Copyright 2023 Gemini Trust Company, LLC. For a liquidity pool with three assets, the equation would be the following: (x*y*z)^()=k. The constant product market maker protocol is a form of the much known automated market maker (AMM) model. $$(x + r\Delta x)(y - \Delta y) = xy$$ Most AMMs use a constant product market maker model. Impermanent Loss is the potential for a market maker to experience a loss due to changes in the relative prices of the assets that they are holding as part of their market making activities. collateralized options) and security tokens (e.g. For example, Bancor 3 has integrated Chainlink Automation to help support its auto-compounding feature. it simply prices the trade based on the Constant Product Formula. Constant Sum Market Makers The simplest CFMM is the constant sum market maker (CSMM). Jun Aoyagi and Yuki Ito. The second type is a constant sum market maker (CSMM), which is ideal for zero-price-impact trades but does not provide infinite liquidity. Adding a bid-ask spread on top of a CFMM breaks the constant-function invariant. Curve (a.k.a. Your trusted source for all things crypto. The equation x * y = k governs asset swaps on Uniswap, where x and y represent the quantities of two different assets in a liquidity pool, and k represents a value called the constant product invariant . In a traditional exchange workflow, market makers need to create orders, orders need to be published on exchanges, market takers need to browse orders, and market makers need to wait for the orders to get filled. There are a variety of other approaches to AMMs for information aggregation, such as Bayesian market makers (often good for binary markets) and dynamic pari-mutuel market makers (often used for horse racing). Shell Protocol has similar goals but takes a different approach. Users may contribute their assets to the CFMM's inventory, and receive in exchange a pro rata share of the inventory, claimable at any point for the assets in the inventory at that time the claim is made.[1]. A constant-function market maker (CFMM) is a market maker with the property 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. First introduced by Balancer, constant mean markets satisfy the following equation in the absence of fees: where R is the reserves of each asset, W is the weights of each asset, and k is the constant. For example, if an AMM has ether (ETH) and bitcoin (BTC), two volatile assets, every time ETH is bought, the price of ETH goes up as there is less ETH in the pool than before the purchase. The formula used to determine the number of tokens to withdraw when removing liquidity. Liquidity Pool:a liquidity pool is a collection of assets that is used to facilitate trading in an AMM.they help to ensure that there is always a sufficient supply of assets available to buy and sell in the market. Many of first-generation AMMs are limited by impermanent loss and low capital efficiency, which impacts both liquidity providers and traders. it doesnt matter which of them is 0 and which is 1. When does the tail wag the dog? Follow More from Medium Jessica Doosan 5 AI Coins For the Next Crypto Trend Ren & Heinrich in DataDrivenInvestor I analyzed 200 DeFi Projects. It's the nature of any competitive industry and the only constant is Change. (DEX). put some amount of one token into a pool (the token they want to sell) and remove some amount of the other token from the pool 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. the higher the asset volatility, the higher A should be). Suggested . 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. [8] It has been noted that this includes the intrinsic value of any negative-gamma derivative contract. 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. Recently, liquidity providers have also been able to earn yield in the form of project tokens through what is known as . The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged: Uniswap, Curve, and Balancer. It sets the trading price between them based on the . The constant product formula . In many markets, there may not be enough organic liquidity to support active trade. How does the Constant Product Market Maker (CPMM) work? $$r\Delta x = \frac{x \Delta y}{y - \Delta y}$$ In this constant state of balance, buying one ETH brings the price of ETH up slightly along the curve, and selling one ETH brings the price of ETH down slightly along the curve. 1.0.0. . 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 technology is decentralized, always available for trading, and does not rely on the traditional interaction between buyers and sellers. remains unchanged from the reference frame of a trade, it is often referred to as the invariant. 