forward contract when entering and the low volume period of the near contract while exiting. The slippage values should also include some "insurance" for the possibility of being caught in a gapping or limit move.
Only when all of these costs are calculated into the equation should traders begin to consider evaluating the profitability of a system.

Evaluating trading systems on the basis of total profit can be valuable, but since most high return systems include a large amount of risk, it can expose the traders' accounts to unacceptable losses. For some traders a 50% drawdown may be OK, for others it's not. Large drawdowns can effect ones account, mental health and track record. It is possible to have a highly profitable system without large drawdowns. But as a general rule, systems achieve greater profit at the expense of greater risk.

Also, comparing results on the basis of total profit doesn't tell traders many things. For example, traders would have no idea how the margin was allocated, how efficient the system was in terms of time in the market, etc. These kinds of factors can play heavily into the viability of a trading system. So, in this respect, evaluating a trading system on the basis of profit is taking a very narrow perspective on that system.

It is impossible not to be concerned or look at the profitability of various systems. After all, that's why people trade, to make a profit. On the other hand, many traders should do more to down play this method of analysis, since there are many important things it does not tell them about their systems. Analysis on the basis of profit is a valuable tool only when it is combined with other methods and should not be trusted as the sole form of analysis.


Comparing Techniques for the Smallest Drawdown (Smoothest Equity Curve)

As most traders know, the markets are run by Murphy... As Murphy would have it, almost every system runs into its drawdown period shortly after its inception. For traders that have little experience with drawdowns, comparing trading systems on the basis of the smallest drawdown might be the superior method for selecting a system that works best with the their personality. (Often margin is added to this figure because it represents the total capital necessary to trade a system. However, adding margin into the total equation does not reflect the actual amount the traders might lose.)

The drawdown period for a system is the largest drop in account equity from a peak in the account to a valley. The drawdown period can span across winning periods, to connect large losing periods, to form a large account decline. There are two forms of drawdowns. Neither one is the "correct" form, but traders will find they are usually pulled to one or the other.

1.Largest drop in equity, in terms or percent.
2.Largest drop in equity, in terms of dollars.

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The following graph shows an example of how these different kinds of drawdowns can appear at different times, in a trading system's life:



These two types of drawdowns appeal to different types of traders. What primarily separates these two types of traders are their professional goals. Traders interested in becoming fund managers, or other types of trading professionals, would be wise to limit their drawdowns to around 20%. Most successful professional traders have less than a 30% drawdown. Funds that have large drawdowns tend to scare off investors. For institutional clients of a fund, consistency of results can often supersede the return of an account in importance. Additionally, it's bad press. The drawdown is frequently calculated when magazines are comparing different fund managers.

For traders who do not intend to be money managers, the maximum dollar value of the drawdown becomes more a thing of personal taste. What are you willing to bear? (No pun intended.) Some investors are willing to risk a large percentage of their expendable capital on trading, while others are only trying to get a good return on their capital. In either case, it's a personal decision.
Systems analysis on the basis of the smallest drawdown can be very important to traders for another reason, mental peace. It is easier to stick to a system that does not have large losing periods. Many traders fail because they do not stick to a well-tested system. Having a system with small drawdown periods can make it easier to stay with the system during the hard times.

The only real disadvantage for evaluating trading systems on the basis of drawdowns, is profit. Often limiting drawdowns means limiting the risk. Limited risk usually translates into limited profit. Contrary to popular belief, it is OK to limit the profitability of a system. Often, professional traders limit the risk to their accounts and forgo potential profits at the expense of assured consistency. There sometimes seems to be this testosterone/ego thing about having the most profitable system. The same thing applies to people who like to dive off high places into water. It is good for getting an adrenaline rush or a "Wow" from the audience, but wouldn't you rather let someone else do it, while retiring to your hot tub? To pull together this analogy, it is often more comfortable to grow an account slowly and safely than to take the large risks needed to achieve maximum account growth.


