Welcome to Top Traders Unplugged. In markets success doesn’t come from predicting what happens next, it comes from being prepared for what you can’t predict.

In each episode we go deep with some of the world’s most thoughtful minds in investing, economics, and beyond to understand how they think, how they prepare, and how they decide, and the experiences that shaped how they see the world. No noise, no short-cuts, just real conversations to help you think better and invest with confidence.

Welcome and welcome back to this week's edition of the Systematic Investor series with Richard Brennan and I, Niels Kaastrup-Larsen, where each week we take the pulse of the global markets through the lens of a rules-based investor.

This week we have a very special guest, namely the one and only Dave Dredge, who really needs no introduction, but who officially is the Chief Investment Officer at Convex Strategies in Singapore. Rich and Dave, it is really wonderful to have you both here this week. Hope you're doing well. What's going in your part of the world, so to speak?

I'll let Dave go first since he is the guest.

It's summer in Singapore, which is just like any other time of the year in Singapore. So, it's hot and humid and rains a lot. But business wise we're super busy. There's obviously a lot going on in the world and the need for effective explicit loss mitigation that effective explicit, negatively correlating, explicit, true diversifying has never been higher.

And so, we're pretty busy, and markets are active across all kinds of asset classes, and I've got some presentations coming up. I'm down in Australia in a couple of weeks speaking at a conference down there. So, everything's going here as usual.

That's fantastic. Good stuff. How about you, Rich? How are you doing?

It's a bit colder for me, Niels. So, down in the southern hemisphere here. I'm not too far away from Dave in Singapore, but sufficiently south to know it's winter down here. So, I noticed that Dave and I have both got our merch on for Top Traders Unplugged. And the only one who's absent of that, Niels, is you. And I assume it's because it's a boiling summer heat up there and you can't afford to have anything over that top of yours.

Well, I mean that is definitely one excuse. The other more truthful excuse is I completely forgot it. But there we are. I will have to improve my prep skills, that is for sure.

It's great to have you here and it is really wonderful knowing what topics we're going to be talking about, which I appreciate both of you help put together. And I think really the audience is in for a treat this week.

Now, it is coming up to month end in July, and my trend barometer yesterday finished at 45 which is pretty neutral, probably more or less in line with what we see in terms of the indices. And for those who listen on a regular basis, you'll notice that I skipped the ‘what's been on your radar’ because we’ve got so much stuff to cover with Dave and Rich that I thought we would just simply go onto that a little bit quicker today.

Now we're recording on Thursday. We’ve got one and a half days left of the month of July, so we'll see how it goes. But so far the data looks like the following, and this is as of Tuesday evening. BTOP50, down 23 basis points, up 8.32% for the year. SG CTA index down 79 basis points for the month, and up 8.50% for the year. SocGen Trend down 75 basis points for the month, up 8.3% for the year. And the Short-Term Traders Index (that's struggling a bit more), down 1.71% in July, and up 3.34% so far this year.

In the traditional world, MSCI world is down 1.63%, and if we exclude US and Canada (which was suggested by Andrew - not the Andrew that comes on as a co-host but another Andrew) that is down 26 basis points only for the month, and up 9.56% so far this year. The S&P US Aggregate Bond Index down 91 basis points, so no relief on that, and it's flat for the year. And the S&P 500 Total Return down 2.39% so far in July, up 7.58% so far this year.

Before we dive into all the topics, just wanted to ask whether there was anything from the month of July. I mean obviously there's been some activity I think, to say the least, over in Taiwan if I'm not mistaken. But anything else going on from your vantage point?

Well, there's a lot going on in my world. So, you've got sort of multi-year, multi-decade highs in long-dated bond yields in Japan, in the US, in Britain. You've got a whole bunch of central bank policy meetings over the end of the month. Obviously, the Fed overnight last night, standing pat with three dissents in the vote. Very unusual there. And a huge disappointment in the bond market. You've had a ton of noise out here, as you mentioned, across some of the equity…

Yeah, I said Taiwan, Dave, but I meant Korea, didn't I?

Korea, but Taiwan also. Taiwan hasn't been quiet. Japan hasn't been quiet. And so in particular the big semi chip manufacturers in Japan, in Taiwan, in Korea. But Korea most particularly, where you've had this proliferation of levered ETFs that has fueled this boom/bust there that's been extraordinary. I was just looking at it is these two times levered ETFs in Hong Kong on the listed chip makers in Korea. So, one of those being SK Hynix.

So just over the last three months, SK Hynix itself as of the close today is up 1%. The two times levered ETF is down 47%.

Wow.

And so, it's such a perfect example, and I'm sure we'll talk about it, of what in the business is known as volatility drag. And so, at some point in that three month period, the underlying stock was up as much as 125% and is now all the way back down to up 1%. But the volatility drag of the 2x leverage, which is a 2x the daily move, not 2x over the period, has been up as much as 300%. It is now down 47% from the start. And something I say all the time, and Rich will get this particularly, over a long enough time horizon, all levered ETFs approach zero.

Not to hijack the conversation on that topic right now, but you kind of wonder why authorities keep giving people these nuclear instruments, right? I mean you really have to wonder.

In fact, Korea's talking a lot today. There's an article today from one of the big normal ETF managers in Korea saying we shouldn't allow these things. These things are again, they're just volatility drag. It's just transferring wealth away from the end investor and it's inevitable that way. It's simply the mathematics of geometric returns and the impact of that variance on the draw down versus the draw up over time. It's inevitable that they go to zero.

Yeah. Anything in your part of the world, Rich, that we want to highlight before we move on?

It's just been a volatile time for us, Niels. It's a bit like, what is it, those magnificent men in their flying machines, goes up, and then it goes down, and it goes up, and then turns around. And so, that's what we're getting for this month, especially with the KOSPI, that was a significant decline. So, it's been a challenging couple of months for us, Niels.

Yeah, absolutely. All right, let's move on. Let me try and set up the conversation the best I can and then we move into these questions, topics that we prepared. So, obviously, Rich, you've been a regular contributor to the podcast for many years, and Dave has been one of the most popular guests each time he has joined this show. But something has been kind of nagging me over the years.

Now, you both come at markets from completely different directions. So, Dave, from the world of options, convexity and tail protection. And Rich, you come from trend following and quantitative research. Different backgrounds, different tools, different terminology entirely, actually. And yet when I think back to all those conversations we've had, the two of you sound like echoes of each other.

So, I went looking for why, and I think I found it. Both of you see markets as complex adaptive systems rather than as statistical distributions to be sampled and estimated. That one commitment, and almost everything else you believe, seems to follow from that. So that is what I want to explore today; take that idea, examine it properly, and follow it wherever it goes. Because it takes both of you to the same uncomfortable conclusion that the wrong mathematics is being deployed in markets and that risk is not volatility, it's something deeper than that.

So, I'm going to put questions to each of you, knowing full well that we will most likely end up going in a little bit different directions and it'll be more of a fluent conversation. But anyways, I hope you're up for it. And this may turn out to be kind of the lecture where the student, being me, has two professors to ask questions to and will feel a little bit underprepared as the lecture begins. But there we are.

Wonderful.

Anyways, let's start with kind of the shared lineage. So, Dave, what do you actually mean when you say that market is a complex adaptive system? And what does the conventional view assume it to be?

I think I'll give Rich his flowers. I think he said it best, maybe ever, on one of your interviews with him when he said that the future isn't hidden, it hasn't been written yet.

True.

We don't know what it is because there's too many moving parts. And so, the way we think of it and we talk about it here is Ed Lorenz's Butterfly Wings, that it's infinite paths inside a finite space chasing an unattainable strange attractor. And our job is always to do everything we can to understand initial conditions and where we are; understand the now and then be resilient to an unknowable future path.

And so, you guys have heard before, everybody's heard my race car analogy. It's not about forecasting the future circumstances of the race. It's about making your car as resilient as it can possibly be and then being able to react and respond to the unknowable path of the future. Because the future is so much more than simply this shape of the race course. It's what other drivers doing. It's what you're doing. It's weather, it's wetness, it's wear and tear. It's all these things that are impossible to predict that all interact and affect each other.

And, as Rich will say so eloquently, the emergent outcome of all those different parts that create a whole that is unexplainable by the individual parts. And so, we see the world that way and then we see our task on behalf of the investors that we work with is to prepare them with a car that has braking capacity, that makes it the best car for achieving that resilience and the ability to accelerate and decelerate and react as things occur in the ever evolving initial conditions chasing that strange attractor through this infinite loop of a finite universe.

Yeah, absolutely. Now, as Dave alluded to, Rich, you've arrived at the same place but in a completely kind of different way. What has convinced you about this?

Well, first big fan of yours, Dave, have been a long-term big fan of yours and sort of, I'll quietly go to sleep at night reading one of your memos, and yeah, I just feel as though we're very much aligned in the same space.

But my interest stems from a strong passion in science which co-evolved with my strong interest in finance. But recognizing that the two weren't aligned. I think you see that science has progressed from the world of linear outcomes, the world of Newton, into a world that's much more dynamic, a lot less stationary. It's a world of reflexivity, where matter tells space how to curve and space tells matter how to move.

