 In my view, 2019 was something like a founding year for what I call Bitcoinometrics. And with Bitcoinometrics, I mean the application of statistical methods to Bitcoin. So it's pretty similar to econometrics that many of you might know from your economics studies, if you have studied economics at least. And what Bitcoinometrics does also like econometrics, is that you first derive hypotheses from economic thinking in the case of econometrics, and then you test them using statistics. And the same applies here to Bitcoinometrics, that we first derive certain hypotheses not only from economic insights in this case, but also from technological, mathematical stuff from cryptography, and then we still test them using statistics. So in order to understand why 2019 was so special, we have to go back a bit in time. So in the earlier years 2013, 14, 15, there were already the first quantitative approaches to Bitcoin, especially to model the Bitcoin price. So for example, there were models out there that used transaction volume to explain the Bitcoin price. But the problem back then was, and that's also why I called the Mickey Mouse models, that there was no real robustness testing going on. So there was just someone putting out a model, sometimes not even himself did the robustness checks, and especially not other researchers did those robustness checks. So there was no peer review that you know from academia. And the other problem was that you had the impression that those models were just a bit random. So people were just throwing random variables into the equations without having any foundations, any theoretical foundations beforehand. So then this whole quantitative approach was a bit put on ice, and the focus was more on the qualitative analysis of Bitcoin. So mainly by the Austrian economists who went back basically to the work of Mises and Rothbard, and they were looking from those perspectives, and they were looking for the insights that those thinkers had regarding what makes a good form of money, because after all, Bitcoin is a money candidate. And this whole approach, this more qualitative approach from the Austrians, culminated in the book of Saifidina Moussa, a very good friend who already gave two talks here at the bank, and the book is called The Bitcoin Standard, and I mean he wrote about a lot of stuff there, but one thing was very important that he identified hardness as one of the major driver or the major features that a good form of money should have. And what he also did, he introduced the stock-to-flow approach to Bitcoin. So this is originally coming from mainly the commodities analysis, so the gold analysis, and he introduced this in his book, especially to compare gold with Bitcoin and other forms of money like euro and dollar. So just to recap a bit why is stock-to-flow a good measure for hardness, you can have different approaches there. I mean one way of looking at it to say, okay, if you have a very high stock, a very huge amount already outstanding of a certain asset, and only little amounts are coming each additional year, for example, onto the market, you have a very resistant, a very robust asset against supply shocks. So it's very difficult to inflate or dilute this asset. You can also think about the fact that if you have a very high stock-to-flow ratio that it takes a lot of time to reproduce the current amount outstanding. And obviously this only works if it's very hard to produce new units of this certain asset. And what happened then is that the anonymous investment manager, Plan B, took this stock-to-flow approach and published an article in March this year, and he used the stock-to-flow approach as a quantifiable variable for hardness. And so what he was actually doing in my view at least is he was testing a hypothesis, and the hypothesis was hardness is the major or the predominant driver for the valuation of Bitcoin. And this is why, and it's the first reason why I say this is like a very crucial year or even the founding year of what I call Bitcoinometrics because you had this two-step approach now. So he had first a theoretical foundation mainly coming from the Austrians, and then you had guys with a strong statistic background testing in case this certain hypothesis. And what also happened that this was very interesting and it also reached us at some point was that the publication sparked the interest of other quantitative-oriented researchers. So this was not only Plan B who was working on this model, and we will look later in greater detail at the model, but very soon other quants and other statisticians jumped onto this wagon and refined and criticized this whole approach. So there was extensive robustness checks going on, completely different to what we had here. So this was the second ingredient why I say there was this founding year of Bitcoinometrics. And in the end we ended up and we will see later why it's such a robust model. In the end we had the first robust valuation model for Bitcoin. Before we get into the model I wanted to point out two specific statistical features when it comes to Bitcoin. The first one is you have a very extensive data availability. You actually have in the end an open database, so the Bitcoin blockchain is something like an open database that is updated every 10 minutes, so you have more or less real-time data when it comes for example to the stock-to-flow data on this data, and you also have other data like addresses that we will use later as well. And if you compare this for example, and I came across this during our study, if you compare this for example to gold it's very hard to get