 So, yes, we are moving from the lightning session directly to session three, which is already the final session of the conference. Session three is devoted to new challenges for macro-interpolicy, and we have three papers in the session that are each very interesting on a range of topics. The first one is on a liquidity risk and an interest rate risk and the interaction between the two. Then we'll have a paper on how banks respond to climate stress tests as a second paper, and then we'll have a paper also looking at the nexus between banks and non-banks. One paper will have just before the coffee break, and this is the paper on banking on uninsured deposits, and I'm very happy that Alexi Savov has come all the way from New York NYU to present the paper here, and we'll have Anjesi Leonelo from the ECB to discuss the paper. So, Alexi, the floor is yours. Thank you very much. Thank you, everyone, and thank the organizers for inviting me to present this paper. It's a joint work with Emma Drexler at Wharton and my colleagues at NYU, Philip Schnovo and Olivier Wang. This paper was very much inspired by the events of March 23 in the banking world, so let me just remind you briefly what happened. Since early 2022, the Fed in the U.S. raised interest rates very aggressively up to five and a quarter percent or so. Long-term interest rates, which in part are driven by the expected path of short rates in the future, also went up by something like two and a half percent at points. Now what does this have to do with banks? Well, going into this period, banks in the U.S. had about $17 trillion worth of long-term loans and securities, and the average duration on those was something around four years. And you can do the math. It's pretty simple. Rates have increased by two and a half percent on four-year duration assets. That means that the fall in the value of those assets is about 10 percent, and 10 percent of 17 trillion is about $1.17 trillion of implied losses on those long-term loans and securities. This is a very big number. It's big just in raw dollar terms, but it's also very large compared to the amount of equity that banks in the U.S. had, which is about $2.2 trillion. And so the obvious concern, therefore, is that, well, maybe there's widespread insolvency resulting from this kind of a large loss. Indeed, you know, here it's a little representative quote from Larry Summers who said, specifically talking about SBB, that SBB committed one of the most elementary heirs in banking, borrowing money in the short term and investing in the long term. When interest rates went up, the assets lost their value and put the institution in problematic situations. All banks borrow short-end land logs, so it's like, okay, gulp. It sounds like it would be more widespread than that. So it's pretty concerning. All right. The most elementary error in banking is banking. That sounds like a problem. Okay. Well, let's see what happened. Here's one piece of interesting data, is the stock market. What does the stock market think about all this? And the stock market wasn't very worried. So like bank stocks actually, despite, so as interest rates are going up, right, this is the Fed funds rate in black, bank stocks roughly track the overall market. Didn't go down much. The market went down some, but so did bank stocks. And so there wasn't much evidence that the market was pricing in. These very large losses from the rise in interest rates. Once SBB happened and there was a run, and this will be a big focus of the talk, then bank stocks dropped and haven't really recovered. So it was more the run that hit the bank stocks as opposed to the implied losses from the rise in interest rates. So what's going on? Why would that be? Why would the market be kind of whistling past the graveyard as they say? It turns out that there's more going on than just the losses on the asset side of the balance sheet. And what's going on is on the deposit side, on the liability side of the balance sheet. What happened, and what always kind of happens, is that as the Fed was raising interest rates here, the black line, again, the Fed funds rate starting in early 2022. Sure, banks were making losses on the asset side, but they were making greater profits on the liability side. And the reason for that is that deposit interest rates, here, I've picked out three representative deposit products. I know there are slightly different names in Europe and different countries. But checking accounts is kind of like the most liquid demand deposit. You can think of savings account is still, you can take it out any time, but you can't write checks against it. And then time deposits where you lock in your money for term, those three pretty representative. And you can see that they went from paying zero when the Fed funds rate was zero. So banks weren't earning any profits on those deposits. In fact, during that period, given that there's costs in operating deposits branches and so on, they're probably losing money on them. But since the Fed started raising interest rates, deposit rates staying low while the Fed funds rate is going high, there's a very large spread that is opening up between the market rate and the rate that they're paying on deposits. And that represents a very large and significant source of profits for the banks. So the deposit franchise, in a sense, provides a natural hedge to the asset side of banks from increasing interest rates. I haven't looked too closely at Europe, but I do have this chart showing a similar picture in European countries. Of course, there's a lot of variation. In terms of deposit betas, I should define what that is. Deposit betas like the fraction by which the deposit rate goes up per 100 basis point increase in the policy rate. So not too different. Now, so if you do a little bit of math back at the envelope here, you'll find that on the deposit side, the picture looks like this. There are, again, about $17 trillion or so of deposits. This is just back to the US. If you assume an average beta of 0.4, 0.4 is actually kind of the historical average. One of the puzzling things recently is that betas have been a little bit lower. But let's say, perhaps to