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Duration, convexity and rate sensitivity
Updated 4 August 2026 · 4 min read · 16 Contents
Plain-language meaning
Duration, convexity and rate sensitivity means examining contractual debt cash flows, prices, yields, interest-rate sensitivity, credit evidence and deposit terms with the identity, period, unit, source and limitations kept visible. It is a disciplined way to describe evidence, not a shortcut to an investment conclusion.
Learning objectives #
After this chapter you should be able to define duration, convexity and rate sensitivity, identify the evidence needed to use it, distinguish a reported zero from unavailable evidence, and explain why unlike instruments or periods may not be comparable.
Prerequisites #
Read “Clean price, dirty price and accrued interest” first. Be comfortable checking an exact listing or instrument, its source, observation date, native currency and unit. When any one of those is unknown, pause the comparison and record the gap.
Core concept #
Duration approximates first-order rate sensitivity; convexity refines curvature for larger changes. Preserve raw facts separately from interpretation, and retain the denominator, time window, classification rule and provenance that make the evidence reproducible.
Method #
For duration, convexity and rate sensitivity, first identify the exact evidence named in this chapter: Duration approximates first-order rate sensitivity; convexity refines curvature for larger changes. Then freeze identity and period, collect source-backed inputs with units, calculate or classify only compatible evidence, and record contrary facts and unavailable fields.
Where it appears in XMarketRadar #
Use fixed-income research and source documents. Some instruments lack reliable current pricing, so the concept may be educational-only when licensed evidence is absent. A displayed field is useful only with its source and as-of context. If XMarketRadar does not calculate this chapter’s concept directly, use the chapter as an educational checklist and retain the supporting primary document or screen URL in the research workspace.
Worked example #
Modified duration 4.2 estimates about -4.2% for a +1 percentage-point yield move before convexity. Module context: Illustrative bond has face value CU 1,000, 5% annual coupon paid semi-annually, 31-Dec-2030 maturity, Actual/Actual day count and 4% annual yield compounded semi-annually; each CU 25 coupon is contractual subject to issuer payment. This is an illustrative audit trail, not live data, a target or an expected outcome.
Interpretation #
Interpret the result in the direction defined by the field, not by an assumed desirable outcome. Higher, lower, positive and negative can each have different meanings by context. Compare the observation with its own history or a compatible benchmark, and label conclusions as observations, interpretations or user decisions.
Limitations and common mistakes #
Using duration as an exact forecast for large rate moves. Yield is not a promised return: default, calls, reinvestment, taxes, accrued interest, illiquidity and model assumptions can change the realized result. A precise calculation can still mislead when the source is stale, the denominator changed, or a classification hides important detail.
Market and jurisdiction differences #
Government and corporate conventions, day counts, settlement, clean/dirty quoting, rating scales and deposit guarantees differ by market and instrument. Exchange rules, accounting conventions, calendars, taxes, disclosure timing, quote scale and licensed coverage can differ. Verify the current primary source for the relevant venue; registry support alone does not prove that every field is available.
Key takeaways #
For duration, convexity and rate sensitivity, remember this boundary: Using duration as an exact forecast for large rate moves. Keep the evidence exact, dated and source-backed; publish missing information as unavailable rather than manufacturing a value.
Practice #
Reproduce this historical scenario from source-labelled inputs: Modified duration 4.2 estimates about -4.2% for a +1 percentage-point yield move before convexity. Then change one input, preserve the original period and unit, and explain whether the result changes or becomes unavailable. Write the identity, source, date, unit and failure condition, then state exactly what would display as —.
Knowledge check #
Reveal answer and explanation
Question: which mistake would invalidate a review of duration, convexity and rate sensitivity? Answer: Using duration as an exact forecast for large rate moves. Explanation: the chapter requires the stated identity, period, unit and compatible evidence; a missing required input remains — rather than 0.
Educational use only #
This chapter is descriptive education, not investment advice, a forecast, a recommendation, a suitability assessment or an instruction to buy, sell, rebalance, trade or place an order. XMarketRadar’s broker connections remain read-only.