Hi everyone. um now you um probably wouldn't need any um any introduction and um I just wanted to tell about how um I'm how I'm solving the problem of uh impermanent loss which I decided to spin up as a separate project and at the same time I would mention few changes to uh to curve uh crypto pools which apart from yield basis will also power um swaps of currencies like euro and dollar for example like foreign exchange swaps or um also um also probably swaps of assets like gold for example. uh apparently the same changes in crypto pools which are needed to in a yield basis are also needed for these sorts of applications. So let me um let me switch to the slides. All right.
And um maybe um maybe some people uh saw them already and maybe it was even in the context of uh Bitcoin but actually it's not about Bitcoin it's about solving the problem of impermanent loss. So what is what is impermanent loss? Um why is it such a big deal? Imagine that you put um crypto liquidity liquidity in volatile coins in um in some let's say simplest unis swap to pool for example this uh and or maybe maybe in curve crypto pools because they have the same impermanent loss although they are slightly different. If you um if you do that that then your portfolio will be always rebalanced.
So let's say you put um Ethereum and USDC in uh in a liquidity pool. If your um well if your um ether goes up then u obviously the pool starts um starts selling this ether to some external traders and value starts a little bit deviating from the value of ethers and stable coins which are doing nothing and it appears that value in the pool so if you deposit it here and If the price went up, it appears that value in the pool would actually be smaller than value of your um portfolio of the same coins doing nothing. So imagine that you have um you know over here you have 5050 I don't know if USD USD right and um well if you if it is still ETH and USD you have the same number of same same number of USD along this straight line but if you put in liquidity pool you actually you actually have less value. Now imagine that price of ETH actually went down not up. So you move moved along along this line while you are in liquidity pool and got in here and again it appears that assets which are doing nothing they they are worth more than your liquidity and liquidity pool.
So maybe maybe this old black line is going up because you earn fees while you are in AMM, right? And some people may hope that this movement up will cover this gap, but usually it doesn't. For example, over over several years, you you may get APR in let's say ETHUSD pools like several percent. Or in WBTC to USD pool and maybe Bitcoin went up by factor of five and but you earned maybe only a few% and lost quite a bit more over here. This is why a provision of crypto liquidity is not very popular and that's why crypto like volatile crypto liquidity is dominated by market making firms not really uh not really by uh like by passive liquidity providers in DeFi while in stable coins actually defy is probably holding the most the most of liquidity capacity.
Anyway, is it possible to solve this problem and actually the answer is yes. So, let me explain how. Um, imagine that you have crypto let's say BTC like red bitcoin and USD stable coin. So if you put your liquidity in um in liquidity pool this price of your LP token is apparently proportional to square root of crypto price right so it's um if you look back at this graph the uh the solid line is looks awfully similar to square root and it actually is um of course you get get it multiplied by by whatever factor which which means that you're earning fees but it is still square root fundamentally and this is what is causing us troubles. So we want to really get rid of this square root somehow.
How do we do it? Apparently it is possible to construct a position which um which actually squares this uh this square root so it disappears. Um so what what this position would be apparently it is compounding leverage. Well it's a little bit different from normal leverage. So in normal leverage you borrow against some asset and uh keep the loan size constant.
So you get the growth but you you kind of get less capital um than you bring less capital than than your collateral is. Here you uh here we would always change the loan size. So imagine you create this position. You bring some uh BTC USD liquidity, right? You take a loan um which is over size equal to what you brought and borrow kind of the same amount of BTC USD liquidity.
So that um BTC USD uh liquidity size is two times bigger than the loan. So let's say um well this size is uh 2x this value is 2x of the loan size right and um if it so so happens that bitcoin price goes a little bit up then maybe value of your cholesterol goes up right and if if that happens then this loan is not 50% of the value of your collateral anymore. So what we do, we borrow more uh take let's say a piece uh this piece which we borrowed and buy even more um well even more collateral. So the the ratio again stays 50%. So the new loan size you know this one is 50% of this new collateral size.
