Bank Capital & Leverage
Capital is the sliver of assets funded by the owners. Thinner capital lifts leverage and return on equity, but a fall in asset value burns through that cushion faster. How much loss can the bank absorb before it is insolvent?
Return on equity (ROE)
12.5%
ROA × leverage = 1.0% × 12.5
Capital after shock
8.0%
c − loss = 8.0% − 0.0%
Leverage
12.5×
Capital cushion
8.0%
Max loss before insolvency
8.0%
Leverage 12.5× turns a 1.0% return on assets into a 12.5% return on equity — but the same 12.5× means a loss above 8.0% of assets erases the owners' stake.
Try this: (1) drop capital to 2% and watch ROE soar while the survivable loss shrinks; (2) set the loss to 8% at the default 8% capital — the bank sits exactly at the insolvency edge; (3) raise capital to 12% and confirm the same 8% loss now leaves a positive cushion.
Reflect: If higher leverage always raises ROE, why do regulators force banks to hold minimum capital? Who bears the loss once capital is gone?