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FRM Part II · FRM Exam Part II · Capital Structure in Banks

A bank has equity of USD 8 billion against assets of USD 100 billion, with a return on assets of 0.80% and a pre-tax cost structure unchanged by leverage. Management plans to buy back equity and raise deposits so that equity falls to USD 5 billion with assets unchanged and ROA still 0.80%. What is the change in ROE and the main risk implication?

Net income of USD 0.8 billion gives ROE of 10% on USD 8 billion equity and 16% on USD 5 billion. Higher leverage boosts ROE but thins the loss-absorbing buffer, so the bank's probability of insolvency increases even though ROA is unchanged.

  1. AROE rises from 10% to 16%, and the probability of insolvency rises because the loss buffer shrinksCorrect
  2. BROE rises from 10% to 16%, and risk is unchanged because ROA is unchanged
  3. CROE rises from 8% to 10%, and the probability of insolvency falls
  4. DROE is unchanged at 10% because net income is unchanged

Explanation

Net income = 0.8% × 100 = USD 0.8 billion. ROE before = 0.8/8 = 10%; after = 0.8/5 = 16%. Equity falling from 8% to 5% of assets means a smaller loss absorption cushion, so a given asset loss more easily wipes out equity. Constant ROA does not mean constant risk.

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