C (40:46)
With his colleagues at AQR at the time, or in Bitterson, Lasse Peterson. So it's called kind of time, you know, non linear time series momentum. It's quite catchy to talk about nonlinearities in the trend following space. I think my honest opinion before we go into the details is that they spend time discussing a topic that I don't think it's necessarily completely new and this is how past information predicts future information and whether that is a linear or a nonlinear transformation. And I'm going to go into details. I think the novel thing that they bring about is that if there are those nonlinearities, instead of us forcing them by some sort of a parametric approach, let's say we utilize something that is called the sigmoid. So it's a signal that goes from negative to positive, but it flattens out in the tails. Their point is that we know, maybe we let the data speak and maybe we use a neural network that allows us to uncover those relationships and then we can determine the positioning on the basis of those models. So let's kind of break it down into, I guess, into pieces, into components, I guess. Let's think of trading signals in the trend space. What are the possibilities? I would probably say that the simplest of them all is a binary signal. The market goes up, you buy the market goes down, you sell, and maybe you size your exposure statically or dynamically by some level of volume. Fine, let's assume that all volatilities are the same. So you just buy a unit of oil when oil goes up and you sell a unit of S and P. If S and P falls, that's it. Assuming that they have the same wallet. Now, maybe one step of, I guess, of departure from that is to say, well, maybe if my signal is too close to zero, then yes, the sign is positive, but in fact, I don't have so much confidence on it, so I might as well just. But it used my bet as a function of how big that signal is. In other words, if it's a basis point positive, then maybe I should do a basis point allocation rather than a 1% allocation. And if it's 1% of a positive return, then maybe I should do a 1% allocation. So I should scale linearly my exposure to the signal estimation. And that moves us from a binary mindset into a linear mindset. The bigger the magnitude of the signal, the bigger the risk or the sizing that I should do. But there comes now kind of the third iteration of that signaling, which again has been studied in some form or fashion, maybe not as much in academia, even though there are some nice papers that do some empirical analysis on that topic. But certainly I would want to believe in the industry, and certainly if I were to speak about the work that we do, is to acknowledge the fact that, yes, fine, you might actually use the magnitude to scale. But how about an extremely positive or an extremely negative signal? Let's say now you witness S and p up by 3 units of Sharpe ratio. How confident are you to size your exposure so much that this three is going to kind of repeat? So there comes a point whereby confidence and maybe estimation noise and maybe reversion dynamics come into play. And then you kind of say, like, you know what, there is a point whereby I just want to flatten out my exposure. So I get it, the higher the better. But, you know, probably there should be some sort of a concave form on the positivity side and more of a kind of a convex profile on the negative side that flattens out the exposure so I still maintain my linearity around zero. So positives are positive, negatives and negatives. But then in the extremes I should just flatten it out. And I call it the sigmoid, you know, they call it in the paper, S shaped. I'm using the kind of the Greek, if you like, translation of what an S is called like the sigma. So that's if you like the third iteration. So again to repeat binary long or short linear, just use the magnitude sigmoid, maintain the magnitude but then bring some non linearity. And if we stick to those three, before we go to what the paper really really focuses on, there is some form of a benefit, performance wise. If you look into empirical analysis, going into that more like of a sigmoid type of mindset or going into this kind of linear space, maybe the only places that you see some loss of performance is when a tiny bit of a trend is enough for you to get full into the position with a binary signal and then benefit from an early start. But imagine a signal that goes bit positive, bit negative, a bit positive, bit negative with 2 full positive and 2 full negative exposure, you'll end up accruing a lot of costs. So net of costs. It can be a debate how the binary signal can actually help. So this transition is always a bit helpful. So there is empirical evidence and they also showcase it that this non linearity, even if we force it to be like a sigmoid and there are a variety of ways that we can produce that mathematically and parametrically you get good performance or better performance. Their point is why would you have to force the shape of that sigmoid as in everything I've discussed so far is not necessarily driven by the data, it's almost as if we're forcing it. So the sign of past return is our determination, the linear is our determination, the smoothening of the tails is our determination and the signal we put in place is our design. And yes, maybe after the fact we look into the empirical stats and say hey, you're actually doing better. That in itself almost says that yes, probably the data generating process is such whereby you have this continuation of return, but in the tails it ends up reverting. So they say, why don't we let the data speak? So instead of us scaling up and then smoothing in the tails, or scaling down on the negatives and then smoothing it out in the tails, let different markets, be it equities or rates or commodities on and so forth, force this non linearity while still preserving. And that's important, the fact that the signal is positive, I buy, the signal is negative, I sell. And that's important why? Because the minute we depart from it, it is no longer just a trend strategy. Imagine me being here and telling you hey, your signal is positive, you're going to short. Well this is no longer a trend strategy. It's something of a mixture. So they use a neural network. Don't want to bother you too much with the details, but they use a neural network to effectively, if you like, extract the way that past return translates into future return. What's the transfer function? How do I document a signal and how do I determine my position? And should my position be linearly related to my signal? Should it be fading out? If it's too extreme, should it maybe just fall? Let's say to my earlier point, if my sharp ratio is three possible just go to zero. I think crossing zero and going to negative. I see the value of that. Because if the data tells you you need to actually go short, then it basically tells you that there are reversion dynamics. Now, whether we bring the reversion dynamics into a trend system or we use them as a separate engine, to my earlier point, that's maybe cleaner from an ASTA location and from a performance attribution standpoint. But they do show, I guess to go probably closer to the end of my overview, that empirically the data spits out transfer functions that have the non linearity that we're discussing, which is the smoothening in the tails. But even you can end up having reversion dynamics as well in the very extremes. Now I said that those pictures of fitting data at the end of the day, just like if you put past returns, future returns and you like a non parametric analysis, you'll see it. So there are some papers a couple of years back, I believe some of them we have discussed here. But maybe my memory is kind of failing me now that show this relationship. But what they say is that they are now actively monitoring it and fitting it to get to that point. So to conclude, basically the paper says, look, there are non linearities, those nonlinearities exist in details. This is something that we should at the minimum be aware of. Whether we design that parametrically or non parametrically. It's a good question whether the neural network is bringing value. Maybe it brings value. That's why one of the findings that the neural network agrees with the theory and the fact that in the tails possibly the estimation error is greater, and so on and so forth. And some reversion dynamics are there. I would probably say it is an important discussion to be had as to whether this incremental complexity will bring significant value versus having a sigmoid that in itself behaves in line with expectations. So I leave it in this regard, but by all means very good work. And I'm sure people will spend time looking at it and maybe trying it.
