Key rate exposures

[verma.rahul]

Dear David

I am quoting Bruce Tuckman "Since the two-year par yield is a key rate, changing any other key rate does not, by definition, change the two-year par rate. Consequently, two year par bonds have no exposure to any key rate except the two-year key rate. Similarly, five-, 10-, and 30-year par bonds have no exposure to any key rate but that of the corresponding maturity."

But I feel that five-, 10-, and 30-year par bonds will be affected by change in other key rates (not only by maturity key rate) as the coupons are paid for all the year semi-annually. Will the change in 2 year key rate not affect the coupon paid between 0.5 years to 5 years for 30-year maturity par bond ?

Moreover I tried to evaluate key rate exposures for 8% premium bond for change in 2-year key rate as per Table 7.2 pg132, Bruce Tuckman
10 year premium bond
Year Coupon Rate PV (after change in key rate 2-year)
0.5 4 5.01% 3.902249
1 4 5.01% 3.806886
1.5 4 5.01% 3.713854
2 4 5.01% 3.623096
2.5 4 5.0083% 3.534699
3 4 5.0067% 3.448511
3.5 4 5.005% 3.364486
4 4 5.0033% 3.282564
4.5 4 5.00167% 3.202679
Total 31.87902

Without change in 2-year key rate: Price of the premium bond (only 4.5 years coupon to calculate the difference/exposure) = $31.88346
Difference 0.004439
But the key rate exposure given in Table 7.2 is 0.00122

Please help !!! Kindly explain the mistake in my calculation.

Thanks
Rahul

P.S. I have uploaded a excel for your reference.