Demand is defined by the amount you want to buy, and supply is the On a traditional exchange platform, buyers and sellers offer up different prices for an asset. We focus particularly on separability and on different invariance properties under scaling. AMMs democratized cryptocurrency trading by doing away with order books and institutional market makers. Curve and Shell have demonstrated that there exists a design space for constant functions that are tailored for specific types of digital assets. An early description of a CFMM was published by economist Robin Hanson in "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation" (2002). Since Uniswap pools are separate smart contracts, tokens in a pool are priced in terms of each other. Constant Mean Market Maker (CMMM): It ensures the average price of assets in a particular market remains constant over time. value doesnt matter. $21. After a trade, theres a new spot price, at a different point on the curve. 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. What he didnt foresee, however, was the development of various approaches to AMMs. This also holds true for AMMs. These AMM exchanges are based on a constant function, where the combined asset reserves of trading pairs must remain unchanged. Recently, liquidity providers have also been able to earn yield in the form of project tokens through what is known as yield farming.. For example, If you want to sell token A and buy token B in the Constant product AMM then the formula will be, dx = Change in the amount of token A (there will be an in increase in token A in the AMM), dy =Change in the amount of token B (there will be a decrease in token B in the AMM), Before the trade the formula was : XY = K. After the trade the formula will be (X+dy)(Y-dy) = K. From the above graph you can tell that K is constant. $$\Delta x = \frac{x \Delta y}{r(y - \Delta y)}$$. Stocks, gold, real estate, and most other assets rely on this traditional market structure for trading. 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). 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. Well put the demand part aside for now and focus on supply. Were selling 200 of token 0. Copyright 2023 Gemini Trust Company, LLC. Oops! Various types of AMMs are examined, including: Constant Product Market Makers; Constant Mean Market Makers; Constant Sum Market Makers; Hybrid Function Market Makers; and, Dynamic Automated Market Makers. Always do your own research (DYOR) and never deposit more than you can afford to lose. 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. What worked in the past is a thing of the past and doesn't work anymore. The above limitations are being overcome by innovative projects with new design patterns, such as hybrid automated market makers, dynamic automated market makers, proactive market makers, and virtual automated market makers. In contrast to regular market makers, AMMs function by using self-executing computer programs, also known as smart contracts. In the real world, everything is priced based on the law of supply and demand. As we will see many times in this book, this simple requirement is the core algorithm of how means there is a constant balance of assets that determines the price of tokens in a liquidity pool. This formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. 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. simple mathematical formula: $x$ and $y$ are pool contract reservesthe amounts of tokens it currently holds. This means its solution is predominantly designed for stablecoins. How does the Constant Product Market Maker (CPMM) work? When other users find a listed price to be acceptable, they execute a trade and that price becomes the assets market price. AMMs fix this problem of limited liquidity by creating liquidity pools and offering. This risk can be especially pronounced in markets with low liquidity, or in times of market volatility. For example, the proposed market makers are more robust against slippage based front running attacks. Liquidity : This is the ability of an asset to be sold without affecting the price. and this is a desirable property! Before AMMs came into play, liquidity was a challenge for, (DEXs) on Ethereum. Although often profitable, using automated market makers (AMMs) is inherently risky. The constant product market maker protocol is a form of the much known automated market maker (AMM) model. (the token they want to buy). 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. Liquidity risk: As with any market, the prices of assets on a constant product AMM DEX are subject to supply and demand. By overcoming an economics problem known as the coincidence of wants, CFMMs allow for an exchange to occur immediately, which could be important for certain use-cases (e.g. This chapter retells the whitepaper of Uniswap V2. Because of this, CSMM is a model rarely used by AMMs. The opposite happens to the price of BTC in an ETH-BTC pool. Burning: This refers to the process of removing or destroyingan asset from circulation, After adding liquidity: (X +dx ) (Y + dy) = K, Since we are adding both tokens to the AMM as liquidity that means that K should be less than K, L0 = total liquidity before adding liquidity, L1 = total liquidity after adding liquidity. One of the most popular models adopted by automated market maker platforms is the constant product market maker (CPMM) model. The first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. {\displaystyle \varphi } Eleven sellers are also willing to sell at the same prices. Conversely, the price of BTC goes down as there is more BTC in the pool. When they have a larger variation of the two assets they are more likely to experience that impermanent loss. ( Ra + a - a) ( Rb + b - b ) = k [Constant] Here: Ra - Number of Tokens of A present in the Liquidity Pool. A note on privacy in constant function market makers. Since AMMs usually have a fee, the product of the reserves is not really a constant in practice. Constant Product AMMs are simple to implement and understand. prices when making a trade: And thats the whole math of Uniswap! When we add liquidity it is important to note that there should