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IAI Actuarial Core Principles · Business Economics · Role, structure and stability of the financial system

A bank has Rs 1,000 crore of assets financed by Rs 50 crore of equity and Rs 950 crore of liabilities. The assets then fall in value by 4%. Ignoring any other changes, what happens to the bank?

Equity falls to Rs 10 crore. The 4% asset fall is a Rs 40 crore loss, which equity absorbs because liabilities are fixed, leaving assets of Rs 960 crore against liabilities of Rs 950 crore, so the bank survives but with a thin buffer.

  1. AEquity falls to Rs 10 crore and the bank stays solventCorrect
  2. BEquity falls to zero exactly, so the bank is just insolvent
  3. CEquity falls to Rs 40 crore because losses are shared with depositors
  4. DEquity is unchanged because liabilities are fixed in value
  5. Equity becomes negative at Rs 10 crore below liabilities, so the bank is insolvent

Explanation

A 4% fall on Rs 1,000 crore is a Rs 40 crore loss. Liabilities are fixed at Rs 950 crore, so equity absorbs the loss: 50 - 40 = Rs 10 crore. Assets are Rs 960 crore, above liabilities, so the bank remains solvent though highly stretched. This illustrates how leverage of 20 times magnifies small asset losses.

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