Hello and welcome to our monthly meeting of virtual seminar series on central banking and digital currencies Today's host is the Federal Reserve Board and I will now turn things over to our moderator today, Francesca Kerr-Peller Thank you, John Adam. Welcome everybody. Today we have the pleasure of having Harold Ulling present a paper and Michael Salkin discusses paper Harold is the Bruce Ullin and Barbara Ritzenhaler professor in economics at the University of Chicago where he's been since 2007 and he is also a fellow of the econometric society since 2003 and since he graduated from the University of Minnesota in 1990 he has done extensive work on applied Dynamics, stochastic general equilibrium theory on a variety of fields including growth, dynamic contract, business cycle, but also financial crisis and monetary economics Michael Salkin is an assistant professor of finance at the McCombs School of Business at the University of Texas at Austin and since he graduated from Princeton in 2015 he has significantly contributed to the literature on information aggregation learning and noise in financial markets and more recently to the fast emerging literature on digital innovations so we're very happy to have Harold present his paper on the crash of the Terra Luna stablecoin pair and Michael discuss the paper. I will be moderating keeping track of time and keeping track of the questions, so I welcome everybody to ask questions in the chat and I will bring up those questions to the speakers and Harold will have 25 minutes after which Michael will have 10 minutes for the discussion and then we will have a Q&A session for the remaining 20 minutes in the seminar and Harold you are welcome to start put up the slides and Okay, well, thank you. Thank you so much for the kind introduction and thank you for the invitation to speak here So that's really really good and I'm hoping there will be some interesting feedback and look forward to the discussion by Michael obviously So, yeah, so let me get right right into this. So this is about the The title of the papers lunatic lunatic stablecoin trash and it's about the as Francesca said about the Terra Luna system that crashed in Mela steers. So let me let me just briefly explain Roughly what happened. I mean, it's now a year ago But not quite a year ago actually but you know these these instabilities in stablecoins You know seem to keep on coming back and to say something about that a little bit more Now what happened was? that You know a group, I think it's all Korea essentially claded this algorithmic stablecoin Terra UST And I'm going to explain the moment how that worked But it lost more than 75 percent of its value in May 2022 so it certainly, you know Depegged and then and then just you know It just went down and from there and that led to price collapse of the underlying lunar token of 99.9 percent an increase in lunar supply by a factor of 19,000 in the range of more than 50 billion US dollars. So, you know, that's that's quite a bit of money and it seems like you know We're thinking through what happened there this so how did the system work the system work by allowing traders To convert a Terra UST coin into one US dollar worth of lunar tokens and vice versa. So these lunar tokens, they were Really floating What that was a freely floating cryptocurrency with a price, you know bumping up and down You know, let's say it was supposed was worth a hundred dollars, right? Then you could take a hundred Terra UST tokens and get one lunar token for it And then maybe saw the lunar token on exchange like Binance or some other some other exchange And if the lunar token was only worth, you know, 50 dollars Well, then you would then one Terra, you know 50 Terra would would buy one and vice versa So the system was set up to do this course You could also buy Terra directly on the exchanges and could buy and trade Luna directly on these changes but the plea and I would argue clever idea here was this You know Blockchain based system based exchange of one was the other so when one wanted to burn Luna into terror The system would somehow look up the current price to Luna and give you the appropriate one of Terra tokens and vice versa Eventually sustained outflow on or burning of the UST tokens of Terra tokens into Luna results in the collapse of the system Many have argued that this accepted that this affected the cryptocurrency market as a whole there's an estimate by Barons that say that That market cap of the crypto market declined by 600 billion US dollars or that 600 billion US dollars were wiped out and that obviously is you know That's a substantial number. So that's a key figure that was cited the White House proposed on crypto regulation and then You know the lunar crash the recent FTX crash and other things also important driving drivers of the Mika regulations in in Europe, which are actually pretty far advanced and in introducing You know tailor-made regulation to the crypto asset market Okay now oops So here's here's a picture I'd longer slides that show this a little bit like a movie, but here's a picture of what happened So the cherry the UST price isn't black and it actually has fairly stable for nearly years It was you know spot on a dollar the system worked right at all would was nicely and here's the Luna price and now you're seeing Here down here the blue is is the burning. So that's how many people take the the terror talking the The token that's picked to the dollar and turn it into Luna and you see this picking up here But it's not entirely clear if you look at this picture, you know, what was cause and effect You know was it that this was picking up and therefore this started to Peck or this started to decline and what what was going on and in any case the bulk of the burning took place much much later It took in terms of you know the way these financial markets work, right? I mean it took took 24 hours for the for the burning to really you know go full-scale and eventually The price of the underlying Luna token because Luna talk so now gets increasingly diluted diluted by all the terror that was That was converted to you know dropped so far that That the blockchain was halted and the convertibility was halted now There are a couple of interesting things here That that I that I want to understand one is what's evolution of the price You know can you understand the evolution of the price of Luna? Why did it take time? I You know, there's also something interesting that one can say about the evolution of the price of UST, but I probably won't get to that you know today because there's what's going on here in this paper And I can only talk about the subset of it. Okay, so I want to understand these events qualitatively and quantitatively So I'm going to build a theory for the underlying Luna token That gives me a Gradual unfolding of the Luna crash given a certain rate of the terror burning that is assumed that there are people that just want to convert Their UST dollars into Luna for some reason and you know that rate You know what should be happening to the price of Luna and I can't get a price I get some differential equations. I can some get some close-form solutions So that's very nice and I can compare them qualitatively to the data and I can will argue that that already looks pretty good and I can do the same thing for terror UST again I'm not going to talk about that much today I'm in the paper if you want to look but the theory then also allows me to interpret the data So the theory contains key pieces that investors essentially think about and I can try to back out these pieces from the theory variables To deduce what it was that investors must have in mind in light of the theory and then I don't