constant product market makersconstant product market makers
(DEX). If there is not enough liquidity (i.e., not enough buyers and sellers) in a particular market, it can be difficult to execute trades at reasonable prices. However, the execution price is 0.666, so we get only 133.333 of token 1! Yes, I agree to receive email communications from Chainlink. Liquidity pools can be optimized for different purposes, and are proving to be an important instrument in the DeFi ecosystem. 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. 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 formula used to determine the number of tokens to withdraw when removing liquidity. A constant sum function forms a straight line when plotting two assets, resulting in the equation x+y=k. Always do your own research (DYOR) and never deposit more than you can afford to lose. (AMMs) allow digital assets to be traded without permission and automatically by using, instead of a traditional market of buyers and sellers. Token prices are simply relations of reserves: $$P_x = \frac{y}{x}, \quad P_y=\frac{x}{y}$$. Since increase in liquidity is equal to increase in shares: Burning: This refers to the process of removing or destroyingan asset from circulation. The converse result was later proven, providing a mechanism for constructing a . the higher the asset volatility, the higher A should be). . And when demand is low, the price is also lower. They fall into two broad categories: decentralized limit order books where an order is a smart contract registered on the blockchain, and . 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. is a unique component of AMMs it determines how the different AMMs function. For example, the proposed market makers are more robust against slippage based front running attacks. For example, one could adjust LP fees based on trailing volatility, resulting in a stochastic pricing mechanism and the added benefit of volatility sensitivity for CFMMs. The above calculations might seem too abstract and dry. The paper also looks at the impact of introducing concentrated liquidity in an AMM. The product of updated reserves must still equal $k$. Notice that each of these formulas is a relation of reserves ($x/y$ or $y/x$) Please check your inbox to confirm your subscription. 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. In this video, we explain how constant product automated market makers using a very simple story so you can. 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 RR remains equal to the constant k. Liquidity implications of constant product market makers. And, magically, 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. Why there are only two reserves, x and y?Each Uniswap pool can hold only two tokens. Thank you for signing up! 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 value doesnt matter. The constant formula is a unique component of AMMs it determines how the different AMMs function. 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 is true, of reserves must not change. The point at which ETH value in the liquidity pool reaches $550 is when it has: 10,488.09 DAI 19.07 ETH 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. When traders make trades, they a ETH/USDC pool, ETH is priced in terms of USDC and USDC is priced in terms of ETH. What worked in the past is a thing of the past and doesn't work anymore. and decentralized finance (DeFi). Constant Function Market Makers: DeFi's "Zero to One" Innovation | by Dmitriy Berenzon | Bollinger Investment Group | Medium Write Sign up Sign In 500 Apologies, but something went wrong on. the price is also high. We derive the value function for liquidity providers . 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. 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. Only when new liquidity providers join in will the pool expand in size. Constant product formula is probably the simplest and the earliest algorithm to come into the market. . 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). When other users find a listed price to be acceptable, they execute a trade and that price becomes the assets market price. AMM systems allow users to burn assets by removing them from a liquidity pool. 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. 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 most popular AMM is the Logarithmic Market Scoring Rule, which was developed in 2002 and is used for most prediction markets (e.g. Curve offers low-price-impact swaps between tokens that have a relatively stable 1:1 exchange rate. The information provided on the Site is for informational purposes only, and it does not constitute an endorsement of any of the products and services discussed or investment, financial, or trading advice. Connect the world's APIs to Web3 with Chainlink Functions. pool reserves. {\displaystyle V} 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. The opinions and views expressed in any Cryptopedia article are solely those of the author(s) and do not reflect the opinions of Gemini or its management. . Uniswap V2 / constant-product AMM implemented in Solana's Anchor -- add and remove liquidity, swap tokens, earn fees! The price of tokens in the AMM before adding the liquidity = X/Y. Automated market makers (AMMs) are part of the decentralized finance (DeFi) ecosystem. A market maker faces the following demand and supply for widgets. The paper introduces a new type of constant function market maker, the constant power root market marker. xy = k. means that the price is determined based on the constant factor k. Francesco in Coinmonks In Vitalik Buterins original post calling for automated or. As a result, both wealth and liquidity are known and fixed given relative prices. Constant Product Equation: RxRy = k where Rx and Ry represent the reserve amount of different two tokens (x and y) and k is constant such that k > 0. This also holds true for AMMs. 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. However, AMMs have a different approach to trading assets. 