Swap Slippage

The swap slippage is given by:

$$S_{i \rightarrow j} = S_i + (-S_j) = S_i - S_j$$

and

$$S_i = \dfrac{g(r'_i) - g(r_i)}{r'_i - r_i}$$

$$r'_i + r_i$$

where is the original coverage and is the final coverage.

If the swap amount is small, the slippage can be give by

$$S_{i \rightarrow j} = g'(r_i) - g'(r'_i)$$

Practical example of slippage calculation

We take the coverage ratio of USDT at 0.909 and ETH at 1.033. Working this out, we’d get:

USDT:

$$g'(0.909) = -\dfrac{0.00002*7}{0.909^8} = 0.03\%$$

ETH:

$$g'(1.033) = -\dfrac{0.00002*7}{1.033^8} = 0.01\%$$

Hence we have

$$S_{USDT \rightarrow ETH} = 0.03\% - 0.01\% = 0.02\%$$

This represents the marginal slippage when someone is performing a small amount of swap at this coverage ratio. And yes, the slippage is positive and user can benefit from the swap!