Modified duration

What it means

The approximate percentage change in a bond’s price for a one percentage point change in yield.

The exam angle

A linear approximation. It always overstates the loss from a rise in yields and understates the gain from a fall, because the true relationship is convex.

Where it appears in the syllabus

• Fixed IncomeCFA Level I · exam weight 11–14% · Pricing, yield measures, duration, convexity, credit spreads.
• Valuation & Risk ModelsFRM Part I · exam weight 30% · VaR and ES, option valuation, bond risk, stress testing, credit and op risk.

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

• ConvexityThe curvature of the price–yield relationship — how duration itself changes as yields move.
• DurationThe sensitivity of a bond’s price to a change in yield, and equivalently the weighted average time to receiving its…
• 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.
• Yield curveThe relationship between yield and maturity for bonds of the same credit quality.
• Yield to maturityThe single discount rate that equates a bond’s price to the present value of its cash flows.