# Dynamic Risk Management

For each Collateralized Debt Position (CDP) available on Ratio, there is a Collateralization Ratio in place based on the risk rating of the liquidity pool which is determined by the Ratio Risk Ratings (RRR). For example, the liquidity pool of USDT-USDC on Saber is rated as ‘AA’ according to the RRR, for which a Collateralization Ratio of 110% is in place. So, this will require at least $110 worth of collateral to be deposited to mint $100 worth of USDr.

## Protocol's Risk Metrics

Due to different market forces, it may happen that the collateral value goes below the Collateralization Ratio. As a result, a liquidation process will be initiated to protect the protocol from the potential downside. Therefore, each user has to monitor their position and the health of the position by means of the collateral deposited and the debt,

$$
\text{Collateral to Debt} = \frac{\text{Collateral Value}}{\text{Debt}} .
$$

where the maximum borrowable debt in USDr is given by

$$
\text{Maximum borrowable USDr} = \frac{\text{Collateral Value}}{\text{Collateralization Ratio}} .
$$

When the user is in an unhealthy position (CTD < CR), Ratio has the right to liquidate the collateral given by the borrower. However, since the protocol's interest is aligned with that of the user, Ratio Finance has additional cushions in place to protect the borrowers in the event of liquidation. These cushions are called **Delta** and **Gamma**, and allow the protocol to leave the borrower's debt in a much healthier position after liquidation. **This effectively means that, in a liquidation event, the protocol will not unwind and liquidate the full position of the borrower, but instead, just a portion of the collateral will be liquidated and the borrower will return to a healthy position.**

## **Delta**

To allow for better monitoring of the borrower's position and a cleaner output after liquidation, we have defined a variable called **Dynamic Collateralization Ratio** **that acts as additional protection to leave the borrower's debt in a healthier position after liquidation.** Mathematically it is defined as:

$$
\text{Dynamic CR} = \text{Collateralization Ratio} - Delta ,
$$

and, depending on market conditions, could be higher or lower than CR depending on the set risk tolerance of the protocol. **Delta** is a variable that sets the risk tolerance (appetite) of the protocol and has the functional form:

$$
Delta=-Δ\_{min} \bigg( \frac{(1-Ratio)^2}{(1-Tolerance)^2}-1\bigg),
$$

where $$\Delta\_{min}$$ is the maximum difference between the Collateralization Ratio and the Dynamic Collateralization Ratio, $$Ratio = \frac{\text{Market Price}}{\text{Fair Price}}$$ is a measure of the real-time conditions of the market, and $$Tolerance$$ is the protocol's risk tolerance to the deviation of Fair Price with respect to the Market Price.

<figure><img src="https://lh4.googleusercontent.com/VTrGvxSa3soeuDlzWmbdK0DqVmsLS39FUJmKJNvA4ADoIU_ZYc16WGey9tdi_AK5owiYkqbtoM9XFr6CdZnVHTmjnKAKhXC_2MQHHLpMTwjybDHeHIMv7kHgZAjb-caoIqVurG5Uap57d3MCdhHqYnNPZWmHK5qQQVKcraNC6O1we-W_FRL8l5Oc" alt=""><figcaption><p>Functional form of Delta with respect to the Fair Price of the LP Token.</p></figcaption></figure>

Since the Fair Price of an LP token reaches its maximum value when the pool is completely balanced ($1 USD in the graph above), then Delta increases exponentially when the Fair Price of the LP token drops, which means that the borrower's health is decreasing and liquidation may be initiated.

### Gamma

While the Delta buffer protects against volatility in the pool composition, **Gamma** is an additional buffer defined by Ratio Finance to provide a cushion before liquidation between the CTD and Dynamic CR. The result is that this buffer will leave the user in a healthier position after liquidation to protect from cascading liquidations.

## Borrower's perspective

Since Delta and Dynamic CR are variables set for the entire Vault and depend on market conditions and risk tolerance, it is important to know what is the key value that the borrower should keep in mind during high volatility events. Consequently, we defined the borrower's health by the difference between the Collateral to Debt and the Dynamic CR:

$$
\text{Health} = \text{Collateral to Debt} - \text{Dynamic CR}.
$$

Borrower's Health is a number that can be positive or negative but **only when the condition**

$$
\text{Health} < \Gamma ,
$$

**is met, would the borrower's position be partially liquidated.**&#x20;


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