Astrophysicist: The Best Bitcoin Explanation You've Ever Heard | Stephen Perrenod

Stephen, welcome to the show. So glad to have you here with us today.

Hi Charles. Uh, great to join you today.

Can you tell us where you're calling in from and also, um, along with that, can you give us a quick overview of your background? You know, what did you study in school? uh, your first steps professionally and also what was the path that led you to Bitcoin and what was basically your Bitcoin aha moment?

Okay. Um, sure. Well, what what I studied in school was astrophysics. Um, so I had an undergraduate degree in physics and then masters in PhD in astrophysics and I worked in that field for a few years as post-doc. And I was approaching age 30 and I thought, well, you know, these jobs are a little bit, uh, hard to come by for long term, it doesn't pay that well and maybe I should, if I'm going to make the leap into, you know, the business world or the real world, I I should do it then. And so I did and I ended up, uh, getting a position in software development for high performance computing working for an oil company. I did that for a few years and then after that, I just started working for a series of computer companies, um, in business development, sales, technical marketing kinds of roles. So companies like Cray and SGI and Sun Microsystems and various technical market business development roles, really interesting customer set because it ranges everything from aerospace to automotive to, you know, defense applications to things in the life sciences. So got to see a lot of different areas. Um, and I continued with that for three decades and then kind of quasi-retired. It's been 15 years now. Um, and decided to do that here in Asia. I had had two job positions in here. One out here, one in, uh, Tokyo very early on and then my last corporate job in in Singapore. And I got interested in Bitcoin in in 2014. I had had from really actually a young age, I had an interest in coin collecting. When I was young, you could go to the bank and you could find silver coins even from the 19th century, you know, so I'd go with a couple of dollars and get a roll of dimes and so forth. And so I had that period of time when I was sort of interested in silver and gold coins. I even worked in a bank, uh, in high school part-time and in college, so I had that a little bit of interest in in the monetary side of things. But I got interested in Bitcoin because of the technology, really, in late 2014 and, uh, I've been consulting as part of Orion X for the past decade and a half. We're a boutique Silicon Valley based technology and marketing consulting firm and we've got a small group of analysts and we've, you know, we track everything from AI to quantum computing. But, uh, I decided to to track cryptocurrency at that time and really what orange pill was reading the white paper itself because as I read it, once I saw the plus one equation, a derivation for how hard the blockchain becomes, how hardened it becomes exponentially as you add each new block. I said, "Wow, this is kind of amazing." And so I, you know, I tracked it and went down the rabbit hole like everybody else and had as much confusion as everybody else did about cryptocurrencies in general. And at one time wondered if Ethereum would ever flip. You know, it went through the hash wars and the block wars. And I think that's really what turned me into a a a maximalist was the the blockers in 2017.

Why was why would you say that, uh, that was?

Well, it it just became clear that Bitcoin was dominating and the reason it was dominating was because of proof of work. And with my background in supercomputing, I cared about how much compute power was going in. So from very early on, I was comparing the amount of Bitcoin hashing to the supercomputer or how did it look relative to that. And as part of Orion X, I've produced reports now for like seven and a half years, every, you know, twice a year about, uh, the Bitcoin network is a supercomputer network. It is the largest global decentralized cooperative competitive supercomputer network in the world and you can make some comparisons to, you know, the largest supercomputers of traditional time.

Very interesting. And going back to your background, so you said you, you know, have an academic background in astrophysics. Um, you've worked in software engineering. Um, you obviously have this, um, interest in tech and, uh, cryptography, um, you know, computing, um, but you're also now, you know, doing work in the marketing space. Can you help help us bridge the gap between that transition? How did you get into the marketing space and how does your sort of tech background, um, drive your work there?

Well, I got into marketing kind of early actually because, you know, I, the first few years I worked in software development at this oil company using supercomputers and the Cray salesman was in there calling on us. We didn't have a Cray. We had a Control Data supercomputer, but we started using external cycles from a service bureau. The name of that service bureau is now Sprint. They had a huge supercomputer.

Service bureau at that time called UIS. And so we were using Cray cycles for to run certain models. And I kind of thought it was fun. You know, the guys that I was the customer of, they were taking me to lunch. And I thought, this is kind of fun, taking customers to lunch. And, uh, then the Cray salesman said, why don't you come to work for us, you know, and you can be my sales engineer and work alongside me to develop accounts. So I became involved in technical sales and then that migrated towards technical marketing. And then Orion X is really a group of ex-Sun people, uh, many of whom were involved with high performance computing in in their past lives and, uh, it was founded by an ex-boss of mine and so that was kind of a natural thing.

Gotcha. Okay, great stuff. And speaking about sort of jobs and work career, um, there are a lot of people today, you know, facing job uncertainty because of AI, you know, there's economic uncertainty because of asset price inflation and and all the volatility that we see in the markets. If you were starting from scratch today, what would you do and focus on and why?

Well, I would certainly focus on figuring out how to make AI your something you manage, right? Make it your intern or your associate that you're the manager of so that you don't end up the other way around because it's, it's going to try and manage us. Uh, and so we we need to understand it and and defend against that. It, it obviously varies across all different disciplines, but, um, it's hitting the software development area very, very hard, right? So you, you have to be able to uplevel so that you can manage it and have it do the development. You know, I didn't do any coding for about a quarter of a century until the past year and a half. I had never looked at Python. I had seen a number of other languages. I can sort of read it, but I don't know how to find all the libraries and know about the formatting and so forth. And I never actually read, you know, instructions about it. But now I can just use it and use chat GPT or other AI to generate the Python. I can read it and then I can iterate it and, you know, use it as a research tool just to accomplish what I want to accomplish, which is what really matters.

Gotcha. And how about on the economic side and thinking about, you know, the all the asset price inflation we've seen, the volatility, how would you sort of think about and manage, uh, that and prepare yourself for the future?

