By the FinLingo Team | Capital markets practitioner, front office experience at a major European investment bank. FinLingo covers 342 lessons from bonds to exotic derivatives. About · Last updated:
Duration measures a bond's sensitivity to interest rate changes. In its simplest interpretation: a bond with duration of 5 years will lose approximately 5% of its value if interest rates rise by 1%. It is the single most important risk metric in fixed income.
Macaulay duration is the weighted average time to receive a bond's cash flows, where the weights are the present values of each cash flow. A 5-year bond paying a 4% coupon with a yield of 5% has a Macaulay duration of approximately 4.45 years — less than 5 because the coupons arrive before maturity, pulling the average earlier. A zero-coupon bond's duration equals its maturity exactly.
Modified duration converts Macaulay duration into a direct price sensitivity measure: D_mod = D_mac / (1 + y/n), where y is the yield and n is the compounding frequency. Modified duration tells you the percentage price change per 1% change in yield. For the bond above: D_mod = 4.45 / 1.025 = 4.34. A 1% rate rise causes a 4.34% price decline.
DV01 (Dollar Value of a Basis Point) is the dollar price change for a 1 basis point (0.01%) move in yield. For a $1 million bond with modified duration 4.34: DV01 = $1,000,000 × 4.34 × 0.0001 = $434. Every basis point costs $434. This is the metric traders use daily because it translates duration into money.
Three factors. Maturity: longer maturity means higher duration. Coupon: higher coupon means lower duration (more cash flows arrive earlier). Yield: higher yield means lower duration (future cash flows are discounted more heavily, reducing their weight). A zero-coupon 30-year bond has the highest duration of any standard bond — it is pure rate exposure.
Duration tells you how much a bond price will move when interest rates change. A duration of 5 means the bond loses roughly 5% if rates rise by 1%, and gains 5% if rates fall by 1%. Higher duration means more sensitivity to rates. It is the primary risk measure for any fixed income portfolio.
Macaulay duration is the weighted average time to receive a bond cash flows, measured in years. Modified duration divides Macaulay duration by (1 + yield per period) to produce a direct price sensitivity measure. Macaulay tells you when you get your money back on average. Modified tells you how much the price moves per unit change in yield.
Because all its cash flow comes at maturity. There are no intermediate coupons to pull the weighted average earlier. A 10-year zero-coupon bond has a Macaulay duration of exactly 10 years, while a 10-year bond with a 5% coupon has a duration of roughly 8 years. The coupons reduce duration by delivering cash flow before maturity.
FinLingo covers duration, convexity, and bond pricing in Level 1 — 9 units on fixed income fundamentals. Completely free.
Start Free