May i ask why negative duration means increasing in value when interest rate “increases” but not “decrease”?
with positive duration, an increase in interest rate decreases bond value, so i guess it goes the other way when duration is negative.
but i’m curious how can negative duration happen?
First, note that you’re talking about effective duration; neither Macaulay duration nor modified duration can be negative.
Second, recall the formula for effective duration from Level I:
Dureff = (P− − P+) / (2P0Δ_y_)
If effective duration is less than zero, then,
(P− − P+) / (2P0Δ_y_) < 0
If rates increase (i.e., Δ_y_ is positive), then, multiplying both sides by 2P0Δ_y_ gives:
P− − P+ < 0
P− < P+
Thus, when rates increase, the price increases, and, consequently, when rates decrease, the price decreases.
Can someone give us insight as to when this would be possible?
Not insight, but understanding:
Interest only (I/O) strips at low YTMs can have negative effective duration because the increased prepayments means that the bondholders ultimately get less money.