Empirical analysis of AMM loss versus rebalancing on layer 2 chains by Elaine Hu | Devcon SEA

[Music] hi everyone I know it's near lunchtime you must well be a bit hungry thinking about lunch um hopefully after this talk you'll be more hungry not just hungry for food but hungry for more information on this topic so loss versus rebalancing whenever I talk about loss people tend to wish they didn't hear about this term because nobody wants to talk about loss but actually this kind of loss um you could avoid and you could potentially turn it into a profit so if you're a liquidity provider you've never heard of lvr loss versus rebalancing hopefully by the end of this talk you'll get a better idea uh you will probably know how to reduce it so let's get started first why do we care and what is lvr some people say that this is bad blood in the amm system and I tend to agree but first let me quote the original authors who defined this idea in their paper in 2022 they say the lvr is the cost incurred by amm LPS due to stale prices that are picked off by better informed arbitrages well today at Devon I say this is my quote that LPS live on an isolated island and they don't know what's going on outside so they rely on the arbitrages to bring them information and they pay this unjustifiably high cost which is what I call lvr so in this scenario um the a the LPS are always worse off because they're waiting for the arbitragers to come in and snipe the mm stale price make a profit so whenever the sex price moves away from the Dex price um you it's like leaving cash on the table right so at the moment this cash on the table is only picked up by the arbitrages some of it goes to the block proposes but none of it goes to the lp so that that doesn't seem right and surely there's something we could do about it but before we try to tackle this problem we want to know what's the magnitude of the problem right how much our is out there so these are some key questions we're trying to address today first how much lvr is out there not just on E theem but also on base arbitrum because there are more users using L2 we want to know how much lvr is out there on all the l2s and secondly we want to understand if this theoretical value that's proposed by this paper is anywhere close to the empirical value because the theoretical value is an easier calculation it will give you a very easy bull bullar number of the estimation right so if it's close then that's good news lastly we want to see what are the factors that affect lvr um and this includes looking at different hedging frequencies looking at uh hedging on centralized exchange like binance um or Perpetual um platforms like dydx we also want to look at block time um and also the design of the transaction ordering for different chains these are all very important questions we want to answer and see if we can find ways to reduce lvr I need to talk a little bit about methodology here because I'll be referring to empirical versus theoretical lvr and it's important to understand what these terms mean so in the original paper the lvr is defined as a function of liquidity providers p&l the rebalancing strategies pnl and also the lp fees so on the left hand side here we have the hedged lp pnl so if you are liquidity provider you hold we usdc and you don't want to be exposed to the risky assets let's say you don't want the price volatility of e so you can perform this so-called Delta hedging strategy or rebalancing strategy by selling exactly the same amount of risky asset you hold in the liquidity pool in a centralized exchange such as binance so if you do that you're expected to be risk neutral um you won't be exposed to any risk key assets so on the right hand side the only expected return should be your RP fees but in in reality this is not the case right because we always have some kind of residual left uh because the sex price is not exactly the same as the Dex pricee you'll always have something um that can't balance this equation and that residual is defined by the um authors of this paper as the lvr so my analysis I reshuffle the equation a little bit on the left hand side this is what I call empirical lvr you can calculate this using observable on chain data and you can also perform a rebalancing or Delta hedging strategy using binance price you can calculate everything on the left hand side on the right hand side you have the theoretical lvr here I'm just showing uh one of the formula which is uh for constant product pool it's a simple enough equation you just plug plug in these parameters you can calculate a theoretical alv so the point is that we want to understand if the theoretical is anywhere close to the empirical if it is then we can avoid all the hassle on the left hand side or we just apply this simple formula on the right hand side to give a b bullar number measurement now enough of the theoretical empirical let's take a look at the analysis so first we want to know how much lvr right we just want to know not only ethereum but also base arbitrum we want to compare the empirical versus the theoretical we want to compare different hedging frequencies here is a chart showing if um on ethereum West usdc pool that if you're an LP you provide liquidity from the beginning of March and you hold it for seven months until the end of September what is your cumulative expected lvr so this is a loss number right even though it's showing as positive we want this number to be as low as possible because it's a loss and the theory goes that if you hedge more frequently your loss will be lower and these different lines I'm showing here actually aligns nicely with this Theory because you see that one minute hedge lvr is the lowest you're only losing 800,000 usdc but if you're lazy you hedge every day you're losing almost 3 million for the whole s months holding period just remember that this number is the maximum number because I'm calculating it for for the entire liquidity pool right so if you're only a single LP this is only um uh this is the maximum number you're only getting a portion of that loss so don't worry you won't be losing 3 million if you just provide a small portion of the liquidity um you also see some theoretical values here so that's the two dotted lines that's more smooth in the middle and uh these are the theoretical formula I mentioned about and why there are two lines I'll explain the next slide so in the original paper in 2022 the authors have made an important assumption it assumes that there is no trading cost to the arbitragers assumes that the arbitragers trade against the Dex pool they don't pay any fees