Comparing the Profit/Margin Ratio

Using a profit/margin model to evaluate systems is often the technique used by advertisers of trading systems, when stating profit results. This usually is not the best or the most accurate way to represent systems. Since, as stated above, many of the high yield trading systems have large drawdown periods, thus making the entire system unacceptable to most traders. The same system, being analyzed by this method might seem impossible to pass up, since a margin/profit ratio usually looks pretty good. Who wants to turn down a system returning 300%? Often commercial trading systems of this type are targeted for a particular commodity; hence, the results can be skewed by the margin requirements for that particular commodity. A trading system making the same profit in the S&P 500 as in Soybeans, would look better in Soybeans due to the lower margin requirements. This combination of facts can frequently make the profit/margin ratio a misleading number.

Despite what was said above, comparing systems on the basis of the profit/margin ratio does have some utility to traders. It can help them to know if the capital in their account is being leveraged correctly. Simply put, the margin required to enter a particular trade is capital that cannot be used to enter new opportunities. This money could be used as margin in other systems or as risk capital for new entry signals. Analyzing different systems on the basis of the profit/margin ratio allows traders to maximize the utility of the capital in their accounts. Given that a trading system will earn the same amount in two different commodities, it is reasonable to trade the commodity with the smallest margin requirement. This approach will allow traders to enter more trades and/or for each trade put on more units/contracts than they might have been able to do trading the instrument with the larger margin requirements.

Of course, developing strategies that limit the commitments to margin, may not be suitable for all traders. For professional money managers, margin is usually of little concern, since only a fraction of the account is being risked at any one time. In cases like this, it is not necessary for the money mangers to maximize the utility of their margin capital. In fact, doing so may work against the traders' overall risk/reward goals by enticing them to take more trades than would be feasible to meet certain risk criteria.

On the other hand, for small and aggressive traders, leveraging margin requirements may allow them to get the best bang for their buck. To give an example, for small traders it may be possible to take only one contract in the S&P due to the large margin requirements ($12,000+ or -), with a potential reward of $3,500 for the trade. If these traders considered other markets, for example the Canadian dollar ($400+ or - required margin), they may be able to enter thirty times as many contracts. Each contract may have the potential to make only $250, but when you add them all up, you would still make more money than trading just one S&P contract.

Overall, this method of analysis may have some utility to traders, but it is important to remember the things it's not telling you. It says relatively little about the risk to the account and does not even give a clear picture on the profit of the account, since margin requirements are very diverse. It can give a picture of how effectively the margin is being used by traders, but not even this applies to all the traders' needs.

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Comparing the Profit /Drawdown Ratio:

Evaluating a trading system based on the profit/drawdown ratio is perhaps the most useful way to compare two systems. It gives traders a solid base to compare different systems by standardizing the risk reward aspects of different trading systems/money management techniques. This standard is easily compared across both trading systems and commodities. Additionally, this method gives traders a simple view of what kinds of risk to expect with certain profit objectives. In this sense, traders can find a system that has a suitable profit/drawdown ratio and begin to customize the results of the system to their needs.

Consider the following example:



This method allows traders to see that systems A, B and C all have a profit to draw down ratio of 2. This is evident even though the profit, drawdown and the risk per trade are different for each system. In this sense, traders can say these systems are similar, in respect to risk/reward expectations. Additionally, this method has the advantage of standardizing all three systems across two of the most important features to look for in a system, profit and drawdown.

This approach is a very powerful method for comparing trading systems to each other while still allowing traders additional tools for optimizing a particular system. If traders also have the appropriate data on the drawdowns, it may be possible for them to scale their systems up or down to meet the risk goals for their accounts. This can be achieved while maintaining the same relationship between profits and drawdowns.
Consider system B above, this system made $1,000 on an average risk of $50 per trade. Knowing this, traders may be able to take four times as many positions in the market for every trading signal. In essence, doing this quadruples the traders' profits and drawdowns. Since this system had such a low drawdown to start with, a draw down that is four times as large, is still reasonable. On the flip side, traders are often able to reduce a system using the same process. Traders could take half as many positions, and still maintain the same profit to drawdown ratio. Using these kinds of processes allows traders to scale their systems up or down in order to better accommodate their risk/reward objectives.