Um, majority of your assets in Bitcoin and I will show you some of that on my slides.

Okay. Wonderful. Yeah. Let's, let's, uh, let's go there for sure because I'm, I'm curious like one of the questions I had about, um, you know, your research on Bitcoin and your forecasting in terms of prices. What's your best mechanism for forecasting price and where it will go? Is it the rate of inflation in the economy? The power law I know you've talked a lot about that or something else and how did you arrive at that as the best metric to follow?

It, it is the power law and, uh, I first heard of it in late 2019 and, um, you know, it kind of was an aha thing for me because it looked like such a good fit. Once you put it onto a log log chart, um, it becomes pretty apparent as long as you're willing to accept that the volatility is substantial. Um, so it clicked right away and then I just kind of pursued working with it and I learned pretty quickly and got connected with Giovanni Santosi who was the, you know, the original discoverer of this power law relationship for for Bitcoin that back in, you know, five years prior to that, so a dozen years ago now and just keep monitoring it and it's held up and I, I, I think I've got a slide that shows you how the power law index has been very, very consistent over the past decade.

Can we take a look at that?

And just to mention, we're, we're in the process. We've now founded this scientific Bitcoin institute and, uh, Giovanni is the director and I'm the associate director. um, headquartered in California, set up as a non-profit, but we're going to have substantial operations in in Europe as well. Here's some agenda. I, I want to start out with a couple of kind of broad philosophical ideas. One is that we have an absolute monetary standard in Bitcoin. And the other is a word you probably haven't seen before. I had not seen it before a month or two ago, auto poiesis, and Bitcoin is unique. It's the only cryptocurrency that really adheres to that and gold and fiat do not and I will show you why. And then an introduction to the power law and the distinction of that from what exponential behavior is, which is much more typical of traditional financial assets. And why a power law is good because it, it speaks to the stability of a network. So it comes from the network and a network provides stability and it ends up kind of channeling things into a power law and then I'll show the distinction between the power law core and the bubbles that we get. I'll show you evidence that the bubbles have gotten smaller over time. And then I'll talk about the periodic timing. People have talked about four-year cycles. Um, I assert that there has never been a four-year cycle, and that people were just conveniently ignoring the 2011 bubble, which was just as significant as the others. And I'll show you that log periodic timing gives a better fit. And then we'll talk a little bit about gold. And then I've got the Kelly criterion about portfolio sizing. How much might you commit to Bitcoin in your portfolio?

Great.

Okay. So I like to make this statement that Bitcoin is the first scientifically precise monetary standard in human history. This is not a new new idea with me. I mean, Saifedean laid it out in The Bitcoin Standard that the fixed supply and predictable issuance schedule make it fundamentally different as sound money, not only from fiat systems, but from gold, which, you know, always had some supply, uh, expansion and sometimes large finds that that could cause quite substantial inflation for brief periods of time. Uh, and I would assert that humanity has been in need of a monetary standard really for centuries and that we've struggled to try to have one. And we have a meter that's very well defined. We have a kilogram. We have a second. We have other, you know, standards that get enshrined in NIST, the Institute for Standards and Technology and the other standards bureaus. And there's no reason why we shouldn't have one for money. And Bitcoin fits the bill because it's fixed. It's absolutely finite and it's highly precise to 15 digits of accuracy. And it's a good foundation for a scientific standard because it's created from energy and math and and game theory. And those ensure that there's no tampering. You know, when they have the meter, they have to have a a bar. I forget whether they use titanium or what they use of a certain length traditionally, you know, and they keep it under glass and so forth. You've got to make sure the standard doesn't get tampered with and Bitcoin has those sort of properties.

Stephen, quick question on that. So, you know, if there's a technology that humanity has needed for centuries, besides the '08 crisis, was there anything special about that time maybe in terms of way technology was developing that enabled something like Bitcoin to come to the scene?

Well, I think all the, you know, it took four decades of various technology components to come together, right? And so I don't think we had it in terms of cryptography and computation and networks. It really would not have been available, uh, even 15 years earlier. Say you can imagine it a decade sooner, but not 20 years. First, you had to have the internet develop to a certain scale, right? And then you had to have developments in cryptography and you had to have some other developments, um, you know, around the construction of the proof of work and so forth. Um, so I, I don't, I think it happened when it's was kind of ready, more or less, as often happens in discovery.

Yeah. And I think to your point there, it wasn't like an overnight thing. It had been in, uh, been a work in progress for the past several decades.

Okay. So, this this word that may be unfamiliar, probably is auto poiesis. And it's a, it's a new word. It's only been around for 50 years or so. It means self-creation and self-production. And the first use of it was in biology. And the canonical example is cells. So cells kind of create their internal structure. You know, they take in resources through the cell wall and then they assemble everything inside the cell under the governance of DNA and messenger RNA and, you know, the creation of the proteins and so forth. And that, you know, I don't know any more than that, but, but they are autopoietic in terms of managing everything and reproducing that structure. So creation and production is what you can think of in an automatic way. And if you look on the right side chart, Bitcoin satisfies all the necessary conditions as a result of its fixed protocol, its scarcity, having no issuer, no foundation, the security scaling with value, the global neutrality. And this path dependent monetary memory means it kind of knows where it's been and it fluctuates around that and it turns out that it kind of locks into a power law. So it, that relates to the power law. So the system kind of, um, finds its way and gets to a certain level and then locks in with this overall behavior, which is called closure. Here, the dollar is nothing like that. It's, it's all of its rules are determined by committees, right? By the Fed and the Treasury and also by the money center banks whenever they make loans, their loan committees are part of the process. And also it, it tends to have to restructure under severe stress. So, Bretton Woods, you know, the gold window got closed in 1971. We had all the QE since the great recession in 2008. We had a huge break with COVID and, you know, they added 40% of the money supply in too. Um, gold is kind of in between. It's between those two extremes, but it's only autopoietic in part because it can, it doesn't really govern its structure. It's just there, you know, as an unchanging, um, atomic weight or defined element, but it doesn't have its own rules. It doesn't create a ledger. You know, it doesn't have its own, uh, capability for auditing. Uh, you have to externally provide the, uh, security and the assay capability and the ledger. And in fact, its role has really been shaped by external institutions, governments in particular, say, okay, I'm going to mint this coin and that's the coin for the nation and it has this defined, you know, fineness or weight and so forth. So the, the monetary role actually gets externally assigned in the case of of gold.