If you do that then this overall position uh squares well is price of value of that is proportional to square of the value of your collateral. But remember value of your collateral was uh square root of bitcoin price. So you square the square root and the value of your uh resultant position would be proportional to bitcoin price plus it would earn some uh some of the exchange fees. So that's the kind of overall idea. But apparently just this idea is not enough.
So if you apply um if you apply this method uh to actual unis swap two pools uh it doesn't quite work. So of course when you leverage the by factor of two that's nice because you earn twice as much fees. You of course pay the borrow rates but let's forget about this for a second. And most importantly you have this loss rate. This loss rate is associated with uh us changing the loan size and buying more cholesterol or selling some collateral to repay some of the loan all the time.
When we do that, we we actually experience some losses or maybe it's good to call it volatility decay because the higher the volatility is, the higher this loss is. And if we actually apply this method to unis swap 2 to xy equals k amm then it appears that what we lose what we lose over here is apparently equal to what we earn over here. So unis swap 2 actually wouldn't wouldn't earn money if we get rid of impermanent loss somehow. It's not like it doesn't have to be this way but I mean that's what simulations show which is interesting but not very useful because uh we actually want to make money on uh on providing liquidity. We don't want to to probably to work for free.
Well um as you probably know I'm um curve founder and we are using curve amn. So how would it work with curve amn curve amns actually do have concentrated liquidity uh but this liquidity is automatically managed and impermanent loss of curve amm is similar to impermanent loss of unis swap 2. So let me explain how curve amm curve crypto pools work. Many of you probably know that curve crypto pools exist since uh 2021, right? So they exist since since then and they they do have concentrated liquidity although it's usually not very concentrated.
How they work? Um imagine liquidity is concentrated around certain price and if the current price is I don't know somewhere here, right? So it's fluctuating around these values. Everything is great because you know liquidity is dense. We are earning uh good fees, slippages are low, APR is high, everything is good.
But if it so happens that the current price changes and you appear to be somewhere at the age of the concentrated liquidity then everything is not so great because you suddenly your liquidity is much much less concentrated and you earn fees way way slower. So what should we do? Well, it's very tempting to move the whole concentrated liquidity to the new place, right? But movement of concentrated liquidity is uh always associated with the loss. Um and this is actually inevitable.
You probably saw that with liquidity managers on on unis swap 3 which kind of rebalanced all the time and for them it was very hard to actually make money and here it's not an exception. of moving concentrated liquidity means a lot. What we do um at curve right uh we have we keep some sort of budget for these movements and if we have some funds in the budget in the budget to move concentrated liquidity then we actually uh then we actually do it right. But if there is no budget to move concentrated liquidity, then uh then the smart contract decides to not move it and it stays where it was or moves just a little bit if there is a little bit of a budget and waits until pool makes more more money to to move this concentrated liquidity. So where where did do the money to move concentrated liquidity come from?
And yeah, that's probably probably the key here, right? Um, as of today and since 2021, the money to move concentrated liquidity comes from uh fees which the pool is making. So 50% of fees is going to liquidity providers and admin fees on but another 50% of fees charged they go to uh to refill this re rebalancing budget right so and that's that's what what's happening today and this is great but the it has one issue and the issue is this uh let's go back here. Imagine that you are sitting somewhere here on the edge of concentrated liquidity and there is no budget to move it. You are earning money with a smaller rate because your liquidity is not concentrated right and you need to move all this heavy beast to the new place.
But it you know but you well you you need to earn a lot of a lot of money to do it and you are not earning money fast. So you need to wait like like forever to do it and to actually not have it happening. What we are doing currently is making liquidity not that concentrated. So the concentration is actually smaller than it could have been exactly because uh well if you make it smaller here then it's not as heavy. or not not too hard to move this concentrated liquidity.