However, there are also some disadvantages to using this type of analysis on trading systems and money management techniques/approaches. The most important of these is that it does not give traders any insight into drawdowns, in relationship to the account size. This is evident from the examples above. Systems A and C have large draw downs in respect to their account size. It is possible traders would enter into a draw down period ($5,000) when they are just beginning to trade their $10,000 account. This would be devastating to many traders.

When comparing trading systems on the basis of profit to drawdown it is best to compare systems that have been traded in approximately the same time frame. If a good system typically experiences $10,000 of drawdowns per year and $20,000 in profits per year, this system has a profit to drawdown ratio of two. However, if you had two years of data, you may find that the system made $40,000 in profit, but still had a drawdown of $10,000. This would give you a profit to drawdown ratio of four. Three years of data may give a profit to drawdown ratio of six. Since the drawdown often does not grow substantially in magnitude over the years, additional years of data frequently improves the ratio value.

Analyzing a trading system on the basis of profit to drawdown can be a valuable tool for comparing systems that have very different results. It also gives traders a convenient way to examine how to scale a system to their particular needs. However, this method can also leave traders in the dark when considering the drawdown to the account, since the account size is not calculated into the formula.


Comparing the Profit/Time Ratio

Although time analysis is not common to most traders, it can be an important statistic to look at. There are two main advantages for evaluating a system on the basis of time:

1.It allows traders to find systems that have less "global" risk, by finding systems that are exposed to the natural variability of the market less than other systems.

2.It allows traders to find systems that will use the capital in their accounts in a more efficient manner.

When looking at the big picture, it is reasonable to say that given two equally profitable trades, the one that is in the market longer is usually exposed to additional risk. An example of this type of risk, is the possibility of losing money due to an unexpected market phenomena such as, a gap opening of the price, a surprise weather pattern that effects the commodity or odd economic reports. Any one of these market phenomenas (and they happen more often than one expects) can quickly change a winning position into a losing position. In this sense, system traders will want to minimize the amount of time their system is in the market.

The risk of being exposed to the market is very hard to quantify, but it does exist as a real concern. In this respect, minimizing this form of risk, is a part of an effective money management approach.

In addition to this, time analysis can help let traders know if they are using their funds in an efficient manner. This may not apply to all traders, but most professional traders, who have a large amount of capital under management, can benefit form knowing how their money is being used.

The argument here is similar to the profit /margin method of evaluating a trading system. With this approach it is important to note what is the average time it takes for a trade to move into a position where it locks in the fixed costs or exits the market at a loss. A certain amount of capital is required to support a position until it has moved in the traders' favour, and they can lock in enough profit to cover the fixed costs (margin, risk capital, commissions, slippage and, if necessary, insurance from limit moves against the position). This "support capital" is money that cannot, or should not, be put into other opportunities, until traders have locked in a profit on their positions.

To illustrate, consider the following:



It should be fairly obvious that given the choice between these two systems, traders should use system B, since it is in the market half the time of system A. Assuming there are the same number of trades in both of these systems, system B has half the market exposure that system A does. If system B is in the market half as much as system A, it may be possible for traders to expand the number of commodities that are monitored by the system and enter twice as many trades with system B than with A, and with the same account size. This approach allows traders to expand the number of positions taken, without increasing the amount of capital that is dedicated to margin. Of course, this depends on the system. It may or may not be possible to take more signals, due to other limitations on the traders. At least in the theoretical sense, applying this kind of analysis can increase the percentage of risk capital traders have in an account. In real time this may or may not have an actual application for the traders.

Application of this kind of time analysis to increase the account's efficiency, will be most useful with systems that are expandable. By definition, expandable means a system that can be expanded in order for traders to get additional trading signals. A good example might be systems that span over multiple commodities. This type of system may allow traders to introduce additional trading signals to the system by using the system on additional commodities. In other cases, this type of analysis may not be appropriate. For example, consider traders who have specialized day trading systems for the S&P 500. These types of traders do not have a method for getting additional valid signals, since their system is customized specifically for the S&P 500. Additionally, with a day trading system, the traders may not have enough time in a day to execute additional trading signals.

