How Much Does a US Bank Failure Cost the Deposit Insurer? Loss Rates in 2,942 FDIC Resolutions, 1980-2026, an Exact Ratio-of-Sums Identity, Size Elasticities and Why the Average Failure Misleads

The cost of a bank failure to the deposit insurer is usually reported as a loss rate, the estimated cost divided by the failed bank's total assets. I use the FDIC's public list of failures to measure loss rates for 2,942 failures from 1980 to 2026 with a recorded cost. There are two natural averages. The ratio of total cost to total assets is 12.4%, while the mean of the individual loss rates is 25.5%. I prove that the gap equals the number of failures times the covariance between each failure's share of total assets and its loss rate, so the aggregate rate is below the mean rate exactly when large failures have lower loss rates. They do: the elasticity of cost with respect to assets is 0.847 (robust standard error 0.030) among failures with positive cost from 1986 to 2026, so the loss rate falls by about 1.4% for each 10% increase in size. Median loss rates are 22.3% for failures with assets under 100 million dollars and 6.2% for the 17 failures above 10 billion dollars. The aggregate loss rate fell from 19.5% in 1986 to 1994 to 10.1% in 2008 to 2013 and 6.8% in 2014 to 2026, but the median failure's loss rate was higher in 2008 to 2013 (23.5%) than in 1986 to 1994 (20.6%). The 2023 failures of Silicon Valley Bank, Signature Bank and First Republic, with 532 billion dollars of assets, pulled the recent aggregate down; without 2023 it is 14.8%. Beta distributions fitted by maximum likelihood overstate the share of failures with losses above half of assets in three of four periods.