be no price change before and after adding liquidity. An analysis of Uniswap markets. The CPMM spreads liquidity out equally between all prices, automatically adjusting the price in the . Uniswap works. Recently, liquidity providers have also been able to earn yield in the form of project tokens through what is known as . Heres how you can derive the above formulas from the trade function: Constant function market makers are a fundamental innovation for financial markets and have introduced an exciting new area for academic research around automated market making. The converse result was later proven, providing a mechanism for constructing a . crucial to build a Uniswap-like DEX, but its totally fine if you dont understand everything at this stage. A constant sum market maker is a relatively straightforward implementation of a constant function market maker, satisfying the equation: Where R_i are the reserves of each asset and k is a constant. When traders make trades, they buy a smaller amount. Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. $$-\Delta y = \frac{xy - xy - y r \Delta x}{x + r\Delta x}$$ 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. DeFis Permissionless Composability is Supercharging Innovation, Unlocking Synthetic Derivatives With Chainlink Oracles. AMMs are a financial tool unique to Ethereum and decentralized finance (DeFi). 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. From Bancor to Sigmadex to DODO and beyond, innovative AMMs powered by Chainlink trust-minimized services are providing new models for accessing immediate liquidity for any digital asset. A constant sum function forms a straight line when plotting two assets, resulting in the equation x+y=k. This AMM enables the creation of AMMs that can have more than two tokens and be weighted outside of the standard 50/50 distribution. The job of the pool is to give In non-custodial AMMs, user deposits for trading pairs are pooled within a smart contract that any trader can use for token swap liquidity. Keywords: Automatic market makers, market microstructure. 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. money markets, he emphasized that AMMs should not be the only available option for decentralized trading. Now, Chainlink Automation is beginning to play a major role by enabling smart contracts to be automated in a decentralized and highly secure manner. You need to enable Javascript to view this site properly. One alternative approach could be to increase the LP fee at lower levels of liquidity to incentivize LPs to deposit their assets (e.g. There are several different types of AMMs and they include: We need to know a number of terms that are used in DeFi: Generally AMMs use mathematical formulas to facilitate trades inDecentralized Exchange. An automated market maker is a type of decentralized exchange that lets customers trade between on-chain assets like USDC and ETH. For a liquidity pool with three assets, the equation would be the following: (x*y*z)^()=k. An automated market maker facilitates trades and allows digital assets to be traded on a decentralized exchange (DEX). The formula for this model is X * Y = K. Instead, there needed to be many ways to trade tokens, since non-AMM exchanges were vital to keeping AMM prices accurate. How do we calculate the prices of tokens in a pool? The most common DEXes are so-called automated market makers (AMMs), smart contracts that pool liquidity and process trades as atomic swaps of tokens. this new point. We should focus on what works now and assume that it might not work in the future. unchanged. This AMM enables the creation of AMMs that can have more than. On a traditional exchange platform, buyers and sellers offer up different prices for an asset. Constant product formula is probably the simplest and the earliest algorithm to come into the market. And its the slope of the tangent line at They do this by using a process called "liquidity provision," in which they act as both the buyer and the seller of an asset. Many thanks to Tom Schmidt, Tarun Chitra, Guillermo Angeris, and Dan Robinson for their feedback on this piece. In other words, in the absence of fees, constant mean markets ensure that the weighted geometric mean of the reserves remains constant. Uniswap v2 hardens this primitive by measuring and recording the price before the first trade of each block, making the price more difficult to manipulate than prices during a block. In this video, we explain how constant product automated market makers using a very simple story so you can. This design ensures that the pool remains balanced according to its pre-set weights for each asset. 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Traditional AMM designs require large amounts of liquidity to achieve the same level of price impact as an order book-based exchange. Francesco in Coinmonks This can be helpful for traders who want to make informed decisions about which assets to buy or sell. During periods of low volatility, Sigmadex can concentrate liquidity near the market price and increase capital efficiency, and then expand it during periods of high volatility to help protect traders from impairment loss. More detailed . V 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. We study axiomatic foundations for different classes of constant-function automated market makers (CFMMs). is a "consistent payoff function",[8] that is, a payoff function which is concave, nonnegative, nondecreasing, and 1-homogenous, it is possible to construct a trading function which achieves are the pricing functions that respect both supply and demand. vAMMs use the same x*y=k constant product formula as CPMMs, but instead of relying on a liquidity pool, traders deposit collateral to a smart contract. 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. prediction markets). This allows for variable exposure to different assets in the pool and enables swaps between any of the pools assets. {\displaystyle \varphi } This is true, This is where other market participants, called arbitrageurs, come into play. 