Analyzing a system for the profit/time ratio can be a valuable method if the traders have either limited capital and/or the ability to increase the type of commodities they are trading. This method, like the profit/margin method, will show traders, which of two similar systems will maximize the utility of the money in their trading accounts.

This method of evaluation is especially useful if traders have a limited account size and cannot take all the signals generated by a system that monitors many commodities.

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However, there are a couple things to watch out for if you use this kind of analysis:

1.This kind of analysis is not always relevant. If the difference between the average time in a trade for two systems is less than twenty percent, it is probably not necessary to worry about. (Twenty percent is a rule of thumb, and can be effected by the size of the account and the type of trading system.)

2.In terms of optimizing the margin efficiency, make sure it is relevant to your system. As mentioned above, if you do not have a method for increasing the number of signals, there is no way to increase the margin efficiency for your system.

One last thought, the profit over time ratio is not a static number. It can, and does, change from month to month. If traders see a change in the profit over time ratio, it can often be an early signal that the market is changing. For example, it is reasonable to see a change in the profit over time ratio when the market is changing from a trending to a choppy market.


How Important is the System's Percent Win Ratio?

In the trading systems the authors have found and used, the reliability of the winning percentage of the system was not a major factor in selecting it over other systems. There are trading systems that win 65% of the time and have the same profit and draw down as trading systems that win only 35% of the time. To some extent, given that most of the other parameters can remain the same, choosing a high reliability versus a low reliability can be a function of taste. Some people prefer trading systems that win frequently, others prefer to go for the big win. Ironically, there are many traders who have good systems that take a reliable profit by exiting the market early in a trend.
These are also the same traders who often kick themselves for the rest of the trend, due exiting too early, even though they have a good system.
Many traders tend to focus on the percentage of winners. There seems to be an assumption that systems that win more often make more money. In some instances this is true. However, in many instances it is not. It is definitely not a conclusion to assume without thorough analysis of the system. It is the authors' experience, that most of the trading systems that traders will find, will only win approximately 50% of the time. Additionally, many money managers have systems that win more like 35% of the time. (Part of the reason for this is because most money managers select trending systems.)
What is strange is that most traders/investors know that professionals use lower probability systems, but their eyes bug out and their mouths start salivating when they hear about an 85% winning system. The simple fact is, the profitability of a system is not directly related to how often it wins.

While reliability is not a major factor in the viability of a trading system, it can have some major effects on the results of the system. Often times, the percentage of winning trades tells traders much more about the potential for loss than gain. In this respect, looking at the downside potential for a system is important. Let's look at a trading system that has a 50% winning percentage. The following table reflects the possible outcomes after ten trades:



Looking at this table, it is clear that traders with 50% winning systems have a 17.2% chance of getting seven losses or worse in a sample of ten trades. (This is calculated by adding the bold figures together.) This level of confidence may not be acceptable to all traders, especially in situations where they have limited capital. Another way of explaining this phenomenon is that after ten trades, there is a 17.2% chance that a 50% wining system will appear as a 30% winning system. (In fact, there is a 75.4% chance a 50% winning system will appear to be anything but a 50% system after ten trades.) In this sense, it can become very hard to trust the value for the percentage of winners in any trading system.

Another issue with the percentage winning value of a system is that it can effect the worst run of a system. From a statistical point of view, the reliability of a system influences the maximum number of consecutive losers a system can be expected to have. The maximum number of consecutive losses can become relevant to traders because it is often associated with the drawdown period of a system. To give the reader a sense about what kind of losses to expect in a row, consider the following table. It contrasts the winning percentage of a system and in turn the probability of getting a run of losing trades in a row:




To use an example from this table, if traders have a 50% system, for any run of three trades, they will have a 12.5% (bold) chance of getting three losses in a row. This table illustrates how the percentage of winning trades can effect the drawdown period for a system.