just get Qualitative goes to the data I can pretty much exactly replicate the data doing that and I call that the method of quantitative interpretation It's a version of sort of related to identification estimation calibration if you like, but I think in some ways It's different I'm not saying that other people haven't used something like that, but a few deserves a new name. So that's what I'm proposing All right now Doing this runs into a challenge and that's how you want to price cryptocurrency currencies The net present value of these things is zero. So they're no different from other fiat currencies And there's literature that that looks at competing fiat currencies and how to price that There's a famous paper a character in Wallace that has pointed out that you know people treat these currencies as equivalent There's then exchange it in the terminology the version that I want to advertise mine from my favorite Linda shilling That's downloadable for free from the Journal of Monetary Economics published in 2019 Where we where we think that through and we argue that the that the that the price for cryptocurrency Should be risk adjusted Martin Gates empty plus one He has his risk factor if you like the expectation of that thing is is one if you don't like that Just think that QT is the expected future price of the cryptocurrency So it doesn't appreciate with interest rate. It doesn't deep appreciate with an interest rate You know if you ask me, you know, what's my best prediction for you know, the Bitcoin price 10 years from now I look at the Bitcoin price today and I will be my prediction I mean that's essentially what's going on and these words these here, you know We are just replicating essentially results that were already in Kirk and Wallace and one really pick All right, so Maybe then the system should have worked right if the price is a martingale and there's people burning the terror into Luna And the surprise movements in the Luna price uncorrelated with this with this, you know Why should that be correlated with these inflows? Then, you know the burning of the terror USD could have just been absorbed by a higher market cap of Luna rather than the price collapse But clearly that's not what we saw. So you need something else. So you need a different you need a new assumption And the assumption that I'm going to make is I'm gonna I'm gonna impose something on the evolution of the market capitalization in particular I'm going to impose that, you know, once the system crashes, you know There's going to be certain market cap There's only limit of how much people want to hold that stuff in terms of you know valuation And how much it would be valued if the system, you know, somehow survives There's clearly tension here to these martingale results that are in the previous slide and it's it's just good to keep that in mind The second thing is how come that the crash unfolded gradually If you just write down a simple model of rational expectation of crash, it'll be immediate, you know, you know, the burning is coming You should immediately say, okay, how much is there for Luna worse and that should be that should be that After that, the price should be constant and clearly that's also not what we saw And I'd solve that by continual hope for resurrection So the model will have the smart to get property despite from the fact that the price visibly, you know, gradually declined It did certainly look like a Graduate decline, you know, obviously rather than anything that looks like the occasion of future price with the same as the current price Okay, so let me start with the pieces. Here's a very very simple Version of the fear that doesn't contain the dynamics yet, but it helps to clarify a few few things So imagine there are two periods one before burning and after burning There's an initial Luna stock. So there's a number of tokens in and there's a price queue or an exchange rate If you like to the US dollars the rational traders, you know They they would only trade this if there's the same price in both periods Otherwise opportunities for arbitrage and let's say there's a burning be of US UST terror tokens to be is now measured in US dollars where MS just units of Luna Okay, then Simple mass tells you what the final Luna stock should be you just take the current stock and you calculate how many in at the current price How many how many new Luna tokens are added and that's just going to be divided by Q and that gives you the new token You can rewrite this equation by multiplying through with Q Okay, that's it right and so now we need an assumption somehow to to get us, you know Q Right and that's that's what we want. Okay, so I'm gonna assume something about the final market cap I'm gonna assume that's on the left-hand side here Now that's a capacity of the market in terms of value of absorbing that stuff And let's just fix that once you fix that you can solve for the underlying price You know just from that equation you're given the initial amount of tokens capital and that's what you know, and that's going to be your price Now the couple of interesting remarks here because I think there was some confusion the discussion What you need here in order for this for getting a positive price is that the eventual market cap has to be higher than the amount of Terror that gets burned, right? I mean here now it's a little and it's now expressing your dollars and little bees expressing your dollars And so the difference better be positive for the Q to be positive But it could well be that the current market cap before the burning starts is smaller than bees So sometimes people have you know compared the current market cap to the amount of outstanding terror tokens And that's just not the right way of thinking about it Now next we need to introduce the dynamics and how to get the graduate crash and let me motivate this a little bit Right, so this is another picture here of this decline of terror I mean the theory is about Luna, but I think they're looking at the it's a pegged service kind of interesting right you saw this price collapse of the terror token here and But did it have to collapse? Well, I'm going to point to another reason collapse that was for the USDC You remember the secret in the valley bank, you know, it went into trouble You know part of the deposits they actually backed up the USDC token and so the USDC, you know depict, right? And they could have been you know like on this picture and then the total crash of the USD system, but somewhat recovered and You know the people running USDC took measures to you know to show the markets and it restored So so the argument that I'm going to make is that why this crash is happening You don't know where they're going to restore the system as it's here or whether it's going to be fully crashing as it's there. All right So let me write this down explicitly. I First do it in this great time then I get a continuous time system and then get eventually patients So at time tick with zero everybody suddenly realize. Oh my god Burning begins, you know, the system is under stress and we I'm going to treat BTS exorgences for this part The second part that I can't talk about In due to time, you know, I would I would talk about how the how to think about this PT here So then a T and within this short next time interval Delta There's going to be burning of BT Delta USD tokens into the corresponding amount of Luna tokens So I have to divide by the current price Qt if to pick out how many looking Luna tokens I get and I get sort of a version of the equation that I just on the previous slide now I'm going to make this assumption to Continual hope for resurrection So with some probability lambda t times Delta this whole