be conservative, or perhaps just things revert to the historical mean, let's say a beta of 0.4, then you'll find that when interest rate is at 5 and 1 half, as it is now the short rate, then banks are earning 0.6. What they're not paying, so if they're paying 0.4, what they're not paying 0.6 is what they're earning, which gives them a deposit spread of about 3.3%. This is average across all the different types of deposits. And 3.3% on $17 trillion is $560 billion a year in increased profitability of the deposit franchise. So that is a very large amount. In fact, if you think that that would be sustained for three years or so, then would fully, and maybe even more than fully offset the losses on the asset side, which were about $1.7 trillion, if you recall. And so there's these kind of two sides of the seesaw. As interest rates went up, yes, the assets are losing value, but the deposit franchise is going up in value, and the two are kind of similar. And so that could explain why bank stocks held up pretty well, even as interest rates rose. Now, just one point I want to make, because it will come in later, is that in a sense, given this behavior of deposits, what we've said so far is that that helps to offset the losses on the asset side. But you might be thinking, well, it would still be better not to have the losses, right? Maybe if they just stayed in short assets, then they wouldn't have the losses to need. They could just have the profits without the losses. The answer is that banks kind of can't just go short on the asset side of the balance sheet. This is something that we focused on in earlier papers, because like I said, deposit franchise is very expensive to operate. And so what happens is when interest rates go down, it starts to, the value declines and could turn negative. And so you actually need long-term assets to offset the decline in value in case interest rates go down. Now, in the world that we live in, interest rates went up. And so we have the opposite problem where assets are going down, the deposit franchise is going up, but the alternative scenario would have been interest rates go down, right? If we, or just even stayed very low for a long time, we would have the opposite problem where banks would be unprofitable if they were holding only short-term assets. And so those really two sides of the seesaw really do hedge each other. Okay, what we're going to do in this paper, what's new, and it's kind of clear in having seen what happened in March, is that sure, the deposit franchise provides banks with a hedge toward interest rate risk. But of course, that is only true if deposit actually stay in the bank in the state of the world in which assets have gone down in value, right? So depositors have to remain in the bank. And so that means that the hedge that they provide is potentially vulnerable. It can be undermined by outflows of deposits. And broadly speaking, there are two types of outflows and we talk about both in the paper. The first are just pure outflows that are just purely driven by the rise in interest rates. There's something that we did in our earlier work called the Deposit Channel of Monetary Policy which just says as deposit spreads, when interest rates go up and deposit spreads widen, some people respond by taking their money out and putting them in money market funds, et cetera. Banks are generally okay with this because they make so much more money on the ones that stay, that it's actually profit maximizing to let some go in exchange for making more money on the ones that stay. But nevertheless, this source of outflow also limits the profitability of the deposit franchise and is potentially hurting the hedge. So we look at that. But the one that is more concerning and the one that was more non-linear is the potential for a different type of outflows. Not so much people just going for higher rates of money market funds but literally running on the bank. And of course that's a bigger issue or mostly an issue for uninsured deposits. And so that's gonna be the focus of the talk today. So here's the main results that are gonna come out of our framework to study this risk is that we are all familiar with the diamond and dipic model of bank runs, the diamond dipic type runs. And usually what you need in order to get a run in a bank is the illiquidity of the loans that the bank has, right? That's the standard diamond dipic model. Loans are illiquid. So if people take their money out, you have to fire sell them and that exposes you to runs in the first place. Hume talked about this in the morning. What comes out of our framework is that the deposit, even if the bank has perfectly liquid loans, in a sense that's how SBB was. SBB had treasuries and mortgage backed securities like some of the most liquid assets in the world. Nevertheless, it suffered a run. Well, our argument is that that's because there's another asset, an intangible asset that the bank has, the deposit franchise. And what I mean by the deposit franchise is the profits that the bank is earning from the deposits. And that is an asset that exposes you to runs if it's uninsured, even if your loans are perfectly liquid. So you're gonna get a diamond dipic type runs even with full liquidity in terms of the loans and securities on the bank's balance sheet. So that's one thing that's new. And then the second thing that's new about this is it interacts very naturally with the level of interest rates. So because the value of the deposit franchise rises with interest rates, the spreads get bigger, it becomes more valuable to have a deposit franchise. And because the deposit franchise if uninsured is a runnable asset, that that means that the risk of a run, the liquidity risk of the bank is gonna be increasing with interest rates. So immediately get a nexus of monetary policy, right, the level of interest rates and financial stability, the run risk or liquidity risk of the banking system. So those two are gonna be inextricably lit, which is not always true in diamond dipic. It's specific to this type of asset that the deposit franchise. We're also gonna highlight issues that arise for the bank internally, which is the bank faces a kind of