All things considered, this table is probably more valuable to traders mentally than to their accounts. It is valuable for traders to have realistic expectations of the worst run in a system. It is often during these periods that traders feel their system has "broken down." Unfortunately, it is during this "broken down" period that many traders give up on good systems.

Therefore, is the percentage of winners an important statistic to look at? On one hand, it can help traders have reasonable expectations about the performance of a system. On the other hand, the profitability of a system is only partially linked to the reliability of winning trades. So, the truth lies some where in the middle.


Z-Scores and Confidence Limits

Looking at the percentage of winners and losers only tells part of the story when it comes to trading. This kind of analysis assumes that all the trades in a sample happened independently of each other. A good example of this kind of independent relationship between examples (trades) would be a coin toss. If you flip a coin, there is a 50% chance you will get heads, regardless of the result of the last coin toss. For independent situations, past events do not effect the probability of current events.


The markets, however, can have a dependency between trades, where the outcomes of the trades effect each other. For example, the fact that a system has lost on a long trade can effect the chances of winning in the future. A good analogy of this kind of situation is most card games. Once a card is played, and it isn't returned to the deck, it will effect the probability of the other cards to be played. However, the next card to be played is still a random occurrence. In this sense the way a deck is played is both random and dependent on past events. This type of situation can apply to trading, where past events effect the future.

Traders may find systems where the wins or losses come in streaks. Conversely, traders may also find that after a win they usually receive losses, or vice a versa. It is also possible to find dependency in the profitability of the trades. For example, traders may find that highly profitable trades are followed by low profit trades, or they may find the profitability going in streaks.

The Z-score is a statistical value that helps traders analyze the dependence between trades. The Z-score is calculated by comparing the number of runs there are in a set of trades, with the number of runs that would be expected statistically. This number is then usually transformed into another value called the Confidence limit. The Confidence limit is expressed in terms of a percentage, such as "90%." However, when the value is expressed this way, it can be a bit confusing to laymen of statistics. We are usually conditioned to consider a 90% value as pretty reliable, but this is not the case when examining the Confidence limit. The reason for the confusion is that unless a system has a Confidence limit of 94% or better, it is probably not a very reliable conclusion. It is possible for traders to make some valid conclusions about a trading system if the Confidence limit is 90-94%. However, usually in this range, it is more likely the traders are only viewing a statistical anomaly, and the system does not have any exploitable dependence.

In order to calculate the Z-score and the Confidence limits, it is necessary for traders to have at least thirty trades in the sample. This is due to the calculations relying on the standard deviation of the system. (The Confidence limit is actually the amount of examples one would statistically expect within X standard deviations. For example, one standard deviation represents the area where 68% of all the events will fall. If the Z-score was one then the confidence limit would be 68%.)

The Confidence level is only a positive number. However, the Z-score can be either positive or negative. Each has a slightly different meaning to traders.

1.A negative Z-score means there are fewer streaks in the sample of trades tested than would be expected statistically. This means winning trades tend to follow wining trades and losing trades tend to follow losers.

2.A positive Z-score means there are more streaks in the trading system than would be expected. This means winning trades tend to follow losing trades and vice a versa.

If traders find a system with a reasonable Confidence level, it is possible to begin to exploit this aspect of the system. The rest of this section will focus on two examples to demonstrate the possible application of this type of analysis.

1.The first example trading system has a positive Z-Score.
2.The second example trading system has a negative Z-Score.

Keep in mind these are select examples. These types of calculations can be used with and/or applied to other techniques of money management equally as well. The point of these examples is NOT to show which is the best method, but to stimulate thinking on this subject.


Example 1 - Positive Z-Score

These are the basic results of a system before any money management method is applied. Basically it made $8,455 on a drawdown of 8%.

