System Quality Numbers and Position Sizing Strategies

In brief, your trading system employs a set of rules that tells you when and how to trade. The purpose of a trading system is to make sure that you can achieve your objectives easily through an effective position sizing strategy.

Your position sizing strategy helps you determine how much equity to risk on every trade. Its purpose is to help you meet your objectives. You could have the world’s best system (for example, one that makes money 95% of the time and in which the average winner is twice the size of the average loser), and you still could go bankrupt if you risked 100% on one of the losing trades.

A position sizing strategy helps you determine how much equity to risk given several inputs: the trading system’s R-multiple distribution, your risk tolerance, the kind of returns you want to make, and your definition of ruin—whether that’s bankruptcy or some level of drawdown.

With a poor trading system, you may be able to meet your objectives, but you are setting yourself up for a hard and potentially frustrating job. However, if you create a Holy Grail system, you’ll find it easy to meet even extreme objectives through an effective position sizing strategy.

How would you know if you have a trading system that easily allows you to reach your objectives through position sizing strategies? There are several ways you could measure this performance, but I’ll focus on a relatively simple method I believe is effective.

Your trading system generates trades that have a distribution of R multiples. What is the relationship of the average of your trade results to the consistency of those results? Scientists and engineers regularly measure the ratio of the signal (that is, music) to noise (that is, static). For our purposes, the trading system “signal” is the expectancy, and the “noise” is the standard deviation of the R multiples. If you look at the ratio of the expectancy to the standard deviation of the R multiples, you generally can tell how easy it will be to meet your objectives by using position sizing strategies. Table 4-1 provides a rough guideline.


Table 4-1 Guideline to System Quality

It’s relatively easy to use standard spreadsheet functions and calculate this ratio for your system trade results. I suggest analyzing your results once you have at the very least 30 R multiples and preferably 50 to 100 R multiples.

In addition to the expectancy and variability of a trading system’s results, there is one other important variable in your system: the number of trades it generates. A system with a ratio of 0.75 doesn’t really qualify as a Holy Grail system if it doesn’t give you enough opportunities. However, if that same system trades 20 times a month, then you truly have a Holy Grail system. It gives you many opportunities to make money.

After a number of years researching position sizing strategies, I’ve developed a proprietary measure of system performance that we call the System Quality Number (SQN). The SQN takes into account several variables. The specific calculation is beyond the scope of this book (although I do cover it extensively in my book The Definitive Guide to Position Sizing). Regardless, let me share a few important observations I have found as a result of my research:

• It’s very difficult to create a trading system with a ratio of mean R to standard deviation of R as high as 0.7. For example, if I take a system with a ratio of 0.4 and add a 30R winner, that single winner actually decreases the ratio because it increases the standard deviation of R more than it increases the mean. For results worthy of Holy Grail status, your system needs a huge number of winners and a small variation in the amounts won and lost.

• It is possible to develop a Holy Grail trading system if you restrict it to one specific type of market. Keep in mind, though, that such a system is in the Holy Grail range only for that particular market type (for example, quiet bull).

You need to understand how your system works in various market types and use it only in the types of markets for which it was designed. This says a lot about developing systems, and it echoes what I said earlier. The common mistake most people make is to try to create or find a trading system that will work all the time. It’s insane to think that any one system will work well in all market conditions. (Buy and hold worked great in the late 1990s and horribly in the early 2000s). Instead, develop multiple trading systems that are close to the Holy Grail level for each market type.

As testimony to the potential of what position sizing strategies can do for your trading results, I received a report from someone a while back. He was trading currencies from July 28 through October 12, 2008, when most people were losing huge amounts of money. According to his calculations, the ratio between the expectancy of his system and its standard deviation was 1.5—that’s double the ratio of what I call a Holy Grail system. Once he realized how good his system was, he started to risk position sizes at levels that are acceptable only with a Holy Grail system.

Table 4-2 shows the unaudited results he reported to me.



TABLE 4-2 Results of Unaudited Holy Grail System

I’ve seen people make 1,000% per year before, but never anything quite like this. However, I’m willing to believe it is possible if he found a system that provided a ratio of an expectancy of R to a standard deviation of R of 1.53, as he indicated by the data he sent me. His stellar return was possible only after he realized that he had a Holy Grail trading system and that he could utilize a position sizing strategy to take advantage of it. As a result, he was able to increase his exposure per trade to a huge level that would bankrupt most traders using trading systems with lower ratios.