There's this combined reflexivity which Einstein found which overturned Newton. And that, therefore, changed concepts such as what is length? Because length became a very frame dependent posture. And I feel that finance is sort of maybe 100 years behind where the science is today in their understanding of what these systems are when we talk about Complex adaptive systems.

When we use the word complex and when we use the word adaptive, I don't think people really understand what we're talking about there. We are truly talking about complexity, and non-stationarity, and evolution of systems. We're talking about processes here. We're not talking about a world of things, we're talking about a world of processes. And these processes are very contingent on constraints.

But finance has really resisted that move for such a long time. It's stuck in this world of Euclid where it's maths, it's a correct form of maths, but it's not a maths to apply to this domain we call the reality, which is the financial markets we observe today. Mandelbrot exposed that. And I think there's two key things. Firstly, there's roughness at every scale. There's a fractal geometry, there's these attractors, as Dave so eloquently put. We have a system that is computationally irreducible.

So, what that means is, as Dave mentioned, the complexity and the decisions that especially in a reflexive system where you get the agents within the system reacting and adapting to the system and the system forcing that adaption and reaction, there's this reflexivity involved which makes our ability to deal with simple linear rulers non-functional. We'll find that the system that we are inquiring and investigating is inherently non-linear, it's unpredictable. The future is being written at every step.

And to understand what happens in five days time, you need to understand the decisions and consequences of all of the agents who will be transacting over that period and their conglomerated positions and all of their effects, which is incalculable from the domain that sits in the now. And therefore, it's not like a future that is hidden in fog. It's a future that is inherently unpredictable.

So, I view these systems, particularly these, what we call complex adaptive systems, which are particularly inherent in living systems where we have agents who react to that system and the system reacts to those agents. There's this dynamic reflexivity. When we have that occurring, which is typically in living systems, we find that they are complex adaptive systems. A bit different to, say, the weather, which is a physical system. The molecules in the weather, they're not reflexive in the same sense that an agent in our market is.

I go back to that famous quote by Richard Feynman. He said, imagine how hard physics would be if electrons have feelings. Now, that is what the market is. And that's why it is a complex system and incredibly difficult to crack. And despite the Nobel laureates we've had, the very clever quants you will be really surprised at the fact that there is very little evidence that anyone has significantly beaten the market. The market is the master.

I remember that movie Margin Call, with Kevin Spacey and Jeremy Irons. Jeremy Irons was eating his steak recounting the litany of collapses that have occurred over the last 200 years and how these very clever people have always sort of experienced these collapses without being able to resolve why these occurred. And it's because they're using a mathematics that is not appropriate for the domain - the reality we exist in. So that's where my interest is. That's why I think Dave and I are very aligned in our views.

Yeah, well, excellent, great stuff. All right, so obviously we're in the world of investing that is directional. We like when price moves. So let me sort of focus on that a little bit.

And we know that also, from the work of people like Mike Green, that a lot of money has been flowing into the markets recently that never looks really at the price, but it has an impact on price, I guess. So, I wonder maybe from your perspective, Dave, what does that do to price that you have this, and I call it new but it's not that new, but it's been there for a little while, this type of investor that looks at price differently, meaning price insensitive.

Yeah, this is something we could go on about for the entire time period. As I think you know, I'm reasonably good friends with Mike Green and with Hari Krishnan. And huge fan of their work and their most recent paper on passive investing and equity flows, which they were kind enough to even give me an acknowledgment in for some feedback I had provided. I'm known for years and years of what some people fondly refer to as Dredgisms in the world. And one of my famous Dredgisms is, ‘positioning is the only thing that matters’. And I love all the time where people want to justify why a market moved, or this, or that reason. I say that positioning is the only thing that matters and sort of that passive flow dynamic.

And again, something that I know you and Rich talk about all the time, talking about price insensitive investors versus price sensitive investors. Similarly, when we model markets, we break markets into, and again this will sound very familiar to you guys, we break them into what I call rational accounting man, which would be price insensitive people that are following accounting rules and regulation or instructions that are non-economic related, and what we would call boundedly rational agents. People who are making decisions based upon the risk they're taking, skin-in-the-game, their own capital, tacit knowledge.

And what we would call boundedly rational agents. People who are making decisions based upon the risk they're taking skin in the game, their own capital, tacit knowledge, right?

And we model things that way. And so you can think of that passive as a subset of bounded of sorry, rational accounting man.

And we model things that way. And so, you can think of that passive as a subset of rational accounting man. And rational accounting man dominates most markets because all bank traders, all pension fund traders, all insurance traders, all central bank traders, all FX reserve managers are rational accounting men.

When they buy something, they're not thinking about the value of it for their retirement, they're thinking about the regulatory requirements around accounting and risk and usually an annual compensation period. That is a very different thought process than somebody who's trying to make a 30 year investment decision to fund his retirement where losses are his and failures to achieve his investment goals impair his own lifestyle. Those are two very different decision making and very much what Rich talks about all the time.

The central banks who bought all the bonds are sitting on massive unrealized losses. The FX reserve managers are sitting on massive unrealized losses. The banks are sitting on massive unrealized losses. The pension funds and insurance companies, that are a big part of some of the other side of stuff we do, with duration extending callable note structures, with embedded Bermuda swaptions, that are masking duration in the form of structured complex derivative products, have really massive unrealized losses and nobody's cut the positions yet.

Nobody's freed the capital that's tied up in those things or the lack of capital. Nobody's recognized the accounting losses. And so, to me, this is one of the biggest drivers of all things in the financial system is exactly this.

It's exactly what you and Rich talk about all the time, that interaction and the growing dominance, at times, of the price insensitive investor, and, of course, the application of leverage in particular in the regulated space where volatility is the measure of risk and low volatility means low risk and adding leverage doesn't increase the risk.

The risk is the volatility, no matter how much leverage you apply to the super senior tranche of a subprime CDO. Now obviously Rich and I know very well that the leverage is the risk. It's the reason why it's a left skewed return distribution. It's the reason why tails are far fatter than a Gaussian normal distribution would hint at.

The lack of capital is the strange attractor, at times, pulling the market that direction because of the proliferation of loss management as that leverage has to get cleansed from the system. So, to me that's what moves prices. It's the accumulating imbalances as some sort of price insensitive flow builds, and builds on itself, reflexively building as the application of leverage through a flawed regulatory construct, not just regulatory, but flawed understanding, builds that and then reverses the other way with the fat tail on the other side as the mistake becomes recognized, the king has no clothes. The knowledge game recognizes that problem and it moves back the other way and in what will be a very fat tail. And that's the way we see the world.

Yeah, absolutely. Now you did an interesting exercise, Rich, because you built, “a market where nobody really is responding to price”. What happened with that?

Well, I suppose this model was influenced by Jean-Philippe Bouchaud's sort of examination of market microstructure, what moves price? And what I'd say is that, well, it's the transaction event that moves price. And all other theories, you might have fundamentals, you might have macro investing, you might have liquidity flows, all of these different theories, they're what I regard as downstream of the transaction. The thing, the mechanistic thing that is actually moving price is the transaction itself.

So, the way I see these markets is a composite, it's an ecosystem of participants in those markets and each of those particular species in that ecosystem, they create a directed force based on the models that they adopt in that market. So, fundamental investors will have a particular force implied to evaluation. Trend followers will be implying a sort of an amplifying force as they respond to price moving.

So, therefore, it sort of comes to this point of what I call or it's feedback in the systems that creates this fractal structure and it's actually what is creating this movement in price. So, when I look at the feedback, I see there's two forms of feedback.

There's the positive feedback or what I call amplifying feedback, and there is negative feedback, which is more the convergent premise, the reduction or the return to the mean, or the mean reverting, the counter trend fade. So, these two forces, divergent and convergent can be expressed by all of these different ecosystems of different species. And these ecosystems, and they all have these different forces being applied in the markets. Some are amplifying, some are destructive or mean reverting.

Now, when I put an agent-based model together, looking at what I call… let's look at the species of a market, I'm going to call one the random trader. They are the trader who has no model that has a preference, a directional preference. They can be amplifying or they could be, negative feedback. They're what I call the random trader.

There's a convergent trader who's always fading the move. So, the markets are oscillating, they're fading the move at each way, trying to bring things back to what they consider an equilibrium-based position.

Then there is the price sensitive, they're price sensitive. And then there's another price sensitive agent who I call the divergent trader. They're the ones that amplify the move. Passive actually fits in that category. It's not that they are responding to price, they are price insensitive, they're responding to a rule. But that rule is invest in the biggest things. So, what that does is it puts an amplifying pressure or directional force into that market.

So, with this agent-based model, what I did was I looked at just applying random participants in that model first and what I got was a Gaussian outcome. No fat tails, no memory, no volatility clustering. It was exactly what the outcomes you'd expect from the efficient market hypothesis, the Gaussian premise.

But as soon as I started putting divergent participants in it, amplifying the move, I got to a position of about 25% and above of participants that are divergent. All of the signatures you see in the real market automatically come back into the market. You get fat tails, you get volatility clustering, you get the memory - market memory. All of these signatures come back in once the agent-based model integrates a small percentage, only about 25% of these divergent participants. And passive, of course, is a divergent participant as well.

