124 - First Principles: Volatility Steals Your Edge

On today's episode of The Trade Busters Podcast, this may quite literally be the most important episode I've ever released. And the reason for that is, so first of all, if you haven't already done so, go listen to my last episode, episode 123, which is called Know Your Edge. And this idea of Knowing Your Edge, and I mentioned right at the top of that episode that it's quite straightforward, and it's just more of an issue that most people don't maybe think about it, or not mindful of what their edge is. But today's episode, I want to talk about something that is basically an extension of that, and it is something that comes to realization of, you know, after so many years of trading, developing strategies, et cetera. And it's the idea that volatility and volatility tax essentially rob you of your edge. So again, if you haven't already done so, go listen to episode 123, and this idea, you know, all of the episodes I've done, and this whole concept of expectancy hacking. So Know Your Edge is knowing why your strategy should work, where your profits are coming from. In expectancy hacking, I've talked about as a way of kind of safely harnessing the edge, shaping your equity curve, your risk profile. And so the equation for expectancy, I've said, is one rate, one size, and loss size, right, and expectancy hacking is the idea of focusing on the one and loss size, or the one loss ratio, and letting the strategy determine the one rate. So the big revelation is that there's actually a fourth variable, and that is the volatility tax. And this can actually be measured. So real quick, we talked, you know, many times in the past, there's even episodes on this asymmetric compounding, or the episode was like one minus one doesn't equal zero, and I'll link those in the show notes. But this idea that compounding is not symmetric in both ways, right, if you, and it kind of extreme examples, if you lose 50% of your account, you need 100% to get back to even. And this basically brings up the concept of arithmetic versus geometric returns. And I want to take a moment to point out and reference an article that I will also link in the show notes, it's literally called the arithmetic return doesn't exist. It's by Matt Hollerbock, who runs the blog called Breaking the Market, and again, that is something you definitely want to go and read, and I'll link that in the show notes. But the idea is once you take into account compounding and the geometric nature of compound returns, what you expect may not be the same as what actually happens over a large sample size and large number of repeated trials. So I set up another spreadsheet that will give you a very clear kind of numeric example of this. And this is going to be initial notes. I haven't linked it at the main trade buses page yet. So I'll link the direct link over in the show notes. The spreadsheet title is Shannon's demon, and let's not focus on that now. We'll get into there's a whole other episode about why, you know, that name and the spreadsheet. But if you go to that sheet, and I definitely recommend you do I'll try my best to kind of explaining the America example on this episode, but it will be very helpful to go to the sheet to see it for yourself, and there's a tool you kind of kind of play around with and see different examples. So at the sheet, there's a tab called geometric return, and this is sort of the usual setup where there's going to be certain cells where you can go ahead and do a user toggle and change the values. And this sheet is set up where you set up a one rate and then average, you know, one size loss size kind of risk reward ratio. And it's going to show you based on varying bet sizes. What the earth matter return and the geometric return are so you can see the difference. So there's three cells you can edit one is the one rate and you'll see that, you know, if the one rate is 50% the loss rates 50% right. It's going to just automatically update if the one rate is 95% the loss rates 5% so that's pretty self explanatory. The next one is the size average loss. Now the reason why I made it so. The average loss is the input and then the average win will be automatically updated because when we talk about expectancy and Kelly ratio. And kind of the risk reward ratio is usually measured as a function of the loss size. So when you say there's a bet size, it means how much you stand to lose. So in this sheet, if you input for example, I'm going to put negative 1%. So let's say you lose 1% when you lose the last input is the reward risk ratio. So basically all this sheet does is it takes your loss size. It takes the reward risk ratio and applies that to calculate the win. So here's the example. I'm going to set it up with a 50% win rate average loss size of 1% and you had to use a negative negative 1% and then I'm setting up reward risk ratio of 1.2. And what that's going to mean is your win size is 1.2 x of your loss size. So if you have negative 1% and a 1.2 reward risk ratio, you'll see that the average win size is going to be 1.2% right because it's 1.2 to 1. So looking along this sheet, I have it set up where it's going to automatically give like just 20 rows and it's trying to show the difference as you increase that size. So on the average loss column, it starts at the 1% and it just automatically steps up, you know, this goes 