The risk of ruin applied to risk management in trading

As a trader, one of the main concepts you need to master is risk management. This is what allows you to stay in the game and have a better chance of earning money off of the markets.

Many traders have no idea how much risk they are taking on each trade, per day, or per week, or their overall risk of going broke. And those traders who do know their risk per trade or per day are often not (or hardly) familiar with the risk of bankruptcy. Most likely because they don’t want to see it as a possibility.

What is your risk of ruin? This is the amount of capital that you are willing to risk before you have to stop trading (commonly referred to as the “ruin point” or “maximum drawdown”). Note that this is not the total capital in your account, as you should NEVER risk 100% of your capital.

The risk of ruin is a statistical concept that matches the probability that you will reach that level of ruin. Ideally, you should never have a drawdown of 50% or less, because then you’ll a 100% return just to break even!

It is obviously not possible for a trader to profit without taking some risk, but it is imperative that he/she knows what his/her risk is and that he/she is prepared to take it. If a trader isn’t prepared to take risks on his/her trading account then trading is not for him/her, it’s that easy.

Ideally, you should be prepared to risk 25-30% of your account as a MAXIMUM point of ruin before you need to stop trading, then revisit your trading plan for new goals and risk settings to determine if you can continue trading, then develop a new plan if necessary. You may also need to consider psychological venture capital, how willing are you to take risks on your own trading account? At what level of loss would you begin to feel uncomfortable trading with confidence?

Considering most traders who are starting out – they’re highly risk averse, and might experience a loss of confidence with just a bit of drawdown, whereas more experienced traders who accept risk may endure a larger drawdown while keeping the confidence to keep moving forward.

As a trader, our job is to avoid reaching our point of ruin. You must therefore calculate your chances of reaching this drawdown level. Simply put, the more you risk per trade per day, the more you increase your risk of going broke. So the easiest way to avoid the risk of going broke is to risk only a small portion of your account each day. I generally recommend a maximum of 1-2% of the account principal per day (1% for new traders). Note that this is per day and NOT per trade!

There is a formula for calculating your risk of ruin, and ideally your risk of ruin should be between 0% and 0.5%.

NOTE: It is mathematically impossible for the risk of ruin to be 0%! The target is therefore less than 0.5%, which, when rounded down, is close to 0%. When you go over 1% and more, you know you are risking too much, and the risk of ruin turns positive, which means that it is only a matter of time before it explodes and reaches its maximum level! It is therefore advisable NOT to trade until you are sure that you can reach (using a trading simulation if you are a discretionary trader or a back-test for an automated system) a risk of ruin level of less than 0.5 % and ideally close to 0% whenever possible.

There are several ways to calculate the risk of ruin, but the most common formula is as follows:

**Risk of ruin = (1 – (B – P)) / (1 + (B – P)) ^ U**

**B** = Probability of winning (Ex. 0.6 for 60%)**P** = Probability of losing (Ex. 0.4 for 40%)**^ U** = Power of the maximum number of consecutive losing trades before ruin.

Sample calculation of the risk of ruin

**“John”** has a $50,000 account and is willing to risk a maximum drawdown of 30%, which is -$15,000. Suppose he has proven by his transactions that he can obtain the following averages: profit = 60%, loss = 40%, risk per transaction 1% of the account ($500) so the maximum number of trades he can take and lose consecutively is 30 trades before he reaches the ruin point (maximum drawdown of 30%).

His risk of ruin is therefore calculated as follows:

**(1-(0.2)/1+(0.2))^30 =**

**(0,666666)^30 = 0,000005214 = 0 % (rounded down to the inferior number).**

This represents a very low risk of ruin! This allows him to take risks knowing that there is very little chance of ruin. Of course, this assumes that he continues to trade in a reasonable manner! If the profit rate and the profit/loss ratio adjust themselves over time, the risk of bankruptcy may thus increase or decrease.

**Another trader, “Veronica”,** takes too much risk and is undercapitalised. She has an account of $10,000 and is willing to risk a maximum Dradown of 30%, which is a ruin point at -$3,000. Profit = 60%, Loss = 40%, risk per trade 10% of the account (-$1,000) so the maximum number of trades she can make and lose consecutively is 3 trades before she reaches her point of ruin (Maximum drawdown of 30%).