Again, I have no verification that the information sent to me was true. I don’t audit trading accounts. My business is coaching traders. This trader, however, sent his e-mail to me as a thank-you note for the insights he got from my advice. Given my understanding of trading systems and position sizing strategies, I’m willing to believe the results are possible.


Quiet Bull Market

Position Sizing Strategies Are More Important Than You Think

Most people think that the secret to great investing is to find great companies and hold on for a long time. The model investor for this, of course, is Warren Buffett. The model that mutual funds work on is buying and holding great investments, and the goal is simply to outperform some market index. If the market is down 40% and they are down only 39%, they have done well.

If you pay attention to the academic world, you learn that the most important topic for investors is asset allocation. There was a research study by Gary Brinson and his colleagues in the Financial Analysts Journal in 19911 in which they reviewed the performance of 82 portfolio managers over a 10-year period. They found that 91% of the performance variability of the managers was determined by asset allocation, which they defined as “how much the managers had in stocks, bonds, and cash.” It wasn’t entry or what stocks they owned; it was this mysterious variable that they called “asset allocation,” which was defined in terms of “how much.”

I recently looked at a book on asset allocation by David Darst,2 chief investment strategist for Morgan Stanley’s Global Wealth Management Group. On the back cover there was a quote from Jim Cramer of CNBC: “Leave it to David Darst to use plain English so we can understand asset allocation, the single most important aspect of successful performance.” Thus, you’d think the book would say a lot about position sizing strategies, wouldn’t you?

When I looked at the book, I asked myself these questions:

• Does he define asset allocation as position sizing strategies?

• Does he explain (or even understand) why asset allocation is so important?

• Is position sizing (how much) even referenced in the book?

I discovered that there was no definition of asset allocation in the book, nor was there any explanation related to the issue of how much or why asset allocation is so important. Topics such as position sizing strategies, how much, and money management were not even referenced in the book. Instead, the book was a discussion of the various asset classes one could invest in, the potential returns and risks of each asset class, and the variables that could alter those factors. To me it proved that many top professionals don’t understand the most important, nonpsychological component of investment success: position sizing methods. I don’t mean to pick on one book here because I can make the same comment about every book on the topic of asset allocation I’ve ever looked through.

Right now, most of the retirement funds in the world are tied up in mutual funds. Those funds are required to be 95% to 100% invested, even during horrendous down markets such as the ones in 2000 to 2002 and 2008 to 2009. Those fund managers believe that the secret to success is asset allocation without considering that the real secret is the how-much aspect of asset allocation. This is why I expect that most mutual funds will cease to exist by the end of the secular bear market, when P/E ratios of the S&P 500 are well into the single-digit range.

Banks, which trade trillions of dollars of foreign currency on a regular basis, don’t understand risk at all. Their traders cannot practice position sizing strategies because they don’t know how much money they are trading. They are trading the bank’s money, not a segregated account. Most of them don’t even know how much money they could lose before they lost their jobs. Banks make money as market makers in foreign currencies, and they lose money because they allow or even expect their traders to also trade these markets. They usually expect their traders to trade each day even when there is no good trade to make.

Rogue traders have cost banks about a billion dollars each year over the last two decades, yet I doubt that they could exist if each trader had his or her own account.

I was surprised to hear Alan Greenspan3 say once that his biggest mistake as Federal Reserve chairman was to assume that big banks would police themselves in terms of risk. They don’t understand risk and position sizing strategies, yet now they are all getting huge bailouts from the government.

By now, you are probably wondering how I know for sure that position sizing strategies are so important. Let me present a simple trading system. Twenty percent of the trades are 10R winners, and the rest of the trades are losers. Among the losing trades, 70% are 1R losers, and the remaining 10% are 5R losers. Is this a good system? If you want a lot of winners, it certainly isn’t that good because it has only 20% winners. But if you look at the average R for the system, it is 0.8R. That means that on average you’d make 0.8R per trade over many trades. Thus, when it’s phrased in terms of expectancy, it’s a winning system. Remember that this distribution represents the R multiples of a trading system with an expectancy of 0.8R. It’s not the market; it’s the R multiples of a trading system.