So, what I'm saying is that over the last 40 years this has been the case and this is why markets exhibit these properties: fat tails, volatility clusters that maybe the orthodoxy has sort of refused to believe persists and they're regarding them as anomalies as opposed to a fundamental feature of market structure. So, that's what I found in my modeling.

And it was very interesting that it wasn't a gradual sort of bring back of the signatures of the real market. It was a transition event. It was once we achieved this 25% influence of divergent participants in there, it was a threshold and we got the typical phase transition as opposed to a gradual change.

So, before we get to that 25%, I can populate this simulated agent-based model with convergent traders – Gaussian, random traders – Gaussian, random and convergent - Gaussian. As soon as I start putting those divergent population in there of 25% and above, boom, all the signatures come back into the market.

So, I found that a very fascinating bit of research that just tells me that over the history of these markets, this is a reality and it's this amplifying position, that's what's creating the tails, that's what's creating the memory, that's what creates the volatility clusters.

Yeah, another reality of markets is that, of course, a lot of the time it's small moves, noise, and then from time to time we get the really big moves. So, I'm curious, from your perspective, Dave, where do these actually come from, these sudden, bigger moves? How do they suddenly occur?

Broadly speaking, it's leverage, but more simply speaking, it's loss absorbing capital. And so, people, because they're following very simplified rules of Gaussian linearity, ergotic single slices of time, they are taking more risk than they have the loss appetite for or the capital to absorb losses.

And so, when that mistake gets exposed because one of Rich's divergent traders comes in or something happens moving it, triggers stop losses for the guys who miscalculated the risk. Now, obviously, the biggest one, I'll argue, maybe in the whole system is the assumptions around stable correlation and what amounts to diversification.

And so, the world, the investment universe says, we're happy with our risk appetite to take this much risk on an assumption of the diversification benefit created across these different assets, strategies, geographies, etc. And then when that correlation, for whatever reason, misbehaves, they've got more risk than they want. And so now they need to reduce risk.

Now, of course, in that reflexive world that Rich speaks so well of, their reduction of risk in response to inconsistent correlation affects the correlation, which affects the risk appetite of the next guy who then also has to adjust his risk, which then triggers the divergent trader who is saying, wait a minute, correlation's moving. I want to go with that moving correlation which then affects the next guy.

And so, again, the way we very much look at the world, the residual risk in most people's portfolios, I say all the time, most people do a pretty good job of managing the risk they manage, or managing the risk they measure. But what they don't do a very good job of is managing the risk they assume, the risk they don't measure. And generally speaking, in large investment portfolios, that's correlation.

And it's where they've made simplifying assumptions around correlation and volatility, which are really the two things that everyone assumes constant in their simplified modern portfolio theory, Efficient Market Hypothesis Methodology is the thing that catches them out. And now they have more risk than the capital they had allocated to absorb the losses.

That, of course, gets more and more extreme as different types, either explicit leverage (in the form of banks, balance sheets or hedge funds) get utilized, or the implicit leverage, obviously, the world that we’re most active in of volatility selling. Which creates then mispriced tails and the need to respond to things that you hadn't previously anticipated, which then leads to above normal standard deviation, what you would assume normal standard deviation, market size moves. That's simply how we see the world.

Yeah, Rich, these endogenous forces, can they be measured in some way?

So, I go back to Dave's forest fire analogy. The big moves that occur in the market, I believe, have an endogenous source as opposed to an exogenous source. It's not coming from news. News isn't actually creating the significant material moves. It's a state of the market. And the news might be the trigger, but it's the state of the market. Whether there's the undergrowth that's been building (as Dave loves to say of his forest fire analogy and I totally understand that).

So, when you look at research like Jean-Philippe Bouchaud, you see when he actually assessed whether it was news that was driving market microstructure, he came out explicitly saying that 90% of the moves were from endogenous sources. And what he was doing there at, I think, the tick by tick or the minute by minute, he was looking at the correlation between news events and market price movements from all sources of news events and seeing if there was a strong correlation between the two. And he couldn't find it. And this is what I also observe in markets. It's the state of the market.

When it comes from endogenous sources, it's not coming from nowhere, it's coming from within the market itself. And you find that it doesn't arrive out of nowhere. It builds progressively. So, activity picks up beforehand. Liquidity quietly thins out. The book therefore gets very fragile. And then bang, it goes with a trigger. It often takes, also, longer to settle afterwards. It's not instantaneous.

So, the traditional orthodoxy was that news events were instantaneously accepted by the market, prices would adjust, but that's not the way. There's a lag. And this lag, I think Gabaix and Koijen, and a lot of research has been done on this that says that markets are very inelastic in their properties. And I think that it's this memory that exists in the market. Markets have memory. And you find this when you examine what this volatility clustering is. When you do the research, you find that calm begets calm, and volatility begets volatility. They're amplifying the state of each other.

Now, what happens during these calm periods? You get a progressive increase in the risk building up in the structure, and it's a transition between the calm state and the volatile state that catches everyone naked. And we'll go into that in later questions. But that's what I found.

In my models I found that with no news events, I didn't need any news events in those agent-based models I was talking about. All I needed was the divergent participant, the convergent participant, the random participant. That's what was creating all of those signatures. It wasn't news that was doing that in my agent-based models. It was just the impact that they're exerting with their models. That's what I found.

Now going into a little bit of deep water on my side because both of you from time to time bring up this word ergodicity. And I'm always kind of, what exactly is it we're talking about now? But anyways, from memory, I think it has something to do with ensemble averages versus time averages, something along those lines. Anyway, Dave, why is this important for people who have money at risk in the markets?

I think it's important for a lot of things and certainly important for money at risk. And you're right, something that is ergodic, basically, time doesn't matter, sequencing doesn't matter. The ensemble average equals the time average. From a portfolio perspective it would be the arithmetic mean equals the geometric mean.

.But in something that is non-ergodic, that is not the case. And it turns out that the path through time makes an enormous difference. And so, the easy one for everyone to think of is the usual problem, that a 50% drawdown isn't corrected with a 50% recovery.

True.

You're not back. You’ve got to get 100% recovery to get back. It's our, again, our race car example where it's a multi-lap race and if you crash, you don't finish, it matters.

Nassim always tells the story about people going to the casino and if you give 30 people money to go play one casino game and they all come back, well, they're going to get the average. And if the 19th guy loses his money, it doesn't affect what happened to the 20th guy. But if you send one guy to go play 30 games and he loses all his money on the 19th game, he's out. He doesn't get to play the 20th game.

And so that's the nature of the investment process because it's a path through time. Sequencing matters is, again, another great Nassim quote. The average of the condition of your trousers is the same whether you launder them first or iron them first. But the end outcome is very, very different. Which way around you do it? Sequencing matters. It's a non-ergodic thing.

And I say it all the time, and I'm sure you guys have either seen me write or say it. I think Ole Peters, who's sort of the most prominent voice in the world of ergodicity right now in his book Ergodicity Economics, should be mandatory reading at every school level. In mathematics, in physics, in finance, in economics, in business, in everything. It is the most beautiful mathematical description of common sense, of bounded rationality, of tacit knowledge that you will ever read. And the fact that it is not universally accepted and universally known is a disgrace.

Well said. Now Rich, you also worked with some examples in this and I seem to remember one of them was where you took like a four decades worth of returns and changed nothing except the order of those returns. Tell us a little bit about what happened.

This is such a…

I totally agree with Dave, here. Mandatory reading, it should be because geometric wealth is what we should all be aspiring to. And all of the traditional metrics, or many of the traditional metrics we find in finance, they avoid that path dependency.

So, the popular statistics you'll hear about Sharpe, Sortino, variance at risk, standard deviation, even what you find in the capital asset pricing model with modern portfolio theory, no matter what order of returns you get, it doesn't change the outcome. You still get the same order, invariance, statistic.

But what you find with path dependency is that the order is essential, the sequence of returns is essential. And what I found when I looked at 40 years of history, reshuffled it, because wealth production is a multiplicative process. So, you're dealing with something multiplied by an accumulated balance at each step along the way. And that accumulated balance really defines what will favor that.

What happens to that accumulated balance? Does it deteriorate significantly, therefore the impact of compounding is significantly compromised? Does it accelerate rapidly, which means the impact of compounding is significantly enhanced? What's happening to that wealth, that accumulated balance?

And if things change along that path, stuff is taken away, taxes, all of these things, stuff is added, redemptions are added into that wealth path. It totally changes the path between the world of what I call additive returns and the world I call path dependent returns.

So, what I found when I reshuffled those returns in the process, all of the standard metrics, Sharpe, Sortino, variance at risk, standard deviation, they all stayed the same. But what did change was the wealth. We either had a decline of 30% and it ranged up to a decline of 84% dependent on the trajectory you took.

This isn't a spread we're talking about. This is the difference between a bad year and not being in business. So, it is such an important property. And Mandelbrot of course, was right to talk about the fractal nature of markets and the scale invariant nature of markets. But a very important sequel to that is the geometry of wealth production. Finance has ignored both of them for many years and they are so important.

So, arithmetic returns are the world of additive returns. But what we're talking about, wealth, is a multiplicative process. It's a contingent, conditional process over the course of time. And the path you take has serious implications regarding the ultimate wealth you end up in.

