The Importance of Position Sizing 2
Last week we talked about the coin toss experiment. You lose whatever you risk when tails comes up and you win twice what you risk when heads comes up. If R stands for you risk, this system is characterized by the two R-multiples it generates: 1) - 1R (when you lose, you lose what you risk and R stands for your risk); and 2) +2R (when you win, you win twice what you risk).
You learned that there were six types of objectives and that when you do simulations of your trading system, you'll find that there is an optimal position sizing percentage to use for each objectives. Those six objectives were:
- Maximum (average) return
- Median Return
- Optimal % Risk to Reach our 100% per month goal
- Less than a 1% chance of ruin (i.e., being down 50%).
- Greater than a 0% chance of ruin
- The greatest difference between reaching our objective and ruin.
In the simulation that we ran, I set ruin at being down 50% and our profit goal at making 50% per month. I could have set a number of different ruin levels - anywhere from being down 1% to being down 100%. I could also have set a number of different objectives - anywhere from being up 1% to up by a million percent or more.
Can you see how there are an infinite number of objectives? And can you see how there is probably a different position sizing algorithm that would maximize the probability of each. That's how important position sizing is. And not very many professionals even understand how important it is.
One of your conclusions might have been that the coin toss experiment was not realistic for trading. It was too good. No one can make 100% per month that easily.
However, remember that there were none of the normal detractors from trading. There were no trading costs involved. And there were no mistakes involved. And the losses were always limited to what you risked.
In real trading, you should always have a worst case loss before you enter into a trade. As you've learned from my other tips, that's what you define 1R to be. And in real trading you could have losses as big as 5R. In fact, when you make a mistake, you frequently will have a loss that is as big as 5R. When you add those considerations into real trading, then it becomes more realistic.
But the problem is that almost all economists who study the markets, and many people who get a degree in finance or become trained as an analyst, understand almost nothing about position sizing. Yet position sizing accounts for about 90% of the variance of performance between individual performance in trading.
Let me give you two examples:
First, I play a marble game in some of my talks. There are ten marbles in a bag that are randomly drawn out in replaced. This is equivalent to a trading system with the following characteristics.
- 20% of the trades are 10R winners (you win 10 times what you risk)
- 5% of the trades are 5R losers (you lose 5 times what you risk, which is pretty typical of what happens when you make a mistake).
- The remaining 75% of the trades are 1R losers (you lose what you risk).
I typically play this game in talks. One marble is pulled out at a time and replaced. The audience starts out with $100,000 and must decide how much to risk on each marble pull. And we typically do 30 trades. With 30 trades, there is an 85% chance that the final result will be positive.
However, let's say that we have 100 people in the audience. Chances are we will having 100 different equities at the end of the game ranging from zero to over a million dollars. Everyone got the same trades, but the results were different. And the primary difference in the results was how much was risked per trade. Position sizing is that critical to the outcome. I've repeated this hundreds of times with the same results.
The second example comes from a study on asset allocation. Asset allocation was defined as how much was invested in cash, bonds, and equities. The researchers studied 82 pension plans over a 10 year period and concluded that over 90% of the variability of their performance was due to this "how much" variable. They called it asset allocation, but I call the how much variable position sizing. And now you are beginning to get a glimpse of how important position sizing is to really understand.
Dr. Van K Tharp
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