risk management dilemma. On the one hand it wants to hedge to interest rates and for that it needs long-term assets because the deposits having these insensitive rates on the liability side make you wanna hold insensitive assets with insensitive cash flows on the asset side, right? So you need some long-term asset to hedge the bank to interest rates. However, when you do that, that means that when interest rates rise, the assets fall and the deposit franchise goes up. Overall, your hedge to interest rates, however, you become exposed to a run. And so hedging to interest rate leaves you unhedged to runs and the reverse is also true. Hedging to runs leaves you unhedged to interest rate risk. So that's the dilemma, you can't do both or at least it would be costly to do both. What I mean by costly, you have to raise additional capital and either, and so the way to solve this problem, and this is a costly solution, I don't mean to sell it as, oh, it's done open and shrug. It's a costly solution is for the bank to have something that looks like an option on interest rates. Basically you need an asset like an option whose value doesn't go down when interest rates go up, but also still goes up when interest rates go down. So that's a call option on interest rates, you need something like swapshroom. Or if it's gonna be implemented through capital regulation, there would have to be regulatory capital or capital requirement that is itself tied to interest rates. And we talk a lot about having cyclical capital requirements, it's come up many times on the last couple of days. This would be a rationale for having them specifically tied not to the state of the economy or not just to the state of the economy, but a component that is literally tied to the level of interest rates. So that's also kind of, so I'll talk about that. Okay, so here's what the framework looks like. So imagine a bank that has some assets that it comes into the period with and some depositor base D, okay? So banks coming in with those assets A and deposits D. There's gonna be infinite time T, but all the action is gonna be in the beginning. So over time, every period the bank has to pay some deposit rate, RD on the deposits that go into that period, right? So the deposit rate you have to pay. In addition, it has to meet any withdrawals, X. So change in deposits from period to period have to be paid. Okay, what's the value of the bank? The value of the bank is the value of the assets minus the value of the liabilities. So the assets are what they are. What about the liabilities? Well, the liabilities are the present value of all the future payouts that the banks have to make, all the future expenses they all have. What are those expenses? Those expenses are the following. So for each period in the future, and there's some stochastic discount factor Q that prices all future payouts, for each period on the future, for the amount of deposits that the bank goes into that period with, it's gonna have to pay the deposit rate, okay? Whatever that is. On top of that, it's gonna have to pay little C, this is the operating cost of running the deposit franchise, having branches, having a deposit franchise, attracting depositors, marketing, et cetera. This is costly, banks spend something on the order of 2% of assets to run that thing. And so that's what little C is capturing. In addition, you have to meet any withdrawals, that happen at time zero or any subsequent withdrawals as well. And the liabilities are the present value of all these expenses that you have, okay? It's actually, now let's make some simplifying assumptions. It's enough to get all the ideas across. Suppose that the interest rate just goes up or down. So changes once at the start of time, right? Time zero. So consider a one-time shock to interest rates. You could have more dynamics, it's gonna get more complicated, but the intuition will come across with a one-time shock to interest rates. Let's further assume that deposit rates are proportional to the market rate. So beta, just like in the data, right? This is what we saw, so it's not cost the assumption to make. Deposit rates are proportional to market interest rates, with beta is the proportionality of that, okay? Let's suppose that following the shock, so after the dust settles, deposit is just decay at a constant rate delta. Think of this as the natural shrinkage of the deposit base, capturing the fact that people won't stay forever, even if they're not running or anything, okay? So given these assumptions, let's do the following. First, let's rewrite the value of the bank slightly. Instead of just assets minus liabilities, you can think of the liabilities of kind of having two pieces. First, D, this is contractually why you owe your depositors in the sense that this is the number of dollars that you've taken in and that are now on your books as a liability to depositors. That's, of course, part of your liability. However, since you're paying on those liabilities a below market rate, you're earning a spread, well, that spread gives you an additional asset, the deposit franchise. So we're now gonna decompose the value of the bank as, of course, it's asset minus liabilities, but decompose liabilities in terms of the book value why you owe plus the deposit spreads net of cost that you're earning the present value of that. And let's call that the deposit franchise. Well, with our assumptions, the deposit franchise has a very nice intuitive form, right? This is the present value of all future spreads net of cost. So what is that? Well, it's the amount of deposits that you go in and here we're, for now, just assume no runs, runs are coming on the next slide. So this is the deposits that you have. On each deposit you have your paying beta in interest. So one minus beta is the spread that you're earning, one minus beta times the interest rate. These are your profits right now, right? This is, and then this is, so that's your deposit spread, what you're earning. But from that, you have to subtract the cost of running the deposit franchise. So spreads net of cost. This is like the income, a net income that you're earning on deposits. And then we're taking present