If you take arithmetic returns, I've achieved 100% return over 10 years. Divide that by the 10 years, that's a 10% arithmetic return. The reality is that my path is never like that. I do not get the straight-line path. I get deviations from that path. And those deviations, the volatility starts creating a different trajectory between the geometric path and the arithmetic path.

And as volatility increases, as Dave talks about volatility drag, you find that difference increases in a compounded manner. And so that you might have two very similar arithmetical or additive statistics saying it's the same thing, but the path has totally different trajectories based on this volatility principle that takes a geometric path away from the additive path of the arithmetic mean.

Rich, you already mentioned it a little bit, but I'd like to maybe talk a little bit more about it from Dave's perspective, because, sadly, over here in Europe, at the moment, we have a lot of forest fires. I know you have them in Australia as well from during the summertime. But anyways, you have used forest fires very actively in your analogy. And it's a very important one because it kind of helps people understand kind of the dangers of things being calm, I think. So, can you talk us through it so that we fully embrace that concept?

Yeah. So, it's based on a physics theorem, a subset of chaos theory known as self-organized criticality, as sort of advanced by a wonderful physicist by the name of Per Bak in, what I would say, is one of probably the most important book anybody will ever read called How Nature Works. And it's about how nature works. It turns out most things in the world are nature.

And so, the forest fire is the simple analogy that most people are familiar with, that the fire risk grows as the forest goes longer and longer without a fire because you get more clogged brush between the trees. And so, as we spoke about earlier, diversification in your portfolio, diversification of your forest solves the problem of a lightning strike that hits only one tree. All your other trees are fine.

The risk is when that fire spreads from that tree to the next tree because of the connectivity, closeness and clogged brush and dry brush between them. In the financial markets, that would be leverage. And so, correlation is the big problem because your diversification lets you down and the fire spreads from tree to tree to tree, again, in physics talk, what might be known as the percolation threshold.

At what point does the density of trees, the density of the forest become dangerous? And you can think that everything behaves that way. Avalanche is another great example. An avalanche, the longer you go with snow building up, the more likely you are to get an avalanche. It doesn't mean there's not likely to be an avalanche, it means it's more likely to be an avalanche.

And very much to Rich's point about endogenous risk, you don't need an exogenous shock. What causes the avalanche? The last snowflake, one tiny little snowflake is all you need and that's enough.

Now financial markets very much behave this way because of this reflexive nature and the building, the waxing and waning of imbalances and corrections. And so that's very much how we think about it and talk about what we do when we're out helping people manage the uncertainty of risk.

Again, people tend to be quite good at managing the risk that they're measuring, but the assumptions they're making about the stability of the correlation, the stability of the forest, because they've diversified well, they tend to leave that out. And they say, but Dave, you don't know which trees we own. And I say, I don't need to know. I just need to know where the most dry brush is.

And as it turns out, conveniently, don't tell anybody this is a little bit of our secret sauce. The biggest fire risk, given the nature of how financial markets work, again, back to rational accounting men and price insensitive players, is where the insurance is the cheapest. Because again, things like value at risk are measuring the frequency, a short-term frequency of past fires.

And it says, well, there hasn't been a fire. So, there's no risk. There hasn't been an avalanche, there's no risk. But that's actually generally where the risk is the highest. And so, this is just a great way to look at anything and everything. And the mistake that everybody makes is, oh, it's been calm for so long, it's been calm. Why do you think that's going to happen?

Why do you think that having survived all the way from 30% of debt to GDP to 130% of debt to GDP and nothing's blown up. So, why should we worry about it? All the more reason why you should worry about it. Obviously, the imbalance, that fragility is building and that's exactly where strategies like ours and yours are looking for, protecting, capturing that tail that the flawed methodology doesn't recognize exists.

Yeah, absolutely. Now, from the world of trend following, Rich, we think about position sizing and we have formulas for these things. What does this concept… What does that look like when we go into that world?

The first thing I need to say is that when people experience a calm market, they think about equilibrium-based systems and they think about calmness being sort of almost at an equilibrium state, not much volatility occurring. But that's not what markets are. Markets are not closed systems that equilibrate, they're open systems and they sit at what I call the boundaries of chaos. They’re sitting right out in the frontier in the boundaries of chaos.

New participants are always coming in, new capital's coming in, going out, participants are leaving, coming in. It's an open system. They're far from equilibrium-based systems. And when you experience calm in these non-equilibrium-based systems, this is not the absence of energy, this is the loose, wobbly rubber band being stretched. And what that is this buildup of risk that the metrics, the traditional metrics are not picking up.

It's the undergrowth, as Dave's talking about, that's slowly progressively building up to this state of self-criticality. And this is what happens with this rubber band stretching. So quiet, markets are certainly not where risk is absent. They are being hidden. They're not being expressed by the traditional metrics. But what I've found in my research is they are the deepest coupled negative feedback states in the entire data set.

And what I'm meaning there is that in these calm periods you get markets oscillating. It's not that there's an absence of energy, it's just that their oscillations are canceling out. Now, what happens in this state? And I'll explain why the risk builds up because let's look at some very popular models that are applied to markets.

Let's look at volatility, position-based sizing or volatility targeted. They will have a period of calm and their models mechanistically increase the position size in that period of calm because they're saying, it's a safe market, it's not a volatile market. So mechanistically that builds up position size, the energy is going in, in, into the market.

But also, behaviorally, because the markets haven't been expressing their trends or higher volatility, you find that people behaviorally are starting to leverage up in that environment because they want to create a living in this environment and, therefore, behaviorally they're encouraged to leverage up.

Now, of course we know that volatility clusters, calm begets calm and volatility begets volatility. But what people assume is that the calm is going to… It often continues for a period of time where this mechanistic and behavioral tendency feeds leverage into the system, feeding leverage. So, when you do get the shock, it's a small perturbation out of that calm period. Suddenly you get an explosion out of that calm period. And that's where the risk events occur.

And this is this impact of leverage coming out of quiet environments. They're the most devastating environments. So do not equate calmness with safety. That's one of the fundamental pitfalls, I think, of so many of the risk metrics that we find and that are accepted as rational reasons why we should increase our position size. The high Sharpe ratio, well that's actually authorizing a higher leverage. And that's exactly what you don't want to be doing. We'll get to that later. But this is where finance really needs to carefully look at what they're doing.

Let's stay with leverage for a little while. And I don't know necessarily, I think I want to leave it as an open question to you, Dave, to maybe talk a little bit about what leverage exposes or the impact dangers, when it comes to leverage. You've obviously already given a great example of that with, I forget, was it SLK leverage?

Hynix, S.K. Hynix.

S.K. Hynix, right. Anyways, talk a little bit about leverage kind of free flow a little bit on that.

Yeah. Again, back to what we've discussed. It's loss absorbing capital, right? Is sort of, in a sense, one of the many strange attractors that are pulling markets around. And so, leverage is obviously reducing the capital that's applied to a potential loss.

And so, as that leverage builds because of the rules, the regulations, the misunderstanding or the misapplication of Gaussian risk measures, volatility is risk, that creates the fragility in the system. And through the active suppression of volatility, central banks, governments, policymakers, they want to take advantage. Rational accounting man, they want rational accounting man to lever up that which they want to grow: economies, house ownership, various assets, government bonds, and so they suppress the volatility.

And then mechanistically rational accounting man, in sort of his form of non-price sensitive participant, goes and applies leverage to that and he's optimizing to the short-term returns, probabilistic returns, accounting returns, of a levered thing that reduces the capital protecting that risk. That then leads to the fragility that should the fire start to spread, that's where the problem is. And that's where fat tails come from.

And so, I say all the time in our world you want to own and invest in things with thin tails, things that have high natural volatility where you're getting rewarded with the upside vol for the downside volatility risk you're taking. And then construct your hedges with things that have fat left tails, that have fat tails, that have artificially suppressed volatility and attract leverage. Leverage explicitly in the form of banking system leverage or repo leverage and implicitly in the form of volatility selling.

And those things are the things that are going to have surprises and fat tails, fat left tails, some fat right tails as well, of course, that you want to go and position yourself, in our case through optionality and convexity, and in yours and Rich's case, by your signals in your trend thing saying, hey, this trend's pushing towards something that has that signal, that's got a fat tail potential. And the good news is, as Rich, again you guys talk about all the time, you only need a few fat tails.

You don't need a whole bunch of winners, you just need a very few winners and then just constantly managing your losses to be small and that will dwarf all the other activities that you're involved. You guys were talking about cocoa, I think, the last time you were on the call. I suspect for years, and years, and years, none of you thought cocoa was a big deal in your trend following diversified portfolios. And then all of a sudden it was the big deal. That's exactly sort of the way we look at the world. And I'll argue that's driven by leverage, by imbalances created by inappropriately applied risk methodology, accounting rules, non-skin-in-the-game participants.

Now you mentioned an important word, actually I think ‘optimal’ because I think a lot of people try to kind of be optimal in many things when it comes to investing. But before I let you loose here, Rich, and maybe you talk a little bit about the dangers of that word, when I think back, you also mentioned this thing, Dave, about the trend following world that we buy these breakouts, or we sell them, or whatever it is. But, and I think a lot of times (I'm going off a tangent here a little bit), I think a lot of times, when people think about trend following, they kind of think that's kind of the secret sauce, or we discovered this idea that you can buy a certain day breakout.

