We recently developed software to model the affects of random chance on money management. Although computers are capable of generating pseudo-random numbers, the pseudo-random process introduces bias into the random distribution.

We opted to source our random numbers from random.org. The web site generates purely random streams of bits taken from atmospheric noise. We then use binary mathematics to change those bits into numbers ranging from 1-10,000. Say, for example, that we want to model a trading system with a winning percentage of 50%. Whenever a number comes out between 1-5,000, we consider that a winner. Anything above 5,000 marks a loser.

Changing the winning percentage to 65% works the same way. Any number less than 6,500 represents a winning trade. Numbers above 6,500 signal a loss. The modeling quality is accurate to the thousandth decimal place. That type of accuracy is way more accurate than the “known” accuracy of your trading system, which can only be known within a few whole percentage points.

Most traders fall into the trap of thinking about their trades as individual outcomes. The more appropriate way to view returns is as the sum of all individual outcomes. Losing on any given trade does not matter. It only matters whether the sum of all your winners is greater than all of the losers.

It gets more complicated, unfortunately. A system with 50% wins and a 1:1 payout will almost never come out at exactly breakeven. The mathematical expectation is that we expect to see a degree of drift in the returns solely due to random chance. I suggest reading more in the random trade outcomes and dollar profits section to get a better understanding of drift.

Lastly, we must define a sampling period for evaluating the final result. I arbitrarily set the default value to 200. That means that the software tells us the range of outcomes after 200 total trades. That may take more than a year for some traders. Daytraders may reach that benchmark in several weeks of trading. The question that we are answering is “what is my account balance likely to be after placing 200 trades?”

## Coin Toss Trading Experiment

The first experiment is to analyze how dollar returns vary with a coin toss game and the most basic money management method. A starting balance of $100,000 is used with a risk of 1%. The risk will not change as in the fixed fractional method. Instead, we will leave the lots fixed in order to strictly understand random chance. Wins always earn $1,000. Losses always lose $1,000. The odds of a coin toss are 50% wins with 50% losses and a 1:1 reward risk ratio.

The average trade comes out to $99,868.36, almost exactly $100,000. It’s what we expect for a 50-50 game with a 1:1 reward risk ratio. What I find interesting is the standard deviation of $14,377 and how it changes. I don’t want to cover scary math topics. The layman’s explanation is that the standard deviation is the “normal” range from the average that you might expect. The $100,000 balance, in most cases, would either lose $14,000 or make $14,000.

Everything beyond those standard deviation boundaries represent the less likely wild scenarios. The minimum outcome comes out to $58,o00, a massive 42% loss. This had a 0.54% chance of occurring. The maximum outcome shows as $158,000, a monster 58% return. This had an even smaller chance of occurring, only 0.1% (1 in every 1,000 trials).

Changing the account risk dramatically affects the standard deviation. 1% strikes most traders as sane and reasonable. Yet, there is a small chance of losing half the account to drawdown strictly because of terrible luck. Decreasing the overall risk by a fourth to 0.25% drops the standard deviation by exactly one fourth. The worst case scenario shrinks to a highly tolerable $11,500 drawdown (11.5%). Most traders would find a number between 10%-20% reasonable. The consequence of the reduced risk is that the best case scenario drops correspondingly down to a 14.5% gain.

Stretching the risk out to 2%, a normal industry practice, turns out to be risking accounting suicide with the coin toss game. The worst case scenario drops the final account balance down to $8,000, a staggering 92% loss.

The goal is to help you define risk from a gut feeling matter into something more tangible and calculated. Too many traders enter the market day dreaming about profits. Risk enters the picture, but too few traders actually understand the relationship between risk and reward. Hopefully, the picture of best, worst and average scenarios is starting to become more clear for you.