Authorised Participants (APs), primarily market makers, create and redeem ETF shares in response to investor demand, making their behaviour crucial for ETF liquidity and price alignment. We formulate a dynamic equilibrium model of APs' trading decisions, explicitly capturing their inventory management incentives and arbitrage motives, and derive predictions linking ETF mispricing to inventory risk and aggregate demand shocks. Using a novel regulatory dataset covering primary and secondary market trades for 128 ETFs between 2018 and 2022, we empirically validate our model's predictions. Results confirm that APs' real-time inventory positions and investor demand significantly explain ETF price deviations from net asset values (NAVs), offering insights beyond traditional economic and fundamental factors. Our model further clarifies APs' incentives and sheds light on mechanisms underlying the severe mispricing episodes observed in March 2020 across various ETF classes.