  Many active funds hold concentrated portfolios. Flow-driven trading in these
securities causes price pressure, which pushes up the funds' existing positions
resulting in realized returns. We decompose fund returns into a price pressure
(self-inflated) and a fundamental component and show that when allocating
capital across funds, investors are unable to identify whether realized returns
are self-inflated or fundamental. Because investors chase self-inflated fund
returns at a high frequency, even short-lived impact meaningfully affects fund
flows at longer time scales. The combination of price impact and return chasing
causes an endogenous feedback loop and a reallocation of wealth to early fund
investors, which unravels once the price pressure reverts. We find that flows
chasing self-inflated returns predict bubbles in ETFs and their subsequent
crashes, and lead to a daily wealth reallocation of 500 Million from ETFs
alone. We provide a simple regulatory reporting measure -- fund illiquidity --
which captures a fund's potential for self-inflated returns.
