My name’s Matt, and I’m addicted to Monte Carlo Simulations.
There, I said it. I’m also addicted to the idea of optimal risk sizing in trading, so you’re probably going to see a few articles covering that on this blog.
You’ve probably heard it a thousand times, “Risk no more than 1% of your account per trade”. You’ve heard it in articles, podcasts, youtube videos and every damn day in whatever forums you read. It’s as if God himself wrote it into stone tablets for ForexKing420 to find and disseminate to the world.
It’s wrong. I’ll tell you why. (Scroll down if you just want to see the test results)
Risking 1% Per Trade
First, let’s look at the reasoning for the 1% rule. It’s called Risk of Ruin, and it’s one of the most important concepts in trading. Essentially it’s just the probability that your account will drop to a level that you can’t recover from, based on your Win Rate (WR), Risk/Reward (RR) and Bet Size. Change any of those variables and your Risk of Ruin changes drastically.
The standard advice of 1% risk per trade is a broad-brush approach to ensure that whatever your WR and RR is, your Risk of Ruin will be 0.
Of course, you need at least a minimal edge for this to be true.
To be specific, you still need at least 10% Expected Value (EV) per trade for your Risk of Ruin to be 0 (e.g. 55%WR and 1RR, 40% WR and 1.75RR etc.) if we define “Ruin” as a 50% drawdown on the account. For context, 10% EV is the equivalent of:
- 55% WR and 1 RR
- 50% WR and 1.2 RR
- 40% WR and 1.75 RR
If you don’t have a positive edge, no amount of risk management will keep you from blowing your account, it’s a mathematical certainty if you trade for long enough.
Same Risk, More Reward
So, what’s the problem? 1% Risk per trade and 0% Risk of Ruin sounds like good advice, right? Well, so was your parents telling you not to talk to strangers when you were a kid, but now you’re a door-to-door buttplug salesman that’s not very helpful for you. In the same vein, the 1% rule is fine for beginners who need a blanket ideology to stop themselves from risking their whole account on every trade. Hopefully, that’s not you.
If you’ve crossed the threshold of profitability, you likely have a good sample size of trades under your belt. You know your average Win Rate and Risk/Reward over that sample. You don’t need to follow the beginner rules any more. You don’t need to drive with hands at 10 and 2 or hold onto the safety bar on the rollercoaster.
If you know your stats and you’re profitable, wouldn’t it make sense to trade the LARGEST risk that still gives you a 0% Risk of Ruin? The downside stays the same, the upside increases. That’s a good risk/reward decision.
Optimal Zero Risk of Ruin
I don’t know if this has a name, so I’m naming it Optimal Zero Risk of Ruin (OZROR)
Optimal Zero Risk of Ruin is simply the largest risk % per trade that still offers 0% Risk of Ruin over n trades, based on your expected Win Rate and Risk/Reward.
Below are the tables of results from the Monte Carlo testing. Each table is followed by a small test comparing 1% risk vs the OZROR for a 55%WR and 1.4RR. I’ve used these numbers because they represent 32% Expected Value – a number I believe to be highly achievable. Larger win rates and expected value would produce far more dramatic graphs.
I’ll go into the details of the testing methodology below.
Ruin Based On % of Starting Balance
Ruin Based On Peak To Valley Drawdown
Methodology
For each combination of RR and Winrate (each value in the table), we iterated through potential bet sizes (risk of balance per trade) from 0.4% up to 5% in increments of 0.2%, for 24 bet sizes tested.
Starting from 0.4%, I ran 10k simulations of 500 trades for each bet size. If at any point the starting capital/peak to valley drawdown dropped below the ruin level, that bet size is considered capable of reaching ruin and is ruled out. All larger bet sizes are then ignored as well. The previous largest bet size that achieved 0% ruins over all 10k iterations is considered the Optimal Zero Risk of Ruin.
Then, I did it again. Repeating the same process and getting 2 tables of results. Each value in the tables shown here is the LOWEST value from the 2 runs.
Each value therefore represents a maximum 10k simulations for 24 bet sizes, tested 2x. 480k simulations of 500 trades for every value in the tables above. Of course, in reality the number tested is considerably less than that. Once we have a simulation that reaches Ruin, we stop that simulation, and then we don’t need to run the simulations for any larger bet sizes for that RR/Win Rate combination.
Self-Criticism of the Methodology
This methodology is deliberately over-sensitive, and as such it does create some anomalous results that don’t appear to “fit” with the results either side of it. This is because a single outlier drawdown can cause ruin, and a single ruin within the 10k simulations is considered unacceptable. This occasionally leads to the value being lower than it perhaps should be.
Again, this is deliberate. If I’m going to make the hypothetical argument that those with high enough Win Rate and Expected Value should be risking more than 1%, I want to be cautious and conservative with HOW much more the data recommends. Therefore, I’m deliberately adjusting the methodology to skew towards a more conservative approach. This is the same reason I am testing twice and taking the lowest value of the 2 tests.
Defining Risk of Ruin
How we choose to define Risk of Ruin is clearly pivotal to these tests, hence why we run the test with a number of different definitions. We test using % of starting capital to begin with e.g. you have a $1000 account and don’t want to drop below $500 capital (50% starting capital).
Then we go on to test Peak To Valley Drawdown e.g. your $1000 starting capital grows to $5000, now your “Ruin level” is $2500, as a drop of 50% from your highest balance represents “Ruin” (50% Peak To Valley Drawdown).
For those more risk averse, we also tested 70% of starting capital, and 30% PTV Drawdown.
It’s important to note that when we say 0% Risk of Ruin, that is within our defined parameters. In particular, this should be thought about as “Optimal bet size with Zero Risk of Ruin over 500 trades”. Sample size of trades is important to consider, because over an infinite number of trades it’s impossible to achieve 0% Risk of Ruin. As the number of trades increases so does the tail risk.
The concept of “Ruin” is quite subjective as a trader. For a hedge fund manager, a 20% drawdown while the market has a green year could be career ending. While a retail trader taking his shot with $5k spare capital may be willing to risk 100%. As such, there is no universal consensus on what percentage lost should be considered your ruin point. I’ve chosen 50% as the largest drawdown to test due to the common wisdom that a 50% drawdown requires a 100% gain to recover from, and past this point it gets more and more ugly.
Interestingly, among “Advantage Players” (read: “card counters”) in Blackjack, there is a more standardised definition of ROR: The % likelihood of complete 100% ruin BEFORE doubling your starting balance. This is an interesting concept I may explore in a future post.
Takeaways
So what can we learn from this? Well, 1% risk as a general rule is not too far from being correct – especially when defining Ruin as 30% – but is also a little too simplistic.
Your Optimal Zero Risk Of Ruin (OZROR?) is influenced by your Expected Value and your Win Rate. Higher win rates particularly are able to withstand higher risk per trade. Nothing groundbreaking there, a study of the Kelly Criterion would yield the same results. SPOILER ALERT – I’ll be doing similar testing of Kelly and its variants in the near future. I told you I’m big on optimal risk size.
If you’re a profitable trader, you may be doing yourself a disservice by following the 1% rule, especially if you’re willing to take sizable drawdowns with “house money”; your profits from the markets. Hopefully, this post has helped to quantify how large of a disservice it may be, and how much you may be able to comfortably risk instead.
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