AMMs as Managed, Customized Portfolios

[Music] thank you for the introduction um hi everyone my name is Theo um I do research at B capital crypto and I'm also going to talk about decentralized exchanges um I want to kind of focus this conversation around the liquidity providers and this talk is really going to be a call to action for some research and then also product development I think would be quite interesting um so let's look at the value of an LP position in an amm I'm going to say that we have two assets one is a numerar and the other is some asset whatever you want with Price p valued in terms of the numerar so you can think of maybe the first asset is ethereum the second asset is uh some other uh some other token and P is the price of that other token in terms of ethereum and uh this amm has a set of allowable States so we can think about it as having some set of reserves and it says I will let the reserves change in particular ways so what's the value of the liquidity provider position well if we assume there's one Arbitrage or at least one arbitrageur who's going to try to extract as much value as possible from the amm we get this minimization function or sorry this minimization problem which essentially says the value of an LP position is the minimum value uh among all the sets of allowable Reserves reses so for what's most common which is the constant function market makers that set of allowable reserves is just going to be essentially some invariant uh evaluate the reserves that has to be greater than or equal to some constant so just to make this very concrete with an example let's take a constant product amm uh so things like Unis swap V2 and for that we're going to have this square root in variant if we plug this in and kind of go through everything we get the value of the liquidity provider position at time T So at t uh amount of time after this position was opened is essentially proportional to the square root of the price plus a term that depends on the fees so we look at this and there's a few questions that one might ask or a few kind of considerations uh first is do I want this derivative uh do I want this product second is what rebalancing cost am I going to pay Arbitrage ORS to maintain this uh position's value for me and then third is can I hedge the price movement let's say I just want fees I just want fees for providing my liquidity I don't want to be exposed to the price movement how easy is it to hedge this so I'll review some of the current research which is mostly on this first question do I want this derivative and there the question is okay well let's say there's something I want so some portfolio value V that I want how do I get to an invariant for a constant function Market maker that gives me said value um we see some examp examples in practice I'm using this Loosely but uh things like zero coupon bonds at maturity some of the yield token pools look kind of like this uh we also see things like weighted portfolios so things like balancer pools geometric mean market makers uh some of the Perpetual exchange lending pools look kind of like these weighted portfolios uh we've seen covered calls on chain and other people build options on top of amm and then we've also seen recent proposals uh for things like prediction Market amms there's a recent blog post from Dan and CMAC on that the general theory for the static case so for the case where the time te doesn't matter uh from replicating market makers papers in uh 2021 2023 says that if that portfolio value function is some concave homogeneous increasing function we could figure out the cfmm that gives us said function however this doesn't really tell us why some of this stuff works in practice some of the stuff doesn't seem to have worked in practice how do we do it in the dynamic case that was only in the static case and there's a few things that I think at least are key factors here for that uh I think the ease of hedging the price movement essentially if LPS desire some delta neutral strategy so they're not taking uh risk on the price of the underlying asset how do they do that with an amm so they just essentially want the exposure to the trading fees second is the amount extracted by Arbitrage so if you've heard lever thrown around or we can think of these as rebalancing fees that you have to pay to Arbitrage ORS how much is that and like essentially how much leakage is there from uh my portfolio value third is just how useful is it to have one of these custom portfolio value functions like what are essentially derivatives that I might want to have is the portfolio value actually useful or not so the reason that I think that looking at this is exciting is there's over 10 trillion dollars of Assets in ETFs there's a lot of passive liquidity out there clearly people are doing stuff in kind of the financial world with this and I think there's a lot of opportunity to bring this liquidity on chain so if you're interested in collaborating on these types of questions on the research side or on the Practical side please reach out thank you thank you so are there any questions no questions raise your hand so I can send you the mic okay okay all clear H there's a question here yep uh you didn't talk uh uh you didn't expand in detail but uh um can you uh is there um a brief uh introduction about uh what are typical ways of hedging the directional move it it depends on the actually I think this is kind of a issue in a lot of amms because for instance if you wanted to uh hedge like say a like a constant product position you have that square root uh function that's your long exposure to the asset and most places to get short exposure are giving you a linear short exposure and so what that means is the amount that you need to be short that asset is going to change as the price changes um and that makes it very difficult because you have to constantly be managing this uh the short position the hedge of the short position um which means that it's like no no longer uh passively providing liquidity and there's um there's a number of blog posts if you um message me I can send you from kind of a few years ago that talk about this but in terms of the question of like how do I design a portfolio value that is easy to hedge um I I I think this is a pretty interesting area of research moving forward especially the dynamic case where the cfmm or the aade market maker might be changing over time there's another question over there in the center how do you how do you think about concentrated liquidity provision in particularly regards to hedging as you described so if I'm an LP and I want to you know only provide liquidity within certain bands you know how do you think about that in regards to the rest of the formula um those also actually do fit in kind of the standard constant function Market maker framework even the constant liquidity pools um there's a there's a paper that I wrote with a number of colleagues called the geometry of constant function market makers that shows that connection um essentially the the high level idea is one way to think about all of these things is there's like some set of reserves that's allowable kind of that first slide that I had and that set has particular properties for let's say like the things that you want to hold so even say a concentrated liquidity position whether that's like the Unis swap V3 hyperbolic type concentrated liquidity or if it's a linear concentrated liquidity you can even in some ways think of an order book as linear concentrated liquidity positions uh because for whatever you're selling it's just kind of a linear amount um so this all falls into similar framework and actually I think that's one of the things where kind of the more we can bring this all into a common framework we can start to use more interesting mathematics and then really push forward um our ability to like understand the stuff and build end products happy to talk more offline thank you for the question there's time for one final question over here what do you think is like the the right way of thinking about these portfolios for users because crypto is quite quite a unique place you need to put like these two tokens in in the AML and traditional Market making market makers are looking for optimizing USD do you think we are looking at maybe the WR metrics when we are measuring this kind of performances should we build portfolios for this on two kind of tokens what's your take on on that um so sorry if I understand the question correctly it's like what types of portfolios should we be what what kind of products are we trying to design I I think that's a good question I I think right now there's the the first kind of step to answering that question is to figure out you know what might we care about and then how do we design for those types of uh for those metrics I I think there's a question of to like what the metric should even be and then after that we can kind of you know look into what actually how to actually construct those portfolios um but that I think the exciting part is the design space is pretty wide open right now and of course we can look to finances along history that we can look for inspiration to thank you well thank you very much please have a nice round of app place for you