We show that a simple and intuitive variable, the return of a bear spread portfolio orthogonalized with respect to the market (H-Bear factor), can serve as a new benchmark for explaining the cross-section of hedge fund returns. Low H-Bear exposure funds (bear risk insurance sellers) outperform high H-Bear exposure funds (bear risk insurance buyers) by 0.58% per month on average, outperform even during market crashes, but underperform when bear market risk materializes. Overall, we identify a new risk dimension that affects hedge fund performance, and we show that this risk factor is distinct from the already popular realized tail risk.