Factor models yield an R2 insignificantly different from zero for one-third of hedge funds in a broad sample. These funds illustrate the concept of market neutrality and feature lower volatilities, higher Sharpe ratios, and higher alphas than other funds, indicating they provide a successful alternative investment. However, large portfolios of zero-R2 funds contain fully half the volatility of portfolios of other funds, suggesting they feature substantial systematic risk. Furthermore, these funds display an increased probability of failure even after controlling for idiosyncratic volatility. These results indicate the presence of an omitted factor that exposes investors to significant downside risk.