key rate shft

[yjhirad]

David,

In the key rates example (5.b.3) it appears that when the 2 year key rate is shifted it affects only the rates above it up to 5 years...shouldn't it also affect the rates below it i.e from .5 years to 2 years?

jy

 

[David Harper CFA FRM]

Hi jy,

But i do shock < 2 years by the full basis point
(Tuckman p 135 "The impact of each key rate is one basis point at its own maturity and declines linearly to zero at the term of the adjacent key rate. To the left of the two-year key rate and to the right of the 30-year key rate, the effect remains at one basis point.") ... I think i do have the < 2 year rates shocked to the full 5.01%

or, do you mean, that it seems like maybe it should taper to zero? (which i might agree with, but I followed Tuckman)

David

 

[yjhirad]

right...it seems like it should taper to 0 but the more I think about it - maybe its a boundary condition definition that is being applied so as to make it consistent with the parallel shift paradigm without having to have an extra key rate (the 0-2 year maturity)...not inconsistent just slightly inelegant.

jy

 

[intuit2k2]

Don't really understand this concept. If you're discounting a FI security by the yield curve, then changes in 2 year yields only pertain to 2 year maturities. Is the question asking you to extrapolate the changes in yields given the change in 2 year yields?

 

[David Harper CFA FRM]

The 2-year rate (in Tuckman's example) is just a key rate, meaning, it gets the full one basis point shock (to par yield). Only four rates get this shock. The technique includes a decision rule as to how to treat neighboring rates; in this case, interpolation. So, for example, the 2 years and 1 month yield gets is also shocked but a little less than one basis point, less a little the 2 year and 2 month rate, and so on, in linear (interpolation) fashion until you get to five years, because five years is a key rate. So, all the maturities get shocked.

David