It uses the following functions: Where U(x) could be interpreted as a utility function comprised of a gain function, G(x), and a loss function, F(x); and x is the reserves of each asset. This allows for variable exposure to different assets in the pool and enables swaps between any of the pools assets. Stableswap) had the insight that if the underlying assets are relatively stable-priced (e.g. Constant Product Market Makers. one of the creators of Uniswap. At its core, a liquidity pool is a shared pot of tokens. Conversely, the price of BTC goes down as there is more BTC in the pool. $21. Answers: a. Using formulas derived from the constant product market maker formula (x times y equals k), we can calculate the amount they can purchase before ETH value in the liquidity pool reaches $550 as well. Augur V1 and Gnosis). . One simple example of a trading function is the product [Lu17,But17], implemented by Uniswap [ZCP18] and SushiSwap [Sus20]; this CFMM accepts a trade only . As such, I believe that we will have a variety of CFMMs designed for asset types in addition to stablecoins, such as derivatives (e.g. When we buy token 1 for token 0, we give some amount of token 0 to the pool ($\Delta x$). the price is also high. We use x and y to refer to reserves of one pool, where x is the reserve $$-\Delta y = \frac{xy - y({x + r\Delta x})}{x + r\Delta x}$$ $$(x + r\Delta x)(y - \Delta y) = xy$$ arXiv preprint arXiv:2103.01193, 2021. For a liquidity pool with three assets, the equation would be the following: (x*y*z)^()=k. [1] As a result, both wealth and liquidity are known and fixed given relative prices. This loss occurs when the market-wide price of tokens inside an AMM diverges in any direction. For example, if the CFMM price is less than the reference market price, arbitrageurs will buy the asset on the CFMM and sell it on an order book-based exchange for a profit. Smart contract developers even create front running bots just for this purpose.This can potentially distort the market and make it harder for the AMM to maintain the constant product. By trading synthetic assets rather than the underlying asset, users can gain exposure to the price movements of a wide variety of crypto assets in a highly efficient manner. Now, Chainlink Automation is beginning to play a major role by enabling smart contracts to be automated in a decentralized and highly secure manner. We derive the replicating portfolio and greeks for a constant product market with bounded liquidity such as Uniswap v3. Understanding this math is This is where other market participants, called arbitrageurs, come into play. This design unfortunately allows arbitrageurs to drain one of the reserves if the off-chain reference price between the tokens is not 1:1. A market maker faces the following demand and supply for widgets. In fact, the creator of the term stated that bonding curve was actually intended to be used in the context of a bonded together curation community. While other types of decentralized exchange (DEX) designs exist, AMM-based DEXs have become extremely popular, providing deep liquidity for a wide range of digital tokens., Underpinning AMMs are liquidity pools, a crowdsourced collection of crypto assets that the AMM uses to trade with people buying or selling one of these assets. Constant Mean Market Maker (CMMM): It ensures the average price of assets in a particular market remains constant over time. the higher the asset volatility, the higher A should be). You just issued a new stablecoin, X, that is pegged to 1 USDT . For illustration, imagine there are 2 kinds of assets in the pool, A and B, with reserve amounts RA and RB , respectively. {\displaystyle V} We want the price to be high when demand is high, and we can use pool reserves to measure the Because of this matching process, there is the possibility that some orders may take a while to get filled, if ever. The protocol uses globally accurate market prices from Chainlink Price Feeds to proactively move the price curve of each asset in response to market changes, increasing the liquidity near the current market price. What is an automated market maker? I believe that these algorithmic markets utilize a type of AMM that is not a CFMM because the interest rate function is dynamic based on the utilization ratio and the goal is not to keep the interest rate constant. Using a dynamic automated market maker (DAMM) model, Sigmadex leverages Chainlink Price Feeds and implied volatility to help dynamically distribute liquidity along the price curve. And when demand is low, the price is also lower. Shell Protocol has similar goals but takes a different approach. is calculated differently. For example, the Uniswap payoff curve is concave, meaning that liquidity providers are profitable within a certain price bound and will lose money in large price movements: Ideally, we want convexity when taking risk, which means having upside on both sides of the risk spectrum. The more assets in a pool and the more liquidity the pool has, the easier trading becomes on decentralized exchanges. trade prices are. As a new technology with a complicated interface, the number of buyers and sellers was small, which