Duration

Two related quantities share the name. Macaulay duration is the average time until a bond's cash flows are received, weighted by the present value of each, and is quoted in years. Modified duration converts that into a sensitivity: the approximate percentage change in the bond's price for a change of one percentage point in its yield. When a desk says duration without qualifying it, the second is usually what is meant.

The drivers are intuitive once the definition is read carefully. A longer time to maturity pushes the cash flows further out and raises duration. A larger coupon returns more of the money sooner and lowers it. A zero coupon bond has a single cash flow at the end, so its Macaulay duration equals its remaining life exactly, which is the cleanest case and the one worth holding as a reference.

Duration is a straight line approximation to a curved relationship, and that is its limit. The true price and yield curve is convex, so duration alone overstates the loss on a large rise in yields and understates the gain on a large fall; convexity is the second order term that corrects it, and it matters most for long dated bonds and big moves. Duration for a portfolio is the weighted average of the durations of its holdings.

The concept reaches well beyond bond desks. Rate expectations move the whole yield curve, and long duration assets are the ones repriced most by that movement, which is the mechanism behind the observation that the shares of companies whose profits sit far in the future react hardest to a change in rates.