Okay. Uh, now into power laws, but first the contrast between exponentials and power laws and it's easily done by having two different kinds of graphs, one log linear and the other log log. So in finance, when we look at stock prices, we're used to seeing either linear linear or log linear. So we'll see always linear time, almost always, and then the price could be a linear scale or a logarithmic scale. So in the center figure here, we have, uh, log price versus linear time and exponential or uniform compound annual growth is the orange line and a power law has a different shape. It's the blue line. Now, if you take a short segment, you may see that, you know, they're tangent and they look rather similar for a relatively short period of time, which could be a few years, and you can't discriminate. But over longer periods of time, you'll know which one you have. If you've got a log log chart where the age and you have to know your zero point for the age, so where the age is in logarithmic time, then you're going to have a straight line. And if it's a power law and the exponential is going to diverge and it's just going to head right up and that eventually becomes unstable. So exponentials are unstable and power laws provide some stability and they can persist for many orders of magnitude. And, and Bitcoin has persisted as a power law for seven factors of 10, seven orders of magnitude and you can see six of those on this chart. Um, this is the kind of candle chart you've probably never seen. It's a log log candle chart. So the candles are not of equal duration. The price is logarithmic and it's running from 10 cents up to $100,000. So, log from minus1 to five. And the age is running from 0.2 to the current day. 0.2 in the log is like a year and a quarter. And, uh, when you see 1.0 on the x-axis, that's age 10 years. But each of these candle widths in duration is longer than the next one by about 25%. So the durations are logarithmic as well. And so they space equally in this case. And it turns out you only need 11 candles in this case. And you can fit using either ordinary least squares regression or quantile regression, which are the two dashed and dotted lines. And you get very similar answers that the slope is either 5.7 or 5.86, 5.9, call it 5.8 on average. And so we've got a straight line on a log chart and that's clear evidence for a power law. And the R squared is very high here. I, I don't know what it is, but it's more than 90%. So the price scale, you go six orders of magnitude from minus1 to five. And the age scale, you go from 0.2 to 1.2. So that's one order of magnitude. That's six times, right? And the, the detail measurement gives you a slope of 5.8. The candle band widths are just 0.1 in log 10 terms and that's about 26% for each additional one. So the first one's 0.4 years and the last one, the width of that candle of the data, you know, absorbed in that is almost four years. So we, we call this continuous scale invariance and this is just a different way to look at it. More typically, you're going to look at it with, uh, just taking price points at intervals and you can easily do this one at home. Just pick any day of the year and then check the price of Bitcoin on that day for the past dozen years or so and then plot on a log log chart and you'll get a more or less a straight line. And the slope here for this one was 5.67, 67, very close to the ordinary least squares that we saw with the candle chart before. And actually, you can do this just in a few minutes once you have these prices, you just give it to AI and say, do a power law fit, then it spits this out. So it says the price is 1.27 cents times the age in years raised to the 5.67 power. That's the equation. It's only got two parameters and the slope is 5.67, 67 and the R squared, which is the goodness of fit, the square of the correlation coefficient is 94%. So it doesn't take much data to demonstrate the parallel nature. Now here's contrast with an exponential. So this is not a log log chart. This is Nvidia on a log linear chart. So this is log price and it increased by, yeah, two and a half orders of magnitude and it did that in a decade. So for a decade, Nvidia was growing at about 69% compound annual growth. It's a straight line on a log linear plot. But this is unstable. If you project this forward another decade, the market cap of Nvidia, which right now is four or five trillion, would grow to be 900 trillion. That's equal to all current global wealth. That can't happen. Therefore, it won't happen. So exponentials are unstable. The, you know, the phrase we use is trees don't grow to the sky, right? And so you see bubbles develop exponentially and sometimes super exponentially, but then inevitably they crash back. Fortunately, in the case of Bitcoin, what they crash back to is is the power law or somewhat under and then they return back to the power law.

What is special with Bitcoin in that sense that it's unlike any other, you know, bubbles that we've seen in that, you know, the price doesn't just collapse to, um, you know, zero and, you know, tends to bounce back and create new bubbles in the future. Like, you know, people often mistakenly compare it to, they'll dismiss it and say, you know, it's, it's another tulip bubble. You don't hear that one as much anymore. But definitely in the last, uh, decade, we did. But what special properties does Bitcoin have that, you know, leads it to be like any other, not like any other, uh, bubbles that we've seen?

It's the maturity of the network and it's the fact that it sets all these intrinsic rules for the network. So that allows the network to develop in a certain fashion. But in order for the network to not be this exponential runaway and then, you know, crash to nothing, it has to develop substructure and basically fat nodes or nodes that get preferential attachment. And that happens with, uh, waves of new capital, larger amounts of capital with different structure. So we met Metcalfe's law describes how communication networks grow and it's was true for the telephone system and it was true for the internet and it's true for some of the social media networks that the value of the network goes roughly as the square of the number of people connected on the network. You have to get to a certain scale for it to lock in and you have to develop some structure and Bitcoin did that and it, you know, it took a few years to do that. It had to have a certain level of desirability in terms of security and in terms of growing value in order to attract players and new tiers of capital. And that's what it's done and that's separated it from the rest. So we can't find any other cryptocurrency that sits that sits with parallel behavior.

