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.)


Fill in your details below or click an icon to log in:

WordPress.com 徽标

您正在使用您的 WordPress.com 账号评论。 登出 /  更改 )

Google photo

您正在使用您的 Google 账号评论。 登出 /  更改 )

Twitter picture

您正在使用您的 Twitter 账号评论。 登出 /  更改 )

Facebook photo

您正在使用您的 Facebook 账号评论。 登出 /  更改 )

Connecting to %s