The United Kingdom established the Pension Protection Fund (PPF) in 2005 to guarantee defined benefit pensions. We model the PPF and show that it is likely to face many years of low claims interspersed irregularly with periods of very large claims. There is a significant chance that these claims will be so large that the PPF will default on its liabilities, leaving the Government with no option but to bail it out. The cause of this problem is the double impact of a fall in equity prices on the PPF: it makes sponsor firms more likely to default, and it makes defaulted plans more likely to be underfunded. We use our model to derive a fair premium for PPF insurance under different circumstances, to estimate the extent of cross-subsidies in the PPF between strong and weak sponsors and to show that risk rated premiums are unlikely to have a substantial effect on either the size or the lumpiness of claims unless they are so powerful that they force weaker sponsors to cut fund deficits and improve the match between assets and liabilities.