value of all that in the future. So then you have to divide by the interest rate plus the decay rate, R plus delta. This is taking that present value to today. So that's the functional form for the deposit franchise with these assumptions. It's nice and simple. And what you immediately see is a deposit franchise has negative duration. Its value goes up when interest rates go up, right? So it's increasing in interest rates as opposed to decreasing. So that's in the parlance of bond world. That's negative duration. So what, how do you do this here? Just take the derivative with respect to the interest rate and you get a positive number. Okay, so that's intuitive. Okay, but now let's think about runs. So you have this asset now, it has negative duration. So the deposit franchise is appreciates with interest rates. So let's see what happens. Well, in order to have runs, imagine having part of the deposit franchise be uninsured. So DFU stands for Uninsured Deposit Franchise. The value of the bank is gonna be, again, assets minus deposits, but now plus the insured franchise, that's fine, that's there. But the uninsured deposit franchise is only there if people stay. So let Lambda be the fraction of people who remain. And so the uninsured deposit franchise times Lambda is taking into account the fact that some might leave, in which case the deposit franchise that they bring to the table gets destroyed. When would people leave? Well, think about the fraction that stay Lambda as an endogenous function of the health of the solvency of the bank. So we're imagining uninsured depositors who are looking at the stock price or the earnings or something like that and deciding whether or not to run based on how concerned they are. Again, just like in the paper that Hume showed this morning. So we're gonna consider a simple threshold strategy where uninsured depositors run if solvency is below a threshold and they stay if it's above. You can have a smoother version using global games, but we're just gonna focus on the extreme. Yeah. Think of them here as going to a money market fund or something like that. But a very interesting extension would be maybe they go into the largest banks, the J.P. Morgan's of the world. There's some interesting general equilibrium implications of that, but maybe we can leave that for the Q and A. For now, just think of them as going to a money market fund. Okay. So what is this bank solvency gonna be that people are running based on? Well, it's the value. So the value of the bank given how many people stay is the value of everybody leaves plus for the people that stay, fraction of the uninsured that stay, these are the profits that you make on them. So that's part of the solvency of the bank. An equilibrium is when the number of people that stay given the solvency is consistent with that being the solvency, right? So it's a fixed point in that space. And the result that we have is that as long as the bank is sufficiently valuable, given no run, so as long as the bank is solvent, if everybody stays, then at least one equilibrium is the good equilibrium. Where people stay, right? That's the good diamond-divac type of equilibrium. However, if the value of the bank, if everyone leaves is below the threshold, then there will also be a run equilibrium. And that doesn't matter how liquid the loans that the bank has are. They can be perfectly liquid again. So this is something that you don't usually get. It's the illiquidity of the deposit franchise, if you will, that is giving us that result. What does this run equilibrium depend on? Well, it's gonna be more likely to arise if they're more uninsured deposits, but more importantly perhaps it's gonna be more likely to arise if the beta of those uninsured deposits is lower, if you're paying them less. So if you're building your franchise on uninsured deposits, on which you're assuming that you'll be paying very low rates, that's really describes SVB pretty well when you could see this kind of run emerge. And also it's more likely when interest rate goes up, because that's when this runnable asset, the uninsured franchise is very large. And so the run is very destructive, making it more likely in the first place. Okay. This is just a picture to show how the run would work. Well, suppose that we have some level of interest rate, I think of a low interest rate where assets are equal to deposits. So just subtracting from equity for a second. What happens is that as interest rates go up, the value of the asset, including the insured franchise goes down, but then the uninsured franchise goes up. So the bank is still head for interest rates, right? If nobody runs, it's fine. But if people run, it's not fine, which makes the run happen, or at least be potentially to happen in the first place. Okay. And so let me just, in the interest of time, skip to some of the solutions that we have. So the risk management dilemma for the bank, the issue that this really highlights is that, in a sense, the bank can't both hedge runs so that not expose itself to runs and interest rates, not have its value vary with the level of interest rates because they demand too conflicting things. In order to hedge interest rate risk, the bank has to stabilize its value outside of a run. But to hedge against runs, it has to stabilize its value if there is a run. And there's a wedge between those two. The wedge is exactly the deposit franchise. That wedge moves with interest rates. And so you can't with one tool can capture both. So what might the bank do? So one thing that we stress is that one solution to this would be for, and again, costly because it requires paying for it upfront. One solution for the bank would be to hedge, it would be to use interest rate options. So why does the bank need interest rate options? Well, remember, the dilemma is that you're trying to hedge, prevent runs, if interest rates go up. For that, you need your assets to keep their value, like your loans to keep their value if interest rates go up. At the same time, you also need the assets to rise and value if interest rates go down because in that world, your deposit franchise is unprofitable, right? So you don't want to