We study the trading incentives of large rational risk-neutral investors who are
uninformed about fundamentals and only observe past prices. It is often asserted that
such investors should not trade. Our key departure from an otherwise standard rational
expectations framework is that average market participants do not know whether large
traders are informed. We find that non-zero price-contingent trading is the optimal
strategy of such investors. Due to superior knowledge of their own market impact, such
investors can infer information from past prices better than the market. Our model
sheds light on existing empirical evidence and yields novel testable predictions.