In this paper, we introduce a new form of asymptotic arbitrage, which we call a partial asymptotic arbitrage, half-way between those of F ollmer & Schachermayer (2007) and Kabanov & Kramkov (1998). In the context of the Heston model, we establish a precise link between the set of equivalent martingale measures, the ergodicity of the underlying variance process and this partial asymptotic arbitrage. In contrast to F ollmer & Schachermayer (2007), our result does not assume a suitable condition on the stock price process to allow for (partial) asymptotic arbitrage.