What the Same Shock Does to Regional-Bank Earnings and Capital

The subject here is not merely whether regional banks have different regression coefficients; it is what those coefficients do to a stress path. The specific question is how lower aggregate sensitivity and higher persistence alter projected earnings, loan losses, and capital when regional banks face the same severe macroeconomic scenario as large banks. The answer helps a reader distinguish a model-based change in the projected path from a claim that regional banks are safe under every shock.

A coefficient is a response pattern, not a safety score

A regression coefficient measures how an outcome has moved with a variable in the estimated relationship. In this setting, a lower coefficient on a Treasury yield means that the modeled outcome changes less, in the short run, when that aggregate rate variable changes by the same amount. It does not mean that the bank has no interest-rate risk, nor does it describe the level of earnings or capital before the shock.

The Federal Reserve’s illustrative comparison makes the difference visible. For interest income, the coefficient on the three-month Treasury yield was 0.255 in the all-bank model and 0.184 in the regional-bank model. For interest expense, it was 0.207 and 0.156. The p-value for each comparison was 0.001. The term-spread coefficients showed the same direction: 0.124 versus 0.0841 for interest income, and 0.0367 versus 0.0249 for interest expense, again with p-values of 0.001.

These values are not percentages of assets and should not be read as a direct forecast of dollars. They are estimated response parameters attached to particular equations and variables. Their usefulness is comparative: holding the model setup and the rate path constant, the regional-bank equations imply a smaller immediate movement in these interest-income and interest-expense components than the all-bank equations.

The scale and sign of a coefficient also depend on the variable and equation to which it belongs. A rate coefficient for interest income is not interchangeable with a coefficient for a net charge-off rate. Nor does a statistically different coefficient by itself tell us how much capital a bank will have at the end of a scenario. The model must combine that parameter with the starting level of the outcome, the path of the variable, past values, and the other equations that feed the projection.

The business model gives that statistical pattern an economic interpretation. Regional banks’ greater reliance on low-cost deposits and longer-duration, often fixed-rate assets can slow the pass-through of a short-term rate change to both sides of the balance sheet. A large bank with more wholesale funding, capital-markets activity, or short-term commercial lending may adjust differently. The regional coefficient therefore captures a historical response pattern associated with a different mix of assets and liabilities; it is not a universal property of every institution in the asset band.

The word “short-run” matters. The study reports that many of the differences remain economically and statistically meaningful when long-run multipliers are considered, but a long-run response is not the same as an immediate response.