Under the model presented in the note, the optimal capital ratio under a risk‑sensitive requirement is a concave function of the risk of a bank’s assets. Because the risk is distributed uniformly on [0,1], Jensen’s inequality implies that the expected value of a concave function of risk is lower than the concave function applied to the expected risk. As a result, the average capital ratio that a bank would maintain under a risk‑based requirement is smaller than the flat ratio that would result from a simple leverage (risk‑insensitive) requirement. In other words, a bank would hold a smaller capital ratio when the requirement is risk‑sensitive than when it is based on a single leverage rule.
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https://www.federalreserve.gov/econres/notes/feds-notes/Outlining-and-measuring-the-benefits-of-risk-sensitivity-in-bank-capital-requirements-20250328.html
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