Duration
What is Duration?
Duration is a cash-flow-weighted measure of a bond's interest-rate exposure and, depending on the form used, a measure of approximate price sensitivity.
Macaulay duration
Macaulay duration is the weighted average time to receive a bond's discounted cash flows, measured in years. Weights are each cash flow's share of present value. It is shorter than maturity for a conventional coupon bond because coupons arrive before principal, and equals maturity for a standard zero-coupon bond.
Duration and price sensitivity
Modified duration translates Macaulay duration into an approximate percentage price change for a small yield movement. Practitioners often use the shorter word duration when they mean modified or effective duration, so reports must label the measure. Effective duration is commonly used when cash flows change with rates because of embedded options.
Example
A ten-year coupon bond might have Macaulay duration of eight years and modified duration near 7.8. The latter implies an approximate 7.8% price decline for a one-percentage-point yield rise, before convexity. The bond still matures in ten years; duration is not simply the time remaining until principal repayment.
How to interpret it
Higher duration generally means greater sensitivity to yield changes. Compare duration by currency and reference curve, and separate government-rate duration from credit-spread duration where possible. Portfolio duration is an aggregated local measure; opposing exposures at different maturities can produce the same total while responding differently to a nonparallel yield-curve shift.
Limitations
Duration is a local approximation and becomes less accurate for large moves. Standard forms assume fixed cash flows and a parallel yield shift. Calls, prepayments, and options make cash flows rate-dependent and can change duration sharply. Duration says nothing by itself about default, liquidity, inflation, currency, or the expected direction of rates.
Practical checklist
Name the duration definition, yield curve, currency, valuation date, and bump size. Reconcile security and portfolio measures, calculate key-rate duration for curve shape, and add convexity for larger moves. Use effective duration for option-sensitive instruments and test explicit scenarios. Match the measure to the portfolio's liabilities, benchmark, and actual decision horizon. Preserve source methodology so every change can be clearly explained and independently reproduced.
Also known as: Macaulay duration
Sources and further reading
- Investor Bulletin: Interest Rate Risk, Investor.gov, U.S. Securities and Exchange Commission