exact data on the stock-to-flow data of gold, so the best you can hope for is annual data for example for the flow, and also for the stock it's very difficult to get an exact number. Basically there is no exact number, every gold analyst. So if you ask 10 gold analysts they will probably tell you 10 different answers to this question. If you ask 10 Bitcoin you only get one answer. And this was really interesting and this also enabled high-frequency testing. So you also have the possibility, for example if you go to coinmetrics.io, you can get daily data as well. You could even use intraday data if you want to. And this is something very special, especially if you compare it for example to gold or other commodity markets. And the other thing is a bit more technical but it's a very interesting and very important concept that we have to understand later and actually we will also test this concept later. So there is something called the difficulty adjustment in Bitcoin and it ensures that the supply growth path that was more or less predetermined or set in stone by Satoshi is insured and can't be manipulated or can't be changed through price movements. So what basically happens if you have a price increase in Bitcoin it's obviously more attractive to mine to produce more of Bitcoin. But through this difficulty adjustment you have an adjustment of the difficulty. This case upwards so it gets more difficult to get new Bitcoins or to mine new Bitcoins. And you have the same in the other direction so if the price decreases and it's attractive to mine Bitcoin it's getting easier to mine Bitcoin. And this is very important because this means that the market valley or the price of Bitcoin doesn't have any feedback mechanism on the stock to flow because the stock to flow will be our regressor, our explanatory variable and usually what you have with econometric phenomenon you always have a feedback mechanism. So it's very rare that you have the statisticians called exogenous regressor that is not influenced by the dependent variable so the variable that we want to explain. Another feature is obviously this was discussed in the very end that we already know future values of the stock to flow which is also pretty handy obviously but usually you don't have future values for your explanatory variable. So let's look at the model in more detail. So if you start by just plotting the time series so you have here the market cap on the left hand scale and the right hand scale you have the stock to flow ratios you might think okay what is all this fuss about I don't see anything here there's no real relationship there can't be the same applies to the scatter plot where you have the stock to flow values and the market cap for a certain period of time and the whole picture changes if you use the logarithm of both variables because then it looks like this and looks already much better. So now you clearly see here that it could be a relationship and if you look at the scatter plot you see this very linear straight line here so this was the starting point to say okay if I have this linear relationship here I could use my standard linear regression models and if you do this you get pretty remarkable results because this here for all of I will always give a little refresher for all of those who missed statistic class at university the r squared basically means that almost everything almost all the variance in the dependent variable so the market value is explained by the x variable in this case the stock to flow and also if you look at the question how likely is that this is just random that the stock to flow ratio has this coefficient you see that it's very very unlikely so this was basically more or less what Plan B published in the beginning and then happened what I described in the beginning this sparked directly the interest of many other quant because a lot of people were saying in the beginning okay this is all fine and good but this is just a spurious regression so the question is what is a spurious regression in the time series this is like the nightmare for every analyst because it means that you think you have found something when indeed you haven't found anything and this is kind of a problem what happens with time series if they look like this so they are not stationary they are not like this and we will see later a stationary variable as well but they are trending upwards and what can happen is that if you use your standard regression analysis in this type of series that you capture a trend of both variables but they are not really connected and this was the first critique that Plan B received and a lot of people also directly delivered the answer they didn't only criticize but they came up with the solution as well so there is especially one also anonymous investment manager probably at least I don't know exactly who is called Nick when he came up with the fact that there is one way out of this problematic situation and this another term that we will explain now and this is called co-integration and co-integration is a very fancy term and it's mathematically also very complex but it can be explained hopefully at least with a very simple example and this is what we will do now the example is the following this is very common basically in a literature that didn't come up with this this is like the basic explanation in the statistical literature that you have a drunk and a dog so in a scenario one you have the drunk and the dog standing outside of the bar and they are not connected so the dog doesn't belong to the drunk so what can happen now is that the drunk starts walking