# Inventory Risk

In the context of our design, enabling single-sided liquidity provision eliminates Impermanent Loss (IL) but is replaced by what we call as Inventory Risk (IR). IR occurs when the total liabilities of the protocol becomes greater than the total assets in the system. In our case, when the sum of total value of tokens across all the pools become less than the total amount deposited as liquidity, LPs are exposed to IR.

## Inventory Risk Factor (IRF)

We have introduced a parameter called Inventory Risk Factor (IRF) to measure IR and prevent a situation where Mantis is unable to pay its liabilities:

$$
\text{IRF} =
\begin{cases}
1 &  \text{if} \  \text{NLR} \geq 1\\
\text{NLR} & \text{if} \  \text{NLR} < 1
\end{cases}
$$

Since the loss due to IR is only realised by LPs upon withdrawal, the IRF comes into effect when the following two conditions are satisfied at the time of withdrawal:

* NLR < 1
* Liquidity ratio of the token being withdrawn is less than 1<br>

In such a case, the withdrawal amount is multiplied by IRF (after fees) and is represented mathematically as:

$$
\text{Withdrawal amount} = \text{IRF}(\text{Liabilities} - \text{Fees})
$$

Doing so ensures that the system remains sustainable. LPs are also incentivised to withdraw in other tokens with a liquidity ratio > 1 when NLR < 1, keeping the system in balance.


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