In the past week, Curve’s lock-up volume once again surpassed AAVE as the project with the highest lock-up volume in the Defi world. As of September 27, the lock-up volume exceeded $13.7 billion. In addition, Curve has also expanded its business to 5 smart contract platforms, and can occupy about 10% to 20% of the lock-up volume of the public chain where it is located, which also makes Curve a veritable cornerstone project in the world of Defi.

Curve locks data on different public chains

(Source: https://defillama.com/home)

This article hopes to re-introduce Curve from the two aspects of project mechanism and operation, and use this to analyze the development status of Curve V2 since the update. (The stable asset transaction mentioned below refers to the transaction of assets with equal expected prices, while the non-stable asset transaction refers to the transaction of assets with unequal expected prices.)

**Project mechanism**

**AMM ****Mathematics**

Curve founder Michael Egorov released the White Paper of Curve V1 in November 2019, and for the first time introduced the StableSwapinvariant function, an automatic market-making mathematical model that focuses on stablecoin transactions. Before introducing this model, first review two basic automatic market making methods: the constant sum equation and the constant product equation. (Xi is the quantity of each asset in the fund pool)

When using the constant sum equation, the price will not change with the transaction and will always remain stable, but once the price deviates too much, the liquidity of the fund pool will be emptied. Therefore, the constant sum formula is only suitable for asset groups where the expected price will never change, and the market-making strategy is to provide liquidity for all funds at a fixed price.

The constant product equation is an AMM model similar to UniswapV2, but the two-dimensional equation is pushed to multiple dimensions. The market-making strategy of this model is to spread the flow over all prices. If the automatic market-making model is applied to stable asset transactions, then because the quantity of each asset is equal to D/n, the constant product is D/n to the power of n.

Curve designed the StableSwap invariant function for stable asset transactions, which is between the two lines introduced earlier. When the coefficient χ approaches positive infinity, the StableSwap invariant function approaches the constant formula; when the coefficient χ approaches 0, the StableSwap invariant function approaches the constant product formula. So set χ as a dynamic coefficient:

When the price is far away from the price equilibrium point (expected price point), χ tends to 0, and the StableSwapinvariant function is also approximate to the constant product equation; when the price is close to the price equilibrium point, χ tends to the coefficient A, and the StableSwap invariant function is also approximately constant. And the equation. Therefore, compared to the ordinary constant product formula, Curve’s StableSwap model has the advantages of ultra-low slippage and concentrated liquidity in the area near the “price equilibrium point” (as shown in the figure below). It is worth noting that the model has an important assumption: **the price of each asset should be stable at a level.**

Comparison of three automatic market-making models (two-dimensional)

(Source: https:// curve .fi/files/stableswap-paper.pdf)

Curve completed the V2 upgrade in June of this year, aiming to adapt V1’s automatic market-making model StableSwap to adapt to the trading of non-stable assets such as USDT, wBTC and ETH. The main updates include: (1) The liquidity of the V1 version is too concentrated and is not suitable for unstable trading pairs. The model is improved to adjust the liquidity concentration. (2) Use the Repegging mechanism of the internal oracle.

Because the V1 model is used to trade unstable assets, and V1 has an important assumption: the price of each asset is the same, so in the V2 model, the balance of each asset is used as the xi in the model. When the price is relatively stable, the balance of each asset is equal. The number of tokens in the pool is linked to the balance through the price vector P:

When P0 is set to 1, the vector P represents the price of all assets for the 0th asset. On this basis, Curve launched the V2 automatic market-making model Crypto invariant function:

The difference from the V1 model is the coefficient K:

The Crypto invariant function is derived from the StableSwap invariant function, where A*K0 is the coefficient χ in the StableSwap invariant function. As shown in the figure below, when the price approaches the equilibrium state, K0 tends to 1, and the Cryptoinvariant function also approaches the Stable Swap invariant function. Therefore, at the point of price equilibrium, liquidity is more concentrated. When the price is far from the equilibrium state, K0 tends to be a very small positive number (ie γ), and the Cryptoinvariant function will also approach the newly constructed constant product formula (the dotted line closer to the origin in the figure below) to prevent large price fluctuations. Liquidity quickly dries up.

The Crypto invariant function determines the amount of change in the balance. To get the specific number of transactions, you must divide it by the vector P. P is initially set as the price at the equilibrium point. However, when the transaction changes constantly, the vector P needs to be updated continuously. Therefore, V2 launched the **price repetging mechanism** , which mainly includes the following three parts:

1) Internal oracle, use the internal exponential moving average (EMA) price oracle to obtain the latest price level P* (t represents the time since the last price update, and T1/2 is half of the time interval for calculating EMA) :

2) Threshold control mechanism, using a variable Xcp to measure constant product:

When Xcp breaks through a threshold, the vector P is updated.

