Duration (finance)

In <a href="/facts/Finance/fLh1GgN8">finance</a>, the duration of a financial <a href="/facts/Asset/o7TARXhB">asset</a> that consists of fixed <a href="/facts/Cash_flows/TM2tHnlW">cash flows</a>, such as a <a href="/facts/Bond_(finance)/qlmpLj0k">bond</a>, is the <a href="/facts/Weighted_average/VHyJfPxb">weighted average</a> of the times until those fixed cash flows are received.
When the price of an asset is considered as a function of <a href="/facts/Yield_(finance)/aRohGR9L">yield</a>, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.
The dual use of the word "duration", as both the weighted average time until repayment and as the percentage change in price, often causes confusion. Strictly speaking, Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years. Modified duration is the name given to the price sensitivity. It is (-1) times the rate of change in the price of a bond as a function of the change in its yield.
Both measures are termed "duration" and have the same (or close to the same) numerical value, but it is important to keep in mind the conceptual distinctions between them. Macaulay duration is a time measure with units in years and really makes sense only for an instrument with fixed cash flows. For a standard bond, the Macaulay duration will be between 0 and the maturity of the bond. It is equal to the maturity if and only if the bond is a <a href="/facts/Zero-coupon_bond/tLBePUFS">zero-coupon bond</a>.
Modified duration, on the other hand, is a mathematical derivative (rate of change) of price and measures the percentage rate of change of price with respect to yield. Price sensitivity with respect to yields can also be measured in absolute (<a href="/facts/Dollar/Mp3qLdHp">dollar</a> or <a href="/facts/Euro/NWG2nlCx">euro</a>, etc.) terms, and the absolute sensitivity is often referred to as dollar (euro) duration, DV01, BPV, or delta (δ or Δ) risk). The concept of modified duration can be applied to interest-rate-sensitive instruments with non-fixed cash flows and can thus be applied to a wider range of instruments than can Macaulay duration. Modified duration is used more often than Macaulay duration in modern finance.
For everyday use, the equality (or near-equality) of the values for Macaulay and modified duration can be a useful aid to intuition. For example, a standard ten-year coupon bond will have a Macaulay duration of somewhat but not dramatically less than 10 years and from this, we can infer that the modified duration (price sensitivity) will also be somewhat but not dramatically less than 10%. Similarly, a two-year coupon bond will have a Macaulay duration of somewhat below 2 years and a modified duration of somewhat below 2%.

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Duration (finance)