Ethereum Finance Math

Decentralized Finance (DeFi) on Ethereum relies heavily on mathematical principles. Understanding this underlying math is crucial for anyone interacting with DeFi protocols, whether as a user, investor, or developer.

Smart Contracts and Basic Arithmetic: At its core, DeFi’s functionality stems from smart contracts, which are programmed to execute financial operations. Basic arithmetic, including addition, subtraction, multiplication, and division, is fundamental. Smart contracts use these operations to calculate interest rates, loan collateralization ratios, trading prices, and much more.

Yield Farming and APR/APY Calculations: A major aspect of DeFi involves yield farming, where users earn rewards by providing liquidity. The returns are often expressed as Annual Percentage Rate (APR) or Annual Percentage Yield (APY). APR represents the simple interest rate earned annually, while APY considers the effect of compounding. The APY formula, (1 + r/n)^n – 1, where ‘r’ is the annual interest rate and ‘n’ is the number of compounding periods per year, becomes vital for assessing the true profitability of a farm.

Liquidity Pools and Automated Market Makers (AMMs): AMMs, like Uniswap and Sushiswap, use mathematical formulas to determine the price of assets in a liquidity pool. The most common model is the constant product formula: x * y = k, where ‘x’ and ‘y’ are the quantities of two assets in the pool, and ‘k’ is a constant. This formula ensures that as the relative quantities of the assets change due to trades, the price adjusts to maintain the constant ‘k’. Understanding this formula is essential for comprehending slippage, the difference between the expected price and the actual price received when trading.

Impermanent Loss: Providing liquidity in AMMs carries the risk of impermanent loss. This occurs when the price ratio of the assets in the pool diverges significantly from the initial ratio when liquidity was added. The AMM formula forces arbitrageurs to rebalance the pool, resulting in a loss for liquidity providers compared to simply holding the assets outside the pool. Calculating the potential impermanent loss involves understanding the percentage change in asset prices and its impact on the pool’s overall value.

Collateralized Debt Positions (CDPs): Platforms like MakerDAO allow users to borrow stablecoins like DAI by locking up ETH or other assets as collateral. These CDPs maintain a collateralization ratio, which is the value of the collateral divided by the value of the borrowed DAI. Maintaining a healthy collateralization ratio is crucial to avoid liquidation, where the collateral is sold to repay the debt. The math behind these ratios, liquidation thresholds, and stability fees is essential for anyone using CDPs.

Oracle Price Feeds: DeFi protocols rely on oracles to obtain real-world price data for assets. Accurately and securely retrieving this data is vital. Protocols may use weighted averages from multiple oracle sources to mitigate the risk of manipulation or inaccurate reporting. The mathematical methods for aggregating and validating oracle data are crucial for the stability of the DeFi ecosystem.

In conclusion, Ethereum finance heavily leverages math, from basic arithmetic in smart contracts to more complex formulas in AMMs and CDPs. A solid understanding of these mathematical principles is key to navigating the DeFi landscape successfully.