![]() V = ∑ i = 1 n P V i is the present value of all cash payments from the asset. The present value of these cash flows is: The denominator is the sum of the weights, which is precisely the price of the bond. Macaulay duration, named for Frederick Macaulay who introduced the concept, is the weighted average maturity of cash flows, in which the time of receipt of each payment is weighted by the present value of that payment. Similarly, a two-year coupon bond will have a Macaulay duration of somewhat below 2 years and a modified duration of somewhat below 2%. 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%. įor everyday use, the equality (or near-equality) of the values for Macaulay and modified duration can be a useful aid to intuition. Modified duration is used more often than Macaulay duration in modern finance. Key rate duration or partial durations measure bond price sensitivity to changes in the shape of the benchmark yield curve. 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. (Price sensitivity with respect to yields can also be measured in absolute ( dollar or euro, etc.) terms, and the absolute sensitivity is often referred to as dollar (euro) duration, DV01, BPV, or delta (δ or Δ) risk). 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. It is equal to the maturity if and only if the bond is a zero-coupon bond. For a standard bond, the Macaulay duration will be between 0 and the maturity of the bond. Macaulay duration is a time measure with units in years and really makes sense only for an instrument with fixed cash flows. īoth 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. Key rate duration is an important metric it is used to assess the sensitivity of bond value. Modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield. Strictly speaking, Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years. 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. ![]() When the price of an asset is considered as a function of yield, 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. In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |