# Deposit Gain and Withdrawal Fee

### Deposit Gain and Arbitrage Protection

Recall that the coverage ratio is defined as:

$$
r\_x = \frac{A\_x}{L\_x}
$$

When a user deposits $$A\_x$$and $$L\_x$$increases by the same amount, pushing closer to 1, the equilibrium coverage ratio increases. Users will receive **deposit gain** as they help bring the pool closer to equilibrium.

However, Wombat’s asset-liability management design could potentially lead to *withdrawal arbitrage*, which drains funds from the pool. We developed a **withdrawal fee** to prevent withdrawal arbitrage.

When $$A$$=0.002, the deposit gains and withdrawal fees are as followers:

<table><thead><tr><th width="216.33333333333331">Coverage Ratio</th><th>Deposit gain</th><th>Withdrawal fee</th></tr></thead><tbody><tr><td>0.1</td><td>+13.49%</td><td>-13.49%</td></tr><tr><td>0.2</td><td>+3.05%</td><td>-3.05%</td></tr><tr><td>0.3</td><td>+1.06%</td><td>-1.06%</td></tr><tr><td>0.4</td><td>+0.44%</td><td>-0.44%</td></tr><tr><td>0.5</td><td>+0.20%</td><td>-0.20%</td></tr><tr><td>0.6</td><td>+0.09%</td><td>-0.09%</td></tr><tr><td>0.7</td><td>+0.04%</td><td>-0.04%</td></tr><tr><td>0.8</td><td>+0.01%</td><td>-0.01%</td></tr><tr><td>0.9</td><td>+0.00%</td><td>-0.00%</td></tr><tr><td><strong>1.0</strong></td><td><strong>+0.00%</strong></td><td><strong>-0.00%</strong></td></tr><tr><td>1.1</td><td>+0.00%</td><td>-0.00%</td></tr><tr><td>1.2</td><td>+0.01%</td><td>-0.01%</td></tr><tr><td>1.3</td><td>+0.01%</td><td>-0.01%</td></tr><tr><td>1.4</td><td>+0.02%</td><td>-0.02%</td></tr><tr><td>1.5</td><td>+0.02%</td><td>-0.02%</td></tr><tr><td>1.6</td><td>+0.03%</td><td>-0.03%</td></tr><tr><td>1.7</td><td>+0.03%</td><td>-0.03%</td></tr><tr><td>1.8</td><td>+0.04%</td><td>-0.04%</td></tr><tr><td>1.9</td><td>+0.04%</td><td>-0.04%</td></tr><tr><td>2.0</td><td>+0.05%</td><td>-0.05%</td></tr></tbody></table>

All deposit gains and withdrawal fees remain in the pool and will be used to keep the system at an equilibrium state.

In most cases, liquidity providers will not be affected by this. Significant deposit gain and withdrawal fees are incurred only if the pool is highly out of balance.

## Incentives for convergence of coverage ratio

In cases where an asset in the pool is high in demand and shows a low coverage ratio, withdrawal in an asset higher in coverage ratio helps converge its coverage ratio. Users are incentivized to withdraw such tokens. Details of data can be found in [#deposit-gain-and-arbitrage-protection](#deposit-gain-and-arbitrage-protection "mention")

Withdrawing from an asset with a low coverage ratio will lead to a withdrawal penalty. You may withdraw your LP in other tokens to avoid the penalty. Refer to the below calculations for reference.

#### Example

Say user owns some LP of x, and he can withdraw in either token x or token y. Assume $$A$$ = 0.002, $$r\_x$$ = 50% and $$r\_y$$ = 90%.

* If token x is withdrawn, the **withdrawal penalty** is **-0.20%**.
* If the user withdraws in token y, he can receive **+0.75%** (swap rate) - 0.01% (haircut) = +0.74% **withdrawal gain** as he converges coverage ratios of two tokens.


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