Curve Finance

By: Aditya Bhandari

Imagine a scenario where you trade two stablecoins, but end up with significantly less value than their exchange rate. That would be frustrating, right? Solving this problem is at the core of Curve Finance’s mission.

What is a stablecoin?

Stablecoins are cryptocurrencies that peg their market value to another asset, such as commodities or fiat currencies. Popular examples include USDC (pegged to the US Dollar), XAUT (pegged to gold), and EURS (pegged to the Euro).

Curve Finance Overview

Curve calls itself an “automated liquidity provider for stablecoins”, but what exactly does that mean? Curve’s automated market maker formula was built around the belief that similar valued assets should be able to be traded with minimum slippage. Slippage is the value that is lost, either due to gas or trading fees, when transactions are made on the blockchain. Currently, Curve’s formula has been able to minimize this to a 0.06% slippage basis, giving users extremely accurate exchange rates. Generally less volatile and within a similar price range of each other, stablecoins enable Curve to provide safety to both its liquidity providers and platform users. Further security measures such as simple smart contracts with a minimal attack surface has led Curve to attain most of the stablecoin market share. It holds 5 to 10 times higher liquidity than the Uniswap variant, and even provides liquidity to other DeFi apps.


Curve shares a similar structure to Uniswap, another decentralized exchange protocol built on the Ethereum blockchain. It consists of multiple liquidity pools that contain a specific ratio of two or more different coins. Liquidity providers can provide currency to existing pools or deploy new pools via the Curve factory in exchange for a certain fee. There are 3 different Curve pools: plain pools, lending pools, and MetaPools. Plain pools are the most simple; all the tokens in the pool are standard ERC-20 tokens. Lending pools are a bit more complex, as they do not actually hold the tokens themselves but instead “wrapped” versions of the tokens. “Wrapped” tokens are tokens that Curve lends to other protocols, which enables liquidity providers to earn interest from both lending and trading fees. Finally, MetaPools are where one token is traded with an entire pool. This enables a user to use one token to obtain multiple other tokens, which prevents diluting existing pools. Standard centralized exchanges, such as the stock market, require there to always be at least one buyer and seller to conduct a transaction; however, Curve’s liquidity provider/pool structure ensures that any buyer will always be able to obtain their desired token as long as the appropriate pool exists.

AMM Formula

At a high level, stablecoins enable Curve to minimize slippage and impermanent loss, but how does Curve mathematically enforce this? Curve’s formula is a balance between a constant-product “zero leverage” and constant sum “infinite leverage” formula. As shown in the graph below, Curve’s formula resembles a constant-sum invariant near the balance (5, 5), however, shifts towards a constant-product invariant as the portfolio becomes more imbalanced.

Curve AMM Formula
Curve AMM Formula
Curve AMM Graph
Curve AMM Graph

We can see this in Curve’s formula through the amplification coefficient, A. Lower values of A move the formula towards the constant product invariant by decreasing the impact of Dnn, while larger values of A move the formula towards the constant sum invariant. When the portfolio is perfectly balanced (the value of X equals the value of Y), the formula is equal to the constant A. The Curve protocol designers initially set A to 100, a balance between the two invariants, but this value can be modified through Curve DAO proposals. This intricate formula allows Curve to give platform users extremely accurate rates at a balanced portfolio, and a restabilizing mechanism at an unbalanced portfolio.

Curve DAO (CRV)

Curve’s governance is fostered by its DAO, CRV. A user can obtain CRV by purchasing the token or becoming a liquidity provider. To further use CRV, a user must “vote lock” their CRV as veCRV (Vote-Escrowed CRV). Locking is not reversible and restricts the user from using the CRV (now veCRV) outside the Curve protocol. veCRV allows users to earn trading fees from the Curve protocol, boost their return on provided liquidity, and vote on DAO proposals and pool parameter changes. It also has a unique time factor: the longer one vote locks their CRV, the more veCRV they receive. To regulate the circulating supply of CRV, Curve periodically buys back some CRV and destroys it. CRV enables Curve to integrate its community into the future of the protocol, while ensuring that governance cannot become corrupt or controlled by only a few major players.


Curve’s unparalleled slippage security makes it the premier trading platform for stablecoins. With a liquidity provider/pool structure, Curve never has to worry about low trading volume and offers liquidity providers substantial rewards to donate to their pools. Its unique formula finds the sweet spot between zero and infinite leverage, allowing it to provide the best rates for the platform’s users. The future of Curve is bright, and we can all become a part of it with the CRV token.

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