# Help! A simple duration question

May i ask why negative duration means increasing in value when interest rate “increases” but not “decrease”?

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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+) / (2P0Δy)

If effective duration is less than zero, then,

(P − P+) / (2P0Δy) < 0

If rates increase (i.e., Δy is positive), then, multiplying both sides by 2P0Δy gives:

P − P+ < 0

or,

P < P+

Thus, when rates increase, the price increases, and, consequently, when rates decrease, the price decreases.

Simplify the complicated side; don't complify the simplicated side.

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Can someone give us insight as to when this would be possible?

avannoord wrote:
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.

Simplify the complicated side; don't complify the simplicated side.

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