Let’s say you made 80 trades with this system in a year. On average you’d end up making 64R, which is excellent. If you allowed R to represent 1% of your equity (which is one position sizing method), you’d be up about 64% at the end of the year.4

As was described earlier in this book, I frequently play a marble game in my workshops with this R-multiple distribution to teach people about trading. The R-multiple distribution is represented by marbles in a bag. The marbles are drawn out one at a time and replaced. The audience is given $100,000 to play with, and they all get the same trades. Let’s say we do 30 trades, and they come out as shown in Table 4-3.


TABLE 4-3 R Multiples Drawn in 30-Trade Game

The bottom row is the total R-multiple distribution after each 10 trades. After the first 10, we were up +8R, and then we had 12 losers in a row and were down 14R after the next 10 trades. Finally, we had a good run on the last 10 trades, with 4 winners, getting 30R for those 10 trades. Over the 30 trades we were up 24R. That number divided by 30 trades gives us a sample expectancy of 0.8R.

Our sample expectancy was the same as the expectancy of the marble bag. That doesn’t happen often, but it does happen. About half the samples are above the expectancy, and another half are below the expectancy, as illustrated in Figure 4-1.


Figure 4-1 10,000 samples from 30 Random Trades

The figure represents 10,000 samples of 30 trades drawn randomly (with replacement) from our sample R-multiple distribution. Note that both the expectancy (defined by the average) and the median expectancy are 0.8R.

Let’s say you are playing the game and your only job is to decide how much to risk on each trade or how to position size the game. How much money do you think you’d make or lose? Well, in a typical game like this, in which you win by having the most money at the end of the game, a third of the audience will go bankrupt (that is, they won’t survive the first 5 losers or the streak of 12 losses in a row), another third will lose money, and the last third typically will make a huge amount of money, sometimes over a million dollars. In an audience of approximately 100 people, except for the 33 or so who are at zero, there probably will be 67 different equity levels.

That shows the power of position sizing strategies. Everyone in the audience got the same trades: those shown in the table. Thus, the only variable was how much they risked (that is, their position sizing method). Through that one variable we’ll typically have final equities that range from zero to over a million dollars. That’s how important a position sizing method is. I’ve played this game hundreds of times, getting similar results each time. Generally, unless there are a lot of bankruptcies, I get as many different equities at the end of the game as there are people in the room. Yet everyone gets the same trades.

Remember the academic study that said that 91% of the performance variation of 82 retirement portfolios was due to position sizing strategies. Our results with the game show the same results. Everyone gets the same trades, and the only variable (besides psychology) is how much the players elect to risk on each trade.

If the topic is ever accepted by academia or mainstream finance, it probably will change both of those fields forever. It is that significant.

The Three Components of a Position Sizing Strategy

Performance variability produced by a position sizing strategy has three components (see Figure 4-2).5 They are all intertwined, and so it is very difficult to separate them.

The first component is the trader’s objectives. For example, someone who thinks, “I’m not going to embarrass myself by going bankrupt” will get far different results from those of someone who wants to win no matter the potential costs. In fact, I’ve played marble games in which I’ve divided the audience into three groups, each with a different objective and a different “reward structure” to make sure they have that objective. Although there is clearly sizable variability in “within-group” ending equities, there is also a distinct, statistically significant difference between the groups with different objectives.

The second component, which clearly influences the first component, is a person’s psychology. What beliefs are operating to create that person’s reality? What emotions come up?


Figure 4-2 The Three Components of a Position Sizing Strategy

What is the person’s mental state? A person whose primary thought is not to embarrass herself by going bankrupt, for example, isn’t going to go bankrupt even if her group is given incentives to do so. Furthermore, a person with no objectives and no position sizing guidelines will position size totally by emotions.

The third component is the specific position sizing method, whether it is “intuitive” or a particular algorithm. Each model has many possible varieties, including the method of calculating the equity, which we’ll discuss later.

