Duration

Definition

Duration measures a bond’s interest-rate sensitivity. It estimates how much the price will change when yields change.

• Macaulay Duration (years): time-weighted average of cash flows.

• Modified Duration (no units): price sensitivity; Price % change ≈ −(Modified Duration × Δyield).

Key Takeaways

• Longer maturity and lower coupon → higher duration (more sensitive).

• Higher yield → lower duration.

• Use Modified (or Effective) duration for risk; Macaulay is mainly a stepping stone.

• Approx rule: if Modified Duration = 5.2, a +1.00% move in yields ≈ −5.2% price move.

Types

• Macaulay Duration: cash-flow timing measure (years).

• Modified Duration: Macaulay ÷ (1 + yield per period).

• Effective Duration: model-based; use for bonds with options (callable/puttable).

Nigeria Example (illustrative)

FGN bond with ~8 years left, 13% coupon. If its Modified Duration ≈ 5.2, then a +100 bps rise in market yield implies about −5.2% price change (all else equal).

Common Pitfalls

• Comparing durations without standardising yield compounding/frequency.

• Using Macaulay instead of Modified/Effective for price sensitivity.

• Ignoring convexity (duration is a first-order estimate).

Mini-FAQ

• Is duration the same as maturity? No—maturity is a date; duration is rate sensitivity.

• Why does high coupon reduce duration? More cash comes earlier, so price is less sensitive.

• Which one should I quote? For risk, use Modified (or Effective if options).

Related Terms

Yield to Maturity (YTM) · Convexity · Coupon · Clean Price · Dirty Price · Yield to Call (YTC)