The Position Sizing™ Game

Background

People are always looking for the ‘real’ secrets of trading success, but mental biases have them looking in the wrong places and at the wrong things. Consequently, they search for great entry systems that they think will help them pick the right stock. Picking the right stock has nothing to do with success and neither does the accuracy of your stock picking.

All Market Wizards agree that the key ingredients to your success are (1) the golden rule of trading (cut your losses short and let your profits run); (2) position sizing (the part of your trading system that tells you how much); and (3) the discipline to do both. The golden rule of trading describes exits-abort losses and ride winners. In this game, position sizing controls how much equity you risk on any given trade.

In the game, as with real trades, there’s only one position sizing question to answer when entering a trade: ‘How much do I risk on each position?’ You establish the risk amount through your initial stop price (what’s your risk per share?) and your decision about how many shares to buy (which determines your total risk). In the first few levels of the game, you will get the result immediately. Later in the game, you’ll have to manage your risk from time period to time period in order to grow your profits (as you would in real trading). .

I've designed The Position Sizing™ Game to help you learn the secrets to trading success before you play the markets. This game does not simulate picking stocks in the market. Instead, it simulates trading a system that has certain characteristics. The system takes care of the ‘stock picking’ for you so that you can focus entirely on the most important aspects of trading-position sizing and letting your profits run. Our game has ten levels that get progressively more difficult to master. However, once you've mastered these principles, you'll know you've mastered some of the skills to trading success. (Levels 1-3 are free).

By the way, in real trading you achieve your objectives through position sizing. Your system (i.e., entry and exit) only determines how easily it will be to achieve your objectives through position sizing.

To complete this game, you must master four key principles: (1) understanding the importance of R-multiples; (2) understanding the difference between expectancy and probability; (3) learning how to let profits run without letting them escape; and (4) using position sizing to make sure you have a low-risk trade. The Position Sizing™ Game is designed to drive these principles home by giving you the experience of making (or losing) money in a game environment where losing is safer. Through this game, you’ll begin to understand these principles experientially without having real money at stake. My book, The Definitive Guide to Position Sizing [http://www.iitm.com/Definitive-Guide-to-Position-Sizing.htm], explains all of these ideas conceptually if you’d also like that.

R-Multiples

First, you must understand the principle of R-multiples. R stands for risk, the risk you take on any trade when you enter the market. It reflects that point at which you plan to get out in order to preserve your capital. For example, if you buy a stock at $50 and you plan to get out if it drops to $47 or below, then your R-value in this trade is $3.00 (i.e., $50 −$47 = $3.00). And if you buy 100 shares of stock then your total risk is $300-which is your total 1R value.

You want your losses to be small (i.e., an R-multiple of one or less) and your profits to be large R-multiples (2R or more). Losses can be bigger than 1R when the market gaps against you and goes through your ‘get me out’ point. They can also be bigger than 1R when you make a psychological mistake and fail to get out when you reach your stop point. Excessive costs (commissions and slippage) can also result in big losing R-multiples.


When you let your profits run, you want your profits to be much bigger than 1R. For example, if R per share is $3 (as it was in our example above), then a $15 gain per share is a 5R profit. Now suppose you have a trading system in which you are right 25% of the time. Continuing our example, when you win, you make 5R and when you lose, you lose 1R. If your system is right one time (i.e., a $15 gain) for every three losses of $3 each (i.e., a total of $9 in losses), you still make a profit of 6R or $6/per share. Imagine that! You are right 25% of the time and you still make money. That's why the principle of cutting your losses short (so you will have small R-multiple losses) and letting your profits run (so you will have big R-multiple gains) is so important. You still make money, even when you are only ‘right’ on 25% of your trades. If you set your total risk at 1% of your equity, then a 6R gain basically translates to a 6% gain.

The first level of this game teaches you position sizing and the importance of large R-multiples. What you win or lose will be expressed as R-multiples and these values are described in the level instructions for each level and are also viewable in the statistics window while playing the simulation.

In Level 1, 60% of your trades (on the average) will be winners. Most of them (55% of all trades on the average) will be 1R gains. Thus, on 55% of your trades, you'll win whatever you risk. If you risk $1,000, then you will win $1,000 on a 1R gain. In Level 1, 5% of all trades will be 10R gains. In other words, if you risk $1,000 when one of these trades comes along, you'll make ten times what you risked or $10,000. However, 35% of your trades in Level 1 will be 1R losers and 5% of your trades will be 5R losers. I hope you'll get a chance to feel the impact of having a 5R trade going against you in this level.