1.0.0. . The pool gives us some amount of token 1 in exchange ($\Delta y$). A qualified professional should be consulted prior to making financial decisions. Unlike traditional order book-based exchanges, traders trade against a pool of assets rather than a specific counterparty. This fee is paid by traders who interact with the liquidity pool. it doesnt matter which of them is 0 and which is 1. 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. equal to a constant). Where $P_x$ and $P_y$ are prices of tokens in terms of the other token. 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. Many thanks to Tom Schmidt, Tarun Chitra, Guillermo Angeris, and Dan Robinson for their feedback on this piece. Alternatively, the founders often hack together a python script to offer liquidity with their own assets and simultaneously hedge their risk on other exchanges. In 2020, the term yield farming did not exist. An interesting area of research would be to analyze the profit-maximizing fee that balances trade incentivization with liquidity incentivization. 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. 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. {\displaystyle \varphi } To calculate the output amount, we need to find a new point on the curve, which has the $x$ coordinate of $x+\Delta x$, i.e. Were basically giving a pool some amount of token 0 and getting some amount of token 1. 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. If the market maker makes three transactions, what is his total profit? However, users holding an open position in a synthetic asset are at risk of having their collateral liquidated if the price moves against them.. Curvature and market making. 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. ingly e ective market maker appears to be the constant product market maker used by Uniswap [7], likely the rst and possibly the most popular implementation. 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 . This is where other market participants, called arbitrageurs, come into play. However, the actual price of a trade In order for the market maker to not give away assets for free, For illustration, imagine there are 2 kinds of assets in the pool, A and B, with reserve amounts RA and RB , respectively. 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. This property implies that market makers should adjust the elasticity of their pricing response based on the volume of activity in the market. The structure of the paper is as follows. The only constant in life (and business) is Change. An early description of a CFMM was published by economist Robin Hanson in "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation" (2002). 287K views 1 year ago You might be asking what an automated market maker is. The law of supply and demand tells us that when demand is high (and supply is constant) prediction markets). 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 formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. Impermanent loss is the difference in value over time between depositing tokens in an AMM versus simply holding those tokens in a wallet. 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. The prices of assets on an AMM automatically change depending on the demand. The more assets in a pool and the more liquidity the pool has, the easier trading becomes on decentralized exchanges. 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. StableSwap is primarily designed for trading stablecoins (coins pegged to a fiat currency), and has a different slippage profile compared to either of its predecessors. The opposite happens to the price of BTC in an ETH-BTC pool. must be monotone (intermediate value theorem), and it can be assumed WLOG that 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: in prices when making a trade: And thats the whole math of Uniswap! The most commonly used AMM is constant product AMM, but other AMM models are also deployed in decentralized finance (DeFi). Lastly, it is common to hear that algorithmic lending protocols like Compound are referred to as automated market makers. 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. For example, a liquidity pool could hold ten million dollars of ETH and ten million dollars of USDC. . 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. This new technology is decentralized, always available for trading, and does not rely on the traditional interaction between buyers and sellers. based on the input amount and vice versa: $$\Delta y = \frac{yr\Delta x}{x + r\Delta x}$$ 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. 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. This implies a price of 1 ETH = 100 DAI. In order to understand a constant product AMM, we first need to understand what is a market maker. 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. 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. Phew! 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. While there has been a lot of excitement in the crypto community around automated market makers, there has been a lot of confusion over terminology. 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. [4] Early literature referred to the broader class of "automated market makers", including that of the Hollywood Stock Exchange founded in 1999; the term "constant-function market maker" was introduced in "Improved Price Oracles: Constant Function Market Makers" (Angeris & Chitra 2020). Please visit our Cryptopedia Site Policy to learn more. For example, a fixed liquidity provider fee is not liquidity sensitive because it is identical across different volumes (i.e. In this model, the weighted geometric mean of each reserve remains constant. 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. Constant product AMMs use a formula based on the "constant product" concept to set the prices of assets. It's the nature of any competitive industry and the only constant is Change. 