patso wrote:I dont get your reply.
I know from first princple, duration is the weighted average of the times until cash flows are received. Say we have two bonds - one fixed and one variable both maturing in 1 year, semi-annual, same face value and interest rate etc… except that one is fixed and the other is variable. One would the duration of these bonds be different ie variable 0.5yr; fixed - 0.75yr.
This is a common problem with people in finance – not you, specifically, but virtually all people in finance: they get very sloppy in their language, which then allows them to confuse ideas.
You’re talking about two kinds of duration here: Macaulay duration and effective duration. Macaulay duration is the
present-value weighted-average time to receipt of cash flows,
assuming that the cash flows do not change. The Macaulay durations of the fixed-rate bond and the floating-rate bond are equal. Effective duration is the (negative of the) percentage price change in the bond given a 1% change in the bond’s yield to maturity; effective duration
does not assume that the cash flows do not change;
it allows that they might change. The effective duration of the floating-rate bond is shorter than the effective duration of the fixed-rate bond because the coupon rate on the floating-rate bond will change when yields change whereas the coupon rate on the fixed-rate bond will not.
Modified duration is a mid-point between Macaulay duration and effective duration: like effective duration, it measures the (negative of the) percentage price change of the bond for a 1% change in its YTM, and like Macaulay duration is assumes that the future cash flows will not change.
So, when you ask why the duration of a fixed rate bond is given as 75% of its time to maturity, your question is ambiguous: do you mean its Macaulay duration, its modified duration, or its effective duration?
And when you say that the durations of bonds in your example should be the same, do you mean their Macaulay durations, their modified durations, or their effective durations?
Note that in my (previous) answer I specified that the
modified duration of a fixed-rate bond is often approximated as 75% of its time to maturity.
And in your example about the 1-year bonds, you’re comparing
effective durations, not
modified durations, not
Macaulay durations.
The fixed-income world would be a lot simpler if people would remember to include the adjective when they talk about
duration.
I wrote an article on these three kinds of duration that may be of some help:
http://financialexamhelp123.com/macaulay-duration-modified-duration-and-...