System Information:
Total Profit : $ 8455.00
Gross Profit : $ 18765.00
Gross Loss : $(-10310.00)
Worst Drawdown on a Percentage Basis
Drawdown as a Percent : -08%
Drawdown From : $ 36025.00
Drawdown Dollar Value : $(-2860.00)
Drawdown To : $ 33165.00

Number of Trades : 45
Number of Wins : 24
Percent Wins : 53%
Number of Losses : 21
Interdependence of trade results
Z score : 2.15
Confidence Limit : 96%

As you can see from the values given, this trading system has a positive Z-score of 2.15. This translates into a confidence limit of 96%. Having a positive Z-score means in this system, wins tend to be followed by losses and via versa. Based on this information, it would seem reasonable to try a Martingale or pyramid money management approach to the system. For example, after traders experience a loss, they will take additional units/contracts on the next signal as a way of recouping losses and/or increasing the system's overall profitability. The following table shows a few methods associated with using this approach to money management:




As this table illustrates, application of the Z-Score can have a dramatic effect on a trading the system. If you would please look at example A, you will see the normal results from this system. If traders had used a Martingale method like in example B, the designated trades would have reduced the drawdown to the account by more than 50% and doubled the profit. Additionally, if traders had used a method like in example C, they would have quadrupled the profit of the system, while only increasing the overall drawdown to the account by 1%. This has moved a fairly average system into a very positive system.

At this point it is often easy to get trade dependence and independence mixed up and say something like, "If I'm doubling up on losing trades and I lose four trades in a row, that would be a loss of fifteen units/contracts! What are the chances of getting four losers in a row?"

Naturally we would grab our calculators and find that for a 53% system, the odds of getting four losing trades in a row is approximately 11%. But this is not true. The chances of getting four losers in a row is less than 11% because we know there is a dependency between the trades and that winners follow losers and losers follow winners.

In summary, a positive Z- score can easily be exploited by using a pyramiding method to correct for losers and winners. Aggressive traders, who have a positive Z-Score for their systems, can turn this fact into cash if they apply proper money management intelligently.


Example 2 - Negative Z-Score

The following results are for a different system with no money management applied to it:

System Information:
Total Profit : $ 3045.00
Gross Profit : $ 17505.00
Gross Loss : $ (-14460.00)
Worst Drawdown on a Percentage Basis
Drawdown as Percent: -22%
Drawdown From: $ 28210.00
Drawdown Dollar Value: $(-6300.00)
Drawdown To : $ 21910.00

Number of Trades : 41
Number of Wins : 20
Percent Win : 49%
Number of Losses : 21
Interdependence of trade results
Z score : -2.21
Confidence limit : 97%

Basically this trading system made $3,045 on a 22% drawdown and has a negative Z-score. This means it has fewer streaks than one would statistically expect from a set of trades. (In other words, the wins and losses tend to come in runs.) One method of maximizing this approach would be to use crossing equity curves to insure that the system is in the market during the good phases and out when it's bad. (Please reference the section of this book on crossing equity curves for more details on this method.)

The following table illustrates the performance of a trading account using different lengths for the moving averages, for the cross over.




As you can see from the table, this approach had a dramatic effect on the account. Consider the bolded combination above, it made $9,470 with only a 7% drawdown. This is an incredible improvement over the results from not using money management. ($3,045 on a 22% drawdown.) Basically, it tripled the profit of the system and reduced the drawdown by two thirds. This is effective money management! Additionally, for a system that has a good negative Z-Score, almost any two averages will work to improve the results of a system.

For systems that have a negative Z-Score, using crossing equity curves is a natural fit for money management. The crossing equity curves technique is an approach designed especially for catching the winning and losing waves in a system, which is what a negative Z-Score implies. Other techniques may also work as well. For example, a pyramiding method that increases the risk after a win and decreases after a loss would also work suitably.

If you have read this book in a sequential manner, then you have already been through the sections describing the "Amount Traded on a Win or Loss" and "Crossing Equity Curves". Both sections warn traders about the pit falls of applying these two forms of money management when there is a low Z-score and Confidence limit. The examples given in these sections also show how the results can be extremely sensitive to optimization, if the Z-scores are too low. If the examples in the other sections did have reliable Z-scores, it is reasonable to assume they would show results similar to the ones above. The examples in the other sections of this book are meant as a warning to traders who blindly try to exploit a trading system in this manner, without having the proper knowledge about the anomalies and characteristics of the system in question.

