(This paper is also available in an interactive version with enhanced digital content - see references. The benefit of this transformation method is that it only requires calculating the risk of a small set of alternate instrument and does not require re-calculating the original portfolio risk. This paper reviews the concepts of partial DV01 and duration and then discusses a simple method for transforming partial DV01s between different rate bases and provides examples.
But partial DV01s or durations can be measured with respect to different rates: forwards, par rates, zero yields, or others.
When valuing instruments off a yield curve, duration and DV01 naturally extend to a vector of partial DV01s or durations (key rate durations) and these are widely used in the finance industry. \Īs will be shown in R code, it is worth noting that a vector of shifts due to a key rate movement is appended horizontally with the name of its key rates as follows.Duration and DV01 (dollar duration) measure price sensitivity and provide the basic risk measure for bonds, swaps, and other fixed income instruments. Using these N shifted zero curves, each effective duration (\(KRD_i, i=1,…,N \)) is calculated with the initial zero curve. When we add up all shifted changes together on the initial yield curve, we can get the parallel shifted curve (red colored solid line).īy shifting each key rates, we can get N shifted zero curves (N is the number of key rates). The key rate duration is also a useful tool for determining the maturities of bonds. The ith shifted yield curve is the sum of the initial yield curve (blue colored solid line) and its shifts at all maturities, which resulted from the change of ith key rate. The key rate duration model describes the shifts in the term structure as a discrete vector representing the changes in the key zero-coupon rates of various maturities. For example, a 10-year bond's sensitivity to a 1 change in only the 5-year interest rate would be that bond's 5yr KRD. In this case, all the key rates except 60M are not affected but two adjacent rates at 54M and 66M are affected linearly. Key Rate Durations (KRD) are essentially some fixed income instrument's price sensitivity to a non-parallel shift in interest rates (i.e., a shift at the 'Key' Rate). (In fact, they can also be used to determine the effect of parallel yield curve shifts, although they’re less efficient than simply using the effective duration of each bond. In particular, the light blue colored line (bottom) illustrates the shifts at all maturities, which resulted from 60M key rate’s change. Using Key Rate Durations Key rate durations are used to determine the effect of non-parallel yield curve shifts on a portfolio of bonds. The key- rate framework imposes no restrictions on how any key rate changes relative to another. Rates outside the range of selected key maturities are set simply by the nearest key rate. The chapter describes key-rate 01s and durations, partial 01s and forward-bucket 01s, proves popular as striking a sensible balance between hedging effectiveness and practicality or cost.
A shift of one key rate by 1% affects its neighborhood of that key rate with linear interpolation. The key rate duration reflects the expected change in value resulting from a yield change for a bond or bond portfolio with a specific maturity. Ho (1992) suggests the size of shift as 10 bp but we use 1%(=100bp) simply for illustration purpose. Interestingly, the shift between these two adjacent key rates is defined by the linear interpolation with the peak at the ith key rate.Īs can be seen in the above figure, yellow colored maturity is assumed to be the selected maturities of key rates. A remarkable result of the tax-neutral method pertains to key-rate durations. In other words, individual effective durations are calculated by shift of each spot rate at each key maturity and the sum of them is the KRD.įormally, ith key rate shift is defined to be zero shift for maturities shorter than (i-1)th key rate and longer than (i+1)th key rate. Unlike the traditional effective duration, KRD is calculated not from a par yield curve but from a zero curve (spot rate) so that the bump and reprice are performed on selected spot rates (key rates). The sum of the product of key rate durations and each yield changes in key rates (with negative sign) is the bond price change due to the non-parallel shift of the yield curve.
The sum of the key rate durations is identical to the effective duration. KRD is a vector of the price sensitivity of a bond to each key rate change. Ho (1992) introduced the concept of the key rate duration (hereafter KRD), which is a new measure of interest rate risk exposure. Ho (1992) introduces KRD to measure non-parallel movements of the yield curve that the existing duration measures can not describe as these are defined under the assumption of a parallel shift of the yield curve.
#Key rate durations how to
This post explains how to calculate the key rate durations (KRD).
0 kommentar(er)
