February 21, 2013

How The Correct Risk Reward Ratio Can Boost Your Profits

Ever wonder why a 1:3 Risk:Reward ratio is so prevalent as a rule of thumb? Ever since I’ve been reading about day trading, I’ve heard people say they ideally look for at least a 1:3 ratio, even they’ll settle for 1:2. In this article I’ll talk about how you can derive this value from the expectancy equation. Further, I’ll show how you can predict what kind of Risk:Reward ratio is right for you.

If you are math-averse, you can skip the equations; examples are given and explained.

What Should My Minimum Typical Gain Be?

risk rewardLet’s say the minimum acceptable performance for your day trading is flat. That is, at a minimum, you should not be losing money over time. How much money should you be making on your winning trades to achieve this performance? If you know your historical win rate, and assume your typical loss is a full 1 R, then this is the equation you need:

Gain = (1 – winrate) / winrate

This equation answers the question “What typical R gain will make my expectancy equal 0, assuming I always lose a full 1 R when I lose?” So obviously, typical gains greater than this value will give you a positive expectancy.

Let’s work an example: Say my win rate is 40%. Then the equation above is (1 – .40)/.40, or 1.5. That means I should only enter trades where I average at least a 1.5 R gain when I win. If I always trade at that minimum my account will not grow or shrink long-term. To intuitively see how this works, imagine I take 100 trades. I will win 40 of them for 1.5 R each. I will lose 60 of them for -1 R each. That’s a gain of 60 R and a loss of 60 R. My account hasn’t budged. Taking trades with a reward smaller than 1.5 R would cause my account to lose money over time, at this win rate. In the same way, taking trades with a reward greater than 1.5 R would cause my account to grow.

Here’s a few more values:

Win Rate Needed Gain
20% 4 R
30% 2.33 R
40% 1.5 R
50% 1 R
60% 0.67 R
70% 0.43 R
80% 0.25 R

Translate this to Risk:Reward

So is the above saying a 40% winner should enter trades whenever they estimate a Risk:Reward of 1:1.5 or better? Probably NOT. You see, if you are like me, or any other day traders I know, you don’t hit your estimated reward target all the time (or even most of the time). So you need to understand based on your trading history, what kind of adjustment to make in order to get the gains you need.

The adjustment is to divide the R gain you need by the percentage of your reward target that you tend to win. The example will make this clearer…

So to continue the above example, recall that my win rate is 40%. I know from the table above that I need to average a minimum of 1.5 R gain on my winning trades. But what Risk:Reward estimate gets me a 1.5 R gain when I win? My records show that I tend to take home about 50% of the reward I estimate for winning trades. So I’ll divide that 1.5 R by 0.5 to get 3 R. That means I should enter trades when I estimate a 1:3 Risk:Reward. That way I’ll tend to win 1.5 R or greater and my account will be healthy.

And there’s our magic 1:3 number! My example case was not an accident. You see, I think the number is so prevalent because of what you can assume about the typical profitable day trader. It’s pretty safe to assume that they generally win 40% or more of the time and that they get around half the gains they thought they would. Given that, 1:3 pops right out as the kind of Risk:Reward they should be looking for.

And, it follows that if your stats aren’t anywhere close to that hypothetical trader’s, then 1:3 is a meaningless guideline for you. For instance, if you win 60% of the time, and tend to take home a third of the projected reward, then 1:2 is a more appropriate minimum ratio. Of course, we are calculating the minimum for profitability here… traders should always strive to find the best risk:reward trades available within their style of trading.

Summary

After reading this article, you should have an idea of why conventional wisdom says 1:3 Risk:Reward ratios are good. You should also have the tools you need to find out what your minimum Risk:Reward targets should be. I hope this aids you in your day trading strategies

Max Hansson

Max Hansson is a guest author to the site. Writing about risk, chart strategies and money management. Max is an active day trader of forex, mainly EUR/USD and GBP/USD.