Right? And why do you think that new flow of capital though continues to come back in, especially after these, uh, you know, periods of of of market pullbacks, right? As opposed to looking at the situation and saying, "Hey, like, you know, Bitcoin already happened. It already had its time." And let's say whether it was, you know, 2017, you know, or again in 2020. Um, why do you think that new flow of capital is willing to come back in and take what looks like a pretty big risk if that moment has already happened in time theoretically?

Well, I think it's the reverse of that. I think that the capital comes in as as the rise happens with the bubbles. So the increase of the bubbles attracts new capital and in fact, you wouldn't get a bubble if you weren't getting the new capital because it requires capital input to grow. It's the derivative of the power law. So if the power law is 5.7, the new capital flow has to be a power of age 4.7. It's a, it's the first derivative. And so it is, act, the bubbles actually attract new tiers of capital. And so that could be, you know, originally it was just, uh, cypherpunks and then it was retail and then it was, you know, some whales and family offices and hedge funds and eventually we got to treasury companies and ETFs and sovereign wealth funds. So you get these larger and larger tiers and those larger tiers are not enabled until the price gets higher because it doesn't become consequential for them unless the market cap is a good bit larger.

And what about capital that flows in to kickstart the next wave of the bubble at the at the end of the bare market? I guess my question was more towards tailored to towards that. What causes new capital to come in during a bare market?

About half of it comes from the intrinsic nature of the bubbles and about half of it comes from external influences. So that's all of your macro influences, the liquidity input that varies, the regulation is the regulation barriers get knocked down, right? Those are enabling functions for things like ETFs, treasury companies, bank custody and so forth.

Gotcha.

This one just shows very simply that Bitcoin has not followed an exponential. If you just take the average return, which is the orange line for each epic, so these are four-year epics up to each halving, monthly returns were 30% in the first epic, and they were half that, 15% in the second epic, uh, 10% in the third epic, you know, seven or eight% in the fourth epic. We're now in the fifth epic. So that came down roughly as the reciprocal of the age. And that's consistent with power law behavior. If it were exponential compound annual growth, it would be a straight line or something close to a straight line. And the blue line is is the volatility. The volatility has come down in a similar fashion, all also similar to the reciprocal of the age of Bitcoin. Now this is a full treatment of the power law using, you know, all the data, uh, a dense amount of data and this shows both ordinary least squares fit, which is the blue line in the center, and then quantile regression at different levels. The red line is the median or 0.5 level. And you see the bubbles clearly in 2011, 2013, 2017, 2021. But you also see that the ordinary least squares and quantile regression median lines are converging and you see the volatility coming down and the bubble heights are smaller as you go from one bubble to the next. And what that's why these quantile regression lines are all collapsing in on each other. We've got the the 0.1 level and the 0.9 level shown and they become closer and closer in, you know, relative log price, but larger in absolute linear space. So again, this is a log log plot. The age in years is marked off. You can see the numbers, numerical values. Right now we're at age 17. Uh, and you can see, you know, what the trend lines say for a month ago or month, a little over a month ago, December 2025, and then the end of this year, what the trend says. So it, it would be right now about 120K is is the trend and we're well below that as we all know and by the end of the year, the trend value would be 160K.