THE CPR Model for Position Sizing Strategies

A simple model for determining “how much” involves risking a percentage of your equity on every trade. We’ve alluded to the importance of this decision throughout this book, but how exactly do you do that? You need to know three distinct variables:

1. How much of your equity are you going to risk? This is your total risk, but we will call it cash (or C) for short. Thus, we have the C in our CPR formula. For example, if you were going to risk 1% of your equity, C would be 1% of your equity. If you had a $50,000 account, C would be 1% of that, or $500.


CPR for Traders

2. How many units do we buy (that is, what is your position sizing method)? I call this variable P for position sizing method.

3. How much are you going to risk per unit that you purchase? We will call this variable R, which stands for risk. We’ve already talked about R in our discussion of expectancy. For example, if you are going to buy a $50 stock and risk $5 per share, your risk (R) is $5 per share.

Essentially, you can use the following formula to determine how much to buy:

P = C/R

Let’s look at some examples so that you can understand how easy it is to apply this formula.

EXAMPLE 1. You buy a $50 stock with a risk of $5 per share. You want to risk 2% of your $30,000 portfolio. How many shares should you buy?

Answer: R = $5/share; C = 2% of $30,000, or $600. P = 600/5 = 120 shares. Thus, you would buy 120 shares of a $50 stock. Those shares would cost you $6,000, but your total risk would be only 10% of your cost (that is, assuming you kept your $5 stop), or $600.

EXAMPLE 2. You are day trading a $30 stock and enter into a position with a 30-cent stop. You want to risk only a half percent of your $40,000 portfolio. How many shares should you buy?

Answer: R = 30 cents/share. C = 0.005 × $40,000, or $200. P = 200/0.3 = 666.67 shares. Thus, you’d buy 666 shares that cost you $30 each. Your total investment would be $19,980, or nearly two-thirds of the value of your portfolio. However, your total risk would be only 30 cents per share, or $199.80 (assuming you kept your 30-cent stop).

EXAMPLE 3. You are trading soybeans with a stop of 20 cents. You are willing to risk $500 in this trade. What is your position size? A soybean contract is 5,000 bushels. Say soybeans are trading at $6.50. What size position should you put on?

Answer: R = 20 cents × 5,000 bushels per contract = $1,000. C = $500. P = $500/$1,000, which is equal to 0.5. However, you cannot buy a half contact of soybeans. Thus, you would not be able to take this position. This was a trick question, but you need to know when your position has way too much risk.

EXAMPLE 4. You are trading a dollar–Swiss franc forex trade. The Swiss franc is at 1.4627, and you want to put in a stop at 1.4549. That means that if the bid reaches that level, you’ll have a market order and be stopped out. You have $200,000 on deposit with the bank and are willing to risk 2%. How many contracts can you buy?

Answer: Your R value is 0.0078, but a regular forex contract would be trading at $100,000, and so your stop would cost you $780. Your cash at risk (C) would be 2% of $200,000, or $4,000. Thus, your position size would be $4,000 divided by $780, or 5.128 contracts. You round down to the nearest whole contract level and purchase 5 contracts.

Position Sizing Basics

Until you know your system very well, I recommend that you risk a maximum of 1% of your equity on any one position. This means that 1R is converted to a position size that equals 1% of your equity. For example, if you have $100,000, you should risk $1,000 per trade. If the risk per share on trade 1 is $5, you’ll buy 200 shares. If the risk per share on trade 2 is $25, you’ll buy only 40 shares. Thus, the total risk of each position is now 1% of your account.

Let’s see how that translates into successive trades in an account. On your first trade, with equity of $100,000, you would risk $1,000. Since it is a loser (as shown in Table 4-4), you’d now risk 1% of the balance, or $990. It’s also a loser, and so you’d risk about 1% of what’s left, or $980. Thus, you’d always be risking about 1% of your equity. Table 4-4 shows how that would work out with the sample of trades presented in Table 4-3.



TABLE 4-4 Results of Risking 1% in the Game

Remember that in this sample of trades you were up 24R at the end of the game. This suggests that you could be up about 24% at the end of the game. We’re up 22.99%, so we almost made it. Equity peaks are shown in bold, and equity lows are shown in italics.