Her risk of ruin is therefore calculated as follows:

**(1-(0.2)/1+(0.2))^3 =**

**(0,666666)^3 = 0,2962954074083 = 30% (rounded up to the nearest number)**

This represents a big difference despite the similar technical performance, but she has a smaller account and therefore more risk. Veronica therefore has a high probability of going broke.

Any probability in favor of ruin is not good! It is therefore essential to determine the size of the position and manage the risk accordingly for each trade and each day so that the risk is minimal and the risk of bankruptcy is kept to a minimum.

So let’s see how you can reduce your risk of bankruptcy:

- Increase your accuracy to get a higher % of winning trades.
- Increase your average profit/loss ratio.
- Reduce the amount of money at risk per trade and per day. (You can do this – at least reduce your risk!)

Risk/return ratio | 1:1 | 1:2 | 1:3 | 1:4 | 1:5 |
---|---|---|---|---|---|

25% of trades win | 100% | 100% | 99% | 30.30% | 16.20% |

30% of trades win | 100% | 100% | 27.70% | 10.20% | 6.00% |

35% of trades win | 100% | 60.80% | 8.20% | 3.60% | 2.30% |

40% of trades win | 100% | 14.30% | 2.50% | 1.30% | 0.80% |

45% of trades win | 100% | 3.30% | 0.80% | 0.40% | 0.30% |

50% of trades win | 99% | 0.80% | 0.20% | 0.10% | 0.10% |

55% of trades win | 13.20% | 0.20% | 0.10% | 0.10% | 0.00% |

60% of trades win | 1.70% | 0.00% | 0.00% | 0.00% | 0.00% |

65% of trades win | 0% | 0.00% | 0.00% | 0.00% | 0.00% |

75% of trades win | 0% | 0.00% | 0.00% | 0.00% | 0.00% |

80% of trades win | 0% | 0.00% | 0.00% | 0.00% | 0.00% |

When using a risk level of 10% of account capital per trade, if you have a winning percentage of 35% and a risk/reward ratio of 1:2, you have a 60.8% chance of losing all of your money. However, if you can increase your market edge (percentage of winning trades) by 5%, then you only have a 14.3% chance of losing your entire account. This shows the power of improving your trading strategies and increasing your percentage of winning trades to gain greater market edge and improve your odds of long term success.

Now, let’s take this same 35% percentage of winning trades, but increase the risk/reward ratio from 1:2 to 1:3. This turns a 60.8% risk of ruin into an 8.2% risk of ruin, so this change actually offers a big advantage. Here is the real challenge:

In trading, it’s actually harder to increase the profit target from 2:1 to 3:1 than to increase the percentage of winning trades or the accuracy by 5%. A 5% increase in the accuracy of a system is not a big change. Jumping from 10% to 20% is a big change and much harder to achieve, but a 5% improvement is not. In a series of 100 trades, it is enough to have 5 other winning trades or 1 other winner in 20 trades.

But it becomes much more difficult to change the profit target from 100 pips to 150 pips, for example, simply because you are trying to catch larger price movements and the market doesn’t always have the right conditions to achieve this. This requires greater precision in the opening of a trade, just to increase the final benefit by 6% (from a risk of ruin of 14.30% to one of 8.2%).

Now, let’s look at the other side of the equation.

Suppose a trader has a 35% win percentage (a highly reasonable goal) and a risk/reward ratio of 1/3. This means that he only has an 8.2% chance of losing all of his capital. However, if this trader is like pretty much every other novice trader who learns to trade and closes their winning trades too early, say 50% of the time, how does that change the above math? The direct consequence of this bad practice is that the 8.2% risk of ruin of soars to 34%. That is 3 chances out of 10 of losing all the capital. Not bad, but definitely less stable. This assumes that the trader effectively gets a 1:3 risk/reward ratio on half of his trades and a 1:2 risk/reward ratio on the other remaining half.

However, as in life, there are things going on in trading that make it much more difficult to maintain discipline, so our math, including our risk/reward ratio remains unchanged. It would be much simpler if trading were like a game of poker where you know the exact profits or losses you can have in each hand, but this isn’t poker, it’s a complex environment that is constantly evolving, sometimes forcing you to leave the market early. Does this increase or decrease the advantage of a system in the market? It is very likely that any adjustment to your system and its risk-reward relationship will reduce your edge, so focus instead on the precision of your strategy to achieve a higher rate of winning.

So if you don’t know your risk of ruin yet, figure it out now!

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