How does duration measure bond interest rate risk?

Duration is a summary measure that captures how sensitive a bond’s price is to changes in interest rates by weighting the timing of its cash flows. The original concept of duration was introduced by Frederick R. Macaulay Columbia University and measures the weighted average time until a bond’s cash flows are received. Practitioners more often use modified duration, described in fixed income literature by John C. Hull University of Toronto, because it directly links a small change in yield to an approximate percentage change in bond price. The approximate percentage change in price equals minus modified duration times the change in yield, making duration a practical proxy for interest rate risk.

How duration is calculated

Macaulay duration sums each cash flow multiplied by the time until it is received and divides by the bond price, producing a time measure in years. Modified duration adjusts Macaulay duration by dividing by one plus the yield per period, translating time into price sensitivity. This adjustment lets portfolio managers estimate that a bond with a modified duration of five will lose about five percent of its value if yields rise by one percentage point, all else equal. Because this is a linear approximation, accuracy declines when yield changes are large; convexity measures the curvature in the price-yield relationship and improves estimates for bigger moves, a point emphasized in John C. Hull University of Toronto’s treatments of fixed income risk.

Causes that change duration

Coupon size, maturity, and yield level are the main drivers of duration. Higher coupons accelerate cash flows and reduce weighted time, shortening duration. Longer maturities extend the timing of cash flows, increasing duration. At lower yields, duration usually increases because early cash flows are discounted less heavily relative to later ones. These relationships explain why the same maturity bond can have quite different interest rate risk profiles depending on coupon and market yields.

Practical implications and limitations

Duration is central to immunization strategies used by pension funds and insurance companies to match asset and liability sensitivity, a practice discussed in supervisory guidance from the Basel Committee on Banking Supervision Bank for International Settlements. For institutions, duration mismatches create funding and regulatory pressures when central bank policy shifts drive rapid rate changes. In emerging market economies, where rates and currency risks are often more volatile, duration management interacts with sovereign risk and capital flow dynamics, affecting local pension systems and household savings behavior. Environmental and territorial concerns emerge when long-term infrastructure bonds with green labeling have long durations, exposing climate-focused investments to shifts in policy rates and investor demand.

Consequences for investors and markets

Misreading duration can produce large mark-to-market swings and force selling into weak markets. Using duration appropriately requires attention to convexity, embedded options such as call features that change effective duration, and portfolio context. When combined with robust risk governance, duration gives a concise, evidence-based way to quantify and manage interest rate exposure.