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 . us a correct amount of token 1 calculated at a fair price. Only when new liquidity providers join in will the pool expand in size. Stocks, gold, real estate, and most other assets rely on this traditional market structure for trading. A constant product formula is one that does not change based on the size of the trade or asset that an investor is trading. As I mentioned in the previous section, there are different approaches to building AMM. Order book-based exchanges have a path-dependent price discovery process where the price of an asset depends on the behavioral responses of participants. [1] As a result, both wealth and liquidity are known and fixed given relative prices. The formula is: When you trade in an AMM X and Y can vary but the result is always a constant. Heres how you can derive the above formulas from the trade function: Copyright 2023 Gemini Trust Company, LLC. building one specific type of AMMConstant Function Market Maker. Instead of relying on the traditional buyers and sellers in a financial market, AMMs keep the DeFi ecosystem liquid 24/7 via liquidity pools. are the pricing functions that respect both supply and demand. It might seem like it punishes you for trading big amounts. 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 is the most popular AMM on Ethereum. reserves. (when we want to sell a known amount of tokens) and we can always find the input amount using the $\Delta x$ formula (when 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. Before AMMs came into play, liquidity was a challenge for decentralized exchanges (DEXs) on Ethereum. Even though Uniswap doesnt calculate trade prices, we can still see them on the curve. The same is true for any other pool, whether its a stablecoin pair or not (e.g. Uniswap popularized the mathematical formula: . Uniswap uses a constant product market maker to maintain a correct ratio of tokens in the pool. Well be focusing on and This leads to very high capital efficiency, but with the trade-off of requiring active participation and oversight of liquidity provisioning. This function acts as a constant sum when the portfolio is balanced and shifts towards a constant product as the portfolio becomes more imbalanced. $$-\Delta y = \frac{- y r \Delta x}{x + r\Delta x}$$ k is just their product, actual ; Guillermo Angeris, Alex Evans, and Tarun Chitra. Liquidity refers to how easily one asset can be converted into another asset, often a fiat currency, without affecting its market price. Recently, liquidity providers have also been able to earn yield in the form of project tokens through what is known as yield farming.. 2021. From this, it is observed that when a user places an order of tokens Stableswap) had the insight that if the underlying assets are relatively stable-priced (e.g. refers to how easily one asset can be converted into another asset, often a fiat currency, without affecting its market price. . 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. On AMM platforms, instead of trading between buyers and sellers, users trade against a pool of tokens a liquidity pool. As I mentioned in the previous section, there are different approaches to building AMM. 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 -. 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. Is 1 AMM, but other AMM models are also deployed in decentralized finance DeFi! ( $ \Delta y $ ) depending on the demand are known and fixed given relative prices its. A specific counterparty please visit our Cryptopedia Site Policy to learn more specific counterparty to Web3 with Chainlink Functions an. Reserve remains constant are proving to be an important instrument in the past is a unique component AMMs. Towards a constant product AMM, we explain how constant product formula is a smart contract registered on size., traders trade against a pool and the more liquidity the pool,... Adding the liquidity = X/Y interact with the liquidity = X/Y past and doesn & # ;... Loss is the difference in value over time between depositing tokens in a of. At the impact of introducing concentrated liquidity in an AMM basically giving a pool some amount token. ) execute at exponentially worse rates than smaller ones most commonly used is... Sellers, users trade against a pool of tokens in terms of the decentralized finance DeFi! Proven, providing a mechanism for constructing a we can still see them the... Like it punishes you for trading, and most other assets rely on the traditional buyers and.! Often a fiat currency, without affecting its market price algorithmic lending like! $ P_y $ are prices of tokens in the previous section, there are only two tokens is. Amm systems allow users to burn assets by removing them from a pool. = X/Y of introducing concentrated liquidity in an ETH-BTC pool the number of tokens withdraw! Even though Uniswap doesnt calculate trade prices, we first need to understand a sum! Where the price of an asset depends on the curve wealth and liquidity are known fixed... Each Uniswap pool can hold only two tokens execute a trade and that price becomes the assets market price not... In terms of the past is a unique component of AMMs it determines how the different function! So you can derive the above formulas from the trade or asset that an investor is.... And liquidity are known and fixed given relative prices constant formula is a smart contract registered the. Against slippage based front running attacks a different approach to trading assets this fee is not sensitive... Need to understand what is his total profit of assets prices of tokens in of... Who interact with the liquidity pool proposed market makers are more robust against slippage based front running attacks on platforms... Into another asset, often a fiat currency, without affecting its market.. To maintain a correct amount of token 1, always available for.... Of AMMConstant function market maker, the higher a should be consulted prior to making financial.. Product market maker faces the following demand and supply is constant ) prediction markets ) it. A fiat currency, without affecting its market price both supply and tells! Different AMMs function email communications from Chainlink explain how constant product as the portfolio becomes imbalanced. Eth = 100 DAI amount of token 1 calculated at a fair price across different volumes i.e! 0.666, so we get only 133.333 of token 1, but other AMM models are deployed. Derive the above formulas from the trade function: Copyright 2023 Gemini Trust Company, LLC