Convexity

What it means

The curvature of the price–yield relationship — how duration itself changes as yields move.

The exam angle

Positive convexity is good for the holder: prices rise more than duration predicts and fall less. Callable bonds and MBS exhibit negative convexity as rates fall.

Where it appears in the syllabus

• Fixed IncomeCFA Level I · exam weight 11–14% · Pricing, yield measures, duration, convexity, credit spreads.
• Fixed IncomeCFA Level II · exam weight 10–15% · Term structure dynamics, arbitrage-free valuation, embedded options, CDS.
• Valuation & Risk ModelsFRM Part I · exam weight 30% · VaR and ES, option valuation, bond risk, stress testing, credit and op risk.
• Market Risk Measurement & ManagementFRM Part II · exam weight 20% · VaR and ES estimation, backtesting, EVT, GARCH, copulas, FRTB.

See it worked through

• Duration and convexity: how good is the approximation?A ten-year bond repriced at four yield shocks, exactly and with the duration and convexity estimates.

There is also a short video: watch it on YouTube.

Related terms

• DurationThe sensitivity of a bond’s price to a change in yield, and equivalently the weighted average time to receiving its…
• Effective durationDuration measured by repricing the bond under small parallel shifts in the benchmark curve, so that changes in cash…
• Forward rateThe interest rate agreed today for borrowing or lending over a future period, implied by today’s spot curve.
• Spot rateThe yield on a single cash flow received at one future date, with no intervening coupons.
• Callable bondA bond the issuer may redeem early, usually when rates have fallen.
• Modified durationThe approximate percentage change in a bond’s price for a one percentage point change in yield.