But I would argue (and I have a feeling that you might agree, but I don't want to be assuming this), I actually think the whole secret that trend followers brought to the table back in the ‘70s is that they understood how to manage the risk and they understood how to size positions differently to what had been understood up until that time. So anyways, don't want to say that because it does tie into leverage and all of that stuff. But anyways, Rich, what I really meant to ask you is what's the problem of being optimal?

Okay, so the problem of being optimal is that it foregoes the room for being wrong. So, let's look at the optimal bit. Let's look at the Kelly criterion. So, the Kelly criterion, it's looking for perfect information, it's asking a specific question. Given an edge, what fraction of your capital should you state to grow it as fast as possible?

Now when you look at it, when you're looking at the optimum condition, it's putting you at a peak because if you go over that peak you become suboptimal. And what you find with the volatility drag, the going over that peak actually puts you into risk of ruin very quickly. If you under bet and you don't go quite to that Kelly limit, that's taking significant risk off the table. It's giving you room for error, giving you room for not being correct.

Now this is the problem. With the Kelly criteria it's assuming perfect information and it's another sort of addition to this Gaussian world. And it's a false premise because what you find is that markets are non-stationary. You find that there's significant noise in the market.

Now what people don't realize is that when they are choosing the optimal bet, they are applying an estimate; not the reality. It's an estimate. Given their sample size, what they're looking at, that's what they're placing as their optimal bet, their estimate. And as when you start introducing fat tails into estimates, your sample size, needing to make that a fair and reasonable sample size, explodes out.

Now, the Gaussian world, it reduces it to a small sample size needing to be a degree of certainty. But when tails are included into that sample, it explodes the sample size out. So, you never have enough sample to be anything other than an estimate. And there is always room for error in that estimate.

And so, because you're trading at that peak, there is no room for error because that's what you give up being optimal. To be optimal means you've got to give up that room for error. That's the biggest mistake. It's putting you at the knife edge. It's increasing leverage to the point where… And I've done this myself, I've looked at Kelly based position sizing models with our trend following approaches, Niels and Dave, and I've compared it to very simple position sizing rules that are regarded as equal weighted risk betting, fractional position sizing that we adopt in trend following world. And it outperforms the Kelly approach when you start introducing things such as regime changes, sufficient noise to your estimate, because the noise is often bigger than the signal that they're looking for to develop that optimal bet. And this is the problem long-term capital management face.

So, they traded that, they used optimal trading positions for as long as the assumptions held. And they were very successful over the time the assumptions held. But when they went over that limit, they went quickly to risk of ruin. That's going over that peak I was talking about.

That's the problem with optimal, to be optimal you've got to have perfect information and we never have that perfect information in these complex adaptive systems.

There is, in podcasting, something called The Optimal Duo for having on a podcast show. And I think we're achieving that today. But there we are. That's a completely different concept - no Kelly here.

Anyways, we're going to move on to something where I think over the years people have heard kind of analogies about football and should a trend follow, is he a striker, is he a defender, Is he a midfielder? But Dave, you and one of your colleagues, I think, Nicholas, have kind of taken this football analogy, and obviously with the recent World Cup, to a brand new level. And I know you published it this morning. (First of all, everybody should follow both Rich and Dave on LinkedIn or Twitter, wherever it is.) But this kind of takes it to, I think, a new level. I've only skimmed it, so I kind of need also, for selfish reasons, for you to take us through this new World Cup scoring system, I guess we could call it.

Unfortunately, that was Nick who just left. We wanted to get rid of him.

Yeah, I saw him leaving there.

So, for forever we've used a football pitch picture in a lot of our presentations. If I speak publicly, I almost always (because I want to frame what I'm talking about and get it in [people’s] heads, because the world, the financial world, has so emblazoned in their mind the Gaussian distribution. So, we draw a football pitch and we draw the Gaussian distribution over it, and explain that that's a measure of frequency. That's a measure of where the ball spends time.

On average, the ball's at the center of the pitch, like the average return of monthly S&P. It's the average. It means nothing. The average is meaningless. It is a wasted statistic.

And then we draw what we call an entropy curve, a Shannon entropy curve, a measure of information value. And then we shade underneath that the long-term contribution to compounded returns of the S&P and show that the 2%iles of returns (the 10 worst months out of 480 months and the 10 best months out of 480 months) contribute almost all of the returns. And just like in a football match, it's what happens in the penalty boxes that matters, not what happens in the center of the pitch. Right? It's goal prevention and goal scoring.

And so, we've been giving that presentation forever, certainly longer than you guys have known me, I've been giving that presentation. And so, Nick (who is who takes geek to a different level here) said, I'm going to build a model and we're going to track it through the World Cup and see if this story you've been telling forever, Dave, is true, that what happens in the penalty boxes is what drives the outcome.

And we did it. And thankfully, nowadays, FIFA provides unbelievable data, and there's all kinds of improved data with the chip that's in the football now. And we came up with what we've called the convex goalkeeper theorem. And without going into all the mathematical complexities, the gist of it is it comes down to three layers. This is how people win a non-ergodic football tournament. Now it's non-ergodic because if you lose, you're out. You hit the ruin barrier, as Rich would say, the insolvency barrier, you're out. You’ve got to stay in to keep going. All right, so it's a very non-ergodic path.

Layer one is defensive resilience. Right? Are you becoming more defensive as the ball moves from the midfield to your penalty box? And we measure it by the 18 yard box and by the 6 yard box. Now, obviously the ultimate defensiveness at the very end are saves by the goalkeeper. But we have other measures and metrics in there about how we're measuring sort of a positive convexity of defensive resilience.

Likewise, the other part of the game is scoring goals. Are you becoming more effective, efficient in your attacking as you approach the other 18 yard box and 6 yard box and goal? And it turns out layer one, most important, layer two next most important.

But then we found a layer three. And layer three was individual tail risk, if you will, and individual performance above and beyond what could be recognized from simply the dominance in the respective penalty boxes. Messi making nine crosses in the last two minutes, right? Or Bellingham's last second two goals, etc. Think of that as a tail risk that, depending on which side of the game you're on, is either a negative tail or a positive tail. And so, staying in the game such that tail can be beneficial to you is very important. That can make a difference in the match.

And so, the model is really fantastic. We put the paper up, a shortened paper. There's a full paper that goes through every single game over the whole course of the thing, we've put a shortened one up with a few key examples.

And so, one of the best examples, and you guys will love this, is the England/Argentina match because you can divide that match into two matches. It was a very normal match until England went up 1 nil. And then England did, as they say in England, parked the bus. Right? They did what is so common in the investment industry. They thought they could reduce risk by capping the upside. By only playing defense. They did what in option space we might call a covered call strategy.

Buy more bonds.

They sold call options, they bought more bonds. They did 60/40. They reduced speed, they drove slower, and yet they're still exposed to the tail, 60/40 can still lose money. A covered call strategy has still got all of the downside. All you've done is forego. The ultimate objective of good defense is attacking.

You can't separate (kid to riches is such beautiful story), you can't separate the parts. The whole is greater than the sum of the parts. The parts must function together. You must be convex to both sides of the magnitude where it matters. It's not the frequency, it's not what's happening in the middle of the pitch where the ball spends most of the time, that matters.

And I found it wonderful watching. And obviously, unlike most Americans, I've played soccer (as we call it in America) my whole life and coached soccer when I was a younger man, some interesting teams. But even watching this World Cup, think how many goals (and Rich will love this), how many goals are the result of a mad scramble? So many, right? Very few are actually a smooth, perfectly orchestrated movement. So many are a rebound, a ricochet, a stumble, a fall, right?

And the act of getting or preventing them is about this unknowable emergent property of defensive resilience and offensive effectiveness. And if you're just trying to play by the numbers, you're not going to find that. And so it's a really interesting model. I'm going to try to… In fact, I told some people today I'm going to speak at a CBOE event in Hong Kong later this year. I'm going to try to somehow form it into one of my presentations, tie it together with total portfolio approach and stuff. So, it's really fun. Everybody should go look at it.

Absolutely. I completely agree. Absolutely.

Now, you've already alluded to, Rich, that we are skeptical of Sharpe. Obviously, Dave has written tons about the Sharpe world that we live in. So, if you have two portfolios with the same Sharpe, what do we not know from looking at those numbers?

Look, before I get into that, I've just got to say, Dave, I can see a sequel to Moneyball coming up. We're applying convexity now in the game. So, looking forward to you doing that coach, and seeing how that goes.

We talk about that all the time actually, Rich, that's spot on.

So, the Sharpe penalizes trend followers. I just wanted to say that. It’s no fault of the ratio. It's not deliberately picking us out, but because when we're employing convexity, the Sharpe is perhaps the worst measure to use to assess that. So, Sharpe, to me, fails in two ways.

The first thing it does is it doesn't let you know the system's failure modes. And I want to give you a good sort of example to consider. So, consider two portfolios, both with a Sharpe ratio of 1.5. So, the first is a single concentrated position. Levered it up using Kelly, resting on one estimate of one edge. That's one of the portfolios producing a Sharpe of 1.5.

