![]() ![]() \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. 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 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. In this case, all the key rates except 60M are not affected but two adjacent rates at 54M and 66M are affected linearly. In particular, the light blue colored line (bottom) illustrates the shifts at all maturities, which resulted from 60M key rate’s change. Ho defines a number of maturities on the yield curve as being the key rate durations, with typical values of 3 months, 1, 2, 3, 5, 7, 10, 15, 20, 25 and 30 years. Rates outside the range of selected key maturities are set simply by the nearest key rate. One of the most popular techniques to accomplish this is the use of key-rate durations (KRDs), introduced by Thomas Ho (1992). A shift of one key rate by 1% affects its neighborhood of that key rate with linear interpolation. 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. 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. Overall, this study revealed the important influence of LOC on soil C fluxes and highlighted the important role of SOM quality and quantity in regulating grassland soil C cycling.This post explains how to calculate the key rate durations (KRD). Grazing and increased soil depth resulted in a greater PE and soil C loss, with soil C/N and SOC content being the most important regulators. LOC addition stimulated SOM decomposition in all soils and increased respiration of SOM by 11.3–92.4 mg C/g SOC, equivalent to 18.7–266.1 % priming. Grazing and deeper soil layers decreased the respiration derived from LOC and their relative contribution to total respiration, mainly attributed to variations in soil C/N and fungal/bacterial ratio (Fu/Ba). We found that soil microbes responded rapidly to LOC input, and microbial biomass controlled by soil organic C (SOC) and C/N was the most important factor directly influencing the intensity of the microbial response to LOC input. The microbial respiration was measured at 9-min intervals across a 105-h period. To address this gap, 13C-labeled glucose was added to six temperate grassland soils with different C/N ratios (9.98–12.0), which were collected from areas with different grazing exclusion durations and at different soil depths. Therefore, variations in soil C and N characteristics may further influence microbial response processes to LOC inputs and the decomposition of LOC and SOM, but a comprehensive understanding of this is lacking. There are some indications that the response of soil microbes to LOC input depends on the microbial demand of nutrients, especially C and N. Furthermore, although numerous studies have explored the priming effect (PE) of soil organic matter (SOM) mineralization induced by LOC addition, few studies have focused on its short-term effects. However, because soil microbial responses to LOC input are rapid, the relative contributions of respiration derived from LOC to total microbial respiration and their influencing factors remain elusive. Continuous and pulsed inputs of labile organic carbon (LOC) into soil are common. ![]()
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