thing stops right the burnings takes place. All right, but then after that You know the the nightmares over and everything returns to normal and the exit this whole situation with a market cap empty plus Delta but then with probably one minus lambda t Delta the burning of the USD continues and we keep on going until The Luna price reaches some very low value and then in we suspend convertibility and In the exit with some exogenous given market cap So I want this I want this empty possibly be different from this empty here and you'd see how that plays a role The rational traders price of Luna tokens that take the solution to count I can write down the equations if I let Delta go to zero I get a system of ordinary differential equations There's lots of things I would love to talk about here But let me not bother you with all the differential equation math that goes on here Let me just show you instead some pictures. So here's some okay, but here's the you know Here's how you can envision this burning right your standard T Yes, it's a total amount of outstanding tokens. He has some market price for these things. There's some burning that take place These are the additional new tokens BT. You know, that's a burning rate, right? So then doing this time interval Delta It's BT times Delta that gets burned divide by the market price either the additional tokens and that gets empty plus Delta Just empty plus Delta will just be empty plus these new tokens here And then, you know, either you're going to be exiting with market cap In order to empty plus Delta in which case these tokens here will be worse into plus Delta And then you can figure out the price or the burning continues and then you get the new indulgence price from this year All right, so differential equations. Let me skip that here Let me just show you some simulations. I imagine the initial market cap is 30 for 30 billion You know, that's a reason why I chose 30 there the initial price I just think that at 100 which was I mean I somewhat less than that, but 100 is just a good number to remember I Fixed the exit market cap as the same 30 so that you know when when the nightmares over sometimes early You just return back to the same market cap as before everybody's happy Let's just assume that and assume that there's an exit rate of or you know has a trade of point or five unit of time That that the nightmare ends, but there's continues burning So I'm gonna fix this burning here, you know in terms of this offer parameter, which is given by be over lumped attempts in That's one way of parameterizing that and it's zero It's a time zero you realize burning is going starting place But I assume it's only going to start a little down the road. It may not start directly at zero So that's assumption here and then for T bigger it's T star it's you get the burning and then the stopping price is epsilon So you can go through these Scenarios here if the burning starts right away, then the price should you know collapse right away essentially If the market cap at the end is the same as exit market cap normal times You would actually get a market pack that goes down and goes up again. That's not what we saw what what happened So instead I'm gonna I'm gonna postpone the actual burning to our 50 So there was initially so the big burning starts later as we have seen in the original data But the price is already collapsing anticipation of this burning that's going to take place The market cap collapses, but then recovers because see I'm still assuming that the capital MT is Equal to the same and as before so I have to make this exit market cap in cases System collapse small and that's what I do this next next pictures So then eventually this market cap is going to be down here and now you get a price dynamic So it kind of looks like the data so next picture is the data and a flip back and forth You know you saw this late burning here that kind of is you know captures this late burning starting at zero You know the late burning starts at 50 It's sort of stylized of the of course the market cap also has this double S shape That would argue the price dynamics kind of looks like this more or less, right? And so I think that's a really success But I can go beyond that I can use The data to actually back out what people must have thought in terms of the empty the lambda t in the empty and Do all that and there's bunch of equations that I need to solve the other creations But I'm gonna worry about it in a nutshell you can only back out either in T or Lambda t you can't you can't separately back out the two of them I mean it's a get two two equations But unless you only get a you know combination of these two parameters So you have to either make an assumption about NT back out lambda t or make an assumption about lambda t and back out Enti and that's what I do in two scenarios and now I can actually replicate the price dynamics pretty much exactly There's some zero constraint that has to be obeyed if you look at the lambda t That's what it looks like. So, you know, you could argue that initially people are still quite hopeful I mean despite bumps here That that the system will restore itself But over time this optimism faded right and this thing went into a tailspin ever faster, right? It's the beginning people thought okay something is happening Maybe there wasn't a venture near that restore people's confidence, but eventually it was gone I think that's a that's a probably reasonable scenario here fix the exit market cap here instead of fix the exit probability and then this exit market cap is becoming very erratic It was kind of high in the beginning and kind of low in the end in the counterpart to what you're seeing here Now what's interesting about this calculation is that you can back out the probability That you will not suspend and it will eventually collapse, right? So initially you're thinking okay, this has to come to an end before we reach the epsilon price But eventually, you know that optimism fades and that probably goes to zero And this essentially provides a price floor for the us t token So that's why that's interesting and you can compare that that's from the theory From the simulations that it before from the last scenario and you can compare that to what happened Now the data is a reconstruct these probabilities Under my two scenarios and be depending on whether fix the lumped and the t and I can think of that as the as a price floor For the for the us t token right and so in this one scenario I get this orange line here is my price floor for the us t token And the other one I get the red line as a price floor and you can see that's the actual us t price I mean it it you know it goes below the orange so it's not a tight tight theory, but it doesn't go below the red So I would say that's that success and from there you can also think about What that what would have taken for us t traders to actually get rid of their tokens When would they be nervous enough to say that's it? I'm going to burn my us t token I'm going to get rid of it. I no longer want it And and and what you find out is you can you can infer that so that in the paper that's constructing more careful detail You can figure out the population distribution of the of the people being nervous enough Of saying now i'm going to burn my us t token remember 60 percent of the us t token for student circulation Even after the system crashed so that's just about the 40 percent of the us t holders that were still holding on And what this says for example that even when the probability of a crash was 50 percent So that will be here here to the right is even higher crash even if that crash in scenario a Only 20 percent of the us t holders were ready to