> For the complete documentation index, see [llms.txt](https://hummus-exchange.gitbook.io/hummus-exchange/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://hummus-exchange.gitbook.io/hummus-exchange/concepts/coverage-ratio.md).

# Coverage Ratio

Coverage ratio `r` defines the system's equilibrium states.

$$
Coverage Ratio = \dfrac{Asset}{Liability}
$$

Liquidity provided to the protocol would become liability. A higher coverage ratio indicates a lower default risk. The coverage ratio is an important parameter to our protocol since it needs to be maintained above certain level to avoid default.

If coverage ratio < 1, the token is under-covered. And if coverage ratio > 1, it is over-covered.&#x20;

![Example: Coverage Ratio of USDT and USD](https://3635384107-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fo6xhq3OTyJ7H1urMeo0S%2Fuploads%2Fy4zGN9tN96i9N3GpfO4a%2Fcov%20ratio%201.png?alt=media\&token=e4c2d825-0a88-4897-87fc-261670acf76d)

In Hummus Exchange, when a swap happens, liquidity (in the system pool) for the swap-from token increases, while liquidity (in the system pool) for the swap-to token decreases

Hummus Exchange encourages convergence towards equilibrium and penalizes the divergence from equilibrium. Therefore, we have established **price slippage** as a function of coverage ratio.

### Slippage Function

The slippage `g(r)` is designed to penalize actions that deviate coverage ratios of two pools and incentivize actions that converge two coverage ratios.

![Marginal Slippage (definition)](https://3635384107-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fo6xhq3OTyJ7H1urMeo0S%2Fuploads%2FO4L9JwQGfWT7A1bxuZ59%2Fslippage%20function.png?alt=media\&token=f991dcf2-4be6-4d68-813b-a7c2d7a9b765)

{% hint style="info" %}
`k` and `n` are fixed parameters to be specified. Our research found that `k = 0.00002` and `n = 7` could be a competent choice of parameters.
{% endhint %}

![Marginal Slippage (graph)](https://lh3.googleusercontent.com/m76mxAXwKBInZRP1M1_ihQ4hUniXSODpSlNvns7FfHh8cH3IFA2b8oVEw-oiTJQKdEzTu8A1WNNRf2elDvFZjL0h5BB3yw5m-tVfDS9LdN3RmZ-OfeWkKUwjJ_4FPTjCSNWjjPnT)

For example, if the coverage ratio is 80%, the marginal slippage is -0.08%. When a swap happens,  0.08% of the swap-to token goes to the pool.

###

### Incentives for Convergence of Coverage Ratio

Hummus Exchange encourages convergence of coverage ratio towards 1. When a user swaps from a pool where the coverage ratio is 80%, he brings the coverage ratio of the from-token to a more healthy position. Hence he is able to receive 0.08% incentives.