We propose the bear beta, i.e. the sensitivity of hedge funds to a bear spread portfolio orthogonalized to the market, as a novel way of classifying funds as insurance buyers or sellers. We find that low bear beta funds (insurance sellers) outperform high bear beta funds (insurance buyers) by 0.58% per month on average. The negative relation between bear beta and future hedge fund returns is not subsumed by a large set of fund characteristics and risk exposures. Consistent with a risk-based explanation, this relation remains negative during market crashes but turns positive during periods of increasing bear market concerns.