Knowing the Z-score about a trading system is one of the best things traders can do. It will allow traders to squeeze additional profit out of a system, without changing any of the parameters of the trading signals to enter the market. It is also one of the most direct ways traders can turn knowledge into money.


Optimal f

Some traders believe the Optimal f is the single best way to analyze a trading system. Others never use this method and do just fine without it.

When comparing the Optimal f value of two systems, all other things being equal, it is wise to pick the account with the larger value. The system with the largest Optimal f value will have the potential to grow the quickest, if the proper Optimal f money management technique/approach is used.

The Optimal f graph is usually displayed as an arch, similar to the one shown below. The optimal value is the peak of the curve. This peak is usually called the Optimal f. (Other places on the graph are usually called, "other values of f".)

In this optimal value lies the tools for growing an account the fastest. But it is necessary to go through a few steps before the data is truly useful to traders. To apply the Optimal f and find the optimal value to risk for an account, follow the steps below:

1.Establish the account size. This is the starting account size and should be obvious to traders.
2.Establish the size of the single largest losing trade. Traders will need to look at the trades to figure this out.
3.Get the Optimal f value from the software.
4.Divide the largest loss by the Optimal f.
5.Divide the account value by the results of step 4.
6.Repeat after each trade.

The results from step 5 will tell traders how many units/contracts to take on each trading signal for maximum growth to their accounts. The following traces through the aforementioned steps with a real example:

1.The account size is $25,000.
2.The largest losing trade is $2,050.
3.The Optimal f is 27%.
4.$7,592 = ( $2,050 / 0.27 ).
5.3.29 = $25,000 / $7,592.
6.Repeat for the next trade.

In a perfect world, traders would enter the next trading signal with 3.29 contracts. Since it is not a perfect world, they need to round the number down to three. Due to the necessity to round down in real-time trading, some traders may find that a value near, but not the optimal, may produce the fastest gain to an account.

Although analyzing different trading systems on the basis of the Optimal f value gives traders insight into which system has the greatest potential for growth, it also has some disadvantages. The Optimal f does not give traders any insight into the risks of using this approach. In many cases, having a high Optimal f, and applying this form of money management to maximize an account, can leave traders susceptible to large draw downs or greatly increase the probability of ruin for an account.


Probability of Ruin

The Probability of Ruin (POR) is the "statistical possibility" a trading system will deplete an account to the point of ruin, before achieving a dollar level deemed as being successful. Ruin is defined as the level of an account when traders will stop trading. Knowing this value can be very important to traders. The POR illustrates to traders the statistical possibility that their trading systems will naturally, by the laws of probability, drift to a point of success or ruin.

To calculate the Probability of Ruin, traders must slog though a horribly long equation. (However, just let the kNOW Software do the math.) In short, the following represents some basic outcomes/elements of the equation:

All other things being equal:

1.The greater the size of the average wins, the lower the POR.
2.The larger the average risk per trade, the greater the POR.
3.The larger the initial account size, ,the lower the POR
4.The higher the percentage of winning trades, the lower the POR.
5.The smaller the account, the greater the POR.

Some authors, have said that the probability of ruin (POR) is not a relevant concept because it does not tell traders anything they can capitalize on. In this sense they are correct. Additionally, it tends to be a small value in winning systems. However, all other things being equal, when given the choice between two trading systems, pick the one with the lowest POR. Also, the probability of ruin should be a value that many small investors/traders look at. Since small investors/traders usually have small accounts, the aggressive forms of money management methods can have PORs that deserve attention.

For the most part, PORs tend to be low. It is usual to see trading systems that have 0-5% for their PORs. For trading systems that work normally and have a reasonable account size, this is what should be expected. The second most common POR is 100%, meaning that failure is almost completely guaranteed. These tend to be trading systems that would fail under most circumstances anyway. Every now and then you get something in the middle range.