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 . We study axiomatic foundations for different classes of constant-function automated market makers (CFMMs). Constant product AMMs use a formula based on the "constant product" concept to set the prices of assets. Surprisingly, there are multiple By tweaking the formula, liquidity pools can be optimized for different purposes. k is just their product, actual AMMs provide liquidity to the DEX by constantly buying and selling assets in order to keep prices stable. CFMMs incur large slippage costs and are thus better for smaller order sizes. Anyone with an internet connection and in possession of any type of ERC-20 tokens can become a liquidity provider by supplying tokens to an AMMs liquidity pool. Because CFMMs encourage passive market participants to lend their assets to pools, they make liquidity provisioning an order-of-magnitude easier. plotting them on the graph. ( Ra + a - a) ( Rb + b - b ) = k [Constant] Here: Ra - Number of Tokens of A present in the Liquidity Pool. Smart contract risk: As with any decentralized platform, constant product AMM DEXs rely on smart contracts to facilitate trades and manage assets. In effect, the function looks like a zoomed-in hyperbola. Decentralized exchanges (DEXes) are an essential component of the nascent decentralized finance (DeFi) ecosystem. 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. The exact mechanics vary from exchange to exchange, but generally, AMMs offer deep liquidity, low transaction fees, and 100% uptime for as many users as possible. Minting: Minting refers to the process of creating a new asset or increasing the supply of an existing asset. [5] First be seen in production on a Minecraft server in 2012,[6] CFMMs are a popular DEX architecture. This mechanism ensures that Pact prices always trend toward the market price. If 1 ETH costs 1000 USDC, then 1 USDC Such a situation would destroy one side of the liquidity pool, leaving all of the liquidity residing in just one of the assets and therefore leaving no more liquidity for traders. As the "virtual . 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. Liquidity implications of constant product market makers. $$r\Delta x = \frac{xy}{y - \Delta y} - x$$ ; Guillermo Angeris, Alex Evans, and Tarun Chitra. Basically, automated market makers are smart contracts that hold liquidity pools. . 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. We should focus on what works now and assume that it might not work in the future. Most AMMs that have recently become popular in Decentralized Finance (DeFi) for trading cryptocurrencies however, are of a new type called constant function market maker (CFMM) [3]. prices when making a trade: And thats the whole math of Uniswap! As I mentioned in the previous section, there are different approaches to building AMM. The structure of the paper is as follows. building one specific type of AMMConstant Function Market Maker. Automated Market Makers for Decentralized Finance (DeFi) Yongge Wang This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. They fall into two broad categories: decentralized limit order books where an order is a smart contract registered on the blockchain, and . Market makers are entities tasked with providing liquidity for a tradable asset on an exchange that may otherwise be illiquid. of the first token and y is the reserve of the other token, and the order doesnt matter. The price of tokens in the AMM before adding the liquidity = X/Y. "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. The same is true for any other pool, whether its a stablecoin pair or not (e.g. $$r\Delta x = \frac{xy - x(y - \Delta y)}{y - \Delta y}$$ $$r\Delta x = \frac{xy - xy + x \Delta y}{y - \Delta y}$$ This property implies that market makers should adjust the elasticity of their pricing response based on the volume of activity in the market. Bonding curves define a relationship between price and token supply, while CFMMs define a relationship between two or more tokens. Eleven buyers are willing to buy at the following prices: $15, $14, $13, $12, $11, $10, $9, $8, $7, $6, $5. Pact offers multiple Automated Market Maker (AMM) capabilities to create the most efficient liquidity for market participants. A constant-function market maker (CFMM) is a market maker with the property that that the amount of any asset held in its inventory is completely described by a well-defined function of the amounts of the other assets in its inventory. This means its solution is predominantly designed for stablecoins. It uses the following functions: Where U(x) could be interpreted as a utility function comprised of a gain function, G(x), and a loss function, F(x); and x is the reserves of each asset. A constant sum function forms a straight line when plotting two assets, resulting in the equation x+y=k. An automated market maker facilitates trades and allows digital assets to be traded on a decentralized exchange (DEX). Yes, I agree to receive email communications from Chainlink. The pool also takes a small fee ($r = 1 - \text{swap fee}$) from the amount of token 0 we gave. Instead of trading directly with other people as with a traditional order book, users trade directly through the AMM.. Liquidity Implication of Constant Product . Since Bancor introduced on-chain AMMs in 2017, there have been several notable improvements on different aspects of AMMs: . Before AMMs came into play, liquidity was a challenge for, (DEXs) on Ethereum. and they also take the trade amount ($\Delta x$ in the former and $\Delta y$ in the latter) into consideration. An early description of a CFMM was published by economist Robin Hanson in "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation" (2002). Curve offers low-price-impact swaps between tokens that have a relatively stable 1:1 exchange rate. If a trader's bid matches the offer of the MM, the trade is executed. Users trade against the smart contract (pooled assets) as opposed to directly with a counterparty as in order book exchanges. V The relationship. Where $P_x$ and $P_y$ are prices of tokens in terms of the other token. Constant Sum Market Maker (CSMM): These market makers ensure the sum of the assets in a particular market is constant.This is achieved by adjusting the prices of assets in the market based on the supply and demand of those assets. Although often profitable, using automated market makers (AMMs) is inherently risky. AMMs democratized cryptocurrency trading by doing away with order books and institutional market makers. 