I have been getting a lot of comments, questions and emails about money management as of late with the market becoming very volatile. This article will show you the most important mathematics you will need to learn to have good money management in learning how to trade this market.

Risk of Ruin
The Risk of Ruin is a statistical model which tells you the chances you will lose all of your account based upon your win/loss % and how much risk you put per trade. This is absolutely critical to know because lets say you are risking 10% of your capital per trade, and say have a 2:1 Reward to Risk Ration or R:R, and have an accuracy rate of say 35%, you have a 60.8% chance you will lose all of your money.

Is this a number you would want to know ahead of time? Lets hope so. Lets first talk about its history and how we can adapt it to trading.
The mathematics of the Risk of Ruin tables were first applied to gambling and rightfully so. In gambling, say blackjack, if you win a hand with the dealer busting, you get a 1-1 payout so if you put $100 on the hand, you will win $100. It helps to know this ahead of time so you can see if your edge (% chance you will win over time) is enough to make you money or lose you money.

However, this is the tricky part. In trading, we rarely know exactly how much we are going to make per trade. We have a limit and a stop (hopefully) right off the bat so we are aware of our risk and potential profit. But here is the harbinger and some questions to consider;

1) How many times have you actually closed a winning trade before hitting your full profit target?
2) Do you have a trading system where the profit target is exactly the same (fixed amount of pips) and therefore you know what your exact payout will be if you hit the target?
3) Do you know exactly how accurate you are going to be with your trading based on the system you use? In other words, have you modelled it so you can predict its overall accuracy within a few % each month?

If the answer to question 1 is around 25% or greater, then we will need to take this into serious consideration when calculating our risk of ruin.
If the answer to question 2 is no, then you will have to also take this into serious account when calculating your risk of ruin.
If the answer to question 3 is no, then you will also have to take this into serious account when calculating your risk of ruin.
Lets explore each question, then the math and then see what is a stable level of risk so you do not destroy your account.

Closing a Winning Trade Before Hitting Full Target
Lets be honest for those of you that are still learning how to trade this market consistently – how many times have you closed a winning trade before hitting the full target? The answer is likely many as I talk to traders all the time and hear this from them time and time again. If you were perfect in your discipline, never made an error in trading and risk management, then I would say go ahead and risk 10% of your capital every time if you could always trade with 40% accuracy and had a reward to risk ratio of 2:1. If you did this, you would have only a 14.3% chance of losing all your capital and likely have a winning account.

However, if you cut your profit targets for whatever reason, say 50% of the time and you cut them in half, your risk of ruin goes up to about 60% – meaning you have a 60% chance of losing all your capital. This changes the game completely and puts the mathematics heavily against you having a long trading career.

In fact, every time you shorten your original profit target, you stack the numbers against you and its more likely you are shortening your profit targets than increasing them.

What this translates into is you have to decrease the amount of risk per trade to keep the same edge or chance you will remain in the game.
A trading system where the profit target is fixed every time (say 50pips)
How many of you are using this as your only method to trade the markets? The answer is likely less than 10% as most of you are probably not using just one system to trade the market but several. Even if you were using one system, the chances are it does not have a fixed target.

The reason why having a fixed target gives you an edge (mathematically) is once you can stabilize the accuracy ratio, you can easily calculate your risk of ruin because your risk and reward are fixed from the outset. This makes the math very tidy.

However, having a fixed target may not always be advisable. Sometimes the market will go for a runner so it helps to take advantage of those big moves when they come. They increase the alpha (the rate of return on an instrument in excess of what would be predicted by an equilibrium model) on your returns and help smooth out losing periods. For a full article on alpha, click here but basically it means if your system is on average 50% accurate, your R:R ratios are 2:1, you should be making $1000 on every win and $500 on every loss. After 10 trades you will have banked $2500. However, if you have an alpha of 5%, you will make an extra $125 which over time adds up.

By staying in trades that go for long runners, although your accuracy remains the same, one winner could count for what you normally get from two so its critical to stay in trades that run or do not give you a signal to exit based on a fixed number. Some systems work best with a fixed profit target in pips but there are many which perform much better when they stay in the runners.
Regardless, if your system does not have a fixed profit target in pips, then you will want to reduce your risk % based upon keeping the mathematics more in your favor.

How Accurate Are You Going To Be?
Unless you have done massive forward and backtesting on your system, you will unlikely know the answer to this question. On top of this, markets change and your accuracy levels will likely change with them. Do you even know your current accuracy ratio as it is for all your trades? Per Pair? Per System? If you do not, then its highly likely you will have the numbers stacked against you and your chance of losing all your capital is more likely than you assume.
Thus, what this means is to be on the safe side of things, you will want to have a smaller amount of % equity at risk per trade. This also becomes more critical in the early stages of your trading where you are likely to make more mistakes, have a lower equity ratio and take profit before hitting your full target.