There's just two parameters. There's a scale parameter and then there's the, the power law index. So it's just T, the age of Bitcoin raised to the K power times some constant that adjusts and then, uh, a little bit about why a power law might be the case. First of all, nature loves power laws. There are four fundamental forces of nature. Some people argue about gravity if it's emergent or fundamental. But it follows a power law. It's 1/r squared. Electromagnetism follows a power law. It's 1/r squared and both the nuclear forces, the strong and weak force have parallel components and other components as well. And, but we also find parallels in biochemistry and in economics and in social networks. So there's some of the biochemistry examples listed here in the upper right and in the gold looking box, the socioeconomic distribution such as income, wealth, consumption, city populations. Cities are interesting because their inputs scale, uh, sublinearly. That is, to build out the infrastructure in a city and all the utilities and transportation networks is cheaper as the population grows larger and they're more compact. You know, you don't have the same last mile problem that you have in rural low population areas. But the outputs, the income, the wealth, the patents, you know, everything associated with the city, the artistic creation is superlinear. Um, and networks, as I mentioned, both communication and social can obey power laws. Uh, Metcalfe's law was formulated for the internet is growing as a square of nodes. And when you actually measure, you observe numbers between one and a half to two or a little bit above two depending on the network. And Bitcoin seems to adhere to something like the 1.8 power. So the idea is that a communication network is more valuable than just the next person added because that nth person can talk to everybody that's already on the network. So actually there's an n squared effect. It's n * (n-1)/2 is the number of total connections on the communications network. So it's n squared in the limit. Now, there's some potential truncation of that because everybody doesn't really want to talk to everybody else, but it does expand people's opportunity horizons a lot. And, uh, what you can do then is measure the users for Bitcoin as wallets or later on as economic participants and you find it grows roughly as the cube of age. So that's a T to the 3. So if the network grows as a square of the number of users and the number of wallets grows as the cube of the age, then the value of the network grows as the sixth power roughly of the age. And so that this is essentially why price is growing is close to the sixth power of the age. And the other point is that is shown in this, uh, black and white box. As Bitcoin matures, the network develops all this structure. You know, the large miners, the institutional holders, custodians, ETFs, and these are called fat nodes in networks. And they stabilize flows, they absorb shocks and they're can be more patient holders of of capital, particularly treasury companies like Strategy that he never sells basically, right? ETFs, it's a little bit different because it's retail flow going on, but when you have these fat nodes, they stabilize the network and they convert the system from exponential style growth to more hierarchical growth. Truth and that manifests as a power law. And then why is the power law so steep? It's because actually there are four different things going on that contribute to that and they kind of sum up to give you this steep power law. One is the network structure, uh, and that's the growth of the user, but also this preferential attachment with these fat nodes. The second is that as it gets adopted as a store of value, then it grows on the balance sheets of the holders and so you get some multiplicative effects from that. The supply rigidity kind of is a strong feedback function that forces price response because you cannot respond with increased supply, right? So, it has to go into price. It's on the traditional supply demand diagram, you're just vertical. And then, uh, the reflexivity that that you get, uh, feeds both into people's beliefs about the system and the leverage that they might be willing to adopt and then the ability to access new capital. And then you can get these bubbles, you know, these reflexive bubbles that can happen because there's more liquidity available because regulations have changed and now you can have ETFs when you couldn't have them before. And then you get herding and FOMO behavior that causes bubbles to overshoot and so forth. If you add all these up, you know, you can get one or two powers from a couple of these and another power from the others. And you add them all up, you could get something like the sixth power. Exactly. What you get is kind of an emergent property. You, you can't predict quite ahead of time, but you just have to measure it and see what happens. Skipped over one. Um, sorry about that. Okay, now let's look at bubbles and also the parallel core. You can separate the core and bubbles in different ways. You can do something complex like hidden Markov models that make the decision for you. You can divide into three zones where you have a neutral zone and a core zone and and you can have a a bubble zone or you can divide very simply at the parallel trend and say everything below is core and everything above is bubble. And all of those methods kind of tell you similar things. So I've just used the simplest method here. So half the data is in the red line and half of it's in the green line. But what they're showing is the rolling average four-year standard deviation as an age of Bitcoin for the lower half of the data, if you will, which I call the core. And all of the bubbles, which is everything above the parallel trend. And when we see the core standard deviation has been very stable around 20%. Whereas the bubbles that started out early on at above 100% volatility have dropped down to below 40% volatility. And if you want the total volatility now, you just take the square root of the sum of the squares of these two components as a rough estimate. And you get 40 something% which is what's observed. And that's a reciprocal fit through there. That dash line, it fits pretty well that it's fallen as one over the age. And so we would expect the the bubble volatility to continue to come down towards the core volatility. Now we're going to look at the bubbles in a little more detail. So we've got, um, in the upper chart, we've got the price history. We've got the best fit with quantile regression. Median is the orange line. And then we have these green triangles. um, there are four large ones and then there are a bunch of little ones. So I was doing this very kind of detailed bubble and anti-bubble analysis and what I found was that really it was just these four big bubbles and the other ones were kind of negligible and you didn't really have any very large anti-bubbles. You had some troughs of long duration, but you didn't have steep anti-bubbles. You had some troughs of long duration, but you didn't have steep anti-bubbles. You had some troughs of long duration, but you didn't have steep anti-bubbles. You had some troughs of long duration, but you didn't have steep anti-bubbles. You had some troughs of long duration, but you didn't have steep anti-bubbles. You had some troughs of long duration, but you didn't have steep anti-bubbles. You had some troughs of long duration, but you didn't have steep anti-bubbles. You had some troughs of long duration, but you didn't have steep anti-bubbles. You had some troughs of long duration, but you didn't have steep anti-bubbles. 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trend, but we did get a new all-time high. We did get this burst, this run-up, um, you know, in October where and then price basically effectively collapsed, right? Um, and that's within that four-year, what would be known as the four-year cycle. So why, why, why do you, why do you identify it as a, as a failed attempt in 2025?

>> If it's not one standard deviation, it's not a problem. So one standard deviation is a factor of 1.58. Even as volatility has come down, and the, the trend price in October, right now, the trend price is a little over 120,000 and it grows at, uh, about 10% a quarter. So in October, it was around 110,000 or a little bit higher. We only exceeded that by 13, 14,000, so a little over 10%. But to even be one sigma, you would have to be a factor of 1.58. You'd have to be 160,000 and above to really, to be in a true bubble that was anything like the prior ones.

>> Okay. So, you're not just defining it as a new all-time high for that year?

>> The power law gives you new all-time highs, right? Theoretically, every month at the rate of 3% a month. But then whether you reach that or not depends on, you know, how you fluctuate around the parallel trend. Um, 2021, the log periodic says that's a first harmonic having no bubble of significance. In 2025, is explained by log periodic, and then we would expect a bubble peak in 2027 with the phase could be in 2028. But, uh, it should be rising very nicely by 2027 and hopefully, you know, later this year. So the four-year model was right three times, wrong twice. The log periodic model was right five, wrong zero times. And also, you can do this RMS error, which is how off were the predictions. And for the four-year model, the error in timing is over one year. But for the log periodic model, the average error in timing was half a year. Uh, so that's much better as well.

Okay, a little bit about gold. If we were on trend, if you could do a power law on gold, and, and it fits very nicely. Um, we're lagging a lot right now. We're, you know, kind of hugging the bottom of the quantile regression or, you know, one sigma kind of on the downside. But it, it's a power law of about 5.3 of age. And, uh, the blue line here shows the Bitcoin price increase, and the gold line shows the gold price increase, but they're on different scales. So the Bitcoin price goes up in this chart by a factor of over 100,000 since 2011. And the gold price, and this was done before the big run-up, but it's kind of dropped back a little bit. The gold price went up by a factor of three since 2011. So, don't let the gold bugs, you know, give you too much grief. A factor of 100,000 versus a factor of three.

>> Yeah, that's, that's fair. But I, I think also we'd have to point out to you that, you know, Bitcoin was just starting out. So it, you know, it had, it had that, uh, that going for it as well. You know, it was starting from a much smaller base.

>> Right. However, if you look at the compound growth rate for gold during this interval, it's about 7 to 8%. And right now, the parallel trajectory for Bitcoin is about 40%. So you can just take, you know, the second half of this, uh, you can go back, you know, eight years, right? And if you do that, uh, Bitcoin went up in order of magnitude, and gold went up, yeah, about a factor of three.