say okay Let me get rid of the token even though there was a 50 chance of a crash And even if you take the morbid nine scenario b it's only about half of the people that were ready to cash in So that's what it can then back out with the theory. Let me conclude You saw the taro luna crash. I think it's interesting to study because we see we seem to be seeing you know stablecoin crashes More often and so just understanding one at a time. I think it's a good idea There the challenges of addressing the character in what is strange in in germany see in the challenge of Being an outward gradual that rather than immediate So I solved this by imposing modern capitalization and impose that that is hopeful resurrection, right? So that gets resolving one or two. I get these ods. I can solve them I get a stylized version of the data but I can even go beyond that I can do a quantitative interpretation of the data I can look at the quantitative movements in burning and the prices to back up the theory variables that the traders must have had in mind And it shows that the threshold collapse probably of collapse in burning was he was about 50 percent It was for more than 80 percent of the us t holders, right? So for half of those that actually burned and there were still 60 percent left. It was all said and done Thank you very much Thank you very much Harold. This is this fascinating Michael the floor is yours. Harold has been as a as a true German right on time I consider because as an Italian we are known to be always late I really appreciate it The floor is yours Michael And yeah, you're muted Is that there? This is great. Now we can hear you Okay, perfect. Yes. So let me just share my screen again. Uh Here we go Wonderful. Well, thank you so much for inviting me to discuss this interesting paper and for the kind introduction So what is the motivation stable coins are often typed? Cryptocurrencies typically to the us dollar or the euro for instance You could even be something in principle like the price of gold They act as a store value and a financial bridge across defi platforms and applications It's just for defi lending often the argument being that they're much less volatile than a lot of prominent cryptocurrencies Like ethereum. So for investors and for traders. It's often something they would want to hold for instance for liquidity So recent collapse of terra luna. However has raised questions about their stability And there's a nice review paper by freola et al and finance research layers that kind of goes through the anatomy Of this collapse And unlike reserve fact stable coins for instance tether or usdc Terra luna is more of a novel algorithmic stable coin arrangement And i'll copy at that a bit because the luna foundation did have roughly three billion In bitcoin that it would use to defend the peg if ever needed But in principle the stable coins should be somewhat self-sustaining because of the algorithmic The arbitrage algorithmic mechanism in the background So terra stable coins are anchored by their native token luna This is often the case and i'll show you an example of another stable coin that's anchored by a token And can always burn one terror for one dollar of luna tokens at the prevailing price and vice versa And that's supposed to be stabilizing because the idea is there's arguably a risk this arbitrage of us Terra is not a little bit off of its peg and that can be resilient for small shocks because For a little bit, you know a less than 1 percent or 1 percent of 1 percent deviation You can make a riskless profit and get out of luna pretty quickly or terra if you're doing the trade But it can be very destabilizing to large shocks because you know once i've traded a large amount Of terror for luna to be able to maintain the peg that price of luna or terror may fluctuate in the next minute Or so before i can unload my position and that can be Stabilizing if i anticipate that the price of luna is going to collapse by 50 five minutes after i try to defend the peg That creates a limits to arbitrage type of argument that makes it difficult for me to want to defend the peg So as this paper do it builds a novel framework for understanding the terror luna crash It has minimal structure which i really like it's very transparent about what ingredients are needed If the law of motion for luna price from the burning rate bt It's very forward-looking so everyone's internalizing what's going on and how terror is going to be burned in the future So everyone's fully anticipating this but we still get a slowly unfolding crash And they implicitly there is that hope for resurrection that how i've discussed Which is there's a market in pride probability lambda t of recovery upon recovery There's an exit market cap for luna and that's the hope that for traders who are willing to hold on to these tokens That there's some chance that the burning will stop and the peg will be restored So you can incorporate heterogeneity in ust holder beliefs to construct a manker for ust tokens based on a threshold perceived probability of recovery and herald briefly discussed that when he was talking about that distribution of Of ust holdings that would lead to burning And he provides an organizing quantitative interpretation methodology for bringing the theory to data And there are many sorts of refinements he does to try to illustrate that his His methodology can be flexible to incorporate some of the nuances of reality such as the two hour observational interval For which he has the data He can also use various different ways in measuring the luna price And what's kind of nice is he's able to infer beliefs lambda t fixing an exit market cap and vice versa Those are the plots that he showed and my one suggestion from a methodological perspective before I talk more conceptually Is I'd like to see the quantitative interpretation to do a bit more I want to get more out of this methodology And what's nice is because you can do the counterfactuals and you can run a variety of counterfactuals You can perhaps provide bounds for lambda t in mt And you can use model based inference, which is nice because with data alone I can follow the price of terror luna and I can say well if I think the price is to first order approximating these recovery Probabilities, I can roughly recover something from the data myself What's nice about this theory is you can do counterfactuals to try to say well The inputs that go into the price are a bit more complicated Let me try to see what seems like a plausible range of probabilities So we can kind of put bounds on these things Which is also very important for not only the luna foundation Trying to figure out whether or not it can defend the peg as well as for arbitrageers trying to defend the peg But also for policy makers and assessing as this thing is slowly unfolding What must be going on from a robust perspective in the minds of every of all the actors involved So as I said, I talk about one other stable point So there's iron finance a two token system backed by the title to a titan token It failed in june 2021 and somewhat similar to as harrell showed for the terror token You can see that it's knocked a little bit off of its peg and then slowly seems to decline Falling first a little bit then then eventually collapsing So one thing to take away from this is that the experience of terra luna is not unique for algorithmic stable coins And in fact, harrell's theory can perhaps be used to understand and rationalize this experience as well And also perhaps on a from a bit more of a negative perspective This means that this sort of risk that we saw with terra luna might just be endemic to this algorithmic stable coin arrangement So it's something to keep