and he's staggering around and he's ending up some part of the city and the dog is also running around chasing something whatever and he's arriving somewhere completely different a different part of the city if you were to run a regression on those two random walks you would get something like we saw earlier because you would pick up a certain dynamic because they're both walking in this direction this direction you would mistakenly think that there is a relationship because of their trends, what they are doing there the second scenario is now that the dog actually belongs to this drunk so you might even think about it like this that the dog is really on a leash so it can't go further than like 2 or 3 or 4 meters so now they are walking again or the guy is walking and the dog is doing whatever and what you will see then is that the distance between them is what is called a stationary variable it's not a case that it can be that it's first 1 meter distance between the two, 1 meter, 2 meter, 3 meter, 4 meter, 10 meter but then we'll get back again, it's again 2 meter, 3 meter it can be a 10 meter again but there are certain boundaries there and this is what is called co-integration so there is even so we have more or less random stochastic variables you still have a certain relationship between them in this case you could think of the co-integration as the leash because this is what it connects you can also think about the fact that the dog cares for the drunk and he doesn't want to leave him alone and he wants to look after him or whatever so there is a certain connection there and this is exactly what you can do with the market value and the stock to flow variable you can also see is there a connection there and this is what is, well it's done with some tests and stuff like this but the basic intuition is that you can also look at something like a difference between the model price and the actual price and what you can see here is that this variable doesn't look like upward trending, downward trending but it looks more stationary and this is exactly the difference between actual price and the model price here it's from a different angle and it's also not the market value but the price here per bitcoin you get the same idea here that you see the actual price is at some points especially here during the bull run but here even more above the model price but it's never overshooting completely and the same applies to undershooting here you get down but you never go completely this way or this way and this is, I mean I spare you the the conjugation results exactly but this is very clearly so you run every conjugation test that you have and you always get the same result that you have a very strong result for conjugation you can also think about it if you don't like the dog and the drunk you can also think about that they are connected through a rubber band so there is some elasticity there but it's always coming back so the actual price always coming back to the model price implied by the stock to flow in the end by the hardness of bitcoin and there was the suggestion and again by Nick that I mentioned earlier to say look the stock to flow ratio is not really that random because as I told you before it's actually more or less predetermined through the difficulty adjustment so it's not really applicable to use a random variable or a random metaphor like the dog so we took out the dog in this case and we put a road here and this is the stock to flow road and the idea is that the drunk the bitcoin price or the market cap whatever is free to move here as it wishes in this case if it's the market value or the drunk but it's never going completely off the road so the idea that the bushes are a problem for him and he can't get over it and so the idea is that you have a certain that you have certain boundaries for the market cap but within those boundaries it can move also in a very random fashion I mean this was very important this was probably for those who were watching or following this on Twitter and said okay now they found a great deal for those nerds what is all about but this was very important because without conjugation you would have had nothing nothing at all, no relationship at all and everything would be irrelevant actually so then the next point was okay we have conjugation so we have this relationship there but what about causality this was the next point what about causality so we can also test here and what we are using here is that you use the error of time so to establish cause and effect and the basic idea is that you use past values of a certain variable in this case the stock to flow and see whether this helps you to predict the current value so for example easier example than this if you have wood prices and you use them to predict furniture price you will see that they have a very predictive power so in this sense are causing more or less if you control for everything else they are causing the furniture prices so what you see here is very clearly that the stock to flow is causing the market cap but not vice versa and this also makes sense because in the beginning I told you that there is no feedback mechanism and this is basically applied with chronometrics if you want to see so we had this hypothesis coming from more or less technological considerations to say okay you have a difficult adjustment and so forth you can't influence this because there will be a rapid change and this is basically the statistical test now where you see okay this seems the data supports that it's really the case that the difficulty adjustment is really working also after