How does duration connect market price risk and reinvestment risk?

Question

AcadiFi · Accepted Answer

The risk-offset interpretation is mainly tied to Macaulay duration for a plain fixed-rate bond.

When yields rise, the bond's price falls, but future coupon reinvestment becomes more attractive. When yields fall, the bond's price rises, but future coupons are reinvested at lower rates. Macaulay duration approximates the investment horizon where those two effects can offset each other.

```mermaid
flowchart LR
  A["Yields rise"] --> B["Price loss today"]
  A --> C["Higher coupon reinvestment"]
  B --> D["Holding return"]
  C --> D
  E["Yields fall"] --> F["Price gain today"]
  E --> G["Lower coupon reinvestment"]
  F --> H["Holding return"]
  G --> H
```

Modified duration is the price-sensitivity version. It answers a different question: how much should price change for a small yield change?

Use Macaulay duration for timing and horizon intuition. Use modified duration for first-order price sensitivity.

How does duration connect market price risk and reinvestment risk?

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