quantitative feel of bond duration – mapping absolute 1% -> relative x%

In the simplest illustration of modified duration, if a bond has modified duration == 5 years, then a 100bps yield change translates to 5% dollar price (valuation) change.

Note that 100 bps is an Absolute 1% change in yield, whereas the 5% is a Relative 5% change in valuation. If original valuation == $90 [1], then 100 bps =>> $4.5 change.

After we clear this little confusion, we can look at dv01. Simply set the absolute yield change to 1 bp. The valuation change would be a Relative 0.05% i.e. $0.045. The pattern is

Duration == 5 years => dv01 == 0.05% Relative change
Duration == 6 years => dv01 == 0.06% Relative change
Duration == 7 years => dv01 == 0.07% Relative change

Note 0.05% Relative change means 0.05% times Original price, not Par price.  Original price can be very different from par price, esp. for zero bonds.

[1] 90 in bond price quote means 90% of par value. For simplicity we would assume par is $100, though smallest unit is $1000 in practice.

(See P10 of YieldBook publication on Duration.)

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