Evaluating Risk and Reward Metrics Part I
I’ve thought about it long and hard, and there is no concrete blueprint by which we navigate our way through determining risk and reward. What I mean by this, is there are often unique or idiosyncratic methods by which we define and specifically determine which is our numerator and which is our denominator.
Depending on which of these formula’s you use your numbers will look somewhat different; one of these ratio’s favoring a number as close to 0 as possible and the other favoring a number as large as possible.
Let’s work through an example. Say that we take a trade on a $50 stock. We buy 100 shares and set our stop loss at $48.00. This represents a total risk of $200. For now, let’s say that our take profit target is $53.00 which would bring us a total gain of $300. We can set up our risk reward ratio either way but for me personally, I prefer it set up as below.
What inferences can we now make about these risk reward ratios? Well, the 3 is obviously a better, larger, and more favorable number than 1.5 right. Yes, but is that all? Maybe, the problem I see with these risk reward ratios is that they are too simplistic. Having a $56 price target with a $50 is stock is all good and fine but does it really tell us much about how likely it is for that stock to hit $56? The risk reward ratio does not at all tell us how likely or probable that scenario is. To compensate for this lack of probability will be easy. We are going to attach a probability to both the numerator and the denominator.
It looks more complicated than it actually is. I have written a lot previously about probability, what it is, and how to go about finding it and calculating it. In this example we are going to apply some speculative probabilities. Yes, made up by me in my head. Let me suggest that the probability of a $50 stock moving to $56 is approximately 0.35 or 35%. (Notice I do not give a defined time frame for this?) Let me also suggest that the probability of the stock moving to $48 is 0.50 or 50%.
Now our risk reward metric has moved against us or not in our favor. Yes, keep in mind that these probabilities are speculative but this exercise is about understanding the reality of placing some hard to reach 12% stock move to a reward target. The reality is that a 12% move in a stock (in a single day) is often huge and not a large probability at all if you are just considering one day of trading time. If these risk reward metrics are for swing trades and held overnight then the landscape changes quite a bit and we might consider a 12% move more realistic. However, for a single day trade 12% is (often) a huge move. While it might seem like I am totally just making these probabilities up in my head (and I am) it might be generally accepted that the further away from the current stock price the less probable it becomes. That is because probability is distributed in greater volume closer to the mean value (assuming standard distribution).
I have heard said, from a couple of different traders that taking a trade with a risk reward ratio of 4 or higher is often a great trade, but I have since come to question this logic based on the actual probability of this trade hitting those targets and what time frame, we might realistically expect either target to be hit.
For a long while I realize one of the mistakes, I was making was setting my stop loss too low and taking profit too early. After doing this exercise and furthering my learning I have since come to realize the futility of setting my stops too low and taking profits too early.
I would like to introduce a postulate that might turn be somewhat contrarian. This idea is determining a reward risk ratio based entirely off of probabilities rather than gains and losses.
A ratio of 0.7 really changes our outlook from the 2.1 we had used the previous formula. The difference between these two results really goes to show just how important having probabilities in your favor are does it not?
What about risk reward metrics for swing traders rather than just day traders. Might there be a difference between the two. I think there is. The difference is opportunity cost. How much it cost to sit around and hold something that might go against you or stay stagnant. We have to somehow factor in a relationship for the role that time plays in our equation.
This is theory in action. Should it instead be an addition or subtraction or another type of function? Maybe, we can revisit this idea done the line. I’ve been thinking about how this element of time should work in this equation, all weekend. I’m probably going to have to set it aside for now and continue on a bit as is. However, my current thinking is that time should be favorable to day traders that are not holding overnight. The longer the swing trade the more time should count against your risk but also for your probability. In this respect it will undoubtedly matter how we choose to go about calculating the Reward/Risk side of the equation. I am likely to make a Part II for risk and Reward using this idea of time for swing trades.
I remember it must have been about a year ago, I was trading uranium equities all day long and thinking to myself that there must be some sort of risk reward math out there. At the time, I remember being incredibly frustrated with Uranium equities and thinking my money was best put to use in other sectors with more love from the masses. I don’t know that the math I am using here today can help alleviate or pacify those pains. None the less, I had a goal to go about learning how math is used to define risk and reward in trading. I have certainly not uncovered everything in this arena but I believe I have scratched the surface. From my understanding risk and reward math can be as complex as you want it to be. When this “time” factor comes into play it gets increasingly complex in my opinion. I’m sure some of these huge hedge funds have college boy calculus snobs cranking our derivatives and integrals that would knock my socks inside out. I can be humble in the fact that I do not know everything.
To conclude Risk and Reward for time being. I like using these two formulas below but I don’t give much credit to simply money gained or lost as with no accounting for probability it means very little.
I don’t have much in my personal life to spell out here, but I have made a relationship to risk reward in my personal life that I will share. I love riding motorcycles. When the weather is warm like it is now, I really miss it bad and really want to get back out there on two wheels again. The risk of riding a motorcycle is actually really large (mostly because of other drivers). When I was younger and dumber I didn’t care. Knockback a 6 pack, do all the drugs in front of me, jump on the motorcycle, and throw a fat chick on the back. Whatever it was that was dangerous I did it and somehow survived. I think about it now and wonder is it really worth spending 10k on a new motorcycle to relive the glory days of my youth or could that money be better spent elsewhere? Well, risk and reward thinking has me favorable to throwing that money at my trading account instead of chasing my glory days on a motorcycle.