But to highlight the numbers and their importance, lets take a look at a table below using the Risk of Ruin formula.

risk_of_ruin = ((1 – Edge)/(1 + Edge)) ^ Capital_Units

Lets deconstruct this briefly. Using 10% of capital at risk per trade, if you are 35% accurate and have an R:R ratio of 2:1, you have a 60.8% chance of losing all your capital. However, if you can increase your edge (accuracy) by 5%, you only have a 14.3% chance of losing your entire account. This shows the power of increasing accuracy ratio to gain a greater edge. Now, lets take the same accuracy ratio of 35% but increase the R:R to 3:1 from 2:1, what this does is turn your 60.8% risk of ruin to 8.2% so in actuality, this gives you a greater edge. Here is the challenge;

In trading, it is actually harder to increase the profit target from 2:1 to 3:1 than it is to increase your accuracy ratio of 5%. 5% is not a big shift. 10-20% is a big shift and much harder to achieve but 5% is not. Over 100 trades, you only have to win 5 more or 1 in 20 more. But to increase your profit target from say 100pips to 150 becomes much harder simply because you are trying to capture more of the days range which requires more precision in your entry, all to increase your bottom line edge by 6% from 14.30 risk of ruin to 8.2% risk of ruin. And if you are not hitting your full targets to begin with, does making your profit target larger seem more reasonable? Unlikely.

Now lets take the other side of this equation. Lets say you are 35% accurate (not too demanding a figure) and have a 3:1 R:R. You will only have an 8.2% chance of losing all your capital. However, you are like virtually everyone else learning how to trade and you take profits early, say 50% of the time. Instead of taking profits at 3:1 R:R, 50% of the time you take them at 2:1 R:R. What does this do to your risk of ruin chances? Turns the ratio from 8.2% to 34%. So now you have a 3 in 10 chance of losing all your capital. Not bad but definitely less stable. This is assuming you are perfect in taking profits at 3:1 R:R 50% of the time and 50% at 2:1 R:R.

But…the markets change, your positions change, things happen that change the game. Central banks intervene, news comes out that drastically changes your position, you see a pattern which you used as a buy signal but now is posting the exact same signal just reversing the trade against you. Do you stay in the trade and wait till your full stop is hit? If it was just as good a valid signal to take the position, shouldn’t it be for closing it early?

The point is things happen and make it very difficult for us to be not only perfect in our discipline, but also perfect in our mathematics and R:R ratios. It is simple if we are trading blackjack where we know the fixed profits we can make and lose, but this is not blackjack – it is a fluid living breathing market and sometimes it would be advisable to exit early. Does this increase your edge or reduce it? More than likely, any adjustments to the system and R:R ratios decrease your edge, not increase them.

So what does this mean for you?
Risk less than 10% of your capital per trade. Risk a lot less. Put the edge so far in your favor that its almost inconceivable you would lose all your capital. If you have capital, you are in the game but if you don’t, you are out. Your capital is your ammo and without it, your dead in this game. Especially when learning how to trade consistently, keep your risk low like 2%. Even when you are really good, keep it low because you will have losing periods and when you do, you want to absorb them well and not take big chunks out of your account. Risking 10% will do this but risking 2% will not.

Although it may not seem like you will make a lot of money risking 2% and having a 2:1 R:R, over time as your account grows, it will compound and you will take losses with ease of stride. However, by risking 5-10%, you severely alter the mathematics and your edge.

As long as your R:R ratio is 2:1 or better, when you lose you will lose a little and when you win you win much more. Even if you take a series of losers, it will only take just as many wins to be back ahead. Case in point;
Say you have a 10k account and have a 2:1 R:R and risk 2% per trade. Here is how the math works out below after a series of 3 losers and 3 winners:

10k with 1 loss at 2% = $200 loss and acct is at $9800
$9800 with 2nd loss at 2% = $196 loss and acct is at $9604
$9604 with 3rd loss at 2% = $192.08 and acct is at $9411.92
So you lost 3 trades in a row and now win 3 trades, here is the tally:
$9411.92 with 1st win at 4% gain (2:1 R:R ratio) = $376.47 and acct is at $9788.39
$9788.39 with 2nd win at 4% gain = $391.53 and acct is at $10179.92
*thus after 2 trades you are back into profit.
$10179.92 with 3rd win at 4% gain = $407.19 and acct is at $10587.11

so even after two wins you erased 3 losses and with the 3rd win you are way ahead. Thus, hopefully you can see the importance of having a good R:R while having low risk. It is psychologically hard to deal with big losses but little losses have a much smaller impact on your emotions and trading so keeping an edge both mathematically and psychologically is crucial to winning at this game.

Author:

Chris Capre
www.2ndskiesforex.com