>> Yeah. And all the, all the gains for gold came this past year.

>> Right. Hey, congratulations. They had a great year. Um, the right-hand chart is the correlation of log Bitcoin price versus log gold price since there it is so dynamic in terms of price range, and they're not very well correlated. It just moves all over the map. Sometimes they're positively correlated, sometimes they're negatively correlated. This is the rolling 52-week correlation. So, it's an average over over one year, but as you can see, it, you know, it, it can shoot up above 75%, it can fall below minus 75%.

Okay. And this is the regression in the large chart. It's the ordinary squares is the solid line, and then the quantile regression, the green one, the middle one, dash line, they're pretty similar. And, uh, they both give you a power law of index 5.3, and they both give you a high R-squared of 94%. And you can see qualitatively, it looks pretty similar to the chart against the dollar, but it's just because gold does go up over time versus the dollar. The power index is, is, you know, a little less steep at 5.3. So in some sense, that's a, a fair measure of how Bitcoin has done since gold is not, uh, depreciating in the way the dollar is. Now, our on the smaller chart, we're showing the residuals. And so you can see the four bubbles. And you can also see that, you know, Bitcoin versus gold took a dive right during 2025. And we're significantly below the fair value trend, which would be about 48 ounces, depending on what you, which one you want to use. And currently, we're, it's 16 ounces as of today. I just checked. So, we're short by a factor of three. Um, that's equal to about one standard deviation or, you know, one and a half. Um, so it, it's down significantly, and, and Bitcoin has some work to do to catch up. Maybe in the last few days, we saw a partial pivot. And, um, I'm coming towards the end. I'm going to look now at the Kelly criterion for optimal log wealth, which speaks to, um, what amount of your portfolio you might be willing to put into Bitcoin.

This was developed by John Kelly of Bell Labs in the early 1950s. He was an associate of Claude Shannon, who's known as the father of information entropy. And there's a kind of complex derivation, but it turns out to be a very simple answer. If you're doing a series of bets or, you know, investment decisions, you have to define the window. Do you do it daily or weekly or monthly or yearly? And then what percentage of the time do you win? And then what's your edge? How big is your win relative to your loss? And based on those two numbers, which are P and B for our purposes, P is the win percentage. Q is just the loss percentage that you can compute from the win percentage. And B is the absolute value of the win divided by the absolute value of the loss. Uh, which is just minus win average win over average loss. Then the formula is just P minus Q over B. In other words, if you won 60% of the time, you would say, "Oh, should I bet 60% of my stake or my portfolio?" And the answer is no, you should bet less than that. And how much less is this the loss percentage divided by, uh, this ratio? So imagine it's an even bet. The, the win and loss are the same. You know, you win $2 or you lose $2, kind of a thing. If you win 60% of the time, you would subtract 40%. And that would say that the optimal bet size would be 20%. 60% minus 40%. But if your payoff is higher than the loss, the average loss, then you can bet more. So if it would double, you'd have 60% minus 20 over two, right? So you just subtract 10%. And then it would say, uh, sorry, it'd be 40 over two, so it'd be 20%. So now I can bet 60 minus 20, I can bet a large amount, 40%.

So what this does, uh, is it's shown, it can be shown in quite detail that this optimizes the growth of the logarithm of your wealth over time and also avoids ruining. And so I've done this analysis for a bunch of different assets. And this shows 16 different ones and it shows 10 years of returns. And Bitcoin won eight out of 10 from 2015 to 2024. And I'll add in 2025 in a moment. And of course, it lost, you know, horrendously in two years, 2018 and 2022. It was the worst performing amongst these asset classes. But nevertheless, you know, the answer that you get is quite positive. The next best one was broad tech, US broad tech. Uh, gold here is actually marked in green. You can see how gold did. And, uh, a lot of these are debt, so they don't return that much. So I've taken the ones that that actually, you know, can return more. And that's in the next slide. The, the eight out of the 16 that are not debt related things. So, Bitcoin, broad tech, large and small caps, real estate, which is REITs, gold, commodities, international equities. And then the next column shows the win rate, which was 80% for Bitcoin and for broad tech, 70% for small and large caps. And then the average win size was very large. For Bitcoin, the average yield was 290%. But the average loss was 70%. So you take the ratio of that two and you get B, which is 4.2. It's just absolute value of W divided by L. And then you plug into this formula and you get 75. So that says based on that, in theory, you could put as much as 75% of your portfolio into Bitcoin. Uh, broad tech 66%, small caps 26, large caps 52. Not so different from broad tech in recent years. Real estate 19, gold 36%.

However, what you really want to do is consider the risk-free rate. So if you'd say that that's 4% roughly a treasury bill rate now, uh, then what you have to do is subtract from your average win and also subtract from your average loss, and your B values get decreased. Uh, Bitcoin was so favorable that it really didn't matter. You still end up with 75%. Roy Tech still 60, but small caps flipped. You can see that the, the win was 12%. I've got to lower that to 8. The losses was 17%, I've got to lower that to minus 21 relative to a risk-free rate. And so actually now you shouldn't have invested in small caps during those 10 years. You should have been short, at least relative to the risk-free rate. Large caps, it lowers it to 40%. Real estate, it flips it negative. Gold, it, it drops it a lot. Commodities, you shouldn't have been in. And international equities, you shouldn't have been in. Once you consider the risk-free rate and consider the other variables.

Now, Bitcoin, we can say, well, as you were just saying, Charles, I mean, it had those great years starting up. So, what if we just look at the first five years? You still had an 80% win rate, but the B ratio is lower, 2.4, but you still end up with a kind of 70% allocation.

>> No, I didn't have the chart that included 2025.

>> I'm sorry. Is that the first five years or the last five?

