# Deposit Fees

A user can earn arbitrage profit by performing a swap, deposit followed by a reverse swap on a token with liquidity ratio > 1. Thus, the deposit fees is only charged for tokens where the liquidity ratio > 1.

The arbitrage fee is given by:

$$
\text{Deposit fees} = (L+d) \left(f(r\_2)-f\left(\frac{r\_{\text{max}}L+d}{L+d}\right)\right) + L (f(r\_{\text{max}})-f(r\_1))
$$

​Here,

*L = Liability*

*d = Deposit amount*

*r\_1 = Liquidity ratio before deposit*

*r\_2 = Liquidity ratio after deposit*

*r\_max = Maximum liquidity ratio of the token*

r\_max is a weighted average of the maximum liquidity ratio observed over a period of time. It is calculated such that 

$$
r\_{max} \geq r\_1
$$

always holds true.

Deposit fees increases as the difference between r\_max and r\_1 increases, as this denotes a possible arbitrage opportunity. When r\_max = r\_1, deposit fees = 0


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