Because of the drawdowns that came early, you would survive. You have a low equity of about $91,130.99 after the long losing streak, but you are still in the game. At the end you would be up about 23%. Even though you risked 1% per trade and were up 24R at the end of the game, that doesn’t mean you’d actually be up 24% at the end of the game. That would occur only if you’d risked 1% of your starting equity on each trade, which is a different position sizing algorithm.

You wouldn’t win the game with this strategy because someone who does something incredibly risky, such as risking it all on the sixth trade, usually wins the game. The important point is that you’d survive, and your drawdown wouldn’t be excessive.

Types of Equity Models

All the models you’ll learn about in this book relate to the amount of equity in your account. These models suddenly can become much more complicated when you realize that there are three methods of determining equity. Each method can have a different impact on your exposure in the market and your returns. These methods include the core equity method, the total equity method, and the reduced total equity method.


So Many Ways to Calculate Equity

The core equity method is simple. When you open a new position, you simply determine how much you would allocate to that position in accordance with your position sizing method. Thus, if you had four open positions, your core equity would be your starting equity minus the amount allocated for each of the open positions.

Let’s assume you start with an account of $50,000 and allocate 10% per trade. You open a position with a $5,000 position sizing allocation, using one of the methods described in the following section, “Different Position Sizing Models.” You now have a core equity of $45,000. You open another position with a $4,500 position sizing allocation; now you have a core equity of $40,500. You open a third position with an allocation of $4,050, and your new core equity is $36,450. Thus, you have a core equity position of $36,450 plus three open positions. In other words, the core equity method subtracts the initial allocation of each position and then makes adjustments when you close that position out. New positions always are allocated as a function of your current core equity.

If your method of allocation is percent risk, then the risk amount would be your allocation. Thus, if you bought 100 shares of a $100 stock with a stop at $95, your risk allocation would be $500. The total amount invested would be $10,000. But your allocation would just be the risk amount, not the total amount invested.

I first learned about the term core equity from a trader who was famous for his use of the market’s money. This trader would risk a minimum amount of his own money when he first started trading. However, when he had profits, he’d call that market’s money, and he would be willing to risk a much larger proportion of his profits. This trader always used a core equity method in his position sizing algorithm.

The total equity method is also very simple. The value of your account equity is determined by the amount of cash in your account plus the value of any open positions. For example, suppose you have $40,000 in cash plus one open position with a value of $15,000, one open position worth $7,000, and a third open position that has a value of $2,000. Your total equity is the sum of the value of your cash plus the value all your open positions. Thus, your total equity is $62,000.

Tom Basso, who taught me methods for maintaining a constant risk and a constant volatility, always used the total equity model. It makes sense! If you want to keep your risk constant, you want to keep the risk a constant percentage of your total portfolio value.

The reduced total equity method is a combination of the first two methods. It is like the core equity method in that the exposure allocated when you open a position is subtracted from the starting equity. However, it is different in that you also add back in any profit or reduced risk that you will receive when you move a stop in your favor. Thus, reduced total equity is equivalent to your core equity plus the profit of any open positions that are locked in with a stop or the reduction in risk that occurs when you raise your stop.6

Here’s an example of reduced total equity. Suppose you have a $50,000 investment account. You open a position with a $5,000 position sizing allocation. Thus, your core equity (and reduced total equity) is now $45,000. Now suppose the underlying position moves up in value and you have a trailing stop. Soon you have only $3,000 in risk because of your new stop. As a result, your reduced total equity today is $50,000 minus your new risk exposure of $3,000, or $47,000.

The next day, the value drops by $1,000. Your reduced total equity is still $47,000 since the risk to which you are exposed if you get stopped out is still $47,000. It changes only when your stop changes to reduce your risk, lock in more profit, or close out a position.

The models briefly listed in the next section generally size positions in accordance with your equity. Thus, each model of calculating equity will lead to different position sizing calculations with each model.

Different Position Sizing Models

In most of my books, I talk about the percent risk position sizing model. It’s easy to use, and most people can be safe trading at 1% risk.

However, in The Definitive Guide to Position Sizing,7 I list numerous position sizing methods, all of which can be used to achieve your objectives. My goal here is to list a few of the methods so that you can see how extensive your thinking about position sizing strategies can be.

