Bond Duration Calculator

What Is Bond Duration? Duration measures a bond’s sensitivity to interest rate changes. It represents the weighted average time until all cash flows are received, with weights proportional to the present value of each cash flow. A higher duration means the bond’s price is more sensitive to rate changes.

Macaulay Duration Developed by Frederick Macaulay in 1938 in the United States, this measures the weighted average time to receive all cash flows. For a bond paying annual coupons: D_Mac = Sum of [t * PV(CF_t)] / Bond Price. Where t is the time period and PV(CF_t) is the present value of the cash flow at time t.

Modified Duration Modified Duration adjusts Macaulay Duration for the yield: D_Mod = D_Mac / (1 + y/n). Where y is the yield to maturity and n is the number of coupon payments per year. Modified Duration directly estimates the percentage price change: dP/P = -D_Mod * dy. For example, if Modified Duration is 5 and rates rise by 1%, the bond price falls approximately 5%.

Convexity Duration gives a linear approximation of price change, but bond prices actually follow a curved relationship with yields. Convexity measures this curvature. Higher convexity means the bond price rises more than expected when rates fall and falls less than expected when rates rise. Both of those work in your favour, which is why bond managers pay for convexity.

Worked Example A $1,000 face value bond, 5% annual coupon, 10 years to maturity, yielding 4%:

• Price (present value of all cash flows) = $1,081.11, a premium, because the coupon beats the market yield
• Macaulay Duration = 8.19 years
• Modified Duration = 8.19 ÷ 1.04 = 7.88
• Convexity = 77.48
• If rates rise 1%, duration alone predicts a −7.88% price move
• Adding the convexity term softens that to −7.49%

That gap between −7.88% and −7.49% is the whole point of convexity. Duration is a straight line drawn against a curve, and the further rates move the more the straight line overstates your loss. On a small move it hardly matters. On a 3% move it matters a great deal.

Practical Rules Longer maturity means higher duration. Lower coupon means higher duration. Zero-coupon bonds have Macaulay Duration equal to their maturity, which is worth checking here: set the coupon to 0 and the duration comes back as exactly the years you entered. Lower yield means higher duration. Bond portfolio managers use duration to manage interest rate risk.