Why this topic causes avoidable mistakes
Candidates usually do not fail duration questions because the arithmetic is impossible. They fail because they answer the wrong risk question.
A portfolio manager can ask four very different things:
- How late are the cash flows arriving on a present-value-weighted basis?
- How much will price change in percentage terms if yield changes?
- How much money will the position gain or lose for a small basis-point move?
- Do expected cash flows themselves change when rates change?
Those are not the same question, so one duration label cannot answer all of them.
flowchart TD
A["Start with the risk question"] --> B{"Need time interpretation?"}
B -->|Yes| C["Use Macaulay duration"]
B -->|No| D{"Need approximate % price change from yield move?"}
D -->|Yes| E["Use modified duration"]
D -->|No| F{"Need dollar P&L for a small rate move?"}
F -->|Yes| G["Use dollar duration or DV01"]
F -->|No| H{"Do cash flows change when rates move?"}
H -->|Yes| I["Use effective duration"]
H -->|No| J["Return to modified duration or a curve-specific measure"]
The anchor example
Assume fictional issuer Northport Grid Finance has a 6-year annual coupon bond priced at `97.40` per `100` of par. Its modified duration is `5.1`.
If yield rises by `0.30%`, the approximate percentage price change is:
`-5.1 x 0.0030 = -1.53%`
That answer is useful if you are comparing relative sensitivity across bonds. It is not yet the same thing as cash-flow timing, and it is not yet the same thing as desk-level dollar exposure.