The second is a wide book of small positions that are only loosely related. No individual position is carrying the load, unlike that single levered estimate. That also has a Sharpe of 1.5 - same number. So, the metric Sharpe itself calls them equal because by the time it's calculated, the entire construction of Sharpe has been compressed into two figures: an average return at the numerator, and a volatility in the denominator. And every trace of how the portfolio is assembled has been discarded apart from those two values.

Now we've got one failure mode for the single cable but if we get a single failure mode in the ensemble of loosely correlated estimates, we only get a failure in one, and 999 is still keeping them up. So, this is where Sharpe doesn't reveal this property. And it's only through understanding the construction, the architecture of the construction of the portfolio, that's what's telling you: what are the foundations of that architecture, what are its dependencies?

Is there one failure mode or is there potential for many failure modes where your portfolio won't come crashing down. You don't get that out of that Sharpe estimate. You get that from a knowledge of the construction. And that's something none of these metrics is going to give to you.

This is why I believe Dave and I are what I call engineers. We are architecting convexity. We are architecting this geometrical sort of progression that mitigates our downside risk and exploits opportunity. This is this brake, the brake system that Dave talks about in his formula one. It's mitigating the volatility drag and getting the beneficial opportunity, exploiting the opportunity because you've got good brakes. That's exactly this principle. So, that's all I've got to add to that.

Sure. Now, we've talked a lot about risk and how to manage how to mitigate that, and I think. I can't say that for sure, but I think a very popular way of thinking about mitigating risk is just diversification. So, my question to you, Dave, is, does diversification really protect you?

Yes, sometimes, just not when it matters the most. Right? So again, traditional diversification is making assumptions about correlation, making assumptions about ignoring the connectivity between the trees. Now, I wrote one of my papers once years ago, pointing out that diversification across a whole bunch of things, that any one of them can cost you all of your capital is probably not a good idea. Right? Because then any one position can wipe you out. Any of them can go to infinity. Infinity loss will wipe you out.

On the other side, in what we're doing, the more diversification, the better, because everything that we do, as best as possible, we want infinity as a potential benefit. So, I only need to get to Rich's point and your point. You only need one month to make an enormous contribution. Right? You only need one trade. If cocoa goes to infinity and you're on it, you've made your budget forever.

And so, the same thing with us, a big part of what we do and how we construct the convexity for our investors, as much as we possibly can we always want infinity on the other side. I don't know if your listeners or you guys are familiar with the St. Petersburg paradox, which is a coin toss game that has an expected return of infinity but a very low probability of achieving it.

But if I can, at the right price, get someone to commit to let me play the game for an unlimited number of hands, and I've always got infinity on the other side, well, eventually I got a pretty good chance of him begging me to unwind the commitment that I can play forever and ever, and ever, and ever. And that's a big part of how we think about things.

So, diversification needs to be understood for what it is. There are beneficial diversifications, there are faux benefits of diversification, and there are dangers of diversification where you don't have bounded, understood downside across a range of diversified and possibly reflexive items.

Yeah, Rich, you talk about this using words. The fact that diversification is kind of more the engine that shields you. Talk us through that idea.

So, Niels, what I found in my research is that diversification for us classic trend followers, it's giving us exposure to more right tail opportunities. To me, using diversification to mitigate risk, as Dave says, can be good, it can be bad.

Here's an example. We've got those thousand strands going across that canyon, it looks diversified, but imagine if they're all connected to a single anchor at each end of that canyon. There is still one failure mode there, but it looks diversified. And this is the problem. You might borrow short and lend long across a dozen markets during calm regimes and think it's fantastically diversified, but you're exposed to a single interest rate bet, effectively, through that.

So, I think correlations… what I've found in the research, and this is really interesting to me, it's research I've done, I haven't really promoted it. But what I've found is that most people think that markets during calm regimes, ordinary regimes, tend to move independently of each other and then during periods of stress, suddenly they become correlated. Well, I beg to differ in that opinion because I think that markets are always permanently coupled.

Now imagine this. So, you know how I was talking about ecosystems of participants. Now, the individual agents in that system, they are rarely holding a single position in anything. They are diversified across products. Now, that model that they are applying, diversified across products, is creating this permanent coupling. So, as long as diversification exists in the market, and most investors apply it, I think we will find that the markets are permanently coupled.

But what does change is that the phase of where it's sitting in that coupling. And what you find during calm regimes, we get this oscillation effect canceling effect. This is what creates this apparent benefit of diversification.

Diversification works during calm environments, but it works specifically at the wrong time. You want it to work during periods of crisis, but when you get into periods of crisis, the coupling goes from oscillating to trend, and you suddenly find that everything becomes correlated. This is this permanent coupling through diversification, through agent based models, all sort of spreading out across asset classes.

A commodity trader is spread out across its commodities. A global macro trader is spread out across currencies, bonds, all of these things, these forces, this coupling of extremes and where the correlation is, a correlation is an expression of where the coupling sits. It's always on, but people assume it's off during good times.

So, the problem I face is that you've got to use architecture here. So, go back to that example. A thousand strands, one anchor. We see the problems of that. But if we've got a thousand strands connected to a thousand separate anchors, we've got a totally different proposition there.

So, we're looking for not necessarily correlation properties, we've got to know the architecture, we've got to know what are the dependencies that exist in our portfolio. You're not going to get that from the statistics, you're not going to get that from correlation properties. You've got to understand how the architecture, how it's created, what are the dependencies in that architecture?

Another really interesting point in my research I found that diversification doesn't thin the tails. So, if you imagine everyone's assumption is that, oh, with increased diversification, the impact of tails dilutes. But what I found is that with increased diversification we get an initial drop in kurtosis and then a ramping up of kurtosis. Because what you find is that the tail properties, because they're fractal in nature, as you get bigger and bigger samples, you get exposed to more large things.

This is unlike the proposition that with increased diversification the large things dilute. No, not in fractal structures. If I get a big tree and I put a sample over that tree, a small sample, more than likely I'm going to get leaves and small branches, nothing material. Increase that sample, I get more exposure to the trunks, to the large branches. Increase it further, I get the entire tree, I get the major dominant fractal structures of that entire tree. This is what happens with diversification.

So, what I've found in my studies, as you increase diversification, you get more exposure to the right tail. This is, I'm not using diversification here as a solve-all for the correlation argument. I'm not saying it's going to significantly reduce your volatility, but I am saying that you get more exposure to the fractal properties of the market and because of this you get more exposure to the right tail. And an example, who would have been sitting in cocoa? Most traders don't even consider cocoa. But because we're maximally diversified across all of these, we had a position in cocoa, that was the thing that exploded.

Now those people with a small subset small portfolio which had the majors in it, the currencies, the bonds, that sort of stuff, they had no exposure to cocoa. We had that idiosyncratic exposure to cocoa because we are maximally diversified.

And this is what I find this leptokurtic property of markets, the fractal nature of the markets means that as you increase your sample size, you find that the large things actually get larger. And that's why your drawdown is always bigger ahead of you, as the greater returns will always be ahead of you as you increase your sample size.

And I've taken 125 years of market data from the Dow Jones, combining that with the S&P 500, and when I look at the major material moves there, you find that the major material moves, the tail properties that Dave is convincing us about, and I totally agree with him, they are the major drivers. That's where all the information is. The rest of the movement is just noise, it's perturbations. That's all it is.

These drivers, as you extend the sample, you get access to the drivers of the system in this fractal structure. Because fractals are scale invariant, you can go down and the structure always stays there. You can go up and the structure always stays there. But as you go up, you get access to bigger, bigger, bigger structure. This is what happens with sample increase and diversification, at least in my research.

Sure, super interesting. Now we've got a couple questions left that I love to talk to you about. The next one is pretty important, I think, because what people will have hopefully gathered from our conversation so far is that asymmetry is important in the way we view opportunities, markets, etc. But you guys come at it in a different way.

So, Dave, you buy this asymmetry. And of course Rich and other trend followers, we kind of built it into what we do. So, let's start with you Dave. Why do you prefer this implementation methodology?

Well, sort of two things that, I would say, differentiates how we go about it. One, I'm creating the trend following type benefit for our investors as opposed to running it ourselves. So, our investors, we are freeing up capital that they have traditionally tied up in poor diversifiers by creating explicit risk mitigation brakes so that they can go out and put that capital to work participating in the positive drift or long-term trend of asset price inflation in compounding assets.

So, the positively correlated side we're allowing them to carry more of on their own books while we focus only on the negatively correlated convexity asymmetry that we need to constantly work to maintain sensitivity and attachment as their assets grow in size, compounding, and price moves through time through this drift and appreciation, asset appreciation through time. So, we need to then actively manage the negative correlation.

So, one, we're trying to create very much what you guys are doing, but the combination of what they do for themselves and what we then provide them creates the long gamma, if you will, on their combined portfolio as opposed to us running both the positive and negative correlation in our books as you guys would as more of a standalone strategy. So, that's one.

Two, now this one, to me, this is my big thing because it's what I do. All of that asymmetry, all of those non-Gaussian distributions that you guys capture the movement of the actual underlying realization of, we're in the business of buying that implicit leverage that allows us to overlay that on the mispricing.

