Convexity
The curve in the price–yield relationship that duration's straight line misses. For an ordinary bond it always favours the holder, so it is priced.
Where you will meet it
Convexity appears in 21 learning outcomes on the CFA syllabus. A few of them:
- Explain how price moves against yield and why bonds trade at a premium or discount
“Convexity is a benefit to the holder, which is why a duration-based estimate always understates the price of an option-free bond.”
- Contrast the effective convexities of straight, callable and putable bonds
“Effective convexity is (PV₋ + PV₊ − 2 × PV₀) ÷ (ΔCurve² × PV₀).”
- Explain sensitivity and scenario risk measures and weigh them against VaR
“Sensitivity measures show how value changes for a small move in one risk factor: beta for equity markets, duration and convexity for interest rates, delta, gamma and vega for options.”
- Assess ways of funding one future liability with a bond portfolio
“The bond portfolio's market value must at least equal the liability's present value, its Macaulay duration must equal the time to the payment date, and its convexity should be as low as possible while still exceeding the liability's.”
Learn it properly
- Duration and convexity explained: how far a bond price moves
- How to memorise CFA formulas: understand them first, then make them automatic
- Bond price, yield and duration calculator
Practise it
Practise convexity until it is automatic: questions that explain every wrong option.
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