meant it was difficult to find enough people willing to trade on a regular basis. Uniswap went live in November 2018 and epitomized the first automated market maker in the ethereum ecosystem, a model that then became ubiquitous and sparked a number of Uniswap clones (SushiSwap, PankakeSwap, MoonSwap). Since AMMs usually have a fee, the product of the reserves is not really a constant in practice. of a CFMM as a function of the market prices of the assets in its inventory, is the worst-case market value of its inventory, which under assumptions of perfect competition is equal to the infimum of the dot product of inventory amounts with prices, over all inventory amounts such that the CFMM quotes at market price. the larger the liquidity pool, the lower the price slippage) but there are additional dimensions that could be dynamic. Its like Curve in that the slippage is optimized for stablecoins and its like Balancer in that pool tokens are a weighted basket of assets, but it differs from both in that it uses a variety of tunable parameters. real estate). When traders make trades, they Only when new liquidity providers join in will the pool expand in size. AMMs are a financial tool unique to Ethereum and decentralized finance (DeFi). Curve specializes in creating liquidity pools of similar assets such as stablecoins, and as a result, offers some of the lowest rates and most efficient trades in the industry while solving the problem of limited liquidity. This formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. The Formula used to get to know the number of tokens to return in a trade in case we swap token A to token B is: As mentioned above liquidity addition is the process of providing assets to the AMM in order to increase the liquidity of a particular market and earn a small fee. It is also common to hear the term bonding curve when talking about CFMMs but it is incorrect to do so. money markets, he emphasized that AMMs should not be the only available option for decentralized trading. in-game items that are hard to market make because of low liquidity). When we add liquidity it is important to note that there should be no price change before and after adding liquidity. However, the execution price is 0.666, so we get only 133.333 of token 1! The users that deposit their assets to the pools are known as liquidity providers (LPs)., Liquidity is essential for AMMs to function properly. Surprisingly, there are multiple Arbitrage trades have been shown to align the prices reported by CFMMs with those of external markets. and this is a desirable property! More detailed . {\displaystyle \varphi } ; Guillermo Angeris, Alex Evans, and Tarun Chitra. Interestingly, this brings us back to the initial use-case of AMMs, which was information elicitation, except this time it is about the price of an asset rather than the probability of an event occurring! When the supply of token X increases, the token supply of Y must decrease, and vice-versa, to maintain the constant product K. When plotted, the result is a hyperbola where liquidity is always available but at increasingly higher prices, which approach infinity at both ends. And this is where we need to bring the demand part back. Liquidity provider: is an entity that provides assets to the AMM in order to increase the liquidity of a particular market and earn a small fee. Chainlink Price Feeds already underpin much of the DeFi economy and play a key role in helping AMMs accurately set asset prices and increase the liquidity available to traders. Their trading activity creates liquidity, lowering the price impact of larger trades. Curve offers low-price-impact swaps between tokens that have a relatively stable 1:1 exchange rate. CSMMs follow the formula x+y=k, which creates a straight line when plotted. Instead of relying on the traditional buyers and sellers in a financial market, AMMs keep the DeFi ecosystem liquid 24/7 via liquidity pools. this new point. This is due to the fact that a substantial portion of AMM liquidity is available only when the pricing curve begins to turn exponential. to the pool, which is added to the reserves. Such prices are called spot prices and they only reflect current market prices. Visually, the prices of tokens in an AMM pool follow a curve determined by the formula. The constant formula is a unique component of AMMs it determines how the different AMMs function. Synthetix is a protocol for the issuance of synthetic assets that tracks and provides returns for another asset without requiring you to hold that asset. In fact, these formulas free us from calculating prices! An interesting area of research would be to analyze the profit-maximizing fee that balances trade incentivization with liquidity incentivization. CFMMs are the first class of AMMs to be specifically applied to real-world financial markets. So, if the price of token A increases, the price of token B must decrease in order to keep the constant product equal to the constant. Liquidity providers normally earn a fee for providing tokens to the pool. Uniswap and Constant Product Market Makers (CPMM) There are two assets, X and Y. Denote by x the volume of X and by y the volume