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Jun 24, 2021

Risk of ruin is a useful metric to help develop trading strategies that suit your risk appetite.

This post will cover:

• Two methods to calculate risk of ruin
• Lowering your risk of ruin

Contrary to what you often see in advertisements, trading is a long-term endeavour, not a get-rich-quick scheme.

You have to stay in the game to win it.

Let’s dive into it!

## What is Risk of Ruin?

Risk of ruin (RoR) is the probability that you’ll reduce your account to a level where trading cannot continue.

This ‘ruin level’ is the maximum acceptable loss of your initial capital.

As capital losses grow, the amount of profits required to break even grow exponentially. If you lose 10% of your capital, you’ll need an 11% gain to break even. But if you lose 50%, you’ll need a 100% gain!

If you’re a new trader, I suggest risking no more than 30% of your initial capital.

If your ruin level is hit, it’s perhaps best to take a pause and tweak your strategy and/or money management. More on that later.

## Calculating Risk of Ruin (Easy Way)

With this method, you only need to know your win rate and the amount risked per trade.

RoR can be calculated using the formula:

Here’s an example:

Suppose I have a \$10000 account and I decide to risk 30% of it.

I start trading a mean reversion strategy with a 70% win rate, and \$200 risked per trade.

1. U = (30% of \$10000) / \$200 = 15
2. A = 70% – 30% = 40% = 0.4

My RoR is thus 0.0003%.

What is an acceptable risk of ruin? This depends on your risk appetite, but anything less than 0.5% would be ideal.

Unfortunately, this simple formula has two major limitations:

1. It only works if your strategy has >50% win rate.
2. It assumes your wins and losses are the same size.

If your strategy uses stop loss and take profit levels that are equally spaced, you may get away with it.

But if you’re a trend follower, where your win rate is likely below 50% and your average winner is much larger than your average loser, you’re out of luck.

The trend following strategy below looks promising, but its 34% win rate gives us a 100% RoR.

To get the RoR for such strategies, we’ll need a more complicated calculation.

## Calculating Risk of Ruin (Hard Way)

Here we’ll use the equations developed by Ralph Vince in his book ‘Portfolio Management Formulas.’

This method does not require your wins and losses to be the same size.

You’ll need to know these variables beforehand:

• Initial capital (\$)
• Capital risked (%)
• Win rate (%) and loss rate (%)
• Average winner (\$) and average loser (\$)

First, calculate the average winner and loser as a fraction of your capital:

Next, calculate Z, A, and P:

Finally, the RoR is:

To illustrate, I’ll use the trend following strategy shown above. Its statistics are:

• Initial capital \$10000
• Capital risked 30%
• Win rate 34%, Loss rate 66%
• Average winner \$286, Average loser \$98
1. Average win% = 286 / 10000 = 0.029
2. Average loss% = 98 / 10000 = 0.0098
3. Z = (0.34 * 0.029) – (0.66 * 0.0098) = 0.0033
4. A = [0.34 * (0.029)2 + 0.66 * (0.0098)2]0.5 = 0.018
5. P = 0.5 * [1 + (0.0033 / 0.018)] = 0.588
6. Risk of Ruin = [(1 – 0.588) / 0.588](0.3 / 0.018) = 0.31%

Vince’s RoR formula can be used on any strategy, so what’s there not to like?

Its biggest limitation is the assumption that your strategy’s performance will remain constant in real-time.

If that were the case, trading would be like running a casino, with returns practically guaranteed over the long-term.

In reality, due to changing market conditions, statistics like your win rate and payoff ratio (average winner/average loser) are always fluctuating. Even a solid strategy could have prolonged periods of stagnation.

This is why you need to monitor your strategy’s live performance and have a plan to revise/replace it when things head south.

You can get a more reliable estimate of your strategy’s long-term performance by:

• Covering different market conditions in your backtest
• Getting a large sample of backtest trades

You can use standard error to help gauge whether your sample size is sufficient. I personally consider anything below 300 trades to be highly suspect.

The trend following strategy above had about 400 trades over 17.5 years, so I’m reasonably confident it has solid long-term performance.

