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Key rate durations3/27/2023 ![]() The only difference is in the way the duration is calculated - modified duration is based on the first derivative of price with respect to yield whereas effective duration is based on estimating a change in price for a given change in yield in either direction, through use of pricing models, for example. In fact, modified duration is more important than effective when figuring out most questions.Įffective duration and modified duration essentially give the same information - the percentage change in price for a 1% change in yield. can i listen to schweser and ignore modified.ĭO NOT ignore modified duration - pretty good chance it will be tested. According to Schweser, you dont need anything besides Effective Dur. I am using both Schweser and analystnotes' notes. There is a key rate duration for every point on the spot rate curve so there is a vector of durations representing each maturity on the spot rate curve. The key rate duration is the sensitivity of the value of a bond to changes in a single spot rate, holding all other spot rates constant. An analyst may want to measure the change in the bond's price by changing the spot rate for a particular key maturity and holding the spot rate for the other key maturities constant. ![]() Parallel shifts in the yield curve rarely occur. The yield curve risk is a bond's sensitivity to changes in the shape of the yield curve.The interest rate risk is the sensitivity of a bond to parallel shifts of the yield curve.It is important to distinguish interest rate risk from yield curve risk. V- and V+ are adjusted to reflect any changes in the cash flows (due to embedded options) that result from the change in benchmark yield curve.Įffective duration should be used for bonds with embedded options. It is very similar to approximate modified duration.Ī pricing model can be used to estimate the price change resulting from a change in the benchmark yield curve instead of the bond's own yield-to-maturity. Macaulay duration is mathematically related to modified duration.Ī bond with a Macaulay duration of 10 years, a yield to maturity of 8% and semi-annual payments will have a modified duration of:Įffective duration measures interest rate risk in terms of a change in the benchmark yield curve. This tells you that for a 1% change in the required yield, the bond price will change by approximately 10.66%. If the yield increases by 20 basis points, the price would decrease to 131.8439. If the yield is decreased by 20 basis points from 6.0% to 5.8%, the price would increase to 137.5888. Due to the linear assumption, the price change measured by duration is P 2 - P 0.įor example, consider a 9% coupon 20-year option-free bond selling at 134.6722 to yield 6%. If the yield falls to Y 1, the price will rise to P 1. The slope of the tangent line is related to the duration of the bond. A tangent line can be drawn to the price/yield relationship at Y 0. Suppose that the bond has an initial yield of Y 0. However, the price/yield relationship is convex, not linear. Modified duration assumes that the price/yield relationship is a straight line. D mod = the modified duration for the bondĭi = yield change in basis points divided by 100 Specifically, modified duration estimates the percentage change in bond price with a change in yield. Modified duration shows how bond prices move proportionally with small changes in yields. The weights are the shares of the full price corresponding to each coupon and principal payment.Īlternatively, Macaulay duration can be calculated using a closed-form formula. Macaulay duration is defined as the weighted average time to full recovery of principal and interest payments. He demonstrated that a bond's duration was a more appropriate measure of time characteristics than the term to maturity of the bond, because duration incorporates both the repayment of capital at maturity, the size of the coupon and timing of the payments. For example, a bond with a duration of three means that, on average, it takes three years to receive the present value of the bond's cash flows.įrederick Macaulay developed the concept of duration approximately 80 years ago. Curve duration statistics measure the sensitivity of a bond's full price to the benchmark yield curve, e.g., effective duration.ĭuration is the weighted average time to receive the present value of each of the bond's coupon and principal payments.They include the Macaulay duration, modified duration, money duration, and price value of a basis point. Yield duration statistics measure the sensitivity of a bond's full price to the bond's own yield-to-maturity.Bond duration measures the sensitivity of the full price change to a change in interest rates.
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