So you can actually make money here on the age and uh at the same time if you make it not as concentrated here probably it is its concentration is a little bit higher here but you know then it's it's closer to XYK really um anyway today this concentration is maybe I don't know maybe 3 5x but not not really more because you it's it becomes too heavy to move. So well um we probably should do something to make it um to make it easier to move when we are so far off peg. And um it appears that there is one way. So one way is this. Now we have curve USD.
Curve USD is a CDP stable coin. So why don't we pair our crypto with curve USD and well when curve USD exists it's um somebody's paying uh somebody's borrowing it so somebody's paying interest rate so why don't we spend this exact interest rate to support uh dense liquidity to refill this budget with the hope to actually get more here than we spend here but that's uh well that's how we can make markets with actually not not bitcoin but with euro with gold and so on over there this method appears to be very very efficient um but here when we are removing impermanent loss uh we actually we ourselves as liquidity providers we are paying interest rate. So if we go back to um go back to this scheme, we have we have this loan and with this loan we are paying some interest rate. So it should go somewhere. Of course it could go to curve system or to yield basis system or whatever.
But why wouldn't it go to uh why wouldn't that rate which we ourselves as liquidity providers pay why wouldn't it go to be invested into efficiency of the pool um which will make fees for us so we in um have some negative APR which is like borrow rate essentially paid towards this um towards this pool which makes plus uh fees and it becomes more efficient. Maybe earns more fees and maybe maybe we get more fees than we invested. Is it true? Let's find out. To do that, I did essentially some simulations, right?
Uh well, the way I'm doing simulations is this. I'm only simulating arbitrage. Arbitrage between liquidity pools and some external uh venue, some external price source. Binance or curve? Well, it appears that curve prices are actually the best.
Uh, surprisingly uh but Binance prices can be to well if remove squeezes they also give the same result and surprisingly these results also correspond to what pools uh how real pools work. So it's they actually match reality which is nice. So if you take data from I think it was from beginning of 2023 till about end of October 2024 right and for this data in XYK bonding curve um in unis swap 2 you would have earned 3%. Right? If you you configured a curve pool between RAF BTC and and USD stable coin and maximized APR there then it would be about 5.
5% APR well before admin fee of course and um if we spend about 5% rate um on like this as an investment in our rebalancing budget Then the pool makes 13%. So actually you know you see the difference here is actually plus 7 and a half%. So we spend minus 5%. Right? Because it was the borrow rate but we've got plus 7 and a half%.
So we kind of we are not positive here which is great. And uh so the method works and well this is just curve pool at the moment. it's curve pool which is still having impermanent loss. So what happens if we get rid of this improvement loss and um to do that uh well instead of using this formula this formula is just to understand what the loss consists of but to actually calculate it precisely I model uh model this uh uh relever process I'm actually doing not doing it not manually um I developed a special AMM which keeps the leverage constant. So it makes compounding leverage of everything you put in there.
And I'm put I'm putting there um liquidity of curve pools. So it appears that if you applied um to the range which I just mentioned so 2023 till end of October 2024 the APR here um is um around 10% right well actually 9% average APR um over kind of kind of bearish part of the market although which had some uh interesting uh bitcoin events. But if you applied over six years, so since uh 2019 till um again end of 2024, then the APR average APR here is 20%. Most of that is happening in year 2021 um where volatility of bitcoin was very very high and actually it makes money on volatility. So it would have earned quite a bit over there but uh well uh our last two years are actually uh actually here right.
So this this part is actually this one. Um so anyway uh it appears that APRs are fairly decent and uh simulations match reality uh so uh like real existing pools. So I thought why not uh make it like removal of impermanent loss live and currently it's um currently it's finished its uh development. Yeah, these are just uh some numbers which of what simulations showed 2021 was crazy. Don't expect that to be repeated.
I think um now it's not as volatile. Uh but yeah um so um yeah just to just to summarize um there is this update to crypto pools incoming which is useful for multiple um well for multiple use cases like um markets like Euro dollar or gold dollar or maybe other um national currencies. But the same way is uh um very well suitable for uh for removing impermanent loss uh which is which is done um you know the way I just described. Thank you.
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