So, we're buying long-dated term periods of the mispricing of the underlying distribution which itself is driven by the supply of volatility dominated by non-price sensitive participants, predominantly structured product vol supply that is itself mispriced relative to its own distribution. And so, you have this sort of double whammy, I'll argue triple whammy, of a price for the flawed distribution of the underlying over a long-term period of playing for that itself is mispriced, that is constructed in product construction that has inherent in it an added level of asymmetry - the non-linearity of explicit option pricing or volatility type products.

And so, you get sort of this triple whammy. And then, again, to my St. Petersburg paradox example, I'm not just getting to play the game one time, I'm committing to play it for three years, at the same price, every time.

And so not only might I get to win the large tail one time, but that one time almost certainly raises to the realization of somebody who's provided this non-recourse leverage that they've mispriced it. So, they may not want me to get to play the game at that price, again, and again, and again, every day, with infinity on the other side, for the next 2, 3, 5, 10 years.

The.

Recognition of the goalkeeping efficiency or the breaks that allows then our investors to go out and be much more aggressive. And so exactly the conversation we were just having about diversification.

And this is again another dredgism that goes back to my banker's trust days running banker's trust businesses during the Asian crisis out here, which was a pretty wild time, more wild than anything I've ever seen, and I've seen almost everything that was wild, that when you're positively convex, more risk is less risk. Exactly what Rich was saying. When we're positively convex, we want the whole tree, not just a branch.

And we're happy to have a room full just exactly like you guys are of opposing views. We don't have actually any views.

If somebody can create great convexity that is positively directional and somebody else wants to create direct convexity that is negatively directional, that is bearish or bullish, the more the merrier.

And so that's how we're going about it in hopes that we create the recognition of the goalkeeping efficiency, or the brakes, that allows then our investors to go out and be much more aggressive. And so exactly the conversation we were just having about diversification.

And this is, again, another Dredgism that goes back to my Bankers Trust days running Bankers Trust businesses during the Asian crisis out here, which was a pretty wild time, more wild than anything I've ever seen, and I've seen almost everything that was wild. ‘When you're positively convex, more risk is less risk’. Exactly what Rich was saying. When we're positively convex, we want the whole tree, not just a branch. And we're happy to have a room full, just exactly like you guys are, of opposing views. We don't have actually any views.

If somebody can create great convexity that is positively directional and somebody else wants to create direct convexity that is negatively directional, that is bearish or bullish, the more the merrier. Right? We're reducing risk and capturing more tails, all the better and go for it.

So, it comes back down to, then, obviously, and this is what Cem and I talk about all the time, Niels, when we're together, is price. What's the price? That price again is heavily, heavily driven by non-price sensitive participants. And flaws, if you will, or I don't know if you want to call them flaws. They just are what they are in the application of regulatory risk and accounting rules on the main market participants that allow them to recognize enhanced return, these repackaged yields of captured option premium, and not necessarily capitalize the tails. And they don't have skin-in-the-game. It's not their money.

And so, they're not thinking about the possibility of what could happen. They're measuring the regulatory probability of it. They're happy to… Another example I use all the time, Rich, is we're going to a casino and because the croupier is getting 10 cents of every dollar he makes, he's trying to attract people to his roulette table because by offering 100 to one payout. But what I'm trying to get him to do is commit to that 100 to 1 payout for a thousand spins, not just one spin at a time.

And when he figures out that he's got a problem, he's likely to try to buy me out of my original agreement. And that's where the big asymmetry comes from - volatility or volatility convexity.

Yeah, that's a great way of explaining it. Share some thoughts on this, Rich, and why trend followers do it slightly differently.

We do it slightly differently, but I think we're playing, Dave and myself particularly, we're playing the same game. So, we're engineers. We're trying to architect the optimal geometry of returns to survive and to capitalize, and exploit opportunities.

So, if you imagine when you look at the market structure, the markets themselves have very little skew in them. But through the processes that both Dave and a trend follower do is that they truncate that left tail with their return distribution. That's the brakes. They truncate that left tail. As we do it with our stops, we do it with our small bets. Dave does it with a small premium you pay for the option. We're truncating that left tail, but we're leaving that right tail open - the positive skew. We're leaving an unbounded opportunity because no one can predict what these markets can do. But the fractal structure tells you that there are things that we've never experienced before which we're going to see and they can be exploited. This is the accelerator on the racetrack - if we predict our downside, if we protect that volatility drag of the down side and we exploit that opportunity.

Dave and our solution; his options and our trend following, it's doing the same thing. If you look at a long position with a stop, that's what we adopt. That's a synthetic call. A short position with a stop is a synthetic put. You get the shape of an option in trend following, but we're just not paying an explicit premium for it.

But there is a premium we are paying for it. It's psychological. It's the losses we incur. It's a foregone growth that we lose. There is a premium that a trend follower pays. They often say, oh, but we don't pay the premium like the long vol specialists out there paying for their options. We do pay it. We do pay it. And we're paying it through the stops that get triggered out to forego future opportunities. We do get those. And it's a psychological cost.

So, Dave gets a line item, where he's got the premium to pay for his option. That's his line item. We don't necessarily have that. We can't see that line item. But it's there, trust me. It's there in how we experience things. We experience lots of losses, whipsaws along the way. That's the price we're paying. That's our premium we're paying to keep that truncated left tail and to exploit the right tail opportunity.

So, I see both of our approaches as architecting a profile to optimize geometry because path dependence is so critically important and that's what we've expressed over this podcast. So, I can only see similarities here. I might see a slight difference in that I think Dave trades what I call discontinuity. In other words, when we put a stop in, there's no guarantee that stop is going to be triggered. We might get a gap through that stop. We'll still have small bets with maximum diversification.

Dave has a guarantee with the explicit premium, so he immediately gets that guarantee. We get it through what I call sort of duration over the course of time. Very similar, but slightly different approaches. So, yeah, I can only see similarities. In fact, what I see is a benefit of perhaps combining both approaches together to get the both of both worlds. But that's how I see it, Niels.

Absolutely.

We advocate that to everybody we work with. There's path dependency. And again, any way you can add positive convexity, add positive convexity. And there are a whole bunch of ways to go about it. And the fact is that the opportunity to capture cocoa, we didn't have cocoa because nobody came to us with a volatility structure and volatility supply that suits how we do it. Now, we might have things that nobody ever thought anybody would do, but that's because there was a volatility supply.

But we're limited in what we can do because there needs to be efficient volatility markets for us to do it in, and there needs to be efficient volatility products, even above and beyond the simplicity of what might be exchange traded and stuff. So, they're very complementary. There are different parts of the distribution. There are different types of scenarios. The breadth of what you guys can do, we can't match in terms of markets. The attachment points are going to be different. Every way you can add convexity, add convexity. That's the answer to everyone's problem.

Yeah, I mean, there are a lot of similarities. I was smiling when I read your June paper where you have this chart where you show what happens when you add 50/50 long vol and the S&P and, of course, you don't just get an average, you kind of almost get the sum. And I use exactly the same chart for trend following. If you add the S&P, and 50%, and 50%, on capital, it's not just the average, it's almost the sum of the two. It's incredible.

Now this conversation will air on Saturday, so a day and a half from now. And what I'm hoping for is that there are a lot of CIOs out there who are going to say, whoa, this is interesting stuff. So, I guess my final question, unless I think of more, what do you want them to do differently Monday morning?... Dave.

It's the same thing I will always say, add convexity, right? So, the first thing that needs to change in the fiduciary investment universe is a change in the incentive structure. So, we have to somehow shift the incentive to being this geometric compounding path. That just doesn't exist. Everybody's getting paid on calendar year, arithmetic returns, time ignoring ergodic processes. So, you need to change the incentive structure and get people to understand that the objective is the growth of wealth.

Expected return is a nonsensical number and it's destroyed more wealth for capital owners than maybe any other simple thing. Now, arguably, it may have transferred wealth to fiduciaries and so there may be some reason why they stick with it, but that's just me being cynical.

So, you need to add convexity. How do you add convexity? Rich and I have talked about optimizing isn't the right answer. It's a ‘learn by doing’ because you're now building resilience to the divergences from the expectation as opposed to optimizing to a backward looking expectation.

So, you can't optimize to the unknown future path. All you can do is put brakes on your car and go out and learn how to drive. Go out and explore how to go faster, aerodynamics, stronger engine, different tires, different steering wheel. But before you start exploring that, you better have brakes, right? So, you need to start freeing capital. (This is sort of my current theme and presentations I give.) You need to start freeing capital from the ballast that you've been using to try to just slow you down.

And you want to then use that capital to invest in brakes, or free the capital by getting brakes, and then use it to go out and find ways to participate in more positive market environments, positive upside participating type assets. And so, learning by doing, trial and error, is how you learn how to drive with brakes, as opposed to trying to estimate the average lap speed. Start trying to extend separation over multiple laps and it's ‘learn by doing’.

Yeah, I've got a follow-up question on that in a second, Dave. But Rich, what do you want people to do Monday morning?

Well, I want them to pay less attention to those damn statistics and more get into the underlying, foundational assumptions of the system you're assessing or look at the dependencies. But specific things I'd like them to do? Here's one - cap leverage in absolute terms.

Now, what I'm doing here, there's no statistical reason for this apart from what we're doing is we are breaking the automatic link between a quiet market and a large position. So, if we cap leverage in absolute terms, we break that link.