in mind going forward that harrell's theory might be useful not only as an autopsy of what happened But as a prescription for what may happen as we move forward in the stable coin universe So what I like about this is a new theory of slowly unfolding crashes in the paper It's often compared to a bank run, you know, you've diamond did vague her and john But there are also several other theories of delayed crashes And I'd like to see the paper speak a bit more to these other mechanisms Like there's the as I mentioned there's a limits to arbitrage literature So you have coordination failure and some of my favorite papers come from this literature For instance a brew and burn a minor. So in brew and brew and a minor There's a lack of common knowledge among arbitrageers that there's common knowledge that The price has moved away from fundamentals and this leads to an endogenous delay before you see a collapse And that's actually the key result of the paper Is that everyone knows that the thing is overvalued by time t But it takes t plus epsilon before the crash occurs. And that's what they would call the strategic delay You've heterogeneous beliefs with short sale constraints and lockup constraints So if we go to the dot-com bubble Hong shakeman john would argue that the release of lockup constraints for insiders slowly increase the asset float for various stocks Tech stocks during the dot-com bubble and this caused the the need to absorb the supply move down the marginal optimist in the market Until eventually this couldn't be sustained and you have a collapse of the dot-com bubble And also just to cite some of my own papers just because they're the most prominent in my mind about this channel There's a lack of common knowledge also fundamentals So in this situation we get price signals that confuse us about the right action Think of the housing bubble in the 2000s We get some early signals from uh new york and san francisco leads us to think that housing is strong We build up and after we build up the price signals become stronger And then we learned we overbuilt and you have this sort of gradual collapse It doesn't occur immediately because we didn't know at the time that things were overvalued. We slowly learned So a comment I have for the paper is what is slowly unfolding in the context of the model It would just be nice to know what is the benchmark is the t star equals 50 instead of zero a notion of slowly unfolding Can we endogenize that it would just be nice to have a clearer sense of the benchmark as I really like this idea And then just from a practical perspective Terra Luna crashed over several days and is that slow compared to the dot-com crash in march 2000 Which took several weeks and if you look at the price for it took about a few months And there's also the suspicions of strategic attacks on terra luna So the lunas foundation depleted about 80 000 bitcoin and reserves about three billion dollars to depend the peg And there's some evidence from that briola paper that there were traders that were shorting bitcoin ahead of time In anticipation of luna having to liquidate its bitcoin Can we use the model at all to evaluate these alternative theories? So next major point. I just want to wake and I'll have one more after this is arguably the terra luna crashes and intrinsically Uh is a crash of an intrinsically worthless asset and it highly relies on self-confirming beliefs Do we believe that we'll be able to support the peg? Do we believe that we believe in the future? That terra and luna will have their value So the algorithmic arbitrage mechanism for stable coins to me is a bit similar to ETFs as authorized Participants would go and make sure the value of the ETF matches the nav of the underlying But there's no underlying fundamentals for the other one side of that trade And the lack of fundamentals makes it vulnerable to being careened off the peg And luna did for first try to defend this peg So it'd be nice to know how did foundations failed interventions impact market beliefs and we can use harrell's models to try to understand that We can actually see the moments of which luna intervened the luna foundation intervened and see what it did for market implied beliefs So we can understand if was defending the peg a credible action by the foundation What's also getting a bit back to that discussion of coordination failure The paper implicitly collapsed a strategic uncertainty into a first order belief pt about the probably going forward probability of resurrection And it would be nice to try to connect that probability through the burning rate back to lambda t to maybe Indochinize it as well as just to discuss the role of higher order beliefs Do I believe that other people believe in this probability as well? And how does that affect my actions? Finally just to conclude that has some implications for policy Algorithmic has different economics from reserve back stablecoins reserve back. They're kind of like high-risk money market funds and algorithmic fuses economic incentives with technological constraints backed by deep-pocketed arbitrageous and devotees Constrained by protocols and burn rates as we had a bit of a discussion before the webinar that there's a lot of technological constraints involved in designing these things and financial stability oversight just has to adapt to the new risks of d5 Smart contracts automated market makers and flash loans and it introduces some new issues such as misdirecting oracles As we said terra luna has to look up the price of luna and terra before the blockchain The protocol can make the conversion. You can also have algorithmic liquidity crashes Cascades that kind of amplify any sort of destabilizing activities and stablecoins So thanks so much for giving me the opportunity to discuss this really interesting paper and with that I will conclude. Thanks so much Thank you very much. Michael. This was a brilliant discussion Harold would you like to respond? Take a moment to respond to michael's before we go to the broader q&a Yeah, sure. I'd be happy to I mean thanks I mean it was really an amazing discussion and Just realized I didn't take enough notes here to to remember all the fine points that you raised michael I think really was excellent You know a few things You know the gradual thing here is about the gradualism in the price and and that's what I want to highlight I mean, it's true that The burning itself was gradual and that was probably gradual because the people that held us t tokens Maybe came late to the game or maybe the us t tokens were tied up in contracts and so forth Right, so there's probably a reason why the why the people that helped us t tokens couldn't burn them right away Even as they saw the system collapsing But the the intriguing question is when when these when these when the lunar then was priced and was priced Right, you can you can look to finance and look at what price was priced Why was it priced at that price rather than some other price at that point, you know the people that You know were aware of the situation I would imagine And and and that's the harder one to understand why would that gradual so the theory gives us a martingale result and whether You know whether people only became overall aware of this You know crash happening later or earlier, you know that that's still a surprise event But we'd have to trickle out, you know the news of the of this collapsed happening piece by piece And that's just and that's just super hard. I mean essentially in some ways my probability of resurrection if you if you like a sort of a version of this um I actually try to work once with the system where you try to forecast the forecast of others And it became totally unmanageable