1, 2, 3, 4, all over up to 20%. And if you look at the arithmetic return, we look at just kind of row 10. With a 50% win rate, 1% loss and a 1.2 reward risk ratio, your arithmetic return, which is kind of the average return per trade per occurrence, is 0.1%. Now this is kind of a very straightforward kind of probability equation, you take the win rate times the win size, subtract the loss rate times the loss size, negative 0.1. So that says that every time you make this trade, you expect 50% win rate, 1.2 win, win on a loss, you expect to gain 0.1%. So that's pretty straightforward. And there's a column called 100 AR, which I basically just said, if you do this 100 times, which kind of you expect to return. So at a 0.1% per trade, your expected return over 100 trades is 10.5%. Now as you go down the columns, you can see that as you increase the bet size linearly, your arithmetic return also increases linearly. So you double the size, then you double the return, 0.1% on average becomes 0.2%, triple the size, right, 3%, but becomes 0.3% return per trade. And then similarly, the arithmetic return over 100 trades, it also scales linearly. And so this is the thing that at a high level probability, it kind of makes sense, right. But this doesn't take into account compounding. And there's another column called GR, which is geometric return. And this basically, there's a different equation in there that kind of takes the limit to infinity and assumes long term with the effect of compounding. And what I mean is this, again, the idea that losses compound faster than gains. Okay, so you can click in the cell if you want to see the formula for that limit. But going back to your original example, if you have an arithmetic return of 0.1%, your geometric return is 0.09%. Right, it's a slightly less. And if we look at that row, right, you're, you're expected return, automatically, after 100 trials is 10.5%. You're expected trial after 100 trials of the geometric return is 10, right. So 10.5 drops of 10 is a slight drop. And to sort of let you quickly assess the difference, I call this the, the GR, AR gap, right, the gap between geometric return and arithmetic return. So there's a column, which is, I've just taken the, the, the geometric return and divided by the arithmetic return, just set up a ratio. And so for a bed size of 1%, right, the first row, your geometric return is 94% of your arithmetic return. So basically the, the 0.1% return drops like a 0.094. So you, you lost some potential return due to that volatility. And this is just at a 1% bed size, right. And so now this is where kind of you can gain an intuitive understanding as you go down, as you increase the bed size. And remember before their arithmetic return was increasing linearly, but you'll see that the rate at which the geometric return increases slows down. And as a result, that ratio, the GR over AR also starts to increase. So, and I know you can see this as a spreadsheet on yourself, but I'll just go over a few quick examples just to kind of paint that picture visually. So at a 1% bed size, the geometric return is 94% of the arithmetic return. Let's say we 5x that and we do a 5% bet. So lose 5% or gain 6%. Now the difference is greater. The arithmetic return per trade is 0.5 and the geometric return per trade is 0.35. So that geometric return has dropped to 70% or 0.7 of the arithmetic return. So after 100 trials, arithmetic expectancy is 64%, 64.7% return, the geometric return has dropped to 42%. This is just taking those same numbers and applying over 100 trades. Now, one interesting thing to note, and Matt mentioned this in his blog as well, is when you bet at Kelly size, and you know, you can determine the Kelly just using math through the different metrics of the trade that went rate when size and all that. When you bet at Kelly size, that is peak return. So in this particular example, or if you set it up the way I mentioned, the Kelly size is 8.3%. Meaning, if you bet in such a way that your loss is 8.2%, you will have maximized your potential gain. So if we go down, in this case, it's around, let me see here, around row 17. At an 8% bet size, arithmetic return is 0.8% per trade. Geometric return is 0.42%, so you basically cut the return in half due to volatility tax. The GR AR ratio is right around 52%. And that is also the highest your geometric return will go. As you start increasing that size, your gap between AR and GR will actually start, no, it continues to increase. And your geometric return will actually start dropping. So at an 8% bet size, your geometric return per trade was 0.42%. At a 10% bet size, it drops on the 0.4%, at a 15% bet size, it drops on to 0.15%. So arithmetic return continues to trend up. Geometric return starts to trend down. Matt also mentioned that when you bet at about double the Kelly size, you basically hit 0 expectancy. So if we go down to row 27, actually sorry, row around 25. No, between the 16% and 17% bet size from a Kelly ratio is 8.3%. You see that the geometric return basically hits 0. And beyond that, it starts to go negative. And again, I think hopefully you're kind of able to follow this, but you will have a very good intuitive understanding. If you just go to the spreadsheet and take a look, but this has a few kind of profound effects. And the first one, which I find very important to realize is all else constant. Again, volatility