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101 Concepts for the Level I Exam

Essential Concept 68: Duration


Effective duration indicates the sensitivity of a bond’s price to a 100-bps parallel shift of the benchmark yield curve in particular, the government par curve; assuming no change in the bond’s credit spread.

\mathrm{Effective\ duration=\ }\frac{\left(\mathrm{P}{\mathrm{V}}_{\mathrm{-}}\right)\mathrm{-}\mathrm{(}{\mathrm{PV}}_{\mathrm{+}}\mathrm{)}}{\mathrm{2\ x\ }\left(\mathrm{\Delta }\mathrm{Curve}\right)\mathrm{\ x\ (}{\mathrm{PV}}_{\mathrm{o}}\mathrm{)}}

 

The flowing procedure is used to apply this formula in practice.

  1. Given a price (PV0), calculate the implied OAS to the benchmark yield curve at appropriate interest rate volatility.
  2. Shift the benchmark yield curve down, generate a new interest rate tree, and then revalue the bond using the OAS calculated in Step 1. This value is PV.
  3. Shift the benchmark yield curve up by the same magnitude as in Step 2, generate a new interest rate tree, and then revalue the bond using the OAS calculated in Step 1. This value is PV+.
  4. Calculate the bond’s effective duration.

The following figure compares the effective duration of option-free, callable and putable bonds.


Concept 31

The effective durations of various types of instruments are shown in the table below.

Type of Bond Effective Duration
Cash 0
Zero-coupon bond ≈ Maturity
Fixed-rate bond < Maturity
Callable bond ≤ Duration of straight bond
Putable bond ≤ Duration of straight bond
Floater (Libor flat) ≈ Time (in years) to next reset