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FRM Part I · FRM Exam Part I · Anatomy of the Great Financial Crisis of 2007-2009

A bank has $50 billion of assets funded by $47.5 billion of liabilities and $2.5 billion of equity. Suppose the assets fall in value by 3%. Assuming liabilities are unchanged, what is the approximate leverage ratio (assets/equity) before the decline and the percentage fall in equity?

Leverage is 20 (50/2.5). A 3% asset decline is a $1.5 billion loss, which is absorbed entirely by equity, reducing it from $2.5 billion to $1.0 billion, a 60% fall. High leverage magnifies small asset declines into large equity losses.

  1. ALeverage of 20 and equity falls by 60%Correct
  2. BLeverage of 19 and equity falls by 57%
  3. CLeverage of 20 and equity falls by 3%
  4. DLeverage of 20 and equity falls by 30%

Explanation

Leverage = 50/2.5 = 20. Asset loss = 3% x 50 = 1.5 billion. Equity falls from 2.5 to 1.0, a 60% decline (1.5/2.5). Choosing 3% ignores leverage; 30% or 57% reflect arithmetic errors.

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