become insolvent if interest rates go down. So you kind of need your assets both to rise and value if rates fall, not fall in value if rates rise, that's an option. You need an interest rate option. And so we characterize the strike of the option and so on that has to happen. But the way for the bank to implement this would be to buy long-term assets, or just like banks do today, but layer on top of that, something like a swapsion, a call option on interest rates. Banks do this already to hedge the mortgage-backed securities that they have because mortgage-backed securities famously have negative convexity. Well, the same is true we're saying of the deposit franchise. Deposit franchise gives the bank negative convexity, might need some options to hedge that. Again, this requires raising more capital upfront so it's not costless in any sense, but if you're gonna build your deposit franchise on uninsured deposits and trying to make spreads off of those, given the rentability that it has, it is gonna require a solution that is costly, something like that. And of course, if banks don't do it themselves by buying options, then you could do it with your capital requirement. The minimum capital requirement that you would need to take care of this problem is to have the bank issue additional equity that is in proportion to the uninsured deposits that it has, the uninsured deposits that it has times the present value of the profits that it expects to earn on them absent the run. So you need to make sure that there's always enough additional value there to cover the deposit franchise if there's a run. And so we need that much equal to that runnable franchise in additional capital. And again, it's purely tied to interest rates. It's rate cyclical capital as opposed to the broader state of the economy or anything like that. The final thing that I'll comment on is, one thing that the Fed did during the SBB crisis is create this program, the BTFP, where they lent to banks against their mortgage-backed securities at par. So those securities had declined in value. So you bought them for a hundred, they're now worth 80. The Fed was still willing to lend a hundred to you against that, right? So what's going on? Well, our framework gives us a way to think about that. What's really going on is as those assets have declined in value, the deposit franchise, right, what we showed is increased in value. And the two kind of roughly offset, maybe not for SBB, who was a very extreme, but for most banks, on average, the two kind of offset. And so when you're lending against the assets at par, the assets are now worth less, what you're really doing is you're lending against the deposit franchise, right? That wasn't, the policy wasn't announced that way. I think that would be an interesting way, but it's a consistent way to think about it as lending against the deposit franchise. In our framework, that does have the potential to eliminate the run equilibrium. So it's a lender of last resort opportunity. Okay, so just to conclude on this, the point of the paper is that there's a new runnable asset in town, even if your loans are perfectly liquid, it's all treasuries, mortgage-backed securities, and highly HQLA, having a bunch of low-beta uninsured deposits, uninsured deposits that pay a low rate and is a source of runs for banks. And since the value of the uninsured franchise increases with rates, it means that the run risk with the liquidity risk to expose the banks to increases with rates, it exposes banks to risk management dilemma where you can't simultaneously hedge both interest rates and run risk and liquidity risk. And so the only way to solve it is with more capital either in the form of interest rate options or rate cyclical capital requirements. Thank you very much. Thanks very much. So, close to us, Ani Essey. Thank you. It's a great pleasure being here today and having the chance to discuss this very interesting paper. Just waiting for the slides to be loaded. Yeah, very good. So, as you saw, yep, yeah. Okay, so as you saw, it's like some other reason where by the same group of authors, this paper sort of zoom in on the bank liability side, on bank deposit. And we all know that bank's deposits are like certainly a source of instability for the bank because beside few exceptions like time deposit, there's always a rise for the depositors to show up in front of the bank and ask the money back. So essentially, most of the deposits are runnable and this is the source of liquidity risk for banks. But also, as Alexi was mentioning, bank deposits are a very important source of revenue for banks because of what they call the deposit franchise. So essentially, banks invest initially in marketing advertising and other things that attract and lock in depositors. And in exchange, they are able to gain market power with a big depositor, so they are always able to charge a deposit rate that is below the benchmark rate. And so, the deposit spread that changes to the level of interest rate. So operating costs, initial investment stays the same but then what they earn is changes with interest rate. So the deposit franchise is not free of risk because if rates fall, then you already pay the investment upfront, but you are not getting much out of it, so then its value decreases and this is a channel through which the bank is exposed to interest rate risk. And the deposit franchise is also sort of the ground where liquidity risk in terms of large withdrawals and interest rate risk sort of interact with each other because the value of the deposit franchise crucially depends on the depositors staying at the bank. So if there are withdrawals, then the deposit franchise is negatively affected because again, as a bank there was an investment upfront but nothing that is coming back because this deposit is moving somewhere else. But also, this is very nice. This is really the nice and very nice contribution of this paper is that the withdrawal incentive are also dependent on the value of the deposit franchise because it contributes to overall bank's value and well, the depositors cares about overall bank's value when they have to decide whether to withdraw or not. So