Last week, I introduced you to position sizing by talking about the marble game I typically play. The game has 20% 10R winners, 70% 1R losers, and 10% 5R losers. It only wins 20% of the time, but the expectancy, because of the 10R winners, is a very healthy 0.8R. I gave you a sample of 30 pulls from the game, shown in the table below. The audience is typically told to decide how much to risk on each pull and we check to see how much equity they have after 30 trades. In fact, the one with the most equity will win a nice prize.
| R-Multiples Draw In A Game | ||
| -1R | -5R | -1R |
| -1R | -1R | -1R |
| -1R | -1R | +10R |
| -5R | -1R | -1R |
| -1R | -1R | +10R |
| +10R | -1R | -1R |
| -1R | -1R | -1R |
| -1R | -1R | -5R |
| -1R | -1R | +10R |
| +10R | -1R | +10R |
| +8R | -14R | +30R |
In a typical game like this, 1/3 of the audience will go bankrupt (i.e., they won't survive the first five losers or the streak of 12 losses in a row); another 1/3 of the audience will lose money; and the last third will typically have made a huge amount of money – sometimes over a million dollars. And in an audience of say 100 people, except for the 33 or so who are at zero, I'll probably have 67 different equity levels.
So this week, I want to define position sizing; tell you it's purpose, and then tell you a little bit about how to do position sizing. First, what is it? Position sizing is that part of your system that tells you “how much” throughout the course of the trade. And, assuming you have a positive expectancy system, that variable, along with your personal psychology, controls about 90% of the variability of your performance in trading. THAT'S HOW IMPORTANT IT IS. And yet most people totally neglect this variable. Mutual funds, for example, that have to be 95% invested at all times, don't really give it much thought.
What's the purpose of position sizing? I'm currently working on a new book titled, The Definitive Guide to Position Sizing, and the subtitle tells you its purpose. It's how to use position sizing to meet your objectives. Position sizing is that part of your trading system that helps you meet your objectives. Everyone probably has a different objective in trading and there are probably an infinite number of ways you could approach position sizing. It's interesting because even the few people who have written about position sizing get this point wrong. They typically say something like position sizing is designed to help you make as much money as you can without experiencing ruin. But what they are really doing is giving you a general statement about their objectives and thinking that's what position sizing does.
For example, you might have an objective of making as much money as you can, but under no circumstances would you want to drawdown by 20%. Thus, your focus in position sizing will be to not have a 20% drawdown. Someone else might have a goal of making 100% and not having a drawdown of 50%. However, this person would be willing to give up 50% on some years in order to make 100% most years. This person would have a totally different position sizing algorithm.
So let's look at the game. What I recommend for position sizing, until you know your system very well is that you risk about 1% of your equity. That means that on the first trade you risk $1000. Since it is a loser (see Table 1), you'd now risk 1% of the balance or $990, it's also a loser so you'd risk about 1% of what' left or $980. Thus, you'd always be risking about 1% of your equity. The table below shows how that would work out with this particular sample of trades.
| Results of Risking 1% in the Game | |||
| Equity | 1% Risk | R-multiple | New Equity |
| 100,000 | 1000 | -1 | 99000 |
| 99000 | 990 | -1 | 98010 |
| 98010 | 980.1 | -1 | 97029.9 |
| 97029.9 | 970.299 | -5 | 92178.41 |
| 92178.41 | 921.7841 | -1 | 91256.62 |
| 91256.62 | 912.5662 | 10 | 100382.3 |
| 100382.3 | 1003.823 | -1 | 99378.46 |
| 99378.46 | 993.7846 | -1 | 98384.68 |
| 98384.68 | 983.8468 | -1 | 97400.83 |
| 97400.83 | 974.0083 | -5 | 92530.79 |
| 92530.79 | 925.3079 | -1 | 91605.48 |
| 91605.48 | 916.0548 | -1 | 90689.42 |
| 90689.42 | 906.8942 | -1 | 89782.53 |
| 89782.53 | 897.8253 | -1 | 88884.71 |
| 88884.71 | 888.8471 | -1 | 87995.86 |
| 87995.86 | 879.9586 | -1 | 87115.9 |
| 87115.9 | 871.159 | -1 | 86244.74 |
| 86244.74 | 862.4474 | -1 | 85382.29 |
| 85382.29 | 853.8229 | -1 | 84528.47 |
| 84528.47 | 845.2847 | -1 | 83683.19 |
| 83683.19 | 836.8319 | -1 | 82846.35 |
| 82846.35 | 828.4635 | -1 | 82017.89 |
| 82017.89 | 820.1789 | 10 | 90219.68 |
| 90219.68 | 902.1968 | -1 | 89317.48 |
| 89317.48 | 893.1748 | -1 | 88424.31 |
| 88424.31 | 884.2431 | -1 | 87540.06 |
| 87540.06 | 875.4006 | -5 | 83163.06 |
| 83163.06 | 831.6306 | 10 | 91479.37 |
| 91479.37 | 914.7937 | 10 | 100627.3 |
Notice that because of the drawdowns that came early, you would survive. You have a low equity of about 82,018 after the long losing streak but you are still in the game. And at the end you would come up a little ahead.
You wouldn't win the game because someone who does something incredibly risky, like risking it all on the sixth trade, usually wins the game. But the important point is that you'd survive and your drawdown wouldn't be excessive.
Position sizing is that important and I'd suggest that you take a look at chapter 14 of my book because many people have told me that it turned their trading around, making them winners instead of losers.
Dr. Van K Tharp
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