  Decentralized exchanges are widely used platforms for trading crypto assets.
The most common types work with automated market makers (AMM), allowing traders
to exchange assets without needing to find matching counterparties. Thereby,
traders exchange against asset reserves managed by smart contracts. These
assets are provided by liquidity providers in exchange for a fee. Static
analysis shows that small price changes in one of the assets can result in
losses for liquidity providers. Despite the success of AMMs, it is claimed that
liquidity providers often suffer losses. However, the literature does not
adequately consider the dynamic effects of fees over time. Therefore, we
investigate the impermanent loss problem in a dynamic setting using Monte Carlo
simulations. Our findings indicate that price changes do not necessarily lead
to losses. Fees paid by traders and arbitrageurs are equally important. In this
respect, we can show that an arbitrage-friendly environment benefits the
liquidity provider. Thus, we suggest that AMM developers should promote an
arbitrage-friendly environment rather than trying to prevent arbitrage.
