Michael Egorov, Curve Finance | YieldBasis Deep Dive

To to start, I still need to explain how how it works a little bit. So, um let's um let's dive in. Um Well, um as you probably uh you are probably no stranger to using automatic market makers. Uh most of you I I I'm sure provided liquidity in different protocols. And uh probably the most OG uh OG AMM would be the constant product AMM, which was used uh in well, in Uniswap one and two, but later was kind of kind of replaced with concentrated liquidity and curve always was about concentrated liquidity, but still constant product uh AMMs are like AMMs are the foundational.

And um well, basically how they work, you have um let's say two coins in an AMM, let's say some wrapped Bitcoin and uh USD stablecoin, and uh you have product of uh two balances being uh constant if fees are zero, unless uh users deposit more, right? So, you have So, you have let's say constant um square root of product, I would say, um of two balances, the same per user, but growing all the time. And well, um one disadvantage of this kind of AMM is impermanent loss, which is essentially the pricing of these of these deposits. So, if you deposit funds in such an AMM, then a price of your portfolio, which is constantly rebalanced in a in fact would be proportional to square root of your asset price. So, let's say well, if you express everything in USD terms, it would be proportional to square root of Bitcoin price if it's BTC to USD liquidity.

All right. So, uh that's um um well, that's uh how constant product AMMs work and uh if you have this price function being square root of uh your um of your crypto price, then it's actually not good because it appears then then if you that if you held these uh you know, Bitcoins and US dollars somewhere aside, you would have essentially almost always a bigger value if price of the asset changes if you neglect the fees. Uh so, it was some there was some belief that you know, the fees can overcome this impermanent loss, but well, um so far it wasn't true because please Bitcoin was growing uh all the time and um you you know, this uh liquidity in these AMMs always uh always underperformed compared to doing nothing. So, well, uh it appears that it's possible to um well, to get rid of this annoying dependency. You can you just want to get rid of the square root, right?

And to get to do that, you need essentially to construct some position which makes a square of your like uh of price of your liquidity. And well, question is like how how to construct it? Apparently, you can we have all the tools. The simplest way would be to essentially borrow against your uh liquidity and you have size of the loan equal to half of the size of your liquidity. So, then it's like uh and you know, using this loan, you just buy more of this liquidity so until until this ratio of loan to liquidity is 50%.

Then it appears that you have factor of two leverage. And if you leverage this thing by factor of two, you get exactly square root disappearing and you have liquidity price pro- well, the uh the eventual position price being proportional to Bitcoin price. So, it's like a little bit like staked Bitcoin. But anyway, this is a rough idea which apparently doesn't quite work for uh for this constant product. I mean, it works for removing square root, but it doesn't work for making money.

Uh it appears that this liquidity should have concentrated liquidity. And it should be automatically managed. So, if you take automatically managed concentrated liquidity, its pricing will be also similar to this, but when you remove this square root by taking a loan against by by leveraging your liquidity, you will you will have essentially like almost Bitcoin which is uh which is up only in Bitcoin terms, right? Um anyway, under the hood, we have a pool with concentrated liquidity. But concentrated liquidity in Curve way.

So, what does that mean? Um well, um you probably noticed that since year 2021, Curve had crypto pools. And crypto pools, they were not constant product. They were actually having concentrated liquidity. They still are.

Uh and this concentrated liquidity is automatically managed. So, let's say if you had current price being somewhere here, then you are in a good spot. Concentrated liquidity works. But if you move to the new price, then um well, you are here, so liquidity density is not good. And it's good to adjust your concentrated liquidity to move to the new place.

Problem is when you do it, you have some losses happening. And what the curve pools do, they actually measure um profits and losses, and if they earned enough profits, they move concentrated liquidity to the new place. Well, what's interesting, we actually uh started very actively trying this for foreign exchange use case for non-dollar stable coins. And uh it actually works. Uh but we need something more than just spending um spending fees which the AMM earned.

So, well, how the OG crypto pool works, we have 50% of uh well, it it earns fees. 50% of these fees go to LPs, admin fees, and so on. The other 50% go to rebalancing, right? So, they they subsidize sort of well, refuel, I would say, rebalances, right? So, and this is how it was.

And then um the uh question is, why wouldn't we add a little bit extra, right? So, for example, in yield basis, we are borrowing curve USD against liquidity. So, why wouldn't that those curve USD um well, let's say we take interest and we spend all that interest rate also on rebalancing, right? So, then we have a bigger stream of funds going into rebalancing, and then we rebalance more efficiently, and the liquidity becomes more dense on average. Or if it's done with uh um let's say foreign exchange use case, I don't know, we have tokenized Swiss franc, for example, ZCHF and curve USD.

So, why wouldn't the ZCHF guys and us stream some funds to to essentially make rebalances more efficient and then liquidity density will be high and hopefully hopefully the pool will earn more fees. So, anyway, that that was implemented. And in Yield Basis, this is going from from the rate which you set in in Yield Basis itself, right? So, liquidity providers pay this rate essentially. Anyway, so, how does it how did it work?

Let's find out. So, this is a graph from a real pool. Looks like it's been following well what gray line shows is the position where liquidity is concentrated. Ideally, you want it to follow Bitcoin price. And well, Bitcoin price is the black line, so you see that it's actually in reality did not quite follow.

Well, I mean, it Bitcoin price dropped, so it started moving to that direction, but didn't reach it yet. Well, do simulations predict that? Let's find out. Yeah, well, it looks like simulations show similar behavior, but reality is actually better. So, it followed better in reality, but still well, could have been better ideally.

So, simulations do predict things. Simulations which we do on Curve simulate arbitrage. But just arbitrage. They don't simulate anything else. So, if you have natural flow which is coming into the pools or some liquidations happening, our simulations don't see that.

