The Importance of Risk Management and Position Sizing
I often wonder if I could have reached this level of understanding earlier. Would it have been possible to be guided towards this understanding by a mentor, thus shortening the time to reach this zen moment? How much experience, failure, and success is required before a person can earn meaningful insight into the nature of the market? For me, I think I had a distinct advantage because I am a trained scientist and I have always been comfortable with thinking in terms of probability distributions. It was just a matter of seeing that the biggest probability questions were in the risk management category, not in whether a stock was going to go up or down. But what about those people who never had to think about probability in their everyday life? How could they be given a head-start? How could you convince them that stock-picking, economic forecasting, and technical analysis is random luck if it isn’t combined with sound risk management? More importantly, could they be convinced before they lose their trading stake or become too discouraged to continue?
So here is my initial attempt to get others who might not have a strong statistics background to appreciate the nature of trading. The plots below were generated by telling a computer to calculate 100 coin-flips. If head came up, I treated it as a winning trade. If tails came up, it was counted as a loss. In probability terms, there was a 50% chance that a trade would win and a 50% chance that it would lose. Now look at the results if we cut our losses at $100 but only allow the winners to run to $100 (yellow plot). Not surprisingly, the strategy yeilds no gain because, on average, each win is cancelled out by every loss. But what if each winning trade was a gain of $200 and each loss was cut short at $100? The red plot shows the results of this coin-flip run and it shows that a $10,000 account would grow to almost $15,000 in only 100 trades. If the winning trades are allowed to run to 3 times the losses, the account grows to almost $20,000 in only 100 trades.
Now any experienced trader can quickly point out the flaw in this argument. I’m sure they would agree that finding a trade setup that can produce winning trades 50% of the time is relatively easy, the hard part is ensuring that the winning trades are allowed to run up to 2 or 3 times the amount that was risked while making sure that losses are kept to a minimum. But this is exactly my point. The battle over probability takes place in risk management, not in finding the proper trade setups. Luckily, there are other methods to help traders succeed and the most powerful method is position sizing.
Now consider the same 100 coin flips. What if we were to risk more as our equity curve increased and risked less during losing streaks? Thanks to the hard work of professional gamblers and mathematicians, we have many rigorous position sizing methods to chose from (remember the MIT Blackjack Team?). I will use a very simple, yet powerful, anti-Martingale technique based on risking 1% of trading capital on each trade. The results are amazing and it shows how using a compounding position sizing strategy can make up for the deficiencies of a trading system. Let us take a closer look at the plot and how they were generated. Again, we just told the computer to flip a coin 100 times. For each trade, we risked 1% of the total trading capital. In this case the run began with $10,000, so the first trade risked $100 dollars. As the equity curve increased or decreased, the amount risked on each trade increased or decreased with it. For example, if the trading capital rose to $20,000, the amount risked on each trade would be $200. If it decreased to to $8000, the amount risked would fall to only $80 per trade. The beauty of the position sizing strategy is that is automatically compounds your gains while minimizing loses. The yellow curve uses a 1:1 risk-reward risk management strategy and is performs the same, telling us that any trading strategy must have a risk-reward ratio that is greater than 1 (no surprise here). The red curve (2:1 risk-reward) begins to show the incredible power of compounding your winnings on the way up. A simple 2:1 risk-reward coupled with compounding position sizing takes our test account from $10,000 all the way up to $350,000 in only 100 trades. A 3:1 strategy goes from $10,000 to an incredible $18,000,000. (yup, 18 million).
I want to emphasize that this was a very crude simulation, and real trading can never ensure that every winning trade yields 3 times the amount risked, but it does show you why you should strive towards this goal on every trade. It also reminds me how bad most of the trading advice is out there. Most people, amateurs and professionals alike, stubbornly think that success in the market relies on picking the right stocks, when in reality, it has more to do with controlling their risk and knowing when to exit once a trade is entered.