and that's obviously not true it's not very realistic right imagine you're in a very volatile Market of course you have to pay some fee to trade against the Dex pool um so they realized that and they they produced another paper in the next year considering trading fee as a factor in the lvr calculation so that's why here you see two different lines the line with um trading fee in Tak into consideration gives you a lower lvr because a cost to the arbitrager is a gain to the lp that's fees you're collecting so you have a lower lvr here and we want to compare the impact of this fee feature and you can see it's around 0.2% of the total cool value now like let's take a look at base base is similar to ethereum it's a priority gas auction um it only has 2 seconds block time but we expect it to be very similar to ethereum so you see here that we have the different hedging frequency the one minute hedging frequency again gives you the lowest lvr only 13,000 usdc loss but if you hedge 4 Hour it increases to 66,000 although it's not totally monotonic because you don't see the daily number being the highest here uh 4 hour is the highest but we can say that you know pretty much in general we still follow the rule that the more frequently you hedge the less lvr you get and again looking at the difference between considering the swap fee and without considering the swap fee the difference is similar 0.3% of the pool value now let's look at an outlier and this is arbitrum why why do I say it's an outlier because first arbitrum is not a PGA priority gas auction chain uh it's a first come first serve chain which means that if your transaction arrives early it'll be executed earlier and also it block time is very short it's only 250 milliseconds right so we expect something to be different and I used two pools here the the first one on the left is the same U uh usdc West pool from Unis swap V2 but unfortun fortunately the pool is not very liquid it has very few swaps so if you do the same analysis you see different hedging frequencies it doesn't really follow the rule of you know the more frequently your hedge the lower the loss right you see the daily hedge actually has the lowest loss uh doesn't really follow the rule doesn't make much sense so I thought okay then maybe I'll look at a a pool with more volume more swaps so I found this other pool camlo V2 which is also a constant product pool and perform the same analysis and here you see that actually it comes back to the theory that the more frequently you hedge the less lvr you have so the 1 minute you have the least lvr of only 9,000 usdc and again we compare the impact of fees on the left hand side you see the difference is about is about one uh 0.1% of the pool on the right hand side is about 0.3% of the pool so this result is very similar to ethereum and base now the next interesting question is if I'm an LP I want to perform this rebalancing strategy this Delta hedging strategy where should I do it should I do it on a centralized exchange like binance or should I do it on a Perpetual platform like dydx right I might want to just stay in the ecosystem do it on on dyds if uh there's not much difference so here I'm showing you the rebalancing strategy pnl if I hedge every minute this is the chart on the left there's almost no difference whether I do it on binance or dydx but if I hedge daily it seems that I have an edge on uh hedging D on dydx right because my p&l is higher on this chart and we found the same for Bas and also arbitrum so next now let's take a look at the empirical lvr and uh we also um see that the lvr is lower on dox remember I said the p&l was higher on dox X as LP so what does it mean here it actually means the price discrepancies between the dexs on ethereum and dydx is actually smaller than the price discrepancies on Dex and binance this means that the Arbiter has less of an opportunity trading Dex dydx so less opportunity for them to make a profit more opportunity for you to reduce your lvr so you are better off uh doing this hron dydx if you are providing liquidity on ethereum but base we don't see much difference here even you look at the daily chart is quite similar um so you can choose whichever you want for arbitrum again this is very different uh because we see the other way around right this time you're actually better off uh just uh doing the Hedon binance because the dis discrepancy between Dex Finance is smaller than between Dex dydx so that's what you know you can choose based on which chain you provide liquidity the last question we have here is to compare different chains across and see what's the lvr in terms of the percentage out of the total pool value so the theory says that uh lvr is a function of square root of block time so if the theory follows the shorter the block time the lower the lvr and you'd expect arbitrum to have the lowest lvr and let's see if that's the casee I have four charts here with different hedging frequencies also including all the chains and for ariton I've included two pools one is the uh pool with low Activity one is the pool with a high activity but let's just ignore arbitrum for a second because it's the outlier let's focus on the blue line which is ethereum and the red line which is base so you can see for all the hedging frequencies uh throughout the seven months holding period you almost always have a lower lvr for Bas and Bas only has a 2C blockchain time so we could say that this follows the theory that the shorter the blog time the lower the lvr right but arbitrum outcome seems inconclusive because whichever hedging frequency you look at whichever you know High activity pool low activity pool you look at sometimes it's higher than base in ethereum sometimes it's lower so we can't make any consistent conclusions here and this might be because the chain is a first com first serve chain is different right it could also because the volumes I looked at in these two pools on arbitrum is actually quite low so the number of swaps are very low here the US dollar uh USD trading volume is also very low you can see the two at the bottom there from the two pools from arbitral much lower than ethereum and base now we know ethereum has the highest lvrr followed by Bas followed by um arbitrum but this is only the lvr from one single pool I'm showing you right West usdc and there are many many more pools as we all know on each of these chains so imagine if you can capture all of these lvrs all of this is not a loss it could be your profit it could be profit that you can give it back to your user so imagine the potential you can gain a lot more users using