We study front-running by high-frequency traders (HFTs) in a limit order model with continuous trading. The model describes an evolutionary equilibrium of low-frequency traders who compete in portfolio management services by offering investment styles. The introduction of front-runners inflicts heavy losses on speculators, while leaving passive investors relatively unscathed. This encourages investment in the market portfolio and markedly reduces overall turnover. Speculative trading persists despite its lower profitability. By most measures, market quality is not affected to any significant extent by front-running HFTs.