In the percent risk model, which we have described as CPR for traders and investors, you simply allocate your risk to be a percentage of your equity, depending on how you want to measure it. In some of the other methods, you use a different way to allocate how much to trade.

Here are some examples of ways you could allocate assets as a position sizing method:

1. Units per fixed amount of money. Buying 100 shares per $10,000 of equity or 1 contract per $10,000

2. Equal units/equal leverage. Buying $100,000 worth of product (shares or values of the contract) per unit

3. Percent margin. Using a percent of equity based on the margin on a contract rather than the risk

4. Percent volatility. Using a percent of equity based on the volatility of the underlying asset rather than the risk as determined by R

5. Group risk. Limiting the total risk per asset class

6. Portfolio heat. Limiting the total exposure of the portfolio regardless of the individual risk

7. Long versus short positions. Allowing long and short positions to offset in terms of the allocated risk

8. Equity crossover model. Allocating only when the equity crosses over some threshold

9. Asset allocation when investing in only one class of asset. Investing a certain percentage of one’s assets, say, 10%, in some asset class

10. Over- and underweighting one’s benchmark. Buying the benchmark and considering an asset as being long when you over-weight it and short when you underweight it

11. Fixed-ratio position sizing. A complex form of position sizing developed by Ryan Jones; requires a lengthy explanation

12. Two-tier position sizing. Risking 1% until one’s equity reaches a certain level and then risking another percentage at the second level

13. Multiple-tier approach. Having more than two tiers

14. Scaling out. Scaling out of a position when certain criteria are met

15. Scaling in. Adding to a position based on certain criteria

16. Optimal f. A position sizing method designed to maximize gains and drawdowns

17. Kelly criterion. Another form of position sizing maximization but used only when one has two probabilities

18. Basso-Schwager asset allocation. Periodic reallocation to a set of non-correlated advisors

19. Market’s money techniques (thousands of variations). Risking a certain percentage of one’s starting equity and a different percentage of one’s profits

20. Using maximum drawdown to determine position sizing algorithm. Not exceeding a certain drawdown that would be too dangerous for your account

Are you beginning to understand why position sizing strategies are much more important and much more complex than you have conceived of in your trading plans to date? There are many more models in The Definitive Guide to Position Sizing, and some of the models have an infinite number of varieties that could be modified to meet your objectives.

The Purpose of Position Sizing Strategies

Remember that a position sizing strategy is the part of your trading system that helps you meet your objectives. Everyone probably has different trading objectives, and there are probably an infinite number of ways to approach position sizing methods. Even the few people who have written about position sizing strategies get this point wrong. They typically say that position sizing strategies are designed to help you make as much money as you can without experiencing ruin. Actually, they are giving you a general statement about their own objectives and beliefs about position sizing strategies.

Let’s play our game again with the 0.8R expectancy. Say I give the following instructions to the people playing the game (100 people are playing): First, it costs $2 to play the game. Second, if after 30 trades your account is down from $100,000 to $50,000, it will cost you another $5. Third, if you go bankrupt, you will have to pay another $13, for a total loss of $20.

If at the end of 30 trades you have the most equity, you will win $200. Furthermore, the top five equities at the end of the game will split the amount of money collected from those who lose money.

Your job is to strategize about how you want to play the game. I recommend that you use the following procedure; it is also an excellent procedure to follow in real-life trading to develop a position sizing strategy to fit your objectives.

First, decide who you are. Possible answers might be (1) someone who is determined to win the game, (2) someone who wants to learn as much as possible from playing the game, (3) a speculator, or (4) a very conservative person who doesn’t want to lose money.

The next step is to decide on your objectives. In light of the various payoff scenarios, here are possible objectives:

1. Win the game at all costs, including going bankrupt (the person winning the game usually has this as the objective).

2. Try to win the game, but make sure I don’t lose more than $2.

3. Try to win the game, but make sure I don’t lose more than $7.

4. Win the game, but don’t go bankrupt.

5. Be in the top five, and don’t lose more than $7.

6. Be in the top five, and don’t lose more than $2.

7. Be in the top five at all costs.

8. Do as well as I can without losing $7.

9. Do as well as I can without losing $2.

10. Do as well as I can without going bankrupt.

Note that even the few rules I gave for payoffs translate into 10 different objectives that you could have. Creative people might come up with even more. You then need to develop a position sizing strategy to meet your objectives.