That's an important one because most of the capital destruction, you see, is coming out of quiet markets with too high position size, too much leverage. Leverage is the destruction of compounding. This is what I've found.

The second one is size every market to the same risk rather than tilting toward whichever sort of edge looks strongest. Now this comes back to the selection argument. There's selection bias in our selection of things that have recently performed, etc. By selecting or increasing our position size to a particular asset because of its recent performance, what we're doing is we're striving towards that single cable between the canyon again.

We are losing the breadth that we had through the all of the different cables tied to separate anchors. And we don't find it in the noise that exists in that market. We're always estimating the return. But it's not enough to give us the optimal bet (as we talked about with Kelly), this is the problem.

So, size every market with the same risk rather than tilting towards whichever edge looks currently strongest. That way you miss cocoa, that way you miss all of these explosions that we talk about. It's not a refusal to think, it's actually the opposite. You still choose your markets, you still choose your horizons and your rules. That's the whole craft of what we do as trend followers. But what you decline is a step afterwards, ranking those markets by apparent strength and betting the difference. So, the difference between edges is smaller than the noise involved in measuring them. So, a ranking is a signal too faint to trust. Trust in my sort of understanding of how these markets work. And tilting towards the leaders quietly rebuilds that single cable that we've got to worry about.

And the third one is grow by widening the book, not by scaling the bet. So, we are avoiding leverage here. So, when you want more return, the instinct is to increase size on what you already hold. Now, what I'm saying is, I'm not advocating that. I'm saying add markets, add different systems, different diversification. Expand your diversification, don't increase concentration in your single bets. That way you're reducing this reliance on this estimate once again.

So, it's the difference between a heavier load on one cable and rather than look for more cables to that bridge, more sort of unrelated things that won't bring your portfolio down, that gives you more exposure to the tails of the fractal markets that we live in. And the last one is enter small. So, always enter small and let the market build the position out of open profit. This is where I say let the market do the heavy work in lifting your performance. Don't use size, or positioning, or leverage, to try and sort of push your will upon the market. Let the market itself do the lifting power. Keep your bet sizes small on any individual estimate that you make.

Okay, so while you've been talking, I've thought of a question and when you do things sort of on the fly, it may not come out as clearly as you would like. But let me try anyways. So back in the ‘90s we started talking about, in this industry, about portable alpha. Now, that really never came too much but I certainly clearly remember this and the concept of, say, having a equity portfolio who, on top of it, would add trend following. I don't think I talked about long vol back then. It probably didn't really exist in the area that I was working in back then. But, of course, more recently it's coming back with a vengeance. We see a number of managers launching these portable alpha return stack products, etc., etc. So, this is what I'd like to for you to help investors understand or maybe deal with. It's the challenge where, on one side, as Dave says, you need to free up capital.

Now you can do that, in a sense, by doing a portable alpha product because you can replicate the index, and you can add trend following or you can add long vol, and you still have money freed. But that line item is, essentially, more efficient. But if you look at it from a traditional perspective, you would say, well, I've got 100% equities, and now I'm adding another 100% trend, or another 100% vol, that, to me, is a leveraged product. So, on one hand we say don't go down the route of just adding too much leverage. At the same time we're saying this is so much more efficient. And when you combine these two, specifically long vol and trend following with your underlying traditional market, you actually get a much better product.

So, how do investors who may not be spending all their time, like we do, in this world, how do they square the risk of too much leverage with the benefit that we're arguing, saying, well actually in this case you should do it, if you know what I mean.

Exactly. And it comes back to concavity and convexity. So, most people are levering concave risks. So, they're levering risks where their correlation is low to good markets and rising to bad markets. So, they've got volatility drag in that dynamic. Right? The volatility has a negative impact on their geometric path and adding leverage to that will create disasters, the disasters that we talk about in terms of what drives markets.

If you're positively convex, if you have explicitly negatively correlated risk that is growing, so your overall portfolio's increasing correlation to positive markets and reducing correlation to bad markets, and think of it as non-recourse leverage, where you've gone out and bought an option that allows you to participate in the upside and give the downside to somebody else, well, that is risk reducing as you grow that position. So back to what I said before. When you're positively convex, more risk is less risk.

And so, you can see when we play around with examples, well, the more long vol, the more hedge we add, the less risk you have. So, you go take more risk, and then guess what, you could add more negatively correlating highly asymmetric protection. You go take more risk.

And so, you can keep going, and going, and going, with this, ad infinitum. But adding leverage, recourse leverage, to concave positions is exactly what creates the volatility drag and destroys compounding paths and creates the tail risks, literally.

Yeah. Do you want to add something to that?

I can't really add to Dave, apart from the fact that Dave works in this world all the time recommending long vol componentry to add to traditional portfolios. Fortunately, in my trend following world I'm 100% trend, so I never have to face this demon that we're talking about. But if it improves concavity, that's a good move. That's how I'd see it.

But really what we're doing here is we're applying a band aid fix to a bad return stream with that traditional portfolio. It's basically like a band aid approach to fix it, I'd say. Ideally, resurrect the architect and start from Brown principles and construct that portfolio without having to have that demon to deal with that poor old Dave has to deal with long vol integration into traditional portfolios all the time.

I also remember from my early days, in the early ‘90s in this space, that one of my colleagues was using this slogan saying, and of course again, this was about trend following, and I'm sure that could be said about long vol, is that ‘trend following allows you to own equities’. And I'm just thinking all these years later, I mean, it's probably as true as it ever has been, yet most investors have not yet embraced any of the two strategies that they need the most.

But hopefully the last two hours with you, and thank you for going long here, so to speak, will change or challenge some of people's assumptions about their investments. So, very excited about that and super grateful, by the way, for all the knowledge that you guys have shared in the last couple of hours. And I'm sure all our listeners will be as well.

And maybe a little bit of… what I like to do, actually, I’d like to do something a little bit different here. First of all, I’d like to ask a small favor of the listeners and that is to go and show their appreciation to both Dave and Rich by heading over to your favorite podcast platform, leave a rating and review because it really does help with more people seeing this.

But I like to up the stakes for the first time here. Since people watch us on YouTube they will see that I'm the one who forgot the Top Traders Unplugged merch here. So, what I'd like to do, I'd like to make a little challenge here and say there is a Top Traders Unplugged vest at stake here for the best review that is posted in the next month. So, we give it to the end of August, so the people have a chance to go out and leave an amazing review for Rich and Dave.

However, since I don't have infinite time to monitor all these platforms, I need to ask a favor. I need you to email the usual one info@toptraders unplugged.com. I'm probably going to, hopefully, I'm going to regret this with a large number of emails to email us what the review was, where you posted it, when you posted it, so that one of my team members will go and verify and then we will either by democratic vote on the Top Traders Unplugged team, select the best and get in touch to the email that you send us so that you can get your merch or we may ask, if we can figure out a way to do it. We may upload them to ChatGPT and ask ChatGPT who do you think should get this vest?

So, upping the stakes for the first time here, hopefully that will get more people going on that. Anyways, as you can tell I'm super excited about this conversation and I really do hope that lots of people will tune in and listen to it. I mean there are no better people than the two of you to explain these things. So, exceptionally grateful for that.

Next week I will be joined by Harry Moore from Man AHL. That will also be an interesting conversation, not least because I think we may touch also on portable alpha as I have a feeling he's coming out with a paper soon. So, we can put all of these conversations into perspective. But in any event I'm going to give you the chance as I mentioned before, go and follow Dave, go and follow Rich. They put out some amazing information. But also, I want to leave room for both of you to any final words, anything you… I wouldn't say we left out. I think we've been pretty thorough…. But anyways, if there is something that I forgot to bring up you can certainly add it.

I'll throw one last Dredgism out there. And so, this is something that amongst my various other activities I'm involved in a lot of risk councils, and risk conferences, and stuff, and people often are waiting for me to give them some magic formula of what is risk, and what is risk management, and what's the right way to do it? And I end all of those presentations with this slide. ‘Risk is about accountability’, and that there's no (exactly what we're talking about here), there's no magic modeling of risk, there's no magic formula of risk, there's no magic regulatory model rule. The only way that risk can be appropriately managed is through accountability, is through tacit knowledge, is through recognition that if I crash I'm out of the race. And until, somehow, that gets instilled into all of these non-price sensitive rational accounting men, the system will forever be fragile.

And I say this to regulators every time I talk to them since Nassim and I wrote notes saying do not embed value at risk in BIS regulatory capital guidelines and remove accountability from the guys actually making the decisions or you'll get the GFC. And nobody's listened to me yet. GFC or not.

Well, I also like the fact that you often remind everybody that actually risk is everything you didn't think of, which in itself is a problem.

Not in your backtest.

Yeah, but it's not in your backtest. That's right. Anything on your side, Rich, you want to...

It's just been a pleasure for the famous Mr. Dredge. Big fan, as I've already mentioned, but it was great chatting, great sharing ideas and this is a great venue for it, Niels. So, thank you very much for this opportunity.

Sure, absolutely. I'm sure we will do it again. Anyways, to all of you out here, thank you so much for listening. From Dave, Rich and me, we look forward to being back with you next week here from Top Traders Unplugged. And until next time, as usual, take care of yourself and take care of each other.

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