I construct a systemic liquidity risk index (SLRI) from data on violations of arbitrage relationships across several asset classes between 2004 and 2010. Then I test whether the equity returns of 53 global banks were exposed to this liquidity risk factor. Results show that the level of bank returns is not directly affected by the SLRI, but their volatility increases when liquidity conditions deteriorate. I do not find a strong association between bank size and exposure to the SLRI - measured as the sensitivity of volatility to the index. Surprisingly, exposure to systemic liquidity risk is positively associated with the Net Stable Funding Ratio (NSFR). The link between equity volatility and the SLRI allows me to calculate the cost that would be borne by public authorities for providing liquidity support to the financial sector. I use this information to estimate a liquidity insurance premium that could be paid by individual banks in order to cover for that social cost.