very quickly and so that's why uh, why the structure was chosen the way it is But it's this gradual unfolding the so the price again the price on the market should be You know in expectation of what happens in the future the people are buying and selling at that price Why that price and that's a tricky part Now the The other thing that you mentioned is the beliefs itself right because the lunar You know the fundamental value of that stuff is zero right and So of course, there's a possibility that it drops to zero right away and then you know, then then game over right at that point You can't you can't burn any usc tokens anymore, right and that's the Essentially also that's where my assumption about an exit market cap Rescues me right because it says from the construction of the theory can never go entirely to zero and I assume to be deterministic You know richer version you could make that sarcastic in some version And and so it could be zero under certain circumstances. I would imagine that that would be possible But but yeah, I mean you're backing something that's uh, there's something that's intrinsically worthless And the only way that can work is people are willing to sign a value to it anyways because that's in transaction values What they would value? It's a very very good patient. Um, I thought hard about where they could somehow incorporate the intervention by the by the where the terror lunar system It's true that about three billion dollars bitcoin worth of reserves that at some point were gone It's not entirely clear where they're gone The pennies of my paper goes to all kinds of blogs that have been posted on this and people speculating on this and was the speculative attacker and it's it's it's it's super tricky. Um, so um I mean, it's just another site is you know taking the market and Um, you know, you could think of that as an increase in market cap You know, you know, suddenly there are more people willing to hope that stuff And maybe that's lens through each one could see that and given that the NT in one of these simulations once you back it up from data seemed to increase higher So maybe that's a that's a reflection of that But it was unclear when the intervention happened and I think there's uh, you know, can Weird happen. What happened with the money? I'm Sorry in the end. I decided just leaves us all out. Um, yeah So there's so much more to say about, you know, many of the things you raised and the points you raised and Interesting discussion, but but I think it was, you know, fairly slow given this time in age when trades happen Quickly and when they're all these smart contracts out there and you know, we're seeing this now, right? This is no longer 2000, you know in 2022 in that case in our 2023, you know, people can just draw money from svb at the push of a button and In pricing happens practically instantaneously um, so And we have to be recognized of that and I think when you call out for Regulation, you know, take them to count. I think that's that's exactly right. So thank you again. I mean, there are many more things You know, I have to think about them much more and it will help me ultimately to boost the paper. We appreciate it Great. Thank you. Thank you, Arald. Um, then I will move to the q&a and, uh, uh, please everybody feel free to Have questions. I will go with the first one by Chris Cameron and he's asking the So this is so timely your presentation is so timely given the arrest yesterday of douan's And he's observing that given the poor structural design What could terra have done to minimize aggregate losses to luna and, uh, usd holders once things became unstable Yeah, I mean, it's an it's it's an excellent question and um, you know Michael essentially hinted at you know, the system maybe being stable if there was small burning but not stable if there was large burning And when one has to unpack this a little bit more the way the system worked And I think there was there was maybe ultimately the archaeology in my mind Was that the that the system looked at the current price and then gave you the appropriate number of luna tokens But then, you know, it takes time to get that transaction on the blockchain and then you had to get it from your From your wallet into let's say binance that takes time and then you have to sell it there that takes time too And so I think I think what happened was that people were afraid that the arbitrary You know when you see the price of luna collapsing that by the time you get your system out You're actually getting less than what the What the usd was was worth in the to begin with I think there was even a bandwidth that was imposed that later on they tried to lift That maybe have accelerated the whole thing But if there's boundaries that probably creates additional panic of people getting through the exit door and then trying to sell it Even at a lower price on binance And so I think if I think if the system had been more Tissipatory where the price would head, you know once you sell your token on the blockchain The system might have been more stable. That will be sort of a very technical answer, right? And But again, we didn't have we didn't have an idea where the where the price should head now with this theory You can now figure out you can say, okay if the mark that's how the market capitalization evolves and And you know, if you see a certain burn rate, you know what the market capitalization Will have to be next and so you could you could give a few more terror tokens, essentially If we'm alone at luna tokens if there's a lot of burning, right and then and then maybe Maybe then, you know, people are happy and they would just hold on to the token So you have to sort of think about the so the incentives for holding have to be Have to be higher, right if if if people start selling that stuff and burning that stuff Once it's just a bit in the dollar, you know, then Then such a system apparently can unravel very quickly. I mean that's sort of part of the answer and something that Thank you, Harold Jonathan has Yes, and raised Would you like to have a question? Thank you. Thank her. I think It's very nice to have a tractable model that help us You know, develop a quantitative interpretation of the phenomenon and underlying forces I have a question that may be related to michael's comment Which is so since the the underlying beliefs are unobservable So maybe it would be nice if you can talk about how we can apply this method To test the validity of this particular theory and maybe also against alternative You know competing theories, right such as those You know suggested by michael that may involve, you know strategic action of large institute institutional investors or luna foundation gas Intervention things like how can we apply this method to in general differentiate Validities of different competing stories Yeah, no, thanks Jonathan.  