# The Risk of Ruin (and why you should know yours)

## What is Risk of Ruin?

The Risk of Ruin calculates the probability that you will lose a certain percentage of your capital. It’s also known as the Probability of Ruin. It is commonly used by traders to refer a situation where their account balance falls below the minimum requirements for it to continue trading.

For professional traders its probably one of the most important metrics to know since it doesn't only tell if you are profitable in the short term, but also in the long term

If you look at the graph below you will see the risk of ruin for a particular trader. Note that this trader has an +/- 80% chance to lose 1% of his capital. While this might seem very high keep in mind that we usually risk 1%-2% of our capital per trade. So, a single loser will mean you will lose 1%-2%. If you look at it this way, 80% in this example is no big deal and expected. Next note that the curve rapidly goes down and from it, we see the trader has a +/-1% chance to lose 75% of his capital. In general, everything around and below 1% is acceptable but of course, that depends on the trader’s risk appetite. From the graph, you can clearly see how the Risk of Ruin can help you to get a better expectation of the amount of capital you might lose during your trading. Note that that the risk of ruin does not give you an indication of when you will lose it. That might be tomorrow or next year. It will only give you the probability that you might lose a certain amount of your capital.

Example of a Risk of ruin graph from the Improve your trade journal

## Which Methods Are Used to Calculate the Risk Of Ruin?

There are two main methods which are used to calculate the risk of ruin.

• The original method is written by Perry J. Kaufman in his book Smarter Trading

• The advanced method by Ralph Vince in Portfolio Management Formulas (New York: Wiley, 1990)

I will look at both methods in the following paragraphs and explain why I believe the improved version of Ralph Vince is the best one. Now if you don’t like math then just skip the next 2 paragraphs on how to calculate the risk of ruin. While I find it very interesting to know the exact differences between the 2 methods you don’t need to know it to be able to use it. In reality, you probably will use a spreadsheet or trading journal to do all the calculations for you. So, if you are interested in math then continue with the next paragraphs. Otherwise, just know that you should use the Ralph Vince method and just skip the next 2 paragraphs.

## How to calculate the Risk of Ruin using Kaufmanns formula

Perry J. Kaufman came up with the following formula to calculate the Risk of Ruin in his book Smarter Trading.

and

• Win% is your win ratio
• Loss% is your loss ratio
• U= the maximum number of risks that can be taken before the individual reaches their threshold for ruin

Example:

Let’s say we have a win rate of 60%, a losing percentage of 40%, and a \$10.000, - trading account. Now we want to calculate the Risk of Ruin that we might lose 30% of our capital

Losing 30% of our capital means we lose \$3000. In order to calculate our Risk of Ruin we first need to calculate U. We can calculate U by using our risk per trade.

Let’s suppose we risk \$200, - per trade. This would mean we can have (\$3000 / \$200) = 15 losers before we lost a total of \$3000, -

So U, the maximum number of risks, will be 15 then. Now that we have U, we can calculate our risk of ruin.

So, in this example, we have a 5.19% chance to lose 30% of our capital when using the Kaufmann formula which is quite high. Later on in this article, I will give you some ways how you can lower your risk of ruin, but for now, let's continue with the second method to calculate your risk of ruin.

## How to calculate the Risk of Ruin using Ralph Vince formula

One of the shortcomings in Kaufman’s formula is that it only uses the win% and lose%. It does not take into account how big your average winner is compared to your average loser. In reality, your winners would be bigger than your losers (I hope) and that can make a big difference in your risk of ruin. This is why Ralph Vince came up with the following improved version to calculate the Risk of Ruin. The formula becomes much more complex, but it is giving us much more accurate results.

Ralph Vince formula:

Let’s use the same example we looked at in the previous paragraph but now using this formula with our average winner & loser and see how this turns out:

• Our win% will be the same: 60%
• Our loss% will be the same: 40%
• We use the same trading capital of \$10000, -
• Our max risk is the same: 30%
• Let’s suppose our average winner is \$300, -
• And our average loser is \$200, -

Then…

## Calculating your risk of ruin using Monte Carlo simulations

I’ll do an article that explains Monte Carlo simulations in great detail soon. For now, it’s enough to know that Monte Carlo simulations are much like throwing a dice multiple times. But instead of throwing a dice, we are going to take (or simulate) multiple trades and calculate our max drawdown. The trades we simulate are based on your current win rate, the average winner, and an average loser. Now the trick is that we add a little variance to of those trade we simulate. For example, we might change the win rate a little bit or the average winner/loser just a bit. By changing each trade just, a little bit we get all different trades and we can calculate max drawdown for these trades. If we know our max drawdown we can easily check if we hit our risk of ruin or not.

Let’s say we start with \$10000 again at the beginning of each simulation and we simulate 100 trades. Now if the simulation tells us our max drawdown after those 100 trades are \$3000 then we know that our risk of ruin is a 100% chance to lose 30% of our capital. As you might imagine, a single simulation is not enough. To get an accurate result we need to do multiple simulations.  For example, let’s do 500 simulations in which we still take 100 trades per simulation. Now we might found out that 36% of those 500 simulations had a drawdown of at least \$3000 and the 74% had a drawdown below \$3000. This means our risk of ruin to lose 30% of our capital would now be 36%

By using Monte Carlo Simulations, we account for variance in our trading and it allows us to calculate the risk of ruin for a given number of trades. Basically, with Monte Carlo simulations we try to mimic life as good as possible and take all factors we can imagine into account to give us the best risk of ruin results.

Example of a Money Carlo simulation in the Improve your trade journal

## How to analyze your Risk of Ruin?

Now that we have seen What Risk of Ruin is, how to calculate it, and why you want to know yours you probably ask yourself. How do I analyze my Risk of Ruin?

For this, you need a spreadsheet, trading journal or you can use one of the many calculators online.

## How can you reduce your Risk of Ruin?

Once you know your Risk of Ruin the next question becomes. How can I reduce my risk?

There are a couple of ways how you could reduce your risk of ruin:

1. Reduce your position size. We already saw that by reducing your position size you will need more losers in order to lose the same amount of capital. The chances of having more losers (without corresponding more winners) are less likely and thus this will decrease your risk or ruin.
3. Increase your win rate. This might be a bit harder to do. But perhaps instead of looking for more winners, study your losers. Are there any losing trades that you could have avoided? Sometimes being able to remove a couple of losing traders is the best way to get a higher win rate. Also, look at your different trade setups and/or assets your trade. Perhaps some are comparing much worse than others and by simply avoiding those you can improve your win rate.
4. Use an appropriate account size. Most beginning traders open accounts with not enough money in it, making their risk of ruin (together with overleveraging) very high. So either increases your account size or reduce your position size. Luckily today most brokers nowadays let you trade micro futures which require 1/10th of the capital needed or micro forex accounts where you can trade with 0.01 lots

## Erwin

I am the owner of EB-Worx. Together with my wife and dog I live in the Netherlands where I love to day trade the ES-mini and develop software which helps me to become a better trader.

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