Individual Trade Risk and Position Sizing

 I have discussed how “R” works in the past.  If you want a better explanation than mine, check out these two posts from Brian Lund at www.bclund.com:

-           The Most Important Concept for Successful Trading, and

-           Using “Magic” to be a More Profitable Trader.

Not to beat a dead horse, but the steps to determining how R works are as follows:

1.         Determine how much you are willing to lose on any one trade – this is your R.

This calculation is obviously dependent on a lot of factors, but here are some ideas you can use to determine your : 

-           Rule of Thumb.  You can use a rule of thumb – never risk more than 1% of your    capital account on any one trade. 

-           Max Losses.  You can try to simulate your trading system to determine the            maximum number of losses you incurred in a row and then add a safety valve.    Say that through backtesting you found that you had 8 losses in a row.  In the            real world, double that value to say that you would probably have 16 losses in a   row.  Divide your capital account by this amount and you would never run it       down all the way.

-           Maximum Adverse Excursion.   The MAE is the largest loss suffered by a trade   while it is still open.  A position may move against you by 5 ticks but is closed out at a loss of 2 ticks.  The MAE would be -5 ticks.  Link:  “A particularly large MAE       might reveal that actually it would not work in practice because the MAE would    be too       large for the proposed account size, perhaps eliciting a margin call that     would render the backtest results inaccurate and misleading.”

-           Security Specific Calculation.  Using the standard deviation, ATR or other            volatility based calculation could help determine the room that you would have      to give a specific trade to be successful.

2.         Determine the trade specific stop.

This is the risk of the individual trade.  It may vary from trade to trade.

3.         Find the position size by dividing step #1 by step #2.

Looking at an example, assume you have a $20,000 risk capital account and you determine that you are not willing to risk more than 1% or $200 on any 1 trade (Step #1).  The next trade needs a stop of $50 to be successful (Step #2).  Divide $200 by $50 and you get 4, which means that you should buy 4 contracts  (Step #3). 

Position sizing is important.  Assume that you think you have an edge based on some type of indicator (moving average etc).  When this edge presents itself, you put on the trade and never accept less than a risk to reward ratio of 1 to 2.  However, while the ratio of risk to reward may remain the same, the actual outcome of each trade (in terms of ticks) may be different.

To prove that position sizing is important, let’s create a simulation that assumes the following:

-           Risk to reward ratio of 1 to 2

-           Starting capital account of $20,000

-           Tick value equal to $5

-           Winning percentage of 30%

-           Variety of individual trade results.

The table above represents a system that has a broad range of individual trades results but the same risk to reward ratio.  On one trade, you risk 5 ticks to make 10 ticks but on another trade you may risk 20 ticks to make 40 ticks. 

On any given trade, you may win or lose based on your system’s average winning percentage.  This will result in either an increase or a decrease of the capital account.

Running the simulation over 500 trades and repeating the simulation 1000 times, you get the following ending account value statistics (30% winning percentage, 1:2 Risk to Reward Ratio):

On average, using no position sizing, we would draw our account down to 16,937 after 500 trades.  Not great for a 1:2 Risk to Reward ratio system.

Here is what the ending account values looks like over a variety of Winning Percentages (500 trades simulated 1000 times) WITHOUT position sizing and a 1 to 2 risk to reward ratio:

So what happens when we employ position sizing?  That is, we make sure that when we have a trade that risks 5 ticks, we buy more contracts than when we have a trade that risks 20 ticks. 

Here is what the ending account values looks like over a variety of Winning Percentages (500 trades simulated 1000 times) WITH position sizing equal to 1% of the starting capital account and a 1 to 2 risk to reward ratio:

As you can see, using position sizing boosts the ending account value tremendously.  On average, sizing the positions accurately based on a 1R = 1% of starting capital resulted in ending account sizes 2 to 2.5 times in size on average.  This is not insignificant.

Keep ya mind right.