Structured note with no coupon have a duration?

bismarx · September 29th, 2006, 8:10 pm

I was talking with one of my collegue about a structured note linked to a basket of currencies.While I was sure I could compute a duration equal to the maturity of the bond (the same as a zero coupon bond) he told me that a note which doesn't pay any coupon cannot have a duration. Actually I'm not so convinced but....he was a fixed income manager in morgan stanley.I would like to know some other opinion.Thanks

gjlipman · September 30th, 2006, 6:38 am

As you say, a zero coupon bond has a duration equal to its term. And likewise, any fixed cashflow will have a duration equal to its term. Where it gets a bit tricker is if the cashflow isn't fixed. For example, if you get the realised return on some asset, then it will have zero duration, as its value won't change if rates change. And for other things it might be trickier, or even impossible to come up with a duration.

bismarx · October 1st, 2006, 7:09 am

Thanks....i'm afraid I was wrong!! Anyway lem me do just one more consideration. If I know that :-at worst I'll received 100 at expiry -the note has 5 years to expiry-interst rates are now at 3%If interest rates move to 6% from 3%, doesn't it have impact on my note? I mean: the opportunity cost to hold the note should increase and the discounted value of 100 in 5 years should be lower than in the case interest rates were at 3%.

mensa0 · October 1st, 2006, 8:32 am

The MacCauley duration of a zero is equal to its time to maturity. The duration you refer to when you consider changing rates is the so-called modified duration which is (the first derivative of the price function WRT yield)/price.It's an estimate of the % change in the bond price due to a 100bp change in yield. If you have a 5-year zero and rates are 5%, the modified duration is:5/(1.05) = 4.76 so the zero's price will change by appr. 4.76% when yields move 100bp.Mike

bismarx · October 1st, 2006, 12:56 pm

ok so, in contrast with gjlipman said, yor're saying that the structured note linked to a basket of currency has a duration?

Lepperbe · October 1st, 2006, 7:36 pm

breaking down the structured note into it's components ... assuming it has a guaranteed payout at maturity ... this equals a zero coupon bond which definitely has a duration and call options (or put options) on the currencies which probably have a duration as well (interest rate sensitivity) ... combine the two ... structured note has a duration. might be a bit difficult to put an exact number on it, but ... that's question #2.

gjlipman · October 2nd, 2006, 1:58 am

I didn't say that a structured note necessarily has a duration of zero, I said it may not. For example, if you've got a structured note, which puts $100 in a bank account and accrues interest at a market rate, and pays out at the end, that has zero duration (even though there you are guaranteed at least $100 payout).

Lepperbe · October 2nd, 2006, 5:09 am

hm, that doesn't really guarantee a $100 payout, but rather a $100 + interest payout (assuming the bank is safe).