Level 1 has probability on your side (60% winners) and the big R-multiple winners as well. That is, you have the potential of a 10R winner in your favor. That won't be the case in the future levels. This brings up our next topic-expectancy.

Expectancy versus Probability

Expectancy is a mathematical formula that tells you how much you will win on the average per dollar risked. It takes into account both the probability of winning (or losing) and the size of the R-multiples. Casino gambling games are all negative expectancy games; you cannot make money in the long run unless you can do something to change the odds. In trading, you must play a different game from gambling. You must have a positive expectancy game on your side in order to make money in the long run. Expectancy is actually the average R-multiple that your system will give you per trade.

Most people look for games (or trading systems) that make them right. That is a mistake. Such games can have a negative expectancy (meaning that you'll lose money overall) if some of the losers have large R-multiples. More importantly, some of the best trading ideas have large R-multiples in your favor, but only make money 25-40% of the time.

Let's look at an example. Suppose you buy a stock at $50 and plan to get out when it drops against you by a dollar to $49. However, when you are right you expect that stock to move 30%. In this case, a 30% move is an additional $15.

When a trade fails, you lose one dollar per share. When a trade works, you make 15R or $15 per share! What if you were only right 30% of the time and you make money in three of ten trades? In ten trades you'd make $15 per share an average of three times. Your total gain would be $45 per share. In the same ten trades, you'd lose $1 per share on the average seven times. Your total loss would be $7 per share. Over the ten trades you'd end up making $38 per share (or 38R), even though you were only right 30% of the time. Large R-multiples in your favor are much more significant than ‘being right’ for making money in the market. Remember that! And if you had risked 1% of your total equity on this system, you would have been up about 38% at the end of 10 trades.

Even though more trades lose than win in that example, the large size of the winning trades outweigh the losses so the system has a positive expectancy. To calculate expectancy, determine the average R-multiple for the system, taking into account both the positive and negative Rs. The mean R is the system’s expectancy.

Another (more difficult) way to determine expectancy is to multiply each R-multiple (both negative and positive) by its probability of occurrence. Then sum the results (i.e., subtracting the values of the negative R-multiples) to get the total expectancy. All of the probabilities, of course, must add up to 100%. If not, it means that you have missed some. In the case of our stock example just above, you multiply 0.3 by 15 (which is 4.5) and 0.7 by minus 1 (which is minus 0.7). When you add 4.5 and minus 0.7, you have a total expectancy of 3.8R. This means that you will average in gains, over many trades, 3.8 times your risk on each trade.

If the calculation of expectancy seems complicated, we have good news. The game calculates the expectancy for you-both of the system and the mean R-multiple of your trades. You can find the expectancy of each level in the statistics window and your running expectancy within the level is displayed on the trade window. You'll also know the probability of each trade. Since the game randomly generates the trade results from the system’s R-multiple distribution, you could easily get 10 losers in a row, which goes against the expectancy. However, at the end of the level, you'll probably be pretty close to the expectancy of that level. It's just like real trading in that you won't know whether the next trade will be a winner or not. The game will also give you the expectancy of the trades to date as they are randomly picked. This way, you will know how far off the trades are from the likely expectancy that was built into the game.

There is a critical aspect to expectancy that you must understand. Expectancy and probability are not necessarily the same. As I said earlier, you must have expectancy on your side, but you don't need to have probability on your side. Let's look at the example given earlier. You win 30% of the time, and when you win it's a 5R gain. You lose 70% of the time, and when you lose it's a 1R loss. You only make money 30% of the time. Thus, the odds are against you. However, the game has a positive expectancy, giving you an average of 3.8 times your risk each trade or 3.8R

Probability and expectancy will be separate in every level after Level 2. This is a more advanced trading concept for you to master. Beginning with Level 5, you'll even have the option of going long or short on a trade, which means that you’ll be able to go with the probability (i.e., winning most of the time) or with the expectancy. Hopefully, you'll learn how dangerous it is to bet against the expectancy, even though you get to win (or be right) more often.

Winning Trades

In the first six levels, getting a big R-multiple will be easy. If you hit one, you get the big win. If you hit a 10R multiple, you will win 10 times what you risk.

