This paper investigates the interaction between the rise of inelastic intermediaries, e.g. mutual funds and exchange traded funds (ETFs), and exchange rate dynamics. By leveraging regulatory microdata on the universe of mutual funds domiciled in Switzerland, we first document the remarkable rise of the market share of this industry. Mutual funds went from holding 5% of domestic currency fixed income instruments in 2005 to 51% in 2024. We show that these intermediaries have strict mandates and trade only when faced with in(out)-flows. This makes the market more price-inelastic on aggregate in response to asset demand shocks. We develop an analytical model that we bring to the microdata. We find that (i) an inflow into domestic mutual funds with a large portfolio weight on the domestic currency appreciates it and (ii) the reduced aggregate elasticity makes the exchange rate more sensitive to capital flows. Finally, using a weekly panel of five advanced economies, we document the external validity of this mechanism. We show that the currencies whose markets see a higher prevalence of inelastic intermediaries react significantly more strongly to capital inflows.