Imagine a bank subject to both traditional capital requirements (using capital ratios) and a leverage ratio requirement (using the debt-to-assets ratio). The bank is currently considering transactions that will keep the total value of its assets constant. However, these transactions will reduce the share of cash and safe assets and increase the share of risky mortgages on the bank’s balance sheet. These assets have different risk weights for the purposes of banking regulation. The bank is analyzing how these transactions will affect the minimum dollar amount of equity capital required under each of the previous regulations. In this context, consider the following statements about the effects of these changes in the bank’s balance sheet. Which statement is correct?

Question

BlackTom AI · Accepted Answer

Risk-weighted capital rules measure required equity as a percentage of risk-weighted assets (RWA), while a leverage-ratio requirement sets required equity as a percentage of total assets. These distinct bases drive the conclusion.

1) Knowledge points and concepts
- Traditional (risk-based) capital requirement: required equity E_risk = k × RWA, where k is the required capital ratio and RWA = sum(asset_i × weight_i).
- Leverage-ratio requirement: required equity E_leverage = ℓ × A, where ℓ is the leverage ratio minimum and A is total assets (unweighted).
- Safe assets (cash, government securities) typically have low or 0% risk weight; risky mortgages have higher risk weights (e.g., 50–100%).

2) Step-by-step reasoning with intermediate steps
- Let A = total assets (constant). Let s and r be the shares of safe and risky assets (s + r = 1).
- Let w_s be the risk weight of safe assets and w_r the risk weight of risky mortgages, with w_r > w_s.
- Initial RWA_initial = A × (s0·w_s + r0·w_r).
- After the transactions s1 < s0 and r1 > r0, so RWA_new = A × (s1·w_s + r1·w_r).
- Because r1 − r0 > 0 and w_r − w_s > 0, RWA_new − RWA_initial = A × (r1 − r0) × (w_r − w_s) > 0. So RWA increases.
- Required equity under risk-based rule: E_risk_new = k × RWA_new > k × RWA_initial = E_risk_initial. Thus the bank must hold more equity under the traditional requirement.
- Required equity under leverage rule: E_leverage = ℓ × A. A is unchanged, so E_leverage is unchanged.

3) Why the correct answer is correct
Because shifting composition toward higher-risk assets raises RWA and therefore the dollar amount of equity needed under a risk-weighted capital rule, while the leverage-rule requirement depends only on total assets (unchanged), so its required equity stays the same.

4) Why other options are incorrect (brief)
- “Not enough information”: incorrect — risk weights and direction of shift (toward riskier assets) are sufficient.
- “Both unchanged” or “leverage needs more equity”: incorrect because RWA clearly rises and leverage-required equity depends only on total assets.
- “Both need more equity”: incorrect because leverage-required equity does not change when total assets are constant.

Conclusion: The bank will need more equity to satisfy the traditional capital requirement, while the equity required by the leverage ratio requirement will not change. This matches the provided answer.

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