Eureka Case 28 min Undergrad

The Duration Gap

You're the chief risk officer at a bank in Lima. The portfolio is full of government bonds and long-term mortgage loans —assets of the highest credit quality. The board sleeps soundly: "we don't hold junk, we hold sovereign debt." But those 7-year assets are funded with deposits that reprice within months. If rates rise, the bank loses value through a door nobody on the board is watching.

The situation

The bank has S/1,000M in assets with a 7-year duration (long-term bonds and loans) and S/900M in liabilities with a 1-year duration (short-term deposits). Equity is S/100M. That difference —assets react far more than liabilities to a change in rates— is the duration gap. When rates rise, the value of the long assets falls sharply while deposits barely move: the entire loss lands on equity.

Here's the trap keeping the board calm. Credit quality is not the same as interest-rate risk. A sovereign bond doesn't default, but its price falls when rates rise just like any other long bond. A duration mismatch funded short-term is a huge bet that rates won't rise —and a 200-basis-point increase can wipe out the bank's equity even if every asset is AAA. It's the risk that, mismanaged, sank so many savings institutions.

Your job in this case: measure how much equity the bank loses in a rate increase depending on how much of the duration gap you hedge, and decide what to do. The question isn't whether the assets are good, but whether the bank is betting on rates without knowing it.

The decision

What do you do with the gap?

  • A · Leave it: they're government bonds, it's "safe"
  • B · Extend duration to earn more carry
  • C · Hedge the gap with swaps/futures and immunize

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