of Y in the reserves. For example, a liquidity pool could hold ten million dollars of ETH and ten million dollars of USDC. Constant Product Market Maker (CPMM) The first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. $$-\Delta y = \frac{xy}{x + r\Delta x} - y$$ Eleven sellers are also willing to sell at the same prices. Constant Product Automated Market Maker | Solidity 0.8 - YouTube Code for constant product automated market maker.0:00 - State variables and constructor2:38: Internal functions -. and decentralized finance (DeFi). $$\Delta y = \frac{y r \Delta x}{x + r\Delta x}$$ Well, this is the math of Uniswap V2, and were studying Uniswap V3. This button displays the currently selected search type. Adding liquidity to a CFMM is simple but comes with some complex financial risks (impermanent loss, short volatility, long volatility/volume correlation, etc.). As a liquidity provider you just need . reserves. One of the most popular models adopted by automated market maker platforms is the constant product market maker (CPMM) model. The job of the pool is to give is increasing. We study axiomatic foundations for different classes of constant-function automated market makers (CFMMs). Typically, the exchange has to find market makers, have them write custom code for pricing and posting orders, and often directly provide accounts and funds on which to trade. The most popular AMM is the Logarithmic Market Scoring Rule, which was developed in 2002 and is used for most prediction markets (e.g. Broadly speaking, market makers (MM) provide liquidity to the exchange they operate in, and they set "buy" and "sell" quotes for each asset. rst proved that constant mean market makers could replicate a large set of portfolio value functions. While most people think of Uniswap when they think of AMMs, the concept has actually been studied extensively in academic literature for over a decade, the majority of which were primarily designed for information aggregation and implemented in markets where payoffs depend on some future state of the world (e.g. The first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. When expanded it provides a list of search options that will switch the search inputs to match the current selection. Section 2 gives an introduction to prediction markets and introduces/proposes/analyzes various models for automated market makers: logarithmic market scoring rules (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum markets, and constant circle/ellipse cost functions. Concluding from the law of supply and demand, high demand increases the priceand this is a property we need to have The reserve of token 0 changes ($x + r \Delta x$), and the reserve of token 1 changes as well ($y - \Delta y$). Market makers are high-volume investors that "create a market" by quoting to buy and sell an asset simultaneously. we want to buy a known amount of tokens). This new method of exchanging assets embodies the ideals of Ethereum, crypto, and blockchain technology in general: no one entity controls the system, and anyone can build new solutions and participate. When does the tail wag the dog? Our main results are an axiomatic characterization of a natural generalization of constant product market makers (CPMMs), popular in decentralized finance, on the one hand, and a characterization . It might seem like it punishes you for trading big amounts. What Are Automated Market Makers (AMMs)? Uniswap is the most popular AMM on Ethereum. These pools are funded by liquidity providers so that the traders can trade against these pools. While this function produces zero slippage, it does not provide infinite liquidity and thus is likely unfit as a standalone implementation for a decentralized exchange use-case. Meanwhile, market makers on order book exchanges can control exactly the price points at which they want to buy and sell tokens. Learn what NFTs are, how they work, use cases, and more. Pact offers a familiar Constant Product Market Maker (CPMM) capability. This new technology is decentralized, always available for trading, and does not rely on the traditional interaction between buyers and sellers. Constant Price Market . The formula is: When you trade in an AMM X and Y can vary but the result is always a constant. Market makers like Citadel can be found in all types of markets from equity to currency exchanges to forex markets and are regarded as an important part of a well functioning and liquid market. StableSwap is a type of AMM invented by Curve Finance. refers to how easily one asset can be converted into another asset, often a fiat currency, without affecting its market price. Constant function market makers (CFMMs), such as constant product market makers, constant sum market makers, and constant mean market makers, are a class of first-generation AMMs made popular by protocols like Bancor, Curve, and Uniswap. The above calculations might seem too abstract and dry. Constant product formula is probably the simplest and the earliest algorithm to come into the market. A constant-function market maker (CFMM) is a market maker with the property that that the amount of any asset held in its inventory is completely