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IBBC CAPITAL ACADEMY / 2027

Effective, key-rate and empirical duration

Independent IBBC Capital draft content for self-study. Not affiliated with or endorsed by CFA Institute. New lessons await subject-matter review. No CFA designation or official PSM credit is awarded.

Learning goals

  • Explain changing cash flows using mechanisms and limitations.
  • Explain curve shape using mechanisms and limitations.
  • Explain model versus observations using mechanisms and limitations.

Draft · approximately 25 minutes, excluding further revision.

Changing cash flows

Effective duration reprices a security under benchmark-curve shocks while allowing modelled cash flows to respond, making it useful for embedded-option instruments.

A callable bond may lose upside sensitivity as rates fall and refinancing becomes attractive; fixed promised-cash duration can misstate this response.

Curve shape

Central effective duration uses (Pdown−Pup)/(2P0Δcurve); specify the shock size and option model to make the measure reproducible.

Key-rate duration isolates sensitivity at a curve node using a defined interpolation and other nodes held fixed; it can reveal twists hidden by parallel duration.

Model versus observations

Empirical duration estimates observed price sensitivity from data, while analytical duration derives from a pricing model; credit–rate correlations can make results differ.

Effective convexity and scenario analysis complement effective duration; neither removes uncertainty in volatility, exercise behavior or the chosen curve.

Formula and assumptions

Deff=(P−−P+)/(2P0Δcurve)

Original applied case: Effective, key-rate and empirical duration

  1. P0=100, curve-down price=101.8, curve-up price=98.4 for symmetric 0.005 shocks.
  2. Effective duration=(101.8−98.4)/(2×100×0.005)=3.4.
  3. The estimate belongs to that shock and model; it need not stay 3.4 after a large rate move.

Errors to catch

  • Do not assume: Embedded options leave cash flows fixed in every rate scenario.
  • Do not assume: A callable bond has unlimited upside when rates fall.
  • Do not assume: Effective duration needs no repricing scenarios.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.