The last step is to decide when to change the rules. At the end of every 10 trades, I assess the room to determine who has the highest equity. If at the end of 10 trades you are not on track to reach your objectives, then you might want to change your strategy.

Notice how this changes what could happen in the game. Chances are that I’ll still have as many as 100 distinct equities, but chances are also that there will be a strong correlation between the objectives people select and their final equity. Those who want to win the game probably will have huge equity swings ranging from $1 million or more to bankruptcy.

However, those who want to do as well as they can without going bankrupt probably will trade quite conservatively and have their final equities distributed within a narrow range. The game makes it clear that the purpose of position sizing strategies is to meet your objectives. As I said earlier, few people understand this concept.

One Way to Use Position Sizing Strategies to Meet Your Objectives: Simulation

One way to use position sizing strategies to meet your objectives is to use a simulator. We will assume that there is only one position sizing method: the percentage of your equity you are willing to risk per trade.

Here is how we can set up a trading simulator by using the system that was described earlier. Its expectancy is 0.8R, and it has only 20% winners.

We know the expectancy will allow us to make 40R over 50 trades on the average. Our objective is to make 100% over 50 trades without having a drawdown of more than 35%. Let’s see how we can do that with an R-multiple simulator.

I’ve set up a simulation model to run 10,000 simulations of 50 trades for our system. It will risk 0.1% for 50 trades 10,000 times, then it will move up to 0.2%, then to 0.3%, and so on, in 0.1% increments until it reaches 19% risk per trade. We have a 5R loss, and so a 20% risk automatically results in bankruptcy when that is hit. Thus, we are stopping at a 19% risk per position.

The simulation model will run 10,000 fifty-trade simulations at each risk level unless it reaches our criteria of ruin (that is, down 35%), in which case it will say that it has reached the ruin point and move on to the next one in the sequence of 10,000 simulations. That’s a lot of computing to be done, but today’s computers can handle it easily.

The results of this simulation are shown Table 4-5.

The top row gives the risk percentage that delivers the highest mean ending equity.

Typically, this is the largest risk amount simulated because there will be a few samples that may have many, many 10R winners. That run would produce a huge number and boost the average result even if most runs resulted in a drop of 35% or more. Note that at 19% risk, the average gain is 1,070%. However, we have only a 1.1% chance of making 100% and a 98.7% chance of ruin. This is why going for the highest possible returns, as some people suggest, is suicidal with a system that is at best average.


TABLE 4-5 Position Sizing Optimizer Results

The median ending equity is probably a better goal. This gives an average gain of 175% and a median gain of 80.3%. You have a 46.3% chance of meeting your goal and a 27.5% chance of ruin.

What if your objective is to have the largest percent chance of reaching the goal of making 100%? This is shown in the Optimum Retire row. It says that if we risk 2.9%, we have a 46.6% chance of reaching our goal. However, our median gain actually drops to 77.9% because we now have a 31% chance of ruin.

What if our objective is just under a 1% chance of ruin (being down 35%)? The simulator now suggests that we should risk 0.9% per trade. This gives us a 10.5% chance of reaching our goal but only a 0.8% chance of ruin.

You could have your objective be just above a 0% chance of ruin. Here the simulator says you could risk 0.6%. The risk is just above 0%, but the probability of reaching your objective of making 100% is now down to 1.7%.

Finally, you might want to use the risk percentage that gives you the largest probability difference between making 100% and not losing 35%. That turns out to be risking 1.7%. Here we have a 37.9% chance of reaching our objective and only an 11.1% chance of ruin. That’s a difference of 26.8%. At the other risk levels given, it was 15% or less.

Just by using two different numbers—a goal of 100% and a ruin level of 35%—I came up with five legitimate position sizing strategies that just used a percent risk position sizing model.

I could set the goal to be anything from up 1% to up 1,000% or more. I could set the ruin level from anything from being down 1% to being down 100%. How many different objectives could you have? The answer is probably as many as there are traders/investors. How many different position sizing strategies might there be to meet those objectives? The answer is a huge, huge number.

