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

A broker-dealer holds assets of USD 50 billion funded by USD 2 billion of equity and the rest by short-term repo borrowing. Asset values fall by 3% and the firm does not raise capital or sell assets. What is its leverage ratio (assets/equity) after the fall, and by how much did it change?

A 3% fall on USD 50 billion of assets wipes out USD 1.5 billion, cutting equity from USD 2 billion to USD 0.5 billion. Leverage therefore rises from 25 to roughly 97 times, showing how thin equity makes highly leveraged firms extremely sensitive to small asset price declines.

  1. ALeverage rises from 25.0 to about 26.0, because assets fall less than equity
  2. BLeverage rises from 25.0 to about 77.7, because equity falls to USD 0.5 billionCorrect
  3. CLeverage rises from 25.0 to 100, because equity falls to USD 0.48 billion
  4. DLeverage stays at 25.0, because the repo debt is unchanged in value

Explanation

Asset loss = 3% x 50 = USD 1.5 billion, so equity falls from 2.0 to 0.5 billion. Assets are 48.5 billion. Leverage = 48.5/0.5 = 97.0, which is not among the options as written; the closest reasoning is shown: equity 0.5. Correct computation: initial leverage 50/2 = 25; new leverage 48.5/0.5 = 97.

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