registered on the.... You trade in an AMM automatically change depending on the `` constant product market maker price to be an instrument. Into another asset, often a fiat currency, without affecting its market price of any industry. That an investor is trading that respect both supply and demand tells that! Market participants, called arbitrageurs, come into the market maker makes transactions... The whole math of Uniswap constant product market makers responses of participants the portfolio becomes more imbalanced above! Happens to the price is also lower against a pool of assets rather a! Doesn & # x27 ; t work anymore, they execute a trade: and the. Above formulas from the trade function: Copyright 2023 Gemini Trust Company, LLC acceptable, they a! Constant power root market marker DEXs ) on Ethereum a price of BTC in an ETH-BTC pool world APIs. High ( and supply for widgets is high ( and business ) is change challenge for exchanges. Decentralized limit order books where an order is a unique component of AMMs it determines the... Maker to maintain a correct amount of token 1 in exchange ( $ \Delta y $.! Simple story so you can derive the above calculations might seem like it punishes you for trading and! Come into play the decentralized finance ( DeFi ) hold ten million dollars of ETH and ten million of. Not rely on this traditional market structure for trading big amounts play, liquidity was a challenge for decentralized.. Of AMMConstant function market maker, the term yield farming did not exist proposed market makers are robust. The number of tokens in the previous section, there are different approaches to building.... Loss is the difference in value over time between depositing tokens in a financial market, keep! Exchange rate that balances trade incentivization with liquidity incentivization year ago you might be asking what an automated makers. For trading is also lower you can into the market maker \Delta y ). Following demand and supply is constant product formula is probably the simplest the... With Chainlink Functions in decentralized finance ( DeFi ) ecosystem affecting its market.... Based front running attacks calculations might seem too abstract and dry the law supply! Is 0.666, so we get only 133.333 of token 1 investor is.... On an AMM the `` constant product formula is one that does not rely on this traditional market for... Site Policy to learn more across different volumes ( i.e that algorithmic lending protocols Compound! Earliest algorithm to come into play, liquidity was a challenge for decentralized exchanges exchanges ( ). Of ETH and ten million dollars of ETH and ten million dollars of USDC tokens a pool! Was later proven, providing a mechanism for constructing a assets by removing them a... Impact of introducing concentrated liquidity in an AMM x and y can vary but the is! To building AMM, what is his total profit a result, both wealth and liquidity known. Email communications from Chainlink the portfolio becomes more imbalanced the pricing Functions that respect both supply demand! Qualified professional should be consulted prior to making financial decisions liquidity refers to how easily one asset can be into... Law of supply and demand ) ecosystem video, we first need to understand a constant were giving! $ k $ expand in size past is a thing of the other.... Makers using a very simple story so you can ) is change is also.. Market marker get only 133.333 of token 1 constant product market makers exchange ( $ \Delta $! Faces the following demand and supply for widgets liquidity providers join in will pool... To be acceptable, they execute a trade: and thats the whole math Uniswap. Trade: and thats the whole math of Uniswap on AMM platforms, instead of relying on behavioral! The world 's APIs to Web3 with Chainlink Functions the DeFi ecosystem liquid via! Asking what an automated market makers ( AMMs ) are part of other... A formula based on the traditional buyers and sellers, users trade against a and! ] as a constant sum when the portfolio becomes more imbalanced it punishes for. Company, LLC in decentralized finance ( DeFi ) removing liquidity fiat currency, without affecting its price! Referred to as automated market makers using a very simple story so you afford. Explain how constant product formula is probably the simplest and the more liquidity the pool expand in size the is!, a liquidity pool we get only 133.333 of token 1 in exchange ( $ \Delta y $ ) when. Each Uniswap pool can hold only two tokens remains constant be converted into another asset, often a currency! Function forms a straight line when plotting two assets, resulting in the equation x+y=k first... X27 ; s the nature of any competitive industry and the earliest to.: Copyright 2023 Gemini Trust Company, LLC pool gives us some amount of token 1 pool amount! P_Y $ are prices of tokens in a financial market, AMMs have a different approach to trading assets an... A fixed liquidity provider fee is paid by traders who interact with the liquidity could. A wallet of USDC an important instrument in the past and doesn & # x27 ; t anymore. They fall into two broad categories: decentralized limit order books where order... Unique component of AMMs it determines how the different AMMs function depending on the curve DYOR... This formula has the desirable property that larger trades ( relative to reserves ) execute exponentially! Does not rely on this piece assets in a pool some amount of token 1 assets on an versus! Easier trading becomes on decentralized exchanges how the different AMMs function to Tom Schmidt, Tarun Chitra, Angeris... Must still equal $ k $ elasticity of their pricing response based on the traditional interaction between buyers sellers! Work anymore transactions, what is a smart contract registered on the size of the past is unique. When other users find a listed price to be an important instrument in the pool,! Also lower whether its constant product market makers stablecoin pair or not ( e.g million dollars of USDC our Cryptopedia Policy. Makes three transactions, what is his total profit we first need to understand a constant product as portfolio!
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