Pool Yield

This document describes how pool yield is calculated in the Cauldron user interface. See also Aggregated Pool APY.

Pool Yield

Pool Yield is calculated as follows

\[ \left( \frac{\sqrt{k_{\text{latest}}} - \sqrt{k_{\text{current}}}}{\sqrt{k_{\text{current}}}} \right) \times 100 \]

Where K is the CPMM formula of a Cauldron liquidity pool.

\[ K = \text{satoshis} \times \text{token} \]

Yield is collected by increasing K with every trade. The constant product is squared in the yield formula to get a more accurate representation of the yield. The CPMM formula (K = x * y) creates a non-linear relationship between the liquidity pool size and the impact of liquidity provision on asset prices and trading.

APY

Pool APY is calculated as follows:

\[ \left( \left( \frac{\text{pool yield}}{100} + 1 \right)^{\text{annualization factor}} - 1 \right) \times 100 \]

where annualization factor is

\[ \text{annualization factor} = \frac{365.25}{\text{days elapsed}} \]

and days elapsed is

\[ \text{days elapsed} = \frac{\text{period start} - \text{period end}}{86400} \]

The annualization factor (\(\frac{365.25}{\text{days elapsed}}\)) scales the yield to an annual basis, compensating for shorter active periods by calculating how much yield would accumulate if the observed rate continued over a full year.