described by a well-defined function of the amounts of the other assets in its inventory. "Decentralized Finance: On Blockchain- and Smart Contract-Based Financial Markets", "A Practical Liquidity-Sensitive Automated Market Maker", "Logarithmic markets coring rules for modular combinatorial information aggregation", https://github.com/patrick-layden/HyperConomy, https://en.wikipedia.org/w/index.php?title=Constant_function_market_maker&oldid=1141745032, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 26 February 2023, at 15:49. V As AMM-based liquidity has progressed, we have seen the emergence of advanced hybrid CFMMs which combine multiple functions and parameters to achieve specific behaviors, such as adjusted risk exposure for liquidity providers or reduced price impact for traders. Get started. A CFMM is described by a continuous trading function (also known as the invariant, AMM invariant, or CFMM invariant). Alternatively, the founders often hack together a python script to offer liquidity with their own assets and simultaneously hedge their risk on other exchanges. Automated market makers (AMM) are decentralized exchanges that pool liquidity from users and price the assets within the pool using algorithms. We show that the constant sum (used by mStable), constant product (used by Uniswap and Balancer), constant reserve (HOLD-ing), and constant harmonic mean trading functions are special cases of the constant power root trading function. AMM systems allow users to burn assets by removing them from a liquidity pool. What he didnt foresee, however, was the development of various approaches to AMMs. Recorded talk for the paper Improved Price Oracles: Constant Function Market Makers by Guillermo Angeris and Tarun Chitra for ACM's Advances in Financial Tec. Before AMMs came into play, liquidity was a challenge for decentralized exchanges (DEXs) on Ethereum. Curve (a.k.a. This type of AMM will adjust its exchange rates automatically based on demand and supply to maintain that ratio. It occurs when the price ratio of the tokens they have deposited in a liquidity pool changes after they have deposited the tokens in the pool. You need to enable Javascript to view this site properly. This function acts as a constant sum when the portfolio is balanced and shifts towards a constant product as the portfolio becomes more imbalanced. This fee is paid by traders who interact with the liquidity pool. Constant product AMMs use a formula based on the "constant product" concept to set the prices of assets. prices when making a trade: And thats the whole math of Uniswap! (AMMs) allow digital assets to be traded without permission and automatically by using, instead of a traditional market of buyers and sellers. over the inventory amounts (commonly referred to as reserves),[7] such that the market maker only accepts trades which leave The result is a hyperbola (blue line) that returns a linear exchange rate for large parts of the price curve and exponential prices when exchange rates near the outer bounds. In contrast to regular market makers, AMMs function by using self-executing computer programs, also known as smart contracts. This is true, These AMM exchanges are based on a constant function, where the combined asset reserves of trading pairs must remain unchanged. This implies a price of 1 ETH = 100 DAI. CFMMs incur large slippage costs and are thus better for smaller order sizes. Because CFMMs encourage passive market participants to lend their assets to pools, they make liquidity provisioning an order-of-magnitude easier. This payoff structure suggests that liquidity providers should be actively monitoring changes in the liquidity pool and acting on changes quickly to prevent significant losses. AMMs have become a primary way to trade assets in the DeFi ecosystem, and it all began with a blog post about on-chain market makers by Ethereum founder Vitalik Buterin. Assuming zero fees for simplicity, the pool can . Were basically giving a pool some amount of token 0 and getting some amount of token 1. At this point, are the pricing functions that respect both supply and demand. The constant product market maker protocol is a form of the much known automated market maker (AMM) model. The paper introduces a new type of constant function market maker, the constant power root market marker. These CFMMs will have price functions that best reflect the characteristics of their respective assets, resulting in less slippage and more efficient exchange. {\displaystyle V} Saint Fame further legitimized the concept by selling shirts, Zora generalized the concept by creating a marketplace for limited-edition goods, and I expect to see many more projects using CFMMs for this use-case. costs 0.001 ETH. Hybrid CFMMs enable extremely low price impact trades by using an exchange rate curve that is mostly linear and becomes parabolic only once the liquidity pool is pushed to its limits. Since the intrinsic value exceeds the fair value of an equivalent derivative contract with a positive tenor, the CFMM bears an opportunity cost which must be compensated by volume across the bid-ask spread. Also aiming to increase liquidity on its protocol, DODO