So I think in order to get You know, I mean that would be nice if there was another theory out there that could get us as gradual evolution of the You know, I'm gradually within a few days. I mean you could say that's not particularly gradual But still this gradual decline of the luna price and this entire system. So I think the theories that michael alluded to They probably don't give you the full dynamics yet and some and plus, you know, they are They're about assets that have a fundamental value. So where's that coming from? So, you know, I mean there are things that would need to be done first in order to have an alternative theory and then potential One can test it but the absolutely right at this point, you know, there are two variables in the theory That that drive, you know, what participants are thinking And originally I thought well, I have two equations. So at least I can back out these two variables, right? If I three actually have three equations and I have two variables So then I have three equations two variables. I can even write down a test, right? I need additional equations I need additional restrictions on these variables to to allow me to test to to make statements on these things But I don't right and it turns out in the end, you know, I really just have one equation for two variables So there's already a degree of freedom in the theory and I can either fix the exit probability I can fix the market cap upon exit One small test and there was on one of these slides is that the probability that you back out that that the system will live provides a floor for you know risk neutral Traders for the UST terror token and and you know, that's a Maybe a picture again, but that's sort of you like small tests for the theory and It kind of passes that but it's a very it's a very loose test since you only know that the terror So it would have to be between that probability and the one So it's not a very stringent test. So it's really, you know, it's it's how should I say that? I mean you're you're backing out the values of the of the variables in the system that you can't observe from the observations And then it explains the data perfectly and you would need some other implications of these variables Or some other constraints on these variables in order to say well, I don't like these variables Allow me allow me to just super briefly, you know I mean I because I think it's such an interesting and important question Allow me just super briefly to share the slides here again to to talk about this. Let's see. Yeah Hey, here we are again so And I think Michael in essence was was hinting At that too. So when we when I construct these variables from the data Do this quantitative interpretation, you know, this is what I see right? I get this for the exit probability Well, there's already a restriction here, you know, if you know, so one scenario I fix the exit market cap So if the things if the system survives, you just get back to the old market cap That's what I'm imposing here as a scenario And by the way, the the paper and the pennies contains five other scenarios because there's you know and what exactly affects is a little bit You know up up to the user here since they're two variables that need to be inferred from the data and Literally only have one equations one. I think once I think that through So here here back out this exit probability and you can you know, it's it's a raid So it's a raid so that it could exceed one So that's that's not a problem because it's a rate per unit of time And so as a so I should probably call this an exit rage rather than probability But it shouldn't be negative Right, it shouldn't be negative and in fact if you do some calculations then you may see the price go go up Then the then the calculation want that to be due to negative probability Much more likely due to the intervention by the terra luna system, right where they just you know started buying these things But technically in this model, you know, I have to impose that this is smaller equal than zero. So then This restriction, you know, what's one test of this restriction? Are you getting actually close to this price because you don't allow this to be negative? And that's the answer here That's why there's a slight discrepancy discrepancy between the actual price here is and the constructor price here Is you see this here, right? I mean you see this here, right where the the price goes up And in some ways that can't happen in the system The price has to could be continuously going down as we monotonic and that wasn't exactly the case at some moments in the system here So why did the price go up here? Certainly wasn't the the case that there was some negative probability Now, of course, if you allow n to move it could do that But more likely this was maybe due to the intervention that was happening at that time So so that's part of the answer the other part of the answer is You know, it's this oops wait a second here I don't know what's doing See is this underpricing That that I alluded to on the right hand side, right? And so The blue is the price for the UST And if you imagine somebody was trying to trade this on finance, you would say well You know, if the system collapse, maybe I get nothing for it But if if it recovers, I get a dollar for it How much should I be willing to pay? Well, if the if the probability of collapse is 60 percent Then I should be paying should be willing to pay 40 percent of it So I should look at the probability of it not collapsing So the non suspension probability is what is tells tells me the price And so so you can compare this non suspension probability that comes out of my calculation To this price and it's a price floor. Maybe people are willing to pay even more for the UST But if that's if you if you're doing sort of buy and hold until you know, this is all resolved That would be the price floor and I'm sort of, you know, it's nice that that's a floor, but that's I mean, it's a weak test, but that, you know Doesn't doesn't seem to be there's a sense in which you can't test the very because there's no other way of observing that if there was You know, we could do that or if there was some other theory you could test that or we could evaluate that other theory was this theory, but it seems to be Maybe So how can I guess one follow up? I tried to raise my hand, but I I don't see my So it may be It's exactly when Michael mentioned about heterogeneous beliefs related to genocular That kind of the model. So one implication is for example, uh, you are pessimistic. You are thinking high lambda It will recover very soon. I'm the pessimistic guy. I'm thinking low lambda So one implication will be You will try to take leverage And buy more lunar and i'm the pessimistic people. I will try to soft sell the lunar So, uh, maybe we have the implication from other, for example, from the funding rate of the lunar Or the saving volume or boring volume can have some implication Consistent with the heterogeneous lambda story as well Yeah, no, I I I mean I I have sort of heterogeneous beliefs actually heterogeneous costs for the for the terror, right? I mean, why would some people Burn the terror when other people don't so either this was because You know, the the the terror token was still tied up in some contracts or it was due to some Heterogeneous beliefs, but that's tricky. But then it's tricky. How do you think generally equilibrium what this heterogeneous believes? Right, we have some implication on leverage. So, uh, people if I'm the pessimistic people, I will short sell Right, we'd like to short sell. No, that's right. Yeah, right. So that implication can be tested Yeah, I don't think short selling. I'm not sure whether smart contracts allow short selling. They might have It's not something that I check but it but I mean in principle, right? Um You know, how do you get trade going? Right? I mean, that's sort of uh, I think that's a general puzzle many financial markets, right? that That if everybody believes the same thing then I mean, you can't get a price You would agree on a price and the price would be such that neither of us would be Willing to buy or sell at least, you know, maybe we buy or sell because suddenly we have a liquidity need But beyond but not because of you know, but there was active trading Right. So the active trading suggests probably that there are, you know, different beliefs heterogeneous beliefs in the market I'm totally sympathetic with that. But again, you know, then then you get into these Into these, um, you know, grouch marks type