3) Update the price vector P, use the following formula to update the price:

After the price is updated, D can be recalculated to determine a new price curve. At the same time, according to the characteristics of the Crypto invariant function, liquidity will be gathered around the new price.

**Provide liquidity mechanism**

Liquidity providers can deposit a single asset or multiple assets in the V1 fund pool, and the same applies when withdrawing them. Take the following picture as an example, if you deposit 1000 DAI in the pool , you will get 46.1 DAI, 314.5 USDC, 490.2 USDT and 149.2 TUSD. Therefore, the liquidity provider has risk exposure to these four assets, and the size of each exposure is determined by the proportion of assets in the pool. In order to guide the stable asset pool to return to a balanced state, the liquidity provider will receive deposit rewards when a relatively small asset in the pool is deposited (the price is more expensive), and when the asset with the largest proportion in the pool is withdrawn (the price is lower) At times, liquidity providers will also be rewarded with withdrawals.

Stablecoin fund pool

(Source: https://resources.curve.fi/base-features/understanding-curve)

Liquidity providers can also get half of the transaction fees generated by the fund pool, and if they continue to pledge LP tokens into the Gauge, they can also get corresponding CRV rewards. The transaction fee in the V1 fund pool is 0.04%, which is also considered to be the most cost-effective way of stable currency transactions on Ethereum.

The liquidity provision mechanism of V2 is the same as that of V1, and one asset or multiple assets can be selected when depositing and withdrawing. The transaction fees charged by the V2 fund pool range from 0.04% to 0.4%. The fee level will vary according to how close the current price is to the price of the internal oracle, and the fee ratio will be updated after each transaction.

**Token economy**

Curve has a well-designed token economy. Curve’s governance token is CRV, with a total issuance of approximately 3.03 billion, of which: 62% is distributed to liquidity providers; 30% is distributed to shareholders and unlocked linearly within 2-4 years; 3% is distributed to employees and in It will be unlocked linearly within 2 years; 5% will be used as a community reserve. The release plan is shown in the figure below. It is estimated that 2.2 billion pieces will be released by May 2026, which is more than two-thirds of the total circulation.

CRV token issuance plan

(Source: https://resources.curve.fi/base-features/understanding-crv)

There is no benefit to simply holding CRV tokens, but CRV holders can obtain veCRV by locking CRV to the Curve protocol to enjoy the governance functions and protocol rewards of the tokens. The relationship between the amount of veCRV obtained and the pledge time is shown in the following figure:

How to obtain veCRV

(Source: https://resources.curve.fi/base-features/understanding-crv)

After pledged CRV to obtain veCRV, veCRV holders can receive up to 2.5 times the CRV reward when providing liquidity, and 50% of the transaction fees generated by the agreement will also be issued to veCRV holders. In addition, veCRV holders also have the right to vote, and can vote on different CurveDAO proposals and fund pool parameters, the most important of which is the ability to distribute CRV liquidity rewards through the Gauge voting mechanism. The Curve protocol determines the proportion of Gauge based on the amount of veCRV votes obtained by each fund pool, that is, the proportion of CRV liquidity rewards obtained by each fund pool. Gauge weight is recalculated once a week, and users can change their vote every 10 days. This mechanism has also attracted many stable asset operators to pledge CRV to obtain voting rights and attract more liquidity rewards for their own asset pools. This is also the reason why the CRV pledge rate is relatively high.

CRV release scale and lock scale

(Source: https://resources.curve.fi/base-features/understanding-crv)

The current circulation of CRVs is about 760 million, and there are about 300 million CRVs locked in the Curve agreement, accounting for about 40%, and the average lock-up time is 3.65 years, which shows that most CRV pledgers choose to pledge Obtained the most veCRV in 4 years.

**Operational analysis**

Uniswap launched the v3 version in May 2021, hoping to provide a narrower slippage and higher capital efficiency. On UniswapV3, users can choose to provide liquidity to a specific price range. Liquidity providers can therefore choose to provide liquidity for the price range near the equilibrium price of the stablecoin pair, so the slippage generated when using Uniswap V3 to trade stablecoins will be reduced.

One month later, Curve followed Uniswap to complete its V2 update. Although it did not cause a sensation like the UniswapV3 update, it is also an important step for Curve to expand its business territory. After completing the V2 upgrade, Curve also began to support the trading of non-stable assets. The two DEX giants, which focus on different fields, seem to be attacking each other’s business fields at the same time. More than three months have passed. This article will compare with Uniswap from the three aspects of stable asset transactions, non-stable asset transactions, and token valuation levels to discover the current operation of Curve.