your protocol using your chain and the list goes on now coming to conclusions so so we've compared a lot of things we've compared the empirical versus the theoretical we know the theoretical is kind of similar to the empirical we can use it as approximation to give us a bullar number if we want a quick estimation we also look at trading on a Perpetual like dydx and trading on a centralized exchange like binance and the results seem to be very similar if you hedge very frequently then we compare the trading fee uh feature with trading fee you have a lower lvr because the trading fee is a cost to the arbitrager and it's a gain for the LPS so you have a lower lvr we also compare Bas with ethereum and Bas is a shorter block time it has lower lvr so shorter blog time lower lower lvr and we we also know that the more frequently you hedge the less lvr you have there are some inconclusive results from arbitrum uh we don't know if it's because of the first conf first serve chain nature or is it because the pools I choose have too low of a volume too um not that many number of swaps right so these are inconclusive lastly how can we reduce lvr so as an LP you obviously want to hedge more frequently you can reduce lvr by not being lazy um you could also provide liquidity on a pool that has more activities so your price stay stale for less time um and I want to mention something that I I pointed out earlier so the trading volume and the number of swaps actually play a factor um in the lvr because imagine if you only have a 250 millisecond chain but the number of swaps on your pool is only once per hour so at the maximum your price update is only going to be once per hour no matter how quick your block time is right so actually the frequency of the pool the activity of the pool makes a huge difference that's why you need to choose a pool with more activity so as a protocol designer you want to be thinking about how to internalize lvr and redistri uh capture it at your protocol level and redist distribut it back to your LPS and I think that's uh what our next speaker will be talking about they've done something um in this kind of uh design and I think she will show you some of the Practical analysis you could also improve the real ESS of your decks by bringing some Oracle updates or even by just uh charging a dynamic fee lastly if you're a blockchain architect you might want to think about shorter blog time uh you want to think about different transaction ordering designs that potentially will increase the opportunity cost of the Arbitrage so first come first serve chains or prior to gas chains or any other kind of different design that will help your user to reduce lvr is worth looking into and that's the end of my talk uh I'd like to thank this list of people and also the data providers alium and CC data for making this analysis possible question thanks thanks Elaine you can tell you can tell how much the M's not working okay hi yeah thanks elain you can tell how much effort she put into the presentation just by the chart so let's take a look at some of the questions so the first one what percentage of LP rebalance your portfolio with a comparable frequency as arbitragers I would say the LPS are definitely as not as professional as the arbitragers so I would expect the hedging frequency at the max maximum you could do I mean if you can build a b you can do it very frequently right but if you can build a b you're probably an arbitrager so I actually like to ask the audience how many of you actually do hedging if you provide liquidity I only see one hand oh actually a lot more yes yes so that's good to know but yeah it's a lot of hassle I doubt users will actually use uh like a highly frequently hedged position which is why the protocol designer needs to find ways to you know help the user to tackle this problem okay so the next one is how does lvr look on V3 versus V2 yeah so that's something I didn't have time to look into well I had time to look into but I didn't have time to show you here um V3 actually has a lot more lvr just because the trading volume is much more and there are much more activities there um so it's something that's worth looking into for sure yeah and the next one is does liquidity liquidity concentration increase or decrease lvr I think a large part of it um is due to the price discrepancies so liquidity concentration in some sense if you have LPS who have these thresholds right you have the operatic the lower tick if suddenly the price moves and you suddenly have a lot more or a lot less concentrated virtual liquidities in the V3 pool your uh pool's price is going to change right because the less liquidity concentrated liquidity you have you know the more price movement there is so it depends on how fast the price moves versus the centralized exchange I think that makes um it make makes more sense than purely looking at the concentrated liquidity okay on to the next one is there a trading fee for hedging activity I would assume one minute hedging would lead to a lot more trade cost compared to daily um I would say the main fee will be let's say if you hedge on binance I think the fee is around 0.

1% if you hedge on dydx this could be lower based on you know which side of the thing you are if you're a taker you pay you pay a fee if you're a maker you pay a different fee I remember the mid prices like 0.03% so it's actually less uh cost if you h on dydx okay how can you explain that the one minute empirical lvr is smaller than the theoretical lvr well the theoretical value is actually in the formula it's using uh volatility based on a daily volatility so that's why you could so in in the formula one of the parameters is the price vola ility and in the in the paper they use the daily volatility of the binance price that's why you know you get a higher number and one minute if you use a one minute volatility in that equation you probably get a similar number yeah next question does execution prices and size of hedging plus how Hedges are executed is taken into account uh so the execution price in this paper is just the C IED Exchange price right so you're assuming you're hedging on binance so you look at exactly what the price is on binance and the hedging size is just whatever you hold on the lp as the risky asset you want to hedge so in my example it was East so you hedge exactly let's say you provide liquidity to East with I don't know 6,000 usdc then you'll be just shorting two e on the centralized Exchange price using binance price okay so we are out of time for the questions ready but please follow her on X perhaps she can answer it there