In summary, the POR is a method/value that should be curious to all traders, but it usually offers little additional insight, since most of the time the values are below 5%. However, under some circumstances, it can show traders they have a significant risk of ruining their account. When traders are faced with this reality, it means they are risking far too much on each individual trade. With this knowledge, traders should then limit the risk per trade, in an attempt to bring the POR down to an appropriate level. By trading small portions of their accounts, traders are giving themselves, in essence, more chances to win.


Conclusion- For Now

It is the sincere desire of the authors that through the reading of this book and the using of the kNOW Software users of the kNOW Program will become not only very successful monetarily but also very happy traders and investors.

Trading/investing is not easy, even if all you have to do is throw old chicken bones over your shoulder to make a decision to get in or out of the market. Therefore, we hope the kNOW Program will give you the knowledge and the initial foundation to make sound money management decisions and the desire to learn more about the arcane world of "risk management."

It is the authors intent to continue updating this book and adding new money management techniques/approaches and options as they become known and tested.
These new ideas/methods will also be included into the kNOW Software, as they become available. However, in order to expedite this updating effort we will need all the help we can get, so please, forward to us any ideas, questions or new techniques you would like to have us explore and add to the Program.

Thank you again for your time and effort in reading this book and we hope it has been a rewarding experience for you. Creating it has been a real pleasure.

缩水基金

Money Management   


In a chapter entitled "The Secrets of Successful Trading" in Street Smarts, Fernando Diaz concluded:

"Successful traders have a larger edge and better money management than unsuccessful traders. Unlike popular
belief however, this study shows that the smaller edge of successful traders is not the cause of their failure.
Traders' failures can be explained almost exclusively by their poor money management practices."

When trading stocks or commodities the importance of Money Management is underestimated by a lot of traders. It is of much more importance than entry and exit decisions (=timing decisions) will ever be.
Very few indicators are better than a coin toss, and if they are, the edge is eaten up by slippage and commission.

Money Management is also sometimes called asset allocation, position sizing, portfolio heat, portfolio allocation, cash flow management, trade management, capital management, position management, size management, bet size selection, lot size selection, or even risk control, equity control, and damage control.

Money Management is managing the position size while Risk Management is about managing losses and open profits (unrealized trading returns).

Actually I don't like the term 'Money Management' as it also has a very general meaning (it's also used describing the "process" of saving, these "learn valuable skills" pages, talking about piggy banks and how to teach kids about paycheques).
But 'Money Management' tells a trader that (s-)he should concentrate his research on how to optimize capital usage and to view his/her portfolio(-)s as a whole.

Actually there are (at least) 2 steps to implement proper Money Management:

1) Bet sizing is the determination of what (fixed or non-fixed) fraction of a portfolio's total (or again fixed or non-fixed fraction) equity to risk on each trade expressed in Dollar-, Euro-, Yen-, or Swiss Franc-denominated currency values.

2) Position sizing, on the other hand, is the calculation of how many contracts I should hold in my position, once a trade entry is signaled which basically is a function of the BigPointValue (the number of dollars that a 1-point price move represents) and a rounding algorithm as the number of contracts/stocks can't be traded in fractions and must be cut down to a whole integer.


On my desk there are 5 statistics related books and just 2 on trading. So according to the books next to me my focus on statistics is at least 70% :-). A sound knowledge of statistics is a good start into the Money Management arena.

Here a 10 Money Management lessons, including strategies, hints & tips, source code, etc.
They are copied together indiscriminately from several sources from the Internet, from Trading Software, and Trading Literature.

These lessons won't automatically build wealth, but will bring a wealth of experience and knowledge, which will prove invaluable to you if both understood and applied properly. It will steer the course for your success in the global financial marketplace.

I hope you will find and pick what your trading system is desperately looking for.

If you are too lazy to dig deep to both find and understand these lessons I would advise to either refrain from trading or if you are really willing to learn nothing else, then learn this:

Be bright, give up being right, and
   emphaSIZE on Position SIZE !!! empha
   on Position
SIZE !!!



Disclaimer/Copyrights: © All copyrights remain with the authors.

thomas85

good

价值投资理论

It's far helpful. Thank you very much!