>> Oh, of course, it's the latest five. Yeah.

>> Okay. Sorry. I thought you said first, but yeah, I just wanted to clarify.

>> Yeah, it's getting rid of the stuff that's too favorable, right? Potentially. We know from the power law that returns are coming down, but volatility is also coming. And then I've added in 2025 just for Bitcoin. Uh, so we had a losing year. We were down about 5%. So the P value lowers from 80% to 73%. But the B value actually goes up because we only lost 5% and you average it in with the other two that are in the 60s. So the net result is 68%. You could say that I could put as much as 68% of my portfolio. Now, very important, this is annual rebalancing. So the assumption is that I hold it for a year and then at the end of the year, I rebalance to whatever I've calculated the new F to be as I've got one more year of data. So it's, it's I make a series of one-year bets. So I would hold this is for just Bitcoin and cash. The cash is in T-bills. So after I get the next year, I, you know, I would have allocated after 10 years, I would have allocated 75%. But I get this new data and I say, well, I should really only be 68%. And, and if we take just the past six years, uh, then our win rate was 2/3, and it's two of our worst years recently. And then the, it says 59% allocation.

Any question about that?

>> No, no, that, uh, it's, yeah, that makes sense.

>> Okay. All right. I'll close. Has become information energy securely encapsulated electrons to eternal bits. And thank you very much. Thank you. Thank you. Um, one, one thing you've, you've said to, uh, you know, to stick to that, to to the quotes there. Um, you've talked about how, you know, um, people will buy Bitcoin at, you know, sort of the volatility they can handle. You brought up Michael Sailor earlier. He says, everyone will get Bitcoin at the price they deserve. Uh, could you expand on your view, uh, here on that point and, uh, how much do you agree with, uh, what Sailor has said about that?

>> Sure. I mean, we, we've seen that over and over again, right? Um, I, I do think that this price they deserve, um, you know, you kind of have to divide it into the retail and the institutional. And for the retail, it's, do people understand money? Well, most people don't understand how fiat works, right? They couldn't tell you why the gold system failed. And I think it's hard if people don't have that background, that education to then really grok Bitcoin. So I think that it's really important that that people, um, you know, when you're trying to orange pill people, that you have that discussion with them about the nature of money and ask them questions, what do they understand about money? This is why I like Nick Bch's book, you know, or now he's got two, because he kind of goes through it in, in, in that way. I mean, there's some other good books as well. But, uh, with institutional, I have a little bit different view, which is Bitcoin is not interesting to Apple. Bitcoin is not interesting to Nvidia. Not given their current business models and what they do and the size of their treasuries. Bitcoin is not worth enough for them to worry about at a market cap of a little under two trillion. If they bought half a million or a million Bitcoin, it wouldn't change their balance sheet that much. It wouldn't change the outlook for their company. For Sailor, it was transformational. You know, he had a need. He, he believed he had a crisis that, uh, you know, maybe he didn't, maybe he should have gotten into AI and didn't get into AI early enough from his business intelligence model, but he, so he missed that window, and he just couldn't get out of the box he was in. But he was of a moderate size where he could make a difference. For Bitcoin to make a difference for Apple and for Nvidia, and for Microsoft, it's going to have to reach that next order of magnitude. It's going to have to get to that 10 trillion scale. And you can say the same thing for most larger sovereign wealth funds and certainly for nation states. Okay. The US has a strategic reserve, a modest strategic reserve. It's not transformational at this price. For it to be impacting the relative to the 38 trillion of debt, you know, it would have, there would have to be a trillion of Bitcoin on the books, and then it'd have to be growing to two trillion and four trillion. So I, I think this is one of the things that going goes on is that Bitcoin hits these new price tiers. It attracts the attention of these new tiers of capital that are larger and larger and larger, and that helps drive these bubbles. It helps drive this discrete scale and variance, and it helps reinforce this long periodic nature, and also helps the structure of the power as these fatter and fatter nodes get attached into this sort of line of the power.

>> Gotcha. And, you know, actually going back to the, the Kelly criterion there and thinking about gold's performance last year and other precious metals, you know, why do you think they have been the stars of the debasement trade and dollarization over the past year? And then when you think about the, you know, Kelly criterion and how to construct, uh, your model portfolio there, um, how much do you take into account the idea that, you know, past performance isn't necessarily predictive of future performance? And so, you know, you, you make sure not to overweight. So, okay, just because gold, you know, performed really well last year, you know, doesn't necessarily mean it's going to perform well this year or in future years. So, how do you take that into account as you're modeling, uh, what the portfolio might look like?

>> Yeah. Well, with with traditional, what's called gambler's Kelly, the original one that he, uh, derived, um, you just add new data as it comes in. And so you'd add in what happened with gold, and, and that would, you know, that would bump up your allocation to gold, and it would bump down your relative allocation. I mean, I have constructed two asset models where you have just Bitcoin and gold, you know, and, uh, you get something fairly similar, um, something in the 60, 70% range. Gold looks a lot more like fiat than it does like Bitcoin in the long term. So you can, you can construct those, um, you can even construct multi-asset portfolios. It becomes computationally expensive, and you end up changing to a different form of Kelly called continuous Kelly, that uses that looks a little bit like Sharpe ratios. It uses the mean and actually not the standard deviation as in short, but it uses the variance. And, uh, if you just take the mean and the variance with Bitcoin, you can get allocations above 100%. Um, I don't spend a lot of time talking about that. I don't want to encourage people to leverage too much, but you, you can show those. Uh, what you can also do is include skew and and kurtosis, and, and I've done those called MVSK. So it's like what I just described is MV, but then you can add skew and kurtosis. And so I've done three asset portfolios where you have Bitcoin, gold, and, and stocks. And, uh, it depends on how much weight you put on the skew and kurtosis factors, but you'll end up with something like 58, 60% in Bitcoin with those as well. So you just, all you can do is update with the data you have. And I think if you want to be conservative, say you either back off on your Kelly fraction and say, "I'm not going to go full Kelly. I'm going to go half Kelly or two-thirds Kelly because that's how I sleep at night. That's what makes me comfortable." Personally, I, I do kind of go towards full Kelly, but other people may may not want to do that. But it does show that you've got a lot of room to work with between, you shouldn't be in there at one and 2%, right? You should be in tens of percent. I think this shows people that. And then the second thing is, if you don't like the early history, you can throw that out and just use the more recent. The next thing you can do is look at shorter time frames. So you can look at quarterly windows or monthly windows. And if you do, your allocations go way down because, uh, you have more losing quarters or more losing months than you have losing years from a percentage standpoint. You, if you do monthly, you'll end up with something like a 30% allocation, and if you do quarterly, you'll end up around 50%.