we published our work I read a lot of times on Twitter yeah okay this is all fine and good you found the relationship slash co-integration you found the right causality so the causality is running into the right direction but what about variable x, y, z and you could pick whatever you want there and what came up a lot of time was you didn't capture adoption and before we get into the question whether this makes sense at all let's just check it and we just included in this case significant addresses there's also something which is handy as I mentioned before that you get a lot of data from in the Bitcoin sphere so in this case significant addresses means addresses that were really used for spanning and receiving so no random address that you just generated were used but they were really significant in this case and if you include these significant addresses we see in this co-integration relationship so we basically put them on the road and test whether they play any role there we see that they are not significant so they don't add any explanatory power in addition to the stock to flow and what we also see is that the causality is still only running from the stock to flow to the market cap and not from addresses to the market cap and now let's get back to the question whether this makes sense at all so this was not really a bit conometrics approach because we didn't think about this first the thing is that adoption if you think about it and also if you think about it in terms of addresses can't be a driving force in itself it's more like a symptom or a consequence of a driving force for the value of bitcoin so if there is something like a stock to flow like the hardness of bitcoin that's driving the demand and the valuation addresses are just something and adoption in general that follows from that so it's not a driving force in itself so it shouldn't play a significant role or shouldn't play any role at all but we got this out of the way as well you can do this with other variables as well but this was the most, I would say most prevalent critique that adoption was not included here the good news is for all of those who are still hoping to see a funny dog there is still a dog and this dog is called Litecoin so for everybody who doesn't know Litecoin Litecoin is an altcoin, an alternative coin another cryptocurrency or one could also say it's just a copycat of bitcoin and if you run everything that we've just done the whole approach like the regression the conjugation test, the causality test and if you apply everything of those tests and procedures to Litecoin you see that you don't get anything nothing at all but the only thing that you get is you find a relationship between the Litecoin price and the Bitcoin price and this is something that you can clearly see here that the difference between those two prices in this case not the market cap but just the price per Bitcoin or per Litecoin it looks very stationary it's the same with the dog and the drunk that we had before that they can deviate a bit but they are never leaving each other completely they are always somehow connected and the conjugation test clearly shows that you have this relationship so we can come in the end to this picture where we now have a dog with the Litecoin hat there and the Litecoin sign and this is also something that Nick already came up with so it's not my idea just the Litecoin hat actually but it's a very nice picture to think about it if you're not like you're a statistic nerd that if you combine all of those insights that you have a random variable the Bitcoin price you have a random variable Litecoin price but they are just connected so the dog is just following the Bitcoin price and then you have this structure for actually both in this case which is the stock to flow and this is actually the hardness in the end always of Bitcoin so to sum up 2019 was a special year but it was in my view at least a founding year of Bitcoinometrics because a lot of QANs or quantitative oriented people also at financial institutions I think at least delved into Bitcoin much more than before because they had something that they knew so they had statistics that they knew actually from their studies and they could apply it to something new and the other thing is and this is a very strong interpretation or it sounds very strong but this is the logical interpretation of the conjugation result this is the second point here to say if you really have this conjugation and other variables apparently don't play any role in this conjugation relationship that despite all the complexity and all the news around Bitcoin positive well really positive mainly negative about hacks and bands and whatever that the only thing that apparently statistically speaking is striving Bitcoin structurally and predominantly is its hardness and its hardness is captured by the stock to flow value obviously it will be very interesting to see what happens next year with the half thing when this stock to flow or more completely the hardness is increasing tremendously and the third point is this whole stock to flow doesn't work with other cryptocurrencies so if you if you thought ok this guy from Bionic is telling me if I just set up a spreadsheet and I just use a stock to and I come up with a stock to flow ratio of 1000 I would just out compete Bitcoin it's perfect and Jörg will now take over and say ok this is not so easy and it's very difficult and it also makes sense that other cryptocurrencies are not driven by this considerations of hardness and stock to flow ratio that's it from me thank you very much and Jörg it's your stage