phenomena, right? If I buy from you, I should say maybe I shouldn't have, right? Why was why was the idiot buying right when you wanted to sell you wanted to sell to me tells me something and the other way around So how do you and and now mind you know, the theory said you alluded to, you know Take that into account and sort that through and impose short-sale constraints always in the hands of most valued people And suppose and you can do that I I tried that initially the theory gets incredibly complicated and rich going that route and so That's why I'm posh heterogeneous beliefs here Um, homogenous. Sorry homogenous beliefs here at least as far the Luna traders are concerned. It will be interesting I I agree if somebody can write that down successfully. I mean, I will be that would be fantastic I encourage people out there doing that. I'm not saying this year's the last word Thank you, Harle and and uh, Michael Lee has his hand up. Uh, would you like to ask a question, Michael? Uh, yes, uh, thank you for the presentation. It was quite interesting one one aspect that I Uh, it comes to mind is the potential for some more sophisticated suspension and convertibility to be used to better support the market capitalization of Luna in this instance and I wonder if You know in the context of your framework whether useful in this way, for example, you could imagine that Uh, there could they could have allowed for a very a more selective way of burn rate and allow for the market capitalization to to not be directly affected in that at speed In the way that you're showing in this instance where it's kind of treated more as like a probability Um, if you can speak a little bit towards, um more strategic policy Yeah, I mean, I guess algorithmic stable coins, you know, I guess people people aren't particularly interested in resurrecting them But it's an interesting question, right? And and if somebody wanted to do this I mean, I think there were a lot of clever choices made and some choices now in particular night of these theories could be improved upon Right, and I think that's what you are rightly arguing um It's it's good to think through the incentives of the traders here, right? I mean if you What you could do for example, you might think well, um, if you burn, right You don't want large burning because maybe that has too much of an impact on the price You might be tempted to limit the amount of burning that goes on But if everybody understands that a lot of burning is going to come over the next two days Then it doesn't really matter whether the burning takes place kind of right away over the burning takes place over two days As a rational trader, you have to think about what's the price when all is said and done And that's a price you would want to pay for the for luna at the beginning That is what once everybody understands that there's going to be continuous burning for the next two days And that there's no end no exit out under them Then the price would drop, you know by the corresponding amount right away The simple model would would give you the answer there So you'd have to you would have to somehow hope that if you if you slow down the amount of burning that you can somehow Also ended all right, so that's the but where would that be coming from so maybe by slowing it down You know, I mean and I don't think you have a good model of that Maybe you could by slowing down the burning. Maybe you could you calm markets, you know Have a sort of the idea of circuit breakers the ideas of restoring come to the market Of giving some people the opportunity to be on the other side of the market buying Buying the terror and you know and maybe restoring sanity this way, but it's all a You know Even believe the burning will continue the believer, you know, then, you know, so how do we think about panic? I think it's it's very very hard I guess we're seeing a play out of this now with first republic, right? We're some banks the board and says oh no grocery collectibles fine. They deposited their own money didn't have financial market So it's unclear how to stop, uh, you know panic reactions and distrust On markets, and I don't think we have a good theory We have one last question by lucas Thank you I had thank you amazing paper Um, very simple and technical question. Um, what's wrong with the negative burn rate? That's your model implies the negative burn rate would just be, um, interpreted as the La luna foundation putting in this much negative negative supply Yeah, no, nothing won't negative burn right. I totally agree. Um, I have to think whether I um Well, someone has to unburn, but you have an agent in reality who did do that. That's the The one yeah, no, no, no totally right. No the plot that I showed was about the The exit hazard rate, right? I mean the the probability that you think it's it's going to end right about the probability That the system will that the nightmares over and everything goes back to normal That probability can't be negative because it's a probability, right? Probably can't be negative But the burn rate just absolutely can be negative and that will be the you know, could have been the case You know and again, that's about this intervention that that out of a sudden The the the taro luna foundation would go and use their three billion I don't know where they tried there might have I don't think they did But they could have used their three billion to buy lots of taro usd and then actually go the other way right and and uh, and Maybe buy a lot of luna, right? I mean they could have bought a lot of luna and burn it into taro And then we would see negative burn rates But we see the burn rates like we can get data on the burn rates So we we we got the we got the quantity, right? So that was sort of reading the data from coin market cap sort of line by line But we can we can but the but on that we have data So we know how much burning took place and whether it was negative was positive So we know the outstanding stock Of the of the taro coins And that's what I used in order to make the inference and it is true And you go back to the to the beginning of this all there were a few periods where it was slightly negative So at the very beginning there was some creation of taro going on But uh, pretty much throughout the sample it was, you know, nearly always negative I I don't know probably have a plot in the paper somewhere, but Yeah, it can be negative, but it was never sufficiently negative, but you're right in principle That's what something that the jara luna foundation could have done they could have tried to you know, Restore try to restore confidence by going the other way and then the question is would that change beliefs of market participants? And that's the hard one to evaluate I'm just you know, if you just go out there as a politician or as other banks and saying oh, no, no There's no panning. Everything is fine. You know, why should people believe you right? I think that's a It's a generic problem. We even have for monetary policy and financial markets Thank you very much harl. Thank you Michael for the discussion. Thank you for all the questions. I think we're right on time and I Look forward to the next Seminars and I am very thankful for to the organizers for Organizing this very interesting and lively talk And I think it is a very nice contribution to our understanding of developments in the in the crypto industry. Thank you harl. Thank you. Michael. Thank you everybody Thank you. Thank you Thank you again to francesca harrow and michael for the interesting discussion on the Topical issue and to all of you for participating today We hope you will join us again next month until then. I hope you have a pleasant day and a nice weekend Bye