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. An automated market maker (AMM) is the underlying protocol that powers all decentralized exchanges (DEXs), DEXs help users exchange cryptocurrencies by connecting users directly, without an . 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. based on the input amount and vice versa: $$\Delta y = \frac{yr\Delta x}{x + r\Delta x}$$ 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. Constant Product Market Makers A constant product market maker, first implemented by Uniswap satisfies the equation: where x > 0 and y > 0 are reserves of assets X and Y respectively and k is a constant. Unlike . A crowdfunded CFMM is a CFMM which makes markets using assets deposited by many different users. are the pricing functions that respect both supply and demand. This formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. The more assets in a pool and the more liquidity the pool has, the easier trading becomes on decentralized exchanges. Curve and Shell have demonstrated that there exists a design space for constant functions that are tailored for specific types of digital assets. Demand is defined by the amount you want to buy, and supply is the The name 'constant product market' comes from the fact that, when the fee is zero (i.e., = 1), any trade to must change the reserves in such a way that the product R R Concluding from the law of supply and demand, high demand increases the priceand this is a property we need to have If there is a bug in the smart contract, or if it is exploited by malicious actors, it could result in the loss of funds or other problems. Alternatively, the founders often hack together a python script to offer liquidity with their own assets and simultaneously hedge their risk on other exchanges. a ETH/USDC pool, ETH is priced in terms of USDC and USDC is priced in terms of ETH. 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. After a trade, theres a new spot price, at a different point on the curve. Lets return to the trade formula and look at it closer: As you can see, we can derive $\Delta x$ and $\Delta y$ from it, which means we can calculate the output amount of a trade 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. Cryptopedia does not guarantee the reliability of the Site content and shall not be held liable for any errors, omissions, or inaccuracies. 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 constant k. This is often simplified in the form of x*y=k, where x and y are the reserves of each asset. At this point, However, AMMs have a different approach to trading assets. If the AMM price ventures too far from market prices on other exchanges, the model incentivizes traders to take advantage of the price differences between the AMM and outside crypto exchanges until it is balanced once again. The above calculations might seem too abstract and dry. The formula for this model is X * Y = K. Exchanges often have to handle some of the execution themselves by running an internal trading desk with controls to make sure theyre not front-running their customers. A constant product market maker, first implemented by Uniswap, satisfies the equation: Where R_ and R_ are reserves of each asset and is the transaction fee. They were designed by the crypto community to construct decentralized exchanges for digital assets and are based on a function that establishes a pre-defined set of prices based on the available quantities of two or more assets. The product of updated reserves must still equal $k$. This is where other market participants, called arbitrageurs, come into play. Stocks, gold, real estate, and most other assets rely on this traditional market structure for trading. 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. Uniswap is the most popular AMM on Ethereum. And this is where we need to bring the demand part back. Liquidity providers normally earn a fee for providing tokens to the pool. This relationship between the prices of asset A and asset B is known as "constant product price elasticity." 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. Traditional AMM designs require large amounts of liquidity to achieve the same level of price impact as an order book-based exchange. A liquidity pool is a smart contract that holds reserves of two or more tokens and allows anyone to deposit and withdraw funds from them, but only according to very specific rules. the constant product function implements this mechanism! We focus particularly on separability and on different invariance properties under scaling. 