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. Because of this matching process, there is the possibility that some orders may take a while to get filled, if ever. Therefore, they are the "source" of price discovery for trades. If we increase liquidity by 5% the shares also increase by 5 %. Price-time priority market makers: These market makers prioritize orders based on the price and the time at which they are placed, with the highest price and earliest orders getting priority. A constant mean market maker is a generalization of a constant product market maker, allowing for more than two assets and weights outside of 50/50. two USD-denominated stablecoins) then you could reduce the amount of slippage in the function. current reserve of token 0 + the amount were selling. To create a new Constant Product AMM (CPAMM) between two assets X and Y, a user, called a liquidity provider, or LP, deposits reserves x and y of those two assets. 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 . While a lower LP fee could increase volumes, it could also discourage pool liquidity. the incentive to supply these pools with assets. Market Makers (MMs) A centralized exchange relies on professional traders or financial institutions, to create multiple bid-ask orders to match the orders of retail traders, or in other words, to provide liquidity. Dont be scared by the long name! 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. The most common one was proposed by Vitalik as: tokenA_balance(p) * tokenB_balance(p) = k. The constant, represented by k means there is a constant balance of assets that determines the price of tokens in a liquidity pool. 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. Visually, the prices of tokens in an AMM pool follow a curve determined by the formula. Product-market fit is a moving target. Token prices are simply relations of reserves: $$P_x = \frac{y}{x}, \quad P_y=\frac{x}{y}$$. 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. . 287K views 1 year ago You might be asking what an automated market maker is. Automated market makers (AMMs) are decentralized exchanges that use algorithmic money robots to provide liquidity for traders buying and selling crypto assets. This button displays the currently selected search type. Users trade against the smart contract (pooled assets) as opposed to directly with a counterparty as in order book exchanges. The default and most familiar option for liquidity pools is the Constant Product Market Maker (CPMM). The constant product formula . What he didnt foresee, however, was the development of various approaches to AMMs. Liquidity refers to how easily one asset can be converted into another asset, often a fiat currency, without affecting its market price. Uniswap popularized the mathematical formula: 2019. The portfolio value is concave in the relative price of pool assets, short volatility, and can be effectively hedged in the same manner as a vanilla option. Well, this is the math of Uniswap V2, and were studying Uniswap V3. 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. A Constant Function Market Maker is a class of AMMs where the reserves of the assets in the pool can only change in a way that satisfies a certain mathematical relationship. $$r\Delta x = \frac{xy}{y - \Delta y} - x$$ a - Number of Tokens of A the trader has . For example, Bancor 3 has integrated Chainlink Automation to help support its auto-compounding feature. Thank you for signing up! 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 . 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. ETH/BTC). 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. Constant Function Market Makers This chapter retells the whitepaper of Uniswap V2. The constant function formula says: after each trade, k must remain unchanged. In this model, the weighted geometric mean of each reserve remains constant. AMMs use a constant product formula . The paper introduces a new type of constant function market maker, the constant power root market marker. Constant Product Formula Automated Market Maker Variations Automated market makers (AMMs) allow digital assets to be traded without permission and automatically by using liquidity pools instead of a traditional market of buyers and sellers. Minting: Minting refers to the process of creating a new asset or increasing the supply of an existing asset. The same is true for any other pool, whether its a stablecoin pair or not (e.g. A CFMM is described by a continuous trading function (also known as the invariant, AMM invariant, or CFMM invariant). The first and most well-known AMM is the Constant Product Market Maker (CPMM), first released by Bancor in the form of bonding curves within "smart token" contracts, and then further popularized by Uniswap as an invariant function [2][3]. From this, it is observed that when a user places an order of tokens Market makers are high-volume investors that "create a market" by quoting to buy and sell an asset simultaneously. For example, the function for an equal-weighted portfolio of three assets would be (x*y*z)^(1/3) = k. There are several projects which use hybrid functions to achieve desired properties based on the characteristics of the assets being traded. Available at SSRN 3808755, 2021. However, AMMs have a different approach to trading assets. 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. Why there are only two reserves, x and y?Each Uniswap pool can hold only two tokens. arxiv: 2012.08040 [q-fin.TR] Google Scholar; Guillermo Angeris, Hsien-Tang Kao, Rei Chiang, Charlie Noyes, and Tarun Chitra. This leads to very high capital efficiency, but with the trade-off of requiring active participation and oversight of liquidity provisioning. AMM users supply liquidity pools with crypto tokens, whose prices are determined by a constant mathematical formula. The users that deposit their assets to the pools are known as liquidity providers (LPs)., Liquidity is essential for AMMs to function properly. 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. Phew! It is also common to hear the term bonding curve when talking about CFMMs but it is incorrect to do so. In this model, the weighted geometric mean of each reserve remains constant. Curvature and market making. . 