They look only at arbitrage with external price source. And this is why simulations probably earn a little bit less than the actual pool earns, which is good. We want to We want to be on a pessimistic assumptions. All right. So, on a pessimistic assumption, the adjustment of this con- liquidity concentration is happening slower than in reality.

But, still we want it faster, right? And anyway, uh what Mhm. What What does it affect? Well, first of all, well, but Let's actually zoom out. It looks like uh it would have followed actually pretty well over year 2025, but then volatility become a little bit higher than before in the like the short-term volatility.

But, this is comparable to what we would have seen in 2024. So, clearly, it looks like our volatility in 2026 is a little bit similar to 2024. And 2025 was kind of a uh low volatility time, ironically. Um But, anyway, we should be optimizing for like something more volatile, it looks like. Um and well, what it affects also.

When you have uh the liquidity concentration point moving away from the current price, the concentrated liquidity becomes imbalanced. So, you are sitting at the edge of this concentrated liquidity distribution, and this makes your pool not 50/50, not 50% USD, 50% BTC, but let's say 25/75, which is probably not too great, all right? And in simulations, it's it it shows kind of similar, but as I said, simulations are a little bit worse than reality. Reality is better. Which is nice.

Anyway, and um this is just this imbalance plotted in the graph, so you can see that indeed in 2026 imbalance is kind of similar shows similar deviation from 50/50 as in 2024. So, we don't want that. How do we deal with it? And here are several ideas which were validated in Oh, yeah. Well, it's uh uh which were validated in um uh in in simulations.

But, let me also show um like probably the most important for yield basis part, how how the deposits grow, right? So, if we work with pools like they currently work today, we have well, the fundamental growth part, the line to which we actually will return eventually, right? And the redemption uh redemption value, which which is good, like corresponds to fundamental value when pool is balanced, but when well, but when it goes out of balance, we have essentially this, right? So, um Yeah, so this is real data simulations. And uh well, simulations over two years and a little bit.

So, we want we want to avoid these these regions. Uh so, they happens they happen when pool is very imbalanced, right? And we also want to avoid these little spikes here. They they are not very good. They happen when pool suddenly adjusts the liquidity.

So, we want to do it more smoothly. Which was already implemented in ETH pool, but it's not actually uh enough. So, what do we want to change? One thing you probably noticed is that we spend 50% on uh like giving back to LPs and 50% on rebalances. But, who said it should be 50%?

It could be anything, right? So, it's after all it's us writing code, so we can check what happens if if it's not 50%. So, let's I don't know, let's let's do it. Let's replace it with something else. And uh well, um that's what I did in in simulations along with that improvement of moving the liquidity in a little bit more smooth manner.

And here is what what I found out. It looks like if you um plot the well, I started measuring not just the APR which the pool is making, but adjusted APR. So, uh well, first of all, it's APR minus donation rate, right? So, minus refill rate. So, we refill rate is an expense which we uh which goes back into APR, but we want to subtract it because it was an expense, so I subtracted it.

But, I also adjusted the APR by imbalance. So, if the pool is imbalanced, I discouraged the simulator to to treat it as as something big, right? Anyway, it appears that if we had 50% split, 50% to uh refueling, 50% to LPs, we've been in this spot, right? Which which is actually not very stable. Like, you may get into this um you know, dense uh region, but if conditions change a little bit, you apparently earn less or become more imbalanced or something, right?

So, not a good spot. And if you are able to adjust the percentage which you spend on um on rebalances, you apparently can move to this spot which is much much better. You earn more and you can actually choose a more stable point. So, you can uh the whole algorithm can earn more and be more balanced at the same time. Um well, probably we want to to really if if we have a compromise between more stable and earning more, we probably more want more stable actually.

So, let's see what it turned out to be. So, same kind of graphs. Um following uh like liquidity concentration following the price graph, right? So, you can see it's going much better. So, it's it's following well, pretty much here, right?

And the most recent drop um well, you can uh depends on where you start, it either follows it ideally or follows it like here. So, it's uh even if it detaches, it kind of repacks fairly quickly. Um which is what we want. This appears to have pool imbalances up to well, uh what is it? Uh 65 35, right?

Or maybe well, here it would have been like 30 70, right? But it's much better than 80 20 or something. And for shorter time. And uh this also means less pressure on Curve USD peg. Um earnings would also look much much better in this case.

So, fundamental value doesn't have these drops, but it's for a different reason. And redemption value, like the value you actually can withdraw, doesn't reduce for too long. So, it's uh sometimes the pool goes out of balance, so you um you get less withdrawable for like um some time, but not this long time. All right, so this graph looks clearly much better than before. And uh yeah, well, if you look at the summary, so following the price like liquidity following the price goes from this where it didn't follow these peaks at all, right?

To this where it would follow pretty much everything. And the earnings, the value you can withdraw when you deposit it, right? Would pretty much go from this gray line to to this. So, significant improvement I would say. And also the stability of well, the effect on stability of stable coin which is used under the hood, Curve USD in this case, is also reduced, so it's stays much much more stable.

Anyway, so this is kind of the brief brief summary of what I've been researching recently for yield basis. And probably also very important, this finding, so it's a little bit of a research which which helps also the FX pools because it's essentially the same code. This part also applies to FX pools and I think I think we're going to see pretty much the same effect if we are able to tune this fraction we we spend on rebalances for FX pools as well. So, um anyway, a little bit of a um appears a little bit as a test test in prod, but that's kind of uh um well, DeFi ethos we've got anyway. And yeah, I guess soon these improvements will ought to be expected to be live.

Yeah, that's all. That's all. Thanks for listening.