We used only one position sizing strategy: percent risk. There are many different position sizing models and many different varieties of each model.

The Problems of the R-Multiple Simulator

Obviously, there are some huge advantages to simulating your system’s R-multiple distribution to help you learn about that system easily. However, there are also some serious problems with R multiples. Unfortunately, nothing in the trading world is perfect. The problems, in my opinion, are as follows:

R multiples measure performance on the basis of single trades but won’t tell you what to expect when you have multiple trades on simultaneously.

R multiples do not capture many of the temporal dependencies (correlations) among the markets (in fact, only the start date and stop date of a trade are extracted). Thus, you cannot see drawdowns that occur while a trade is still on and you are not stopped out (that is, by 1R).

• As with all simulations, R-multiple simulations are only as good as your sample distribution is accurate. You may have a good sample of your system’s performance, but you never will have the true population. You probably have seen your worst loss or your best gain.

R multiples are a superb way to compare systems when the initial risk is similar. However, they present some problems when one or more of the systems have a position sizing method built into the strategy, such as scale-in and scale-out models. In fact, in these conditions, you would have trouble determining the absolute performance of two different systems. As an example, compare two systems. System 1 opens the whole position at the initial entry point. System 2 opens only half the position at the initial entry point and the other half after the market moves in favor of the system by one volatility. If we get an excellent trade (say, a 20R move), the R multiple of system 1 will be better (bigger) than that of system 2 (larger profit and smaller total initial risk). However, if we get a bad trade that goes immediately against us and hits the initial exit stop, the R multiple is the same for both systems, namely, −1. The fact that system 2 loses only half of the money system 1 loses is completely missed.

• The impact of position sizing techniques (like pyramids) that change the total initial risk of a trade are difficult to test with the concept of R multiples because the R-multiple distributions of the trading systems (with and without the position sizing technique) cannot be compared directly. One way to evaluate the money management technique is to divide the trading system into subsystems so that the subsystems are defined by the entry points and evaluate each subsystem separately. For instance, each pyramid could be treated as a subsystem.

• Since R multiples capture only a few of the temporal dependencies between markets, simulations using R multiples must be based on the assumption that the R multiples are statistically independent, which is not the case in reality. However, one can cluster trades according to their start date or stop date and thus try to introduce a time aspect into simulations. When you do this, the volatility and the drawdowns become considerably larger when the R multiples are blocked. In other words, simulations based on one trade at a time clearly produce results that are too optimistic (1) when you are trying to determine the performance of systems that generate multiple trades at the same time and (2) when you are trading multiple systems simultaneously.

People have asked about obtaining a trading system simulation tool, but we’ve elected not to make one available. All the problems listed above might not be known to or considered fully by someone who might use it.

Getting around the Problems of Simulation

To get around the problems with a simulator, I developed the System Quality Number (SQN). Generally, the higher the SQN, the more liberties you can take with position sizing strategies to meet your objectives. In other words, the higher the SQN is, the easier it is to meet your objectives. For example, I commented earlier on a trader who claimed to have a 1.5 ratio between the expectancy and the standard deviation of R in a currency trading system that generated nearly one trade each day.

Although I don’t know if it is possible to develop such an incredible system, if he does have one, I have no doubt about his results: turning $1,300 into $2 million in a little over four months during a period when most of the world was having a terrible economic crisis.

In The Definitive Guide to Position Sizing, I was able to show how, with 31 different position sizing models (93 total since each can use any of the 3 equity models), it was possible to achieve your objectives easily from the SQN. Nevertheless, there are still precautions you must take because of the following:

1. You never know if your R-multiple distribution is accurate.

2. You never know exactly when the market type will change, which usually changes the SQN.

3. You have to account for multiple correlated trades. I did this with the SQN by assuming that the maximum risk was for the entire portfolio rather than for a single position.

Thus, in our example, with an average (at best) system and a ratio of the mean to the standard deviation of about 0.16, our best risk percentage was 1.7%. However, if we were to trade five positions at the same time, our risk per position probably would have to be reduced to about 0.35%. However, a Holy Grail system might allow us to risk 5% or more per position.

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