Can someone explain what is negative duration ?

[frm.bhb]

As per the definition "Duration is the average time one has to wait till the payment is received". Going by this if, say, duration is 2.5 years means I would receive my money in ~2.5 years. Well.

But, as you may be aware, there are some securities IO strips and FRNs, which are said to exhibit negative duration. I have not seen in terms of numbers but say duration for an IO is -1.0. What does this mean in terms of above definition.

But if I google, the explanation given in terms of the price movement similar to interest rates. For example, they say the price of IO increases when interest rates increase (as opposed to decrease due to inverse price yield relation).

But I would like to understand STRICTLY from the point of view of the definition i.e. Duration is the average time one has to wait till the payment is received. In this case can we say, I receive my money before even I pay something for the security ??? How IOs have negative duration?

Thank you in advance.

FRMBHB

 

[Dmitrij]

1: not the answer to your question: Personally, I would think this has to do with having a short position in a bond or having a long floating rate bond. If you short sell a bond, the other person's gain is your loss. So if he has a duration of 2.5 years, if interest rates fall, the price of the bond increases. The short position, on the other hand, has a decrease in the price of bond if interest rates fall. This would imply negative 2.5 years duration.

If interests rise, the price of the floating rate bond increases too.

I don't think it is possible to have a strictly negative duration vanilla bond without modifications.

For the case of an Interest Only bond or note, if it's part of a CMO, if interest rates rise prepayments slow, meaning the accrued coupon is higher to the IO holder.

*http://accruedint.blogspot.com/2007/07/how-does-cmo-work.html {from: So they create a tranche.}

an attempt to answer your question: I don't think that strictly from the definition of duration this can be called Duration. The reason it's usually called duration is because the mathematical relationship holds for Duration and Interest Rate sensitivity. Typically, the interest sensitivity, which is calculated as the partial derivative of the bond pricing formula, happens to be equal to the Duration formula. When there is negative duration like in CMO IO's, I think the economic intuition of Duration no longer holds and it should simply be referred to as interest rate sensitivity.

So the original formula, let's call it Sensitivity (S), is equal to Duration (D).

D = S, for all D >=0. When D<0, the D loses its meaning in terms of economic intuition, but might still be valid for calculation purposes.

 

[frm.bhb]

@Dmitrij: Thank you for the reply.

Any idea where D more than maturity. Somewhere I read the term 'risk adj D' where in due to default of a security, the recovery may take more time beyond maturity of security, in that case, D > maturity. Any thoughts

 

[David Harper CFA FRM]

@Dmitrij - great answer!

@FRMBHB,

I've definitely been "guilty" of using that duration definition, although from that perspective, more recently I much prefer "[Macaulay] Duration is the weighted-average maturity of the bond, where the weights are the PV of the cash flows" because it precisely characterizes the manual-calc approach to Mac duration (e.g., http://www.bionicturtle.com/how-to/spreadsheet/2011.t4.c.4.-durations 1st tab, right panel).
... although it's still not obvious how to defend this definition in the case of negative duration

But I notice the newly assigned Veronesi text says the following (p 190, Fixed Income Securities) and notice he says pretty much that same thing Dmitrij says [emphasis mine]: "This example [i.e., floating rate bond] shows that even if the average time of future cash flows can be relatively long ... the duration can be very small. Conversely we will see securities for which the duration is actually longer than their maturity, or securities for which the duration is negative. Given that in modern times the notion of duration is mainly used for risk management purposes, and in particular to compute the sensitivity of a security to parallel shifts in the term structure, we must be careful in interpreting duration as an average time of future payments, as this interpretation only holds for securities with fixed cash flows. "

Re: "Any idea where D more than maturity:" The classic example of a security with D > M is an inverse floater.

Thanks, David

 

[niteshkadam05]

IOs have negative duration?

 

[Nicole Seaman]

IOs have negative duration?

Hello @niteshkadam05

The following thread may be helpful in answering your question: https://forum.bionicturtle.com/threads/negative-convexity.5617/post-15879. There are other discussions in the forum regarding IOs having negative duration. If you use the search function and search for "io-strips" or "negative-duration" you will see a list of all of the threads that discuss this. You can also use the tag feature HERE to search for threads discussing this.

Nicole