## How to use Risk of Ruin

### 1. Establish Performance Expectations

Your RoR helps estimate the amount of capital you may lose during trading.

Using Vince’s formula, here’s the RoR as a function of the % of capital risked for the strategy above.

If you’re only willing to risk 1% of your initial capital, there’s an 83% chance you’ll hit that level.

This is to be expected, since the outcome of any one trade is random. You may suffer a losing streak no matter how profitable your strategy is.

If you decide to risk 10% instead, the RoR drops to 15%. If you indeed suffer a 10% capital loss in actual trading, you won’t freak out because 15% is quite a sizeable possibility.

There are very few strategies that can remain profitable indefinitely. Establishing your performance expectations beforehand will help you decide whether you should stop trading a strategy, at least temporarily.

Having realistic expectations, and developing contingency plans based on these expectations, will save you a great deal of anxiety and headaches.

With this strategy, it’s extremely unlikely to suffer a 40% loss of initial capital. It would be prudent to deactivate it if that happened.

Note that the RoR only estimates the probability of losing a certain amount of capital; it does not estimate when this loss will occur.

### 2. Determine Position Sizing

The RoR chart above shows the strategy’s RoR using a fixed 0.1 lots per trade.

If you decide to increase your position sizing, both your average winner and average loser will increase.

The chart below shows how the RoR changes for 0.2 and 0.3 lots.

As you may expect, there’s a significant increase in RoR as your position sizing becomes more aggressive.

If you’re only willing to risk 30% of your initial capital, and want a RoR below 1%, you should be trading about 0.1 lots.

What if your position sizing is already minimal, and you still can’t get an acceptable RoR?

Perhaps it’s time to improve your strategy.

## Improving Your Risk of Ruin

There are two main factors that determine your RoR: Win rate and payoff ratio. Let’s look at each of these:

### 1. Improving Your Win Rate

There are a million different ways to improve your strategy’s win rate.

But I think the easiest way to do it, and without drastically affecting the rest of your strategy, is to add entry filters.

Here I explain how to test the effects of time, trend and volatility filters.

As always, tread lightly when making changes to your strategy. It’s easy to fall into the curve fitting trap, where you unintentionally create a fantastic backtest that fails spectacularly in real-time.

After adding filters, you can verify your strategy’s robustness by running a walk-forward optimization or testing it on different markets.

### 2. Improving Your Payoff Ratio

However, this may be difficult to achieve without affecting the rest of your strategy.

For example, you may try tightening your stop losses to decrease your average losing trade. But this could choke off many potentially profitable trades, reducing your win rate as a result.

I think the best approach is to include strategy elements that are aligned with your trading idea, and then optimize them lightly if you wish. A high payoff ratio will be a natural by-product of a well-designed strategy.

If you’re a trend follower, consider including a loose trailing stop to let your profits run.

Or if mean reversion is your thing, consider using small profit targets and/or time stops.

## Wrapping Up

I recommend Ralph Vince’s RoR formula since it’s applicable to all types of strategies. The calculations are relatively complicated, but hopefully the Excel sheet will make your life easier.

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1. link to excel file not working

• Hi Sam, I just tried it and it downloads fine. The file is called ‘Ralph Vince RoR calculation.’

2. Hi, why does risk of ruin decreases when we increase capital risked? Shouldn’t it be the other way around? Thank you.

• Hi Darwin,
Capital risked refers to the percentage of capital you are willing to lose. It is the ‘ruin point’ that you define for yourself.
So for example, if I’m only willing to lose 5% of my capital, the RoR is high because a small losing streak is enough to make me hit 5%.

3. Sir, regarding avg winner and loser.
1. how do you know it? what if its in %of portfolio (aka size)?
2. is there any formula to calculate risk of ruin:
with following p/m
a)Initial capital (\$)
b)Capital risked (%)
c)Win rate (%) and loss rate (%)
d)Risk/reward
e)Maximum continuous losses b4 you get ruined

• 1. Average winner is your gross profits divided by number of winning trades.
2. The two formulas presented in the article are the only established ones in the literature.

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