Understanding DEX Fees: The Trader's Perspective

The Cost of Decentralized Trading

While price slippage is a well-known challenge in decentralized exchanges (DEXs), traders face another critical cost factor: DEX fees. These fees, typically ranging from 0.1% to 0.3% of trade value, represent a necessary trade-off that users accept in exchange for:

No-KYC anonymity
Faster transaction execution
Complete transparency of reserves and transactions

The Anti-Fraud Advantage

DEX fees serve an important secondary function: they help prevent artificial volume inflation that has historically plagued centralized exchanges (CEXs). Unlike CEXs where wash trading and fake volume have been well-documented, the fee structure of DEXs creates natural economic barriers to such manipulation.

Mathematical Foundation of DEX Fees

Consider a liquidity pool:

x₁: quantity of Token X
y₁: quantity of Token Y
f: DEX fee percentage (expressed as decimal)

For a trade exchanging x₂ of Token X for y₂ of Token Y:

Original Fee-less Formula:

$\displaystyle y_2 = \frac{x_2 \times y_1}{x_1 + x_2}$

Fee-Adjusted Formula:

$\displaystyle y_2 = \frac{(1-f) \times x_2 \times y_1}{x_1 + (1-f) \times x_2}$

The fees are distributed:

Liquidity Providers (LPs) as compensation
In some cases, the DEX protocol itself

Practical Example

Example Pool Parameters:

QD(DAI) = 100,000 DAI
QD(eGHST) = 10,000 eGHST
DF = 0.3%

Trade Scenario:

A trader swaps 1,000 DAI for eGHST

Without Fees:

$\displaystyle Q(\text{eGHST})_{\text{no fee}} = \frac{Q(\text{DAI}) \times QD(\text{eGHST})}{QD(\text{DAI})+ Q(\text{DAI})}$

$\displaystyle \frac{1,\!000 \times 10,\!000}{100,\!000 + 1,\!000} \approx 99.0099~\text{eGHST}$

With 0.3%Fee:

$\displaystyle Q(\text{eGHST})_{\text{with fee}} = \frac{(1-DF) \times Q(\text{DAI}) \times QD(\text{eGHST})}{QD(\text{DAI}) + (1-DF) \times Q(\text{DAI})}$