this is the sort of the setting which this paper is moving. So everything, all the action will be on the deposit side, very little about assets and the question that the authors ask is can the banks simultaneously edge against the liquidity risk so the liquidity does run and at the same time the interest rate risk? And the answer that is provided in the paper is essentially a big no. So the banks are facing a risk measurement dilemma and changes in interest rate are my lead to bank runs and even in a situation in which the bank is fully edge against interest rate risk because essentially edging against this two type of risk requires a very different strategy in terms of portfolio composition. So if you want to get rid of runs, okay, you invest in short term assets and so you match the duration of your deposits with that of your asset. But if you want to ensure against interest rate risk the way I describe it, so I made an investment upfront and you're earning something that's floating, then you have to invest in sort of long or have enough long-term fixed rate assets on your balance sheet. So what the authors then discuss in the paper is that essentially the banks cannot do both and cannot perfectly edge against this two type of risk and then we need the other instrument. So either we need an intervention by someone else so the lender of last resort, we need to think about capital requirements or regulated as a pin and prescribe the banks to do something or capital or the banks itself has to think of different assets to have a convex payoff like options to deal with this management dilemma. And well, I know that this is a theory paper and I'm a theorist but yet I decided to reduce shrink the description of the model to like three bullet points which was a really big sacrifice but this is because the model is very neat. So I'll only discuss some of the elements of the model but this is a discrete time infinite horizon model with multiple equilibrium, this is very important and banks have market power over the depositors and this is what determines the value of the deposit franchise. And there's an interest rate shock to hit the economy at the initial period and then it stays the same throughout. Okay, so my overall take on the paper, this is very interesting, suggests everybody to read, it's extremely policy relevant. The model is stylus but yet you have all the ingredients that you can recognize and connect to the current event and the recent event. So you really have a lot of insight about why we are observing this instability now only for a small group of banks not for the whole banking sector and why in this interest rate cycle and not before. So there are a lot of, you really can really connect the single variables of the model to the more general policy discussion. So this is really wonderful. The model is stylus but yet it's quite intricate. So there are a lot of things that are moving and what I will try to do in the discussion is to sort of focus on some elements of the model. So one element is the withdrawal. So this is really the center and the contribution of this paper. Withdrawals are partly endogenous but my thinking is whether if we are really micro-founding the depositors withdrawals, yes, sorry. But if we are really micro-founding the depositors withdrawals decision, what can we learn from there? And sort of related to that, if we have to think about what banks will optimally do, so if we think that they want to solve a maximization problem and try to think how much of each type of risk they are willing to suffer or to have, how this will work. So let me start from the withdrawals. So this is not really the terminology in the paper but there are essentially two different types of withdrawal you have seen in the presentation. One are the normal withdrawals. I call them normal because they happen all the time. They can happen for any possible level of interest rate and they are just the result of an investor that says, okay, so that's the interest rate, the deposit rate. This is the deposit spread. This is the value of alternative outside opportunity. There's cash always there for me as an option. So what should I do? Should I keep my deposit into a bank or should I move them somewhere else? And it is not where withdrawals occur because as the deposit spread increases then the depositors might find optimal to move out of banks and in alternative investment opportunity. So the substitution is only possible to a certain extent. So these normal withdrawals are not going to occur I think at very high level of interest rate because then the cost of cash is extremely high and banks need something like cash or deposit in order because they provide liquidity services. So their substitution into mutual funds is not perfect because they don't provide such a liquid service. And then there are another type of withdrawal. So they are the diamond in the big kind of withdrawals. That's I think the way to call it because they are like out of pure panic. So there's some strategic complementarity in the model. I'll get there in a second. And then so the depositors find the optimal to withdraw when they expect everybody has to withdraw. So that's why they are like that sort of a diamond and a labeled diamond in the big kind of withdrawals. And this occurs when the deposit franchise is high. So when the deposit franchise is high which is the case when the interest rate is high then the deposit franchise is really the dominant part of the bank value. And since the value of the deposit franchise depends on the people staying at the bank every marginal depositors know that if he leaves then there's a big drop in the deposit franchise. And if you extend this argument you can think that if everybody else withdraw and I'm the only one that stays at the bank while the value of the deposit franchise will be extremely low, the bank's value will be hit severely and I'm here and maybe the value of the bank has gone below the solvency threshold, some threshold of servability which I know that I will get repaid and that will not be better off just leaving. So again it's a diamond in the big kind of withdrawal because I don't want to be the