500 $SOCKS tokens were created and deposited into a Uniswap liquidity pool with 35 ETH, which if ETH were trading at $200, would result in a floor price of $14 for the first pair and around $3.5M for the 499th pair. Balancer stretches the limits of Uniswap by allowing users to create dynamic liquidity pools of up to eight different assets in any ratio, thus expanding AMMs flexibility. However, the CFMM + spread will never underperform the CFMM without a spread (the latter of which will never compensate for opportunity cost). For example: in 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. An arbitrageur notices the price difference between Coinbase and Uniswap and sees that as an opportunity for arbitrage that is basically an opportunity to make a profit. CPMMs are based on the function x*y=k, which establishes a range of prices for two tokens according to the available quantities (liquidity) of each token. Liquidity risk: As with any market, the prices of assets on a constant product AMM DEX are subject to supply and demand. They have applied a deterministic pricing rule in the context of digital asset exchange, redefined the process of liquidity provisioning for market making, and democratized access to global pools of capital. The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged. On a. , buyers and sellers offer up different prices for an asset. On this Wikipedia the language links are at the top of the page across from the article title. The law of supply and demand tells us that when demand is high (and supply is constant) When expanded it provides a list of search options that will switch the search inputs to match the current selection. Please try again. The DODO Market Maker Pool is a product that is geared towards professional market makers with special requirements that cannot be satisfied by the regular liquidity pool models available on DODO (these being the Standard, Pegged, and Single-Token Pools). The purple line is the curve, the axes are the reserves of a pool (notice that theyre equal at the start price). The price of tokens in the AMM before adding the liquidity = (X + dx) / (Y + dy): From the above equation we can find both the amount of token A added (dx) given the amount of token B added (dy) i.e what is dy given dx ? CFMMs are the first class of AMMs to be specifically applied to real-world financial markets. As we will see many times in this book, this simple requirement is the core algorithm of how This AMM enables the creation of AMMs that can have more than two tokens and be weighted outside of the standard 50/50 distribution. As a liquidity provider you just need . CFMMs give issuers the ability to efficiently issue both physical and digitally-native assets and capture secondary market upside while improving liquidity and price discovery for consumers. DeFis Permissionless Composability is Supercharging Innovation, Unlocking Synthetic Derivatives With Chainlink Oracles. The job of the pool is to give a - Number of Tokens of A the trader has . Francesco in Coinmonks $$x + r\Delta x = \frac{xy}{y - \Delta y}$$ An analysis of Uniswap markets. The reserve of token 0 changes ($x + r \Delta x$), and the reserve of token 1 changes as well ($y - \Delta y$). 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. Answers: a. CFMMs are largely path-independent (assuming minimal fees), which means that the price of any two quantities depends only on those quantities and not on the path between them. Constant Product Market Maker (CPMM): A type of automated market maker that holds a fixed value for the ratio of two tokens it is trading, also known as a constant product formula. Path dependence, in a nutshell, means that history matters. Unlike traditional order book-based exchanges, traders trade against a pool of assets rather than a specific counterparty. $$\Delta x = \frac{x \Delta y}{r(y - \Delta y)}$$. Liquidity refers to how easily one asset can be converted into another asset, often a fiat currency, without affecting its market price. Liquidity : This is the ability of an asset to be sold without affecting the price. The most popular of them is the Constant Function Market Makers (CFMM) [37], which maintain a mathematical invariant (for example, a product of the quantity of assets) during the trade. Such a simple formula guarantees such a powerful mechanism! Uniswap popularized the mathematical formula: Uniswap V2 / constant-product AMM implemented in Solana's Anchor -- add and remove liquidity, swap tokens, earn fees! On a traditional exchange platform, buyers and sellers offer up different prices for an asset. Only when new liquidity providers join in will the pool expand in size. saddle.finance. In effect, this acts as a constant sum when the pool is balanced but progressively introduces more slippage as the pool deviates past a specified threshold for the weights of each asset. The first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. In return for providing liquidity, the user may be rewarded with a new asset that is created by the AMM, It is important to note that an increase in liquidity is directly proportional to an increase in shares. 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. Class of AMMs: a powerful mechanism above calculations might seem too and! Although often profitable, using automated market makers ( AMMs ) is inherently risky, come into play also able... In 2012, [ 6 ] CFMMs are the first class of AMMs to be sold without the. Before adding the liquidity = X/Y for constant functions that respect both supply and demand we to... 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