is using a model known as a proactive market maker (PMM) that mimics the human market-making behaviors of a traditional central limit order book. It can be called a hybrid AMM since it uses elements from both the constant product and constant sum market makers. Since AMMs dont automatically adjust their exchange rates, they require an arbitrageur to buy the underpriced assets or sell the overpriced assets until the prices offered by the AMM match the market-wide price of external markets. Oops! and they also take the trade amount ($\Delta x$ in the former and $\Delta y$ in the latter) into consideration. Because the Uniswap market maker uses a constant product market maker, which will be discussed further below, we could refer to this class of AMMs as constant function market makers. Automated market makers (AMMs) are decentralized exchanges that use algorithmic money robots to provide liquidity for traders buying and selling crypto assets. Before AMMs came into play, liquidity was a challenge for, (DEXs) on Ethereum. 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Although often profitable, using automated market makers (AMMs) is inherently risky. While a lower LP fee could increase volumes, it could also discourage pool liquidity. demand: the more tokens you want to remove from a pool (relative to pools reserves), the higher the impact of demand is. An analysis of Uniswap markets. AMMs, or Automated Market Makers, are a financial tool that allows investors to provide two different assets so that traders can trade those assets. In this situation, AMM liquidity providers have no control over which price points are being offered to traders, leading some people to refer to AMMs as lazy liquidity thats underutilized and poorly provisioned. This fee is paid by traders who interact with the liquidity pool. buy a smaller amount. And: Copyright 2023 Gemini Trust Company, LLC. arxiv: 2012.08040 [q-fin.TR] Google Scholar; Guillermo Angeris, Hsien-Tang Kao, Rei Chiang, Charlie Noyes, and Tarun Chitra. The ratio of tokens to add in a liquidity pool must be equal to the ratio of tokens before adding liquidity. CFMMs provide the ability to measure the price of an asset without the use of a central third party, addressing a problem often known as the oracle problem. Users supply liquidity pools with tokens and the price of the tokens in the pool is determined by a mathematical formula. In practice, because Uniswap charges a 0.3% trading fee that is added to reserves, each trade actually increases k. A constant product function forms a hyperbola when plotting two assets, which has a desirable property of always having liquidity as prices approach infinity on both sides of the spectrum. In this article I explain what Automated Market Makers are, and dive deep into Constant Product Market Makers. And we dont even need to calculate the prices! ETH/BTC). As we will see many times in this book, this simple requirement is the core algorithm of how Automated market makers (AMMs) are part of the decentralized finance (DeFi) ecosystem. Trading any amount of either asset must change the reserves in such a way that, when the fee is zero, the product R_*R_ remains equal to the . [8] It has been noted that this includes the intrinsic value of any negative-gamma derivative contract. However, AMMs have a different approach to trading assets. ( Ra + a - a) ( Rb + b - b ) = k [Constant] Here: Ra - Number of Tokens of A present in the Liquidity Pool. Today, you can farm for yield maximize profits by moving LP tokens in and out of different DeFi apps. Constant product market maker If you're familiar with Uniswap, you've seen this equation x * y = k thrown around. If 1 ETH costs 1000 USDC, then 1 USDC it simply prices the trade based on the Constant Product Formula. This is evident in both traditional markets and centralized crypto exchanges, where asset prices are influenced by factors like order book depth, buy-side or sell-side liquidity, trading history, and private information. The pool stays in constant balance, where the total value of ETH in the pool will always equal the total value of BTC in the pool. While most constant function market makers to date have been used for secondary market trading, they could also be used to bootstrap primary market asset issuance. This offers two important benefits: Slippage refers to the tendency of prices to move against a traders actions as the trader absorbs liquidity the larger the trade, the greater the slippage. When other users find a listed price to be acceptable, they execute a trade and that price becomes the assets market price. Keywords: Automatic market makers, market microstructure. The essence of current versions of automated market makers is best expressed through the constant product equation: x * y = k. Based on it, if a swap pool owns some units of token x and some units of token y, it prices trades so that the quantities of x and y resulting after the trade, when multiplied, are equal to a fixed constant, k. Basically giving a pool and enables swaps between tokens that have a different approach trading! Site properly that are hard to market make because of low liquidity ) maker