one left in the bank if everybody else withdraw. And in the current version of the paper the two kind of withdrawals are treated quite separately. So the first one are characterized in an economy in which there are essentially insured depositors and the second one instead are like and play like a lower bound of the deposit, the diamond in the withdrawals, the overall withdrawals in the model with uninsured. So I was thinking whether they could be sort of linked to each other. So think that you only have uninsured and think that these uninsured are also playing the same kind of reasoning of the first guy that when I described the normal withdrawal. So thinking whether they want to leave the money at the bank or not, as if they were the only one. So only for sort of fundamental reason. The only cares about whether the bank is solvent and they will be able to be repaid and whether keeping the money at the bank is sufficiently profitable, relative to a different outside of opportunity. Then I think what you will get is a structure in which probably normal withdrawals or normal driven runs are like something that occurs at level of low interest rate and then the diamond in the big only at a high level of interest rate and then sort of what the next step will be sort of start to think whether the risk management dilemma will always be present. So when withdrawals or runs occur at low level of interest rate at high level of interest rate or whether this is something that is going to only hold for some value of interest rate. And so I think very quickly and then probably I have to stop here. Yes, so I think one of the another reason why to have a very, to push a bit more on the micro foundation of withdrawals is that it allows to potentially move away from the multiple equilibria. There are some post some constraint. For example, it makes very difficult to be able to discuss exactly whatever bank will do. So say that the banks wants to have to choose the asset portfolio composition or for example, the level of the deposit rate or the fix the deposit spread. Well, then it does so anticipating that will be exposed to some interest rate risk or liquidity risk. And if you have a probability of runs, then you're able to solve this problem ex ante and maybe even find something that is already in the literature. So that this liquidity risk and this diamond and db grants that are completely inefficient are still worth to face at least with some reduced probability if you can gain something on something else. And that's up here. Thank you very much. And so. Okay. Thanks so much. I suggest we collect a few questions also from the audience. There is three here and there's one at the back, I think. Thank you. Looks very, you know, a very interesting paper. So two, two issues. So one, you know, part related to what the discuss I was saying. So the, you know, you have withdrawals related to interest rates and withdrawals related to runs and, you know, people limiting others. You know, I guess, you know, one way in which you could kind of think of it is that people don't observe, don't observe whether we draw what is due to interest rates or a run. I mean, this depends of course, if, you know, the depositors are expected to see what people are doing for us in other banks or the specific bank. So if they can observe. So you can create this connection by simply observing that the depositors cannot see in real time whether the nature or the withdrawal. So it will motivate the withdrawal. The other, I don't know if you, I mean, I was a bit late to your presentation. I don't know if you motivated but I know that so there is evidence that people don't switch banks and, you know, somebody said that you are more likely to divorce than to change your bank. Not you, not you personally, I mean, I mean, you were, you were collectively. Collectively. So that could be used as a motivation for franchise value and also, you know, like competitions because it seems to be, I mean, this is Europe, this is to be the case that it's very hard for people to switch banks. Thank you. Interesting presentation and a very interesting solution about the use of the options. But precisely on that, it's a very interesting solution for a few banks. But if we think of all the banks worldwide doing the same, where is the counterparty for that? Will be not counterparties for close for doing for trading all the options? That's the question. Okay, also thanks a lot for the interesting paper. I would have one question or suggestion related to deposits and their composition after a long, long period. So I know in Europe, I think uninsured deposits are not so important, but we know that in many countries, overnight deposits are now a much bigger share than in the past. So many of these might not be like traditional sticky deposits because they actually not held for transaction purposes. So I was just wondering what you think that, I mean, adding these type of deposits in your framework could actually do and might be an interesting extension might be relevant also for Europe. Very interesting discussion, a couple of comments. If you look at towards both European and US banks, the way they've dealt with this problem in the past 10 years I think typically the rule of thumb is that most banks would be holding fixed assets worth let's say 20 to 30% of the deposit, right? So I think all banks understand that you cannot fully hedge or you cannot assume that all the deposits will be there and that the deposit be there's a composite of different behaviors. So they break down behaviorally the different deposits and they say, okay, this behaviorally, I'm still going to have 30, 35% really stable deposits at zero, I can hedge to these and that gives them a bit of room for the more volatile deposits to live or to become more expensive. So that's how they decided to strike the balance which you can think of it as kind of almost dynamic hedging as opposed to like a synthetic alternative to actually the option. So that's one point. The second one is, I think it's an interesting discussion to think whether or not there's such a distinction between the way in which an insured and an insured behave. I