**Stable asset trading**

Stable asset trading is still the core business of Curve. At present, of the 42 fund pools in Ethereum, 40 are all fund pools for trading stable consideration assets. Among them, 26 fund pools are linked to the price of USD, 7 fund pools are linked to the price of BTC, and 4 fund pools are linked to the price of ETH. The 24-hour trading volume carried by the stable asset fund pool exceeds 80% of the total 24-hour trading volume of the project, and the locked-up volume exceeds 90% of the total locked-up volume of the project.

Select 3Pool, the largest stable fund pool in Curve, to compare with the stable currency fund pool corresponding to Uniswap V3. From the perspective of transaction volume, Uniswap V3 is already at the same level as Curve. Considering that Curve has a larger amount of lock-up, compared with Uniswap V3, Curve’s capital utilization rate is relatively low. On the other hand, Curve has fulfilled its promise of low transaction costs and low slippage, and the huge lock-up volume has also given Curve the ability to carry huge transactions.

In addition, Curve has also cooperated with Year to develop the Pool factory function, allowing anyone to configure Metapool. Metapool allows a token to be traded with another underlying base pool, such as [GUSD,[3POOL]], the fund pool assets include GUSD and 3Pool’s LP token 3CRV. This not only supports the transaction of new assets, but also does not encroach on the liquidity of the original assets. The newly prepared fund pool needs to set two parameters: (1) transaction fee, ranging from 0.04% to 1%; (2) parameter A, the Curve team will help set this parameter.

**Unstable asset trading**

After completing the V2 upgrade, Curve also began to support the transaction of non-stable assets, but its scale is small, especially the types of assets that support transactions are still very small. At present, there are only two fund pools that support non-stable assets on Ethereum-tricrypto and tricrypto2, which only support the transaction of three assets: USDT, wBTC and WETH.

Comparing the fund pool involved in the tricrypto2 pool and Uniswap V3, Curve already has more lock-up volume and lower transaction fees, and the 24h transaction volume is also close to the level of UniswapV3’s corresponding fund pool. From the tricrypto2 fund pool, Curve is in non-stable assets, at least the data of USDT, wBTC and WETH are above the level of UniswapV3, but the assets supported by Curve in non-stable asset transactions are still Too few, if you want to compete with UniswapV3 in this field, you must introduce more mainstream assets into its V2 model.

**Valuation analysis**

It is worth noting that more than 40% of the CRV pledged in the agreement is not included in the token circulation, which also causes the low market value of Curve in circulation. But even with these 40% tokens included, the circulating market value of CRV and FDV are far behind Uni. In terms of operational data, Curve has a higher lock-up volume, while Uniswap has a higher transaction volume. Judging from the ratio of the circulating market value or FDV to the locked position, the circulating market value of Curve and FDV is relatively underestimated compared with Uniswap.

Comparing the P/S ratios of the two DEXs, it is found that Curve has a higher valuation level. The annualized total revenue of the Curve project lags far behind Uniswap, and its profitability is far inferior to Uniswap due to its operating model and transaction volume.

**Summarize**

From the operating data of Curve, Curve has the largest amount of locked positions in the Defi world, which proves its appeal to large funds. Compared with Uniswap, Curve’s transaction volume and revenue are at a relatively low level due to its operating model focusing on stable currency transactions and low transaction fees. However, after the V2 upgrade, the operating data of the tricrypto2 fund pool has also been shown in the field of non-stable assets, and Curve also has the strength to compete with UniswapV3.

Judging from the updated automatic market-making mechanism of CurveV2, Curve has embarked on a completely different path from UniswapV3. Uniswap V3 gives liquidity providers the greatest flexibility, and liquidity providers can choose the price range in which they provide liquidity. Different from UniswapV3, the automatic market-making model of CurveV2 can automatically adjust the liquidity concentration range according to the price fed by the built-in oracle, without the need for liquidity providers to redeploy the liquidity range themselves. This design is more friendly to individual investors and does not require liquidity providers to formulate complex market-making strategies themselves.

In general, Curve currently has a clear competitive advantage in the field of stable asset trading, but after the V2 update, it is still in a process of groping for non-stable asset trading. It is foreseeable that as the business scopes of the two DEX giants, Curve and Uniswap, continue to overlap, it is bound to bring greater competition.

Posted by:CoinYuppie，Reprinted with attribution to:https://coinyuppie.com/panoramic-interpretation-of-defis-cornerstone-project-curve/

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