In the last four levels, you'll have to earn your big R-multiples by letting your profits run-just like in real trading. Losing trades will happen quickly, but winning trades will take time to develop. When a winning trade starts, it will probably just be a 1R win. You now have to wait another trade to determine if it will continue and how much of your gain you want to risk. When a winning trade starts, the chances of it continuing are good. However, you'll need to decide if you want to risk it all or just a portion of your profits.

For example, here's the start of a winning trade:

Joe's Foods, Inc. Risk $1,000 Won $1,000 Amount at Stake $2,000

Do you want to risk the entire $2,000 or not? Let's say you do and you again have a 1:1 winner:

Joe's Foods, Inc. Risk $2,000 Won $2,000 Amount at Stake $4,000

You now have a 3R gain (i.e., your initial risk of $1,000 plus another 3R or $3,000). Do you risk it all or just a portion of it? If you risk it all, you could allow a substantial gain to turn into a loss. Risking a portion of it is the equivalent to moving up your stop loss point in real trading. You decide to risk it all one more time. Fortunately, you win and your new situation is as follows:

Joe's Foods, Inc. Risk $4,000 Won $4,000 Amount at Stake $8,000

You now have a 7R gain (i.e., your initial risk plus another 7R). If you risk it all, you'll have a huge profit if you win. On the other hand, you could get a 3R or 4R loser. If that happens, your loss would be huge. As a result, you decide to cut your risk back to $2,000.

Again, you win:

Joe's Foods, Inc. Risk $2,000 Won $2,000 Winnings $10,000

You can now risk any portion of that $10,000 or all of it. You already have a 9R profit on this trade, based on your original $1,000 risk. Do you now understand how letting your profits run can produce big R-multiple gains? The seventh level you play will require that you master letting your profits run in order to make more money.

Using Position Sizing (i.e., how much you risk) so that you have a low risk idea

Imagine that you are playing the first level. You have $10,000 in equity. You know that 60% of your trades, on the average, will be winners. You also know that there is a 10R gain someplace in your future. You decide to risk $2,000 or 20% of your equity. The first trade occurs and it ends up being the 5R loser. You've lost five times your risk of $2,000 or $10,000. You are now bankrupt. You risked too much, despite having both expectancy and probability in your favor.

In any positive expectancy game, there is a percentage of your equity that will give you an optimum return. That optimum percentage will give you the maximum rate of return over time. It will also give terrible drawdowns. Lower percentages of risk will give you less return and smaller drawdowns. Lower percentages could actually increase your chances of meeting your objectives (in the game it is making 50%). But if you risk too much, you risk bankruptcy.

My definition of a low risk idea is ‘an idea with a positive expectancy that is traded at a risk level that will allow you to survive in the short term, so that you can achieve the positive expectancy over the long term.’

At each level, you will have to study thoroughly the Level Statistics under the View Menu to come up with a position sizing strategy for that level and decide how much you want to risk on each trade. One of the main lessons you must master in order to profit will be the art of position sizing. You can think about various strategies, such as playing the market’s money or any of the other strategies presented in Trade Your Way to Financial Freedom [http://www.iitm.com/products/books/trade_your_way_to_financial_free.htm] or in The Definitive Guide to Position Sizing [http://www.iitm.com/Definitive-Guide-to-Position-Sizing.htm] and try them out without risking real money.

The overall objective of the game is to make a minimum of 50% return in each of the ten levels without going bankrupt.

New in This Version of the Game

Some people play this game once, shoot for the moon and try to set a dollar record for their game earnings. With the previous version of the game, we had reports of people finishing with over $1 trillion dollars in equity. While that might be fun, it’s not a useful objective or a valuable use of your time.

We’ve added several realistic influences in this new version that will impact your trading results just as they do in live trading-commissions, slippage, taxes, and trader efficiency. At first, leave those settings alone and play awhile in the easy game mode. After you’ve made it through Level 10 a few times, change the mode to realistic and add in commissions and some slippage. Enable the government to take out taxes. See what a difference those options can have on your results.