drag will not only rob you of your edge, but it can make a positive expectancy trade into a negative one, with no difference besides sizing. That is very important to understand, because again, going back to the idea of knowing your edge. Yes, if you have an edge, you understand why you should make money and where your profits come from. But if you don't understand this idea of geometric return and volatility tax. It's very easy to conflate a strategy not working, or no edge, with simply a strategy being traded too big. And again, this example I walk through can show you, if you have some constructs, some strategy, you know, with this 50% win rate, 1.2 reward risk, it can be anything. Based on those variables, you will have a certain geometric return, and simply increasing the size. To an extent, it will increase the geometric return, and at a certain point, it starts to decrease it, and then at another point, it hits zero. So, simply trading too large will not only distort kind of the net return and the amount of edge you actually get to keep, but can actually drive a trade or strategy negative. That is probably the most important takeaway, and that's why this is kind of behind all of the episodes and the topics of expectancy hacking, credit targeting all of that. This is the kind of the first principle that's behind all of that. So, again, I think this is one of those things where you really have to be mindful, and when you are developing a strategy and trading, you need to be able to pick apart different aspects and how they impact the performance. And I've done episodes about back testing, and why there's reasons to test it as small size, or one lot, you can look at the win rate, evaluate certain things, and then once you're trying to evaluate actual trading, kind of a longitudinal study, you want to plug in the actual dynamic scaling, that affects the keger and return the max drawdown. But all of that goes back to this idea of volatility drag. And this will come in a later episode, but part of the reason I like to ensemble to multiple strategies is basically to have low correlation strategies, which means they can, you know, you don't even have to be inversely correlated. Just a low correlation means that one strategy can go up, or the other goes down, this has the net effect of reducing your portfolio volatility, which in turn reduces your volatility drag, which in turn preserves the amount of geometric return that you can potentially gain. Because I think of this, I think of like arithmetic return as the max potential, right, it's like the expectancy of one trade is the most you can make out of that one trade on average. But because of volatility drag over long term, it's kind of like reducing that max potential, right, and the lower the volatility of your strategy, the more of your potential you get to keep the smaller that gap between geometric return and arithmetic return. And the larger the volatility, the larger the gap. Now that's not to say that you should always bet super small, because remember there is a point at which geometric geometric return is increasing. So there's kind of two opposing forces. Again, go to the spreadsheet and kind of work your way down the rows. You'll see that yes, as you bet bigger, the GR AR gap increases. You are, in fact, raising the absolute level potential return, right, so your geometric return is increasing. The point is that at that Kelly level, it hits a peak, right, that the rate of increase slows down and that curve starts to bend over and pass the Kelly ratio, your geometric return starts to decrease and it eventually hits zero. And so, you know, it's not trying to say that there's a perfect size or you shouldn't, you know, that you have to trade very small. But it's the fact that recognizing volatility attacks is this kind of unspoken fourth variable that I think is very hard to grasp without sort of having a numeric example like the spreadsheet. But once you understand and acknowledge this fact, then you will have sort of another foundational understanding to basically broaden your broadening understanding of edge, you know, how to best accentuate or take advantage of what you have. And be more mindful in developing strategies, not only in the type of strategy as in, hey, if I want to have, you know, obviously selling options, for example, is like a very negatively skewed. And why we want to use stop losses to kind of control the volatility direct. So understanding, not just what kind of strategy and how to size them and how to size them, you know, for running multiple strategies, how to size strategies relative to each other. So, you know, hopefully that helps. And again, I don't want to be hyperbolic, but I really do think this, this concept may be the kind of most important one that I basically had as a takeaway in all the previous years of of trading these strategies. So hopefully that helps and we'll leave it there for today. As always, if you guys enjoyed this episode, please take a moment to rate, review and subscribe to the podcast. You can visit my trading page at www.thetradebusters.com, where you'll find all the strategy mechanics, trade logs, as well as various essays that have written and other podcasts that recommend. Finally can follow me on X or Twitter at the tradebuster. That's it for today. Thank you for listening and I will see you guys next time.