Trying to understand the key rate contributions calculation

[kc]

Hi All,

in chp 13, p.605, I am trying to understand the contribution of the key rate 01.
Per my understandings, I have calculated the opposite percentage for the 5-year and 10-year rates.

My thoughts are :
1. The impact of 5-year rate drops to zero at year 10
2. so starting from year 5, 5 years remaining for the 1 b.p. shock to be completely decreased to zero
3. each year will decrease 1 b.p./5 years, = 0.2 b.p.
4. when reaches year 6.5, total (6.5-5)*0.2 b.p. = 0.3 b.p. has already be gone
5. therefore, 5-year rate contributes 0.3 b.p. to the 6.5-year.

Can someone please help me understand what did I miss ? Thank you so much!

 

[David Harper CFA FRM]

Hi @kc I agree with you through step 4 ("when reaches year 6.5, total (6.5-5)*0.2 b.p. = 0.3 b.p. has already be gone"). However, because 0.3 bp are gone (aka, reduced), there are 1 = 0.3 = 0.7 bps remaining!

Look at this way, between 5 and 10, 6.5 is 30% the distance from the 5 and toward the 10; i.e., at 6.5 (the red line) we are not in the lower half of the blue segment, we are in the upper half because it's only 30% down the slope (aka, as you said "0.3 bps is gone"). Because 6.5 is nearer to 5 and further from 10, the 5-year rate is contributing more of the weight (0.70 bps) while the 10-year rate is contributing less of the weight (0.30 bps). Hope that's helpful!

 

[kc]

Hi @kc I agree with you through step 4 ("when reaches year 6.5, total (6.5-5)*0.2 b.p. = 0.3 b.p. has already be gone"). However, because 0.3 bp are gone (aka, reduced), there are 1 = 0.3 = 0.7 bps remaining!

Look at this way, between 5 and 10, 6.5 is 30% the distance from the 5 and toward the 10; i.e., at 6.5 (the red line) we are not in the lower half of the blue segment, we are in the upper half because it's only 30% down the slope (aka, as you said "0.3 bps is gone"). Because 6.5 is nearer to 5 and further from 10, the 5-year rate is contributing more of the weight (0.70 bps) while the 10-year rate is contributing less of the weight (0.30 bps). Hope that's helpful!

Hi David, thanks for the reply. The last sentence did help!