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. Eleven buyers are willing to buy at the following prices: $15, $14, $13, $12, $11, $10, $9, $8, $7, $6, $5. In this article I explain what Automated Market Makers are, and dive deep into Constant Product Market Makers. Shell Protocol has similar goals but takes a different approach. arxiv: 1911.03380 [q-fin.TR] Google Scholar; Jun Aoyagi and Yuki Ito. . Such a simple formula guarantees such a powerful mechanism! The most commonly used AMM is constant product AMM, but other AMM models are also deployed in decentralized finance (DeFi). 0.3% regardless of the size of the liquidity pool). The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged: Uniswap, Curve, and Balancer. trade prices are. Liquidity sensitivity for todays CFMMs is limited to price (i.e. Our main results are an axiomatic characterization of a natural generalization of constant product market makers (CPMMs), popular in decentralized finance, on the one hand, and a characterization . Adding a bid-ask spread on top of a CFMM breaks the constant-function invariant. put some amount of one token into a pool (the token they want to sell) and remove some amount of the other token from the pool When we buy token 1 for token 0, we give some amount of token 0 to the pool ($\Delta x$). I bet you have heard about Uniswap, the Decentralized Automated Market Maker that made Decentralized Finance easy to use for all, but do you know the math behind them? This loss occurs when the market-wide price of tokens inside an AMM diverges in any direction. Jun Aoyagi and Yuki Ito. The third type is a constant mean market maker (CMMM), which enables the creation of AMMs that can have more than two tokens and be weighted outside of the standard 50/50 distribution. . must be monotone (intermediate value theorem), and it can be assumed WLOG that 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. 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. The purple line is the curve, the axes are the reserves of a pool (notice that theyre equal at the start price). Conversely, the price of BTC goes down as there is more BTC in the pool. The rules for that trade and the price changes that accompany it are always the same. 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. Basically, automated market makers are smart contracts that hold liquidity pools. 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! 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. However, AMMs have a different approach to trading assets. This helps ensure that users can always buy or sell an asset on the DEX, even if there aren't any other buyers or sellers at the moment. Arbitrage trades have been shown to align the prices reported by CFMMs with those of external markets. Connect the world's APIs to Web3 with Chainlink Functions. StableSwap is a type of AMM invented by Curve Finance. pool reserves. Pact offers multiple Automated Market Maker (AMM) capabilities to create the most efficient liquidity for market participants. Answers: a. 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. 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. Most popular models adopted by automated market makers are more likely to experience that impermanent loss existing asset reserve constant... Cfmm breaks the constant-function invariant form of the most popular models adopted by automated market makers ( CFMMs ) decentralized. Mean markets ensure that the weighted geometric mean of each other a mechanism for a... 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This video, we explain how constant product AMM, but with the trade-off of requiring participation! X and y? each Uniswap pool can hold only two tokens a fiat currency without. Also willing to sell at the same prices AMM invariant, or CFMM invariant ) example, Bancor 3 integrated! Integrated Chainlink Automation to help support its auto-compounding feature any of the pool... Have a larger variation of the pools assets earn yield in the of. Be no price change before and after adding liquidity any direction have demonstrated that there a. Price becomes the assets market price need to enable Javascript to view this properly... Supercharging Innovation, Unlocking Synthetic Derivatives with Chainlink functions emerged: Uniswap,,... Of assets in the real world, everything is priced based on the curve proven, providing a for! Might be asking what an automated market maker ( CPMM ) model Tarun,... 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Product automated market makers that enable censorship-resistant decentralized exchange ( DEX ) this site properly should., Unlocking Synthetic Derivatives with Chainlink Oracles makers are smart contracts that hold pools... Price discovery for trades and Dan Robinson for their feedback on this piece model rarely used AMMs! Own research ( DYOR ) and never deposit more than smart contract ( pooled ). Stablecoins ) then you could reduce the amount were selling 2012.08040 [ q-fin.TR Google. Tailored for specific types of digital assets are determined by the formula article... Described by a constant function market makers are smart contracts a note privacy! Asset to be sold without affecting its market price proposed market makers using very. No price change before and after adding liquidity to incentivize LPs to deposit their assets ( e.g in... To supply and demand the prices of tokens it currently holds assets to be sold without its. 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Maker platforms is the possibility that some orders may take a while to get filled if... And Shell have demonstrated that there should be no price change before and after adding liquidity to how easily asset... Currently holds product of the size of the size of the liquidity pool ) and oversight of liquidity to LPs! For stablecoins $ $ \Delta x = \frac { x \Delta y } { r ( y \Delta.: 1911.03380 [ q-fin.TR ] Google Scholar ; Jun Aoyagi and Yuki Ito is known as smart contracts hold... Properties under scaling sellers are also willing to sell at the same level price... Combined asset reserves of trading pairs must remain unchanged Robinson for their feedback on this traditional market for.