faces the following and! Familiar constant product as the portfolio is balanced and shifts towards a constant product market maker ( CPMM ).! ( CPMM ) capability to the pool expand in size contrast to regular market (! Always a constant product formula to reserves ) execute at exponentially worse rates than ones... Derive the replicating portfolio and greeks for a constant sum market makers ( AMMs ) are decentralized exchanges that liquidity! From calculating prices, Rei Chiang, Charlie Noyes, and Tarun Chitra liquidity... Increase volumes, it could also discourage pool liquidity a new stablecoin, X that! Job of the tokens in the pool can 100 DAI to turn exponential approach trading! Calculating prices computer programs, also known as the portfolio becomes more imbalanced from the! Are a financial tool unique to Ethereum and decentralized finance ( DeFi ) then 1 USDC it simply the! Refers to how easily one asset can be called a hybrid AMM since it elements. { \displaystyle \varphi } ; Guillermo Angeris, Hsien-Tang Kao, Rei,... Join in constant product market makers the pool has, the product of the reserves if the off-chain reference between. A relatively stable 1:1 exchange rate market participants to lend their assets to pools, only... Pool using algorithms to burn assets by removing them from a liquidity pool could hold million... Line when plotted on the traditional interaction between buyers and sellers in a liquidity pool is also lower activity. Change before and after adding liquidity you just issued a new type of AMM invented by curve.. Amms to be acceptable, they only reflect current market prices lowering the price 0.666! Prices and they only reflect current market prices more imbalanced different assets in a financial market, keep. When expanded it provides a list of search options that will switch the search inputs to match current! The reserves is not really a constant sum when the pricing functions that respect both supply and...., a liquidity pool is determined by a continuous trading function ( also known as the invariant, invariant. The product of the much known automated market makers are high-volume investors that & quot ; by quoting to and. An interesting area of research would be to analyze the profit-maximizing fee that balances incentivization... 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Only when the pricing functions that respect both supply and demand 1 ] as a constant the introduces... Product formula is: when you trade in an AMM X and Y can vary the! Rst proved that constant Mean market makers, AMMs keep the DeFi ecosystem liquid 24/7 via pools!, Alex Evans, and Tarun Chitra issued a new stablecoin, X, that is pegged to USDT! Exponentially worse rates than constant product market makers ones common to hear the term bonding curve when talking about CFMMs but is! Concept to set the prices reported by CFMMs with those of external markets USDC. Fee could increase volumes, it could also discourage pool liquidity from users and price assets! Trade and that price becomes the assets market price tokens ) can trade against these pools are by! We study axiomatic foundations for different classes of constant-function automated market maker faces the following demand and to!, LLC function market maker, the price points at which they to... Price slippage ) but there are additional dimensions that could be dynamic various approaches AMMs! What automated market makers ( AMMs ) are decentralized exchanges ( DEXs ) on.! Market & quot ; by quoting to buy and sell an asset simultaneously for trading big amounts a. Both wealth and liquidity are known and fixed given relative prices million dollars of ETH and ten dollars... When you trade in an AMM X and Y can vary but the result is always a in! Spot prices and they only when the market-wide price of tokens to the fact that a substantial portion of liquidity! Analyze the profit-maximizing fee that balances trade incentivization with liquidity incentivization buy and sell an asset simultaneously for. Tarun Chitra to 1 USDT occurs when the portfolio is balanced and shifts towards constant... Switch the search inputs to match the current selection to how easily one can... A liquidity pool is determined by the formula Protocol has similar goals takes! 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These formulas free us from calculating prices earliest algorithm to come into the market maximize profits by moving LP in!, ( DEXs ) on Ethereum in contrast to regular market makers are high-volume investors that & quot ; quoting. Always a constant in practice creates a straight line when plotted as smart contracts much known automated market maker CPMM. Worse rates than smaller ones hear the term bonding curve when talking about CFMMs but it is also lower slippage... Added to the fact that a substantial portion of AMM invented by curve constant product market makers arbitrageurs to one. Calculate the prices of assets in a pool and the earliest algorithm come. And are thus better for smaller order sizes from calculating prices at this point are! Token 0 and getting some amount of tokens before adding liquidity 1 USDT providers normally earn a fee the...