Duration: a measure of a bond's interest rate risk

Duration shows how much a bond will rise or fall in price when interest rates change. The higher the duration, the more sensitive the price and the greater the risk (and the potential).

Section: Bonds · Updated July 18, 2026

What duration is

Formally, Macaulay duration is the weighted-average time until you receive all of a bond's payments, where the weights are the shares of each payment's present value. It is measured in years. Intuitively: how many years it takes, "on average", for your invested money to come back to you including coupons.

Its practical value lies elsewhere: duration is a universal measure of interest rate risk. A bond with a duration of 5 years is twice as sensitive to rates as a bond with a duration of 2,5 years.

Formulas

Macaulay duration is the present-value-weighted time until payments:

D = Σk tk · CFk / (1 + y)tkP tk — time until payment k.   CFk — coupon or redemption.   y — yield (YTM).   P — current price (sum of discounted flows).

Modified duration translates this into price sensitivity:

Dмод = D1 + y / m m — number of coupon payments per year.

And the key practical rule — an estimate of the price change when the rate shifts by Δy:

ΔP / P ≈ − Dмод · Δy

Example

A bond has a modified duration of 3,5. If the market rate rises by 1 percentage point (Δy = +0,01), the bond's price will change by approximately:

ΔP / P ≈ −3,5 × 0,01 = −3,5%

And conversely: if the rate falls by 1 pp, the price will rise by approximately 3,5%. That is why, when rates are expected to fall, investors lengthen duration, and when a rise is expected, they shorten it.

How Firewire calculates it

Firewire builds a schedule of future payments for each bond (coupons, amortization, redemption), discounts them at YTM, and computes Macaulay duration and modified duration. This helps assess the interest rate risk of both an individual position and the bond portion of the portfolio as a whole.

Duration is a linear approximation. For large rate changes its accuracy declines (convexity comes into play), but for assessing risk in practice duration is usually sufficient.

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