Re: Continuing the trader/sniper analogy...
So this relentless talking about risk/reward is actually crap, isn't it.
Well no it isn't. Although it is crap when it is considered in isolation which unfortunately seems to be often done by many (which is perhaps what your'e saying?) What most people don't seem to understand is that reward:risk is attached to the hip with win/loss ratio, as you yourself in fact just pointed out. Taking the 2 together as you should, then reward:risk becomes very important and a useful tool to evaluate the overall quality/profitablity of your system.
To reiterate/explain: It's meaningless to talk about risk:reward ratio in isolation. It can only be meaningful if you also always combine it with the win:loss ratio expected for that risk:reward ratio (and vice-versa), because only if you have
both values, can calculate your APPT which stands for "Average Profitability Per Trade" (also known as "Expectancy" as used and described by Van K. Tharp in his book.)
It is obvious that unless you are on average net profitable your account balance will decline over time (even if you have the occassional upswings). We're talking averages here. And that if you *are* on average net profitable, your account balance will increase over time (even if you have occassional drawdowns which are not too severe to overcome).
The formula is (hopefully simple!):
APPT = (Average Winning trades % x Average Win size) - (Average Losing trades % x Average Loss size)
For example, let's say that on average you profit on 2 out of 10 trades (so you lose on 8). This means you have a 20% (0.2) win rate and a 80% (0.8) loss rate. This means your win:loss rate is 1:4. Let's also say that on average, you win $1200 when you win and you lose $300 when you lose. This means your reward:risk rate = 1200:300 = 4:1. You might think that with such a high reward:risk rate you should be profitable. However let's see what the sum says:
APPT = (0.2 x $1200) – (0.8 x $300)
= 240 - 240
= $0 on average
So you're only net break even, on average! Despite having a 4:1 reward:risk ratio! So, looking at reward:risk without taking into account win:loss ratio/probability is... meaningless!
Let's now say you you profit on 8 out of 10 trades on average ( so you lose on
only 2 out of ten.) This means you win on 80% of your trades (0.8) and lose on 20% of your trades (0.2) and your win:loss ratio is 80:20 = 8:2 = 4:1, which one might think is obviously quite high and on the face of it very good. One might think that you have to make money with such a good win:loss rate. (Such a high rate plays into our "wanting to be right bias" of course...)
Suppose further your average win size is $200 while your average loss size is $1000. This means your reward:risk ratio is $200:$1000 so is 1:5. Here some alarm bells should be ringing as that's a very low reward:risk ratio, but the jury's out until the sum is done. The APPT then is:
APPT = (0.8 x $200) – (0.2 x $1000)
= 160 - 200
= -$40 on average
So despite the very good win:loss rate (4:1 or 80% of trades won) you will still be a net loser with a system that trades like this.
But notice, if you can reduce your average loss size to say $500, the sum becomes:
APPT = (0.8 x $200) – (0.2 x $500)
= 160 - 100
= $60 on average per trade
Which is net profitable, despite the fact that the reward:risk ratio is still relatively low at $200:$500 = 2:5 = 1:2.5 = 0.4:1. Which again shows that reward:risk is meaningless without win:loss.
Let's finally do an example where your win:loss rate is 1:2. This means 1/3 of trades are won and 2/3 of trades are lost. Suppose further your average win size is $1500 and your average loss is $500, which makes your reward:risk ratio 1500:500 = 3:1. Then the sum becomes
APPT = (0.333 * $1500) - (0.666 * $500)
= $500 - $333.33
= $166.67 on average
So a system with a relatively modest win:loss rate which only wins on 1/3 of trades, but has a decent reward:risk ratio of 3:1 is net profitable to the tune of $166.67 per trade. As an aside, I'll finally just observe that the
net profitability (per trade) of the system is roughly
one tenth of the
average win size of your winning trades. It would be wildly unrealistic to estimate where you'll be profit wise based on the average size of your winning trades ($1500) and instead should use the more modest net average profitability size which in this example is $166.67. Just something to think about.
What all this hopefully illustrates is that reward:risk and win:loss are equally important when evaluating your trading system's quality. It is meaningless to look at only reward:risk (assuming win:loss will be ok by magic) or only win:loss (assuming reward:risk will ok by magic).
I'll finally emphasise that what further complicates matters is that these 2 measures/variables are in fact interrelated, and not independent variables in a trading system. It's like a complicated machine with 2 dials on, one for win:loss rate, and one for reward:risk rate. One might think you can modify your system to try and improve one of them without affecting the other, but in practice it usually doesn't work like this. Typically you'll find that when you start adjusting your system to increase the win:loss rate (for example), you'll find it in turn affects the reward:risk rate negatively and vice-versa. So the challenge in good trading system development is to tune/design/tweak your system so it's net profitable overall, e.g. get to a point where the 2 variables namely win:loss and reward:risk ratio's gives you a net profitable system, despite these 2 variables being semi-dependent. (As an aside, this is why I enquired in a previous post whether you've calculated the expectancy of your systems.)
For reference, I looked at
this page while constructing this post.
Apologies if you already know all this. Good luck for your trading week.
Edit:
At the risk of stating what might be obvious, what I've not said anything about is how to calculate the APPT for your trading systems. Well you need to basically calculate the following values:
1.) Average Winning trades %
2.) Average Losing trades %
3.) Average Win size
4.) Average Loss size
So for 1.) pull all your trades, count the number of winning trades, and work out the % they make up of the total. For 2.) The difference between that and 100% is obviously the % losing trades (but obviously you can just count the number of losing trades again if you like, and work out the % they make of the total.)
Next for 3.) sum up all the winning trade values only and calculate the average value of them all. Next for 4.) similarly sum up the average losing trades and calculate the average. Finally substitute the found values into the formula as was done above.
As an aside, you may also want to look at the maximum lost trade size, since if this is very much bigger than the average loss size then the resultant APPT/expectancy value may in fact be a bit optimistic in practice. (Van K. Tharp actually uses, if I remember correctly, the maximum loss size for no.4, rather than the average loss size, since that is obviously more conservative as it's "worse case" (and has the effect of forcing one to be strict about stop losses...) But don't quote me on that -- I'll have to go look that up sometime and get back to you to be sure I'm not misquoting/representing him.
Anyway, I hope that's helpful, if not then just ignore it!