Now, you can also experience the effects mistakes can have on your trading. No trader is 100% efficient-no one trades error free. When you have a good feel for position sizing, try lowering your efficiency to 95%. That’s only one mistake out of 20 trades. When you make a mistake on a losing trade (i.e., minus 1R) then it becomes a larger losing trade (i.e., minus 2R). But if it is a winning trade, then it suddenly becomes a losing trade (i.e., +10R might become minus 1R). I believe there are few traders who are 95% efficient in their trades.. Try trading at 90% efficiency in the game. If you want a real challenge, try to get through level 1 at only 85% efficiency. It’s very difficult.

After you go through my recommendations in this section and have completed the game a number of times, I suggest you use the customize feature to plug in the R-multiples from your own trading system. This way you will get a trade-by-trade feel for your system. You can even keep track of your worst R-drawdown without using real money to find out.

Getting Started

When you are ready, go to the ‘File’ menu and choose ‘New Simulation…’ In the window that appears next, make sure ‘Standard Game’ is selected and then press the ‘OK’ button. Begin by reading the instruction on how to play the game as well as the specific instructions for Levels 1 and 2.

Much success and may you learn a great deal from this game!

Van K. Tharp, Ph.D.

Common Questions and Answers

Question:
What mistakes do people make playing this game?

Response:
Most people go bankrupt because they do not understand the most important aspects of trading or their greed gets in the way. Here are some of the most common mistakes: 1) risking too much; 2) risking more after a losing streak; 3) failure to develop a strategy for position sizing; 4) failure to stick with your position sizing strategy; 5) risking too little and not making any money; 6) not letting profits run enough during a winning trade, especially at the beginning of the trade; and 7) risking all of your profits continually during a winning trade.

Question:
You give a breakdown of expectations of winning versus losing trades and payoff. Are those odds and number of winners and losers exact and can I really count on them?

Response:
A random number generator, governed by the given probabilities for the level, generates the trade results in the game. You cannot count on anything, just as you cannot count on the markets. However, over a large number of trades your results should come close to the expectancy for that level.

Question:
I have practically no information about the stock I am supposed to trade. How am I supposed to make a decision?

Response:
Taking every trade in this simulation is a lot like following a system. You don't know which trades will make money, but you know how many of them will on average. If you take all the trades and practice sound position sizing, you'll make money (most of the time) in this game.

You also don't know which trade will go up, but you do know the payoffs and probabilities of the system you will be trading. That's all you need to know to work out position sizing strategies. Those strategies are the key to success and this game is designed to get you away from predicting the market and into thinking about those strategies.

Position sizing is the key to making money in the markets and that's what you need to learn in the first few levels. Most people think that the key to success is analyzing the markets and finding the next winner. And that's why a lot of people have trouble making money in the markets. Instead, the most important question you need to ask is, ‘How much money should I risk on this particular trade?’ This game is designed to teach you success secrets and steer you away from the biases that most people have.

Question:
Why not give us a portfolio to trade?

Response:
I designed this game to be simple so that you can learn some important lessons effectively and efficiently.

Question:
Winning this thing seems more like luck that anything else. Everything is random.

Response:
Even when you don't know the expectancy or the probabilities, it's not luck if you learn position sizing and let profits run.

Question:
What's a good strategy to play this game?

Response:
You'll learn a lot more by experimenting on your own than if I just gave you a strategy to use. After all, you won't lose any real money playing the game and learning in the process. Here’s a general hint: risk a small percentage of your equity-enough to do well, but not so much that you'll be bankrupt if a 5 to 1 loser comes up right away. You might consider increasing the percentage when you are ahead and decreasing it when you are behind. The key is to experiment liberally so that you discover the importance of position sizing and the multitude of ways to implement it in your trading. In addition, make sure you risk a large percentage (if not 100%) of your profits, when you begin winning trades.

Question:
How can I trade a stock without seeing a price chart? I don't want to buy a stock until I know it’s going up or it’s a winning trade.

Response:
This is not an exercise in stock picking or chart patterns. It's an exercise that involves following a positive expectancy system so that you can learn 1) position sizing and 2) to let your profits run. Every trade has the potential to be a winner and in later levels of the game to be the start of a winning trade.

Imagine that you are trying to catch the start of a winning trade; however, you have a tight stop. You might end up getting stopped out three or four times in a row. But you keep the stops tight because you know you'll catch the winning trade one day. That's the same thing as playing this system. Pretend that every one of these trades looks like a winning trade is set to start on the chart. You are ready if it takes off on you as soon as you enter. If not, you get out at a small loss and try again.

If it’s helpful, there are price charts provided on some levels.