H and, and so at this point, um, you know, given the data that we have up until today, would you be adding more gold and less Bitcoin or?

>> Right now, there are two ways to look at it too, which is where am I with respect to the power law, right? So, um, the, if we just take Kelly, we would say, okay, on January 1st, what was the price in January 1st?

>> Of Bitcoin?

>> Bitcoin.

>> I think it was near somewhere between maybe 85, 90K.

>> Yeah, it was in, it was in the high 80s, I think. I think it was sitting around that 87, 88.

>> Right.

>> Right. Level. So now we're at 77.

>> Mhm.

>> Right. So if you had a 70% allocation on January 1st, coming in with 87, and now it's at 77, you're well below. Right.

>> Yeah.

>> Now, you can violate the rules and say, "I'm going to add because I want to push my allocation back up." Or you can wait a year before you make a decision. But that's one set of criteria. The other set of criteria that I use personally is where are we with respect to the parallel? And right now we're down by one standard deviation. We should be up at 120. So just from that standpoint, it's a buying opportunity, and also from a Kelly fraction, it's a buying opportunity. So it's a good place to be adding.

Wonderful. Yep. I definitely, uh, am aligned with that, with that, uh, with that point. Um, great. So I think one other question I had for you here was, how did you invest pre-Bitcoin, and what was the same sort of philosophy? Um, and obviously, you, you have this, uh, this math background. You're very analytical. Um, did you think about investment the same way? I, you know, I imagine, you know, there, before Bitcoin, there was an asset that maybe you'd have be willing to make a 70% allocation to, though.

>> Um, before Bitcoin, it was real estate, actually. So my initial retirement plan was based on having investment real estate plus some stocks, but more in real estate. And, you know, I, I retired in 2010 from corporate and then went into consulting, um, and, you know, real estate was the dominant aspect. But as I've gotten into Bitcoin, I sold off my investment real estate and I only had one property now so that I could have more Bitcoin. So that plus plus stocks and, and actually, as it was early in my retirement, my focus was just on generating yield. So real estate for income and, and stocks, you know, more for the yield at that time. And, uh, you know, real estate was the option for some capital gains as, as well, long-term capital gains. And then when I discovered Bitcoin, it was like, well, let's just grow wealth. Let's, let's just grow log wealth.

Yeah, man.

>> Yeah. And, and maybe to wrap up, so you, uh, you know, we spoke a little bit about Sailor earlier. You know, he's, as you pointed out, he transformed his own company, his own trajectory with Bitcoin. What do you think he's gotten right over these past six years, and where do you think he's been wrong?

>> I think he's gotten most things right. Um, look, he, he went through a process, and he'll tell you he went through a process. So he started out by issuing, you know, traditional debt and inconvertible and, uh, his first preferred, and he kind of went through that in stages and he found his way to getting what looks like the magic bullet with STRC, right? I mean, that's transformational. I, I believe he's redefining the risk-free rate. He's certainly defining the risk-free rate for the Bitcoin economy with STRC, which is now 11.25%. Um, I own most of his products, um, you know, as part of the portfolio. I, I don't know that he's gotten much wrong. It's just that he was able to optimize his financial engineering as he found his way to these different vehicles and saw what the market would accept and what they needed. So, I mean, if he had realized early on, it's something like, hey, money market type pricing or close to it, paying 10%. Uh, that that was kind of a killer app for him. I'm sure he wishes he had done that early earlier, but, uh, he kind of.

>> Yeah, maybe he just needed to get to scale as well, you know.

>> And he, I think he, yes, he had to kind of climb to scale before he could probably do that. Uh, as far as the power law, he's never admitted.

>> So much about the power law. The one thing he got wrong is the model that he created, I think, is, uh, for me, not very informative because he, he created this baseball bull and bear case, and it was just a spreadsheet with a bunch of stair steps in it and arbitrary, uh, percentage increases, but coming down over time. But it turns out that his base case kind of behaves roughly like a paralog going out to 2045, but if you propagate it backwards in time, it looks nothing like the history of of Bitcoin prices. So he, he's, I've never heard him say the words power law. Um, it would be nice if he understood it or acknowledged it, but I, I don't know if that's going to happen anytime soon.

>> Great. Well, Stephen, this has been very, very, uh, informative. Uh, before we wrap here, is there anything else you'd want to share, uh, with the audience about Bitcoin, uh, treasury companies, or anything else?

>> No, I think, uh, those are some of the most interesting things that I've been working on lately. I will say that the analysis with the log periodic behavior and with the modes and including the phases could carry us up, you know, to 350,000 in mid-2027 and to twice that at towards the end of 2028 is what that's showing. And that does not include FOMO and, you know, unusual new, uh, avenues for capital to enter and spiky stochastic razor on top.

>> Wow. Okay. Well, we'll be checking back in. Can't wait to touch base with you again. But again, this is, uh, been super, uh, informative and very interesting to, to, to hear your perspective.

>> My pleasure. Thanks for having me on.

>> Thank you.