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FRM Part I · FRM Exam Part I · The Building Blocks of Risk Management

A bank has total assets of 100 billion USD, with equity of 5 billion USD. Asset values fall by 2% and the bank takes no other action. Another bank has 10 billion USD of equity on the same 100 billion asset base and suffers the same loss. Which statement is correct?

The first bank's equity falls 40%, from 5 to 3 billion USD, after a 2 billion loss, and its leverage rises from 20 to roughly 32.7 to 33. Higher leverage magnifies the loss relative to equity, whereas the second bank loses only 20% of equity.

  1. AThe first bank's leverage ratio (assets/equity) falls from 20 to 19.6 and equity declines 40%
  2. BThe first bank's equity declines 40% and its leverage rises from 20 to about 33.3Correct
  3. CBoth banks' equity fall by 20%, so leverage is irrelevant
  4. DThe second bank's equity declines 40% and its leverage rises to 20

Explanation

A 2% loss is 2 billion USD. Bank 1 equity drops from 5 to 3 (a 40% fall); assets are 98, so leverage is 98/3 = 32.7, approximately 33 on the original 100 basis... computing exactly: 98/3 = 32.67. Bank 2 equity falls from 10 to 8 (20%). Leverage amplifies losses relative to equity, so the first bank is hit harder.

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