A key result in Stochastic Portfolio Theory (SPT) is the existence of relative arbitrage under fairly mild conditions on market diversity and volatility. However, this result is classically derived in a setting without transaction costs. In this talk we build upon the recent work of Ruf and Xie (2020) to incorporate proportional transaction costs in the SPT framework. We study mathematically the structure that these costs impose and consider how the usual assumptions can be modified to allow for relative arbitrage in the presence of market frictions. We empirically analyze if these strengthened assumptions are justified in practice and investigate some portfolios that generate relative arbitrage in our expanded setting.