## A Secret about Mathematics of Risk

ebiesczad Posted 2 Sep. in #Forex #Strategy #Trade #Profit #Drawdown #Math #Risk #Consistent #Breakeven #Risk/rewardIn this article, I’m going to share with you a little secret of mathematics and risk management. I formulated a simple law that expresses a win-win situation in risk management coming from risk/reward ratio analysis and the different mathematical outcomes and ideas that spiral off these simple and yet powerful notions.

As we all know, good trading comes from the triple intersection between good trade location, good risk management and your ability to master yourself. This tripod cannot function properly if one of the elements is out of balance. So, in here I’m going to give you the key and some wise concepts about the second element: risk management. If you apply these principles, you’ll notice that your trading will become more solid and consistent over time. Also, you’ll have the ability to be wrong in your trading decisions most of the time and still come out with a little profit or at least breakeven. By having that in the back of your mind, you'll be able to eliminate some of the bad emotions about trading like risk aversion and the desperate need for absolute accuracy all the time.

Before we worry about how much precise we can be with out strategy with need a insurance plan. A plan to preserve your capital in the worst situations that can and will appear in real life trading. Let’s begin with simple concepts and after that we’ll dig deeper into it to find find some surprising things:

**-Maximum Risk per Trade: **This is the maximum amount of your equity that you’re allowed to risk in any given trade. For example, you can say you’ll never risk more than 1,5% of your total equity in one trade. You can trade less than that obviously, but not more.

**-****Maximum Drawdown of Total Equity:** This is important because it tells you when to stop everything you’re doing and analyze what you did wrong in the last losing trades. For example, you can say your maximum drawdown is 10% of total equity. If you lose 10% of everything you have, you stop everything and analyze what rules you broke and what you did wrong. If we use the example of the last topic, you’ll have to lose 6 or 7 trades at maximum risk in a row in order to reach your maximum drawdown limit. If you have a decent strategy for trade location, that shouldn’t happen at all.

**-****Minimum Risk/Reward Level:** This is probably the most important variable in your risk management arsenal. This is where you’re going to find out about the secret math law I promised in the beginning. First, we need to understand that each specific level of risk reward ratio gives a specific margin of error for your trade decisions. What does that mean? It means that if you set a specific risk/reward level you can be wrong X% of the time and still breakeven. Let’s analyze the different risk/reward levels and their respective margins of error.

If your risk/reward is 1:1, you’re risking $1 to make $1. So, if you have 20 losing trades you need 20 winning trades to breakeven. That means you can be wrong 50% of the time and breakeven since you made 20 losers in a total of 40 trades. Now, let’s imagine you have 2:1 risk/reward ratio. You are risking $1 expecting to make $2. Lets use the same example and say that you made 20 losing trades. Your total loss equals $20, so how many winning trades do you need to breakeven? $20 divided by $2, which is what you expect with your winning trades. Answer: you need 10 winning trades to breakeven. In conclusion, you made 20 losers, 10 winners and a total of 30 trades. In other words, you were wrong 66,67% of the time and broke even.

Do you see what happens and you increase the risk/reward level? You instantly increase your margin of error. From 50% with 1:1 to 66,67% with 2:1. Ok, great, so why don’t we just use 20:1 of 50:1 risk/reward trades? Imagine what the margin of error would be at these levels! There are two reasons why you shouldn’t do that: First, it’s not realistic and second, because of the ** law of decreasing margin of error increments**, which is the secret math law I observed in my research about risk. Let’s study the tables below to understand what this law is about. The table shows the different margins of error for the different risk/reward levels:

The chart to the left shows the size of the increment in the margin of error that you get when you change from one risk/reward level to the next:** (Right click on it and "open image in new tab" to see it clearly).**

This chart to the right shows clearly that the margin of error increment flattens out as the risk/reward levels increase. So, now we can finally make the claim for our special law:** ****(Right click on it and "open image in new tab" to see it clearly).**

*“As the risk/reward level increases, therefore becoming more and more unrealistic, the margin of error increment decreases and flattens out”.*

Can you see how this is a win-win situation? The trades with large risk/reward levels like 8:1 to 10:1 are very hard to find and unrealistic. At the same time, increasing your risk/reward level too much doesn’t add much margin of error after a certain point as we can see clearly on the bar chart. We can also say that, the optimal range of risk reward levels you should shoot for lives where the bars start to flatten out. In other words, the optimal range is between 3:1 and 5:1. These are very realistic and provide an optimal margin of error. In order to find these trades you need a good method for trade location, but that is a completely different animal and a subject for another article.

So there you have it, sticking to those trades between 3 to 1 and 5 to 1, you can be wrong between 75% and 83,34% of the time and still breakeven. If you were looking for an edge in risk management, this is it.