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IBBC CAPITAL ACADEMY / 2027

Convexity and aggregate bond exposures

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 curvature using mechanisms and limitations.
  • Explain price approximation using mechanisms and limitations.
  • Explain portfolio aggregation using mechanisms and limitations.

Draft · approximately 25 minutes, excluding further revision.

Curvature

Convexity describes curvature in the price–yield relation and supplements duration’s tangent approximation; conventional option-free bonds normally have positive convexity.

The second-order percentage approximation is −DΔy+0.5C(Δy)² when duration and convexity share the same yield convention.

Price approximation

Positive convexity raises estimated price relative to the linear prediction for both up and down yield moves, holding cash flows and convention fixed.

Market-value-weighted duration and convexity can summarize a bond portfolio for common parallel yield changes; book-value weights answer a different question.

Portfolio aggregation

Different yield curves, spread shocks and derivatives require consistent risk units; weighted averages can conceal offsetting maturities and basis risks.

A second-order approximation improves many small-to-moderate shock estimates but is not exact full repricing, especially with embedded options or large shocks.

Formula and assumptions

ΔP/P≈−DΔy+½C(Δy)²; Dportfolio=ΣwiDi

Original applied case: Convexity and aggregate bond exposures

  1. Use modified duration 5, convexity 40 and yield rise 0.01 under matching conventions.
  2. Approximate return=−5×0.01+0.5×40×0.01²=−0.048.
  3. Estimated price drop is 4.8% versus the duration-only 5%; no credit shock was included.

Errors to catch

  • Do not assume: Convexity is just another name for coupon rate.
  • Do not assume: The convexity term is linear in yield change.
  • Do not assume: Positive convexity lowers price versus the tangent for both directions.

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.