think if you have an account at the bank and the bank is in the newspapers every day, even if your deposit is insured, you probably take it out. You probably do not want to have $30,000 in a bank that's where there are rumors it will go bust because why would you? Especially it's very easy to move things. So just in case you will move the money to JPMorgan and then you'll see, right? And then there's a whole very interesting discussion about the role of convexity in what's happened in the US, right? Which feels like a very aggressive way to hedge interest rates because I think a lot of the losses comes from the way convexity has behaved and the widening of the spread between mortgage tax securities and long term treasuries. And if you look at Europe, most of the interest rate hedging has been done in short durations with no convexity, right? So with either with swap, so with government bonds with a three, four year duration and that feels like a more reasonable way to manage it as rather than by an NBS that you think has a four year duration and then the duration becomes 20 years, right? So, but that's a kind of a completely separate discussion but I think it contaminates the problem a little bit. Maybe one more. Yes, big round and from FinFSA. I mean, Americans they go with the 30 year mortgage and with the spread of almost 3%, I understand. And what about variable rates? I mean, what do Americans think of variable rates? All right, awesome. First, thank you, Anaisif. I really liked your discussion. I really appreciate your comments and I agree with some of the questions you asked like micro-founding deposits and the interaction between the two different types of withdrawals that actually kind of came up and some of the questions, they're definitely linked. And so in the paper, we tend to separate them but they're linked in the sense that they both erode the deposit franchise. So people leaving the bank at high interest rates either because they're just looking for a high interest rate at a money market fund or because they're concerned for the run, they both diminish the deposit franchise and in that sense one can be the spark for the other. So I think one of those ways in which as we really happened is over the last year they were already bleeding deposits not because there was a run but because these large accounts were moving to money market funds and that then worsened the exposure to the run and potentially precipitated. It's very much related to your question too. Like what happens if on top of that people can't even tell why they're withdrawals? Is it because of interest rates or solvency? That would like then further link them and make them interact and amplify and compound each other. So it'd be an extra source of this problem. You're totally right that people don't switch costs banks unless they get divorced. I think true that this is, we have a series of papers about banks, market power and deposits and this is exactly where it comes from. It comes from the low propensity of people to switch banks. Banks are very good at kind of keeping people and making that relationship as thick as possible. I'll link that in fact to the third question which is too low for too long. It's exactly what I think happened is because interest rates were at the ZOB for so long you had no incentive to switch banks. I think there's like a whole generation of people that never even really had to think about it. And so banks perceive deposits as having become stickier. I mean, I think there's anecdotal evidence and the press for that during COVID, bank CEOs were saying, well, these are probably gonna be pretty sticky deposits and so we gotta put them to work and so on. And so it did change the composition and may have, the bad thing is that that may have contributed to why when interest rates then did go up and people were as surprised as they were. But the good thing about it is that it means that we're less likely to see this kind of problem in the future, right? So because it's less likely that we'll have these giant accounts sitting accepting zero interest rates. So maybe that's the positive. I love the question about who's the counterparty for the options? I think that's a key question. It kind of came up when Klaus asked during the talk, which is the natural provider, if there is one, there might not be one in which case these options are expensive and that would make it even costier. But one natural source would be the banks that experience flight to quality, right? The JP Morgan's of the world where that's where the deposits go during the run. And so these are banks whose deposit franchise actually grows at that time. And so they might be natural providers, a natural counterparty, but again, it's not clear if the supply would be enough given the demand and the price might have to be high enough to induce other sellers. So I totally agree that it really comes down to behavioral assumption about the deposit beta. I think that's what was so difficult about this going into this period. Betas had been trending down. I think some banks, not all, the ones that someone looked good in hindsight, but others assumed that these deposits would stick here than before or stick here than they turned out to be. And so that was part of the issue. And I totally agree that the line between insured and uninsured can get blurred. It is the case. Now, I think in the US in March, what we saw is that really the insured kind of stayed. Not everybody, I totally not, but that was one good thing. Imagine if there was a run on insured deposits as well. For the purposes of our model, you can think of the insured really as being the sticky ones and the uninsured as the flighty ones and what that maps to in the data given the blurriness that you pointed out would be an issue. And the convexity, I don't have a great answer for, I agree, and mortgage spreads are at a record high precisely because of this. Why are they over 300 basis points in the US? It's because of the convexity. It's very high right now and it's very expensive. I think banks have pulled back from mortgage lending partly because of this. Thank you. Okay. Thanks so much again, Alexi and Anisif.