In page 170 (CFA text) it is stated that POs on MBS tend to have high positive duration while IOs have high negative duration…but why? I thought that the value of a PO RISES with falling rates, which would imply negative duration. And a IO should fall in value with falling rates, hence I would have expected positive duration. I would be very grateful if someone could explain! Thanks

When rates fall - POs rates fall - but before that happens the POs get refinanced. So the entire money due to the issuer is returned. Thus duration is low - and positive. Issuer gets his full principal amount back. IOs on the other hand - also would get refinanced, but since the expectation was to receive interest for a long time, and that does not materialize now - the IOs duration is negative. P.S: I am writing this all from some portion of memory. Did I ever read this - seems to be a constant thought that keeps going on in my mind…

Positive duration means negative relationship between interest rates and price of PO Negative duration means positive relationship between interest rates and price of IO. Take care

kingstongal Wrote: ------------------------------------------------------- > > I thought that the value of a PO RISES with > falling rates, which would imply negative > duration. And a IO should fall in value with > falling rates, hence I would have expected > positive duration. > I think You are correct, kingstongal. As mortgage rates fall, there are more Principal Prepayments made in the mortgage pool, which means, POs get paid earlier and their holders dont have to wait the whole long period of average term for that pool. Thus Price of POs rises, showing a NEGATIVE Duration with falling rates. For IOs, reverse happens. As mortgage rates fall and Principals are prepaid, cashflows to IOs reduce as outstanding Principal balances reduce. This causes the Price of IOs to fall too. Showing a POSITIVE duration with falling rates. I have not come to this reading yet, but this is what i understand from similar readings in level 2. Have you checked the errata?

Pretty sure there is no errata. http://www.analystforum.com/phorums/read.php?13,964571 explanation of this phenomenon… excerpted here: Part I: Re: PO vs IO Posted by: McLeod81 (IP Logged) Date: May 18, 2009 11:24AM Null&Nuller, you had it right the first time and it looks like Schweser is ass-backwards on these: PO’s respond VERY positively to decreasing interest rates on the short end because prepayments dramatically accelerate the repayment of principal. If the entire discount from par is repaid immediately, you win. IO’s are nothing but interest payments. The ideal situation for an IO holder is that the bond is NOT repaid at any point, and they end up receiving interest for the entire length of the loan. There is now principal involved, so the longer you receive interest the better. If the loan is repaid immediately, you get nothing. This is why IO’s move WITH interest rates at levels below the coupon rate. Once interest rates are sufficiently high, IO’s start to act like normal annuities (positive duration) because the chance of prepayment fall. From Fabozzi “CMO’s and Stripped MBS”: “If mortgage rates decline below the coupon rate, prepayments are expected to accelerate. This results in a deterioration of the expected CF for an IO. The net effect is typically a decline in the price of an IO.” “Thus we see an interesting characteristic of an IO: It’s price tends to move in the same direction as the change in mortgage rates. This effect occurs 1) when mtg rates fall below the coupon rate and 2) for some range of mtg rates above the coupon rate.” “When mtg rates decline below the coupon rate, prepayments are expected to speed up, accelerating payments to the PO holder. The result is that the price of a PO will increase when mtg rages decline.” “When mtg rates rise above the coupon rate, prepayments are expected to slow down. Coupled with a higher discount rate, the price of a PO will fall when mtg rates rise”. Part II: Posted by: mwvt9 (IP Logged) Date: May 18, 2009 01:48PM If you think it terms of prepayment risk: PO benefit from contraction risk (principal paid back as far as possible). This will happen from refi’s at lower rates. IO benefit from extension risk because you will receive interest for a longer period than was priced into the instrument. Part III: Posted by: null&nuller (IP Logged) Date: May 18, 2009 06:14PM this where my heard hurts - Take a straight bond - rates rise --> price falls. So the duration (the yield/price relationship) is negative mathematically. But because this is normal behaviour for bonds, by convention the industry calls this “positive” duration. (it’s a bit like delta in Puts - it’s always expressed as positive number even tho’ it’s negative price/value relationship) so for example the key rate duration chart on cfai volume 4 pate 152 shows the bars are positive - showing positive duration as per the convention (despite mathematically being negative relationship) then on the chart on the next page shows key rate durations for IOs and POs. POs (for 10+ onward) have “positive” duration in the same way as straight bonds have “positive” duration by convention. IO’s have “negative” duration at 10+ onward in the sense that it is opposite to straight bonds and POs. that’s why my head hurts. “Positive” means “like straight bonds” (which are mathematicaly negatve yield/price relationsihp). “Negative” actually means “the opposite of positive bond duration convention” (so “Negative” actually is mathematically positive yield/price relationship) then on top of all that, the “duration” relationships of both POs and IOs switch at the short end (under about 10 years) appologies for giving anyone else a headache…

Positive duration : negative slope on the yield-price curve (I/R rises => Price falls, I/R falls => Price rises) Negative duration : Positive slope on the yield-price curve (I/R rises => Price rises, I/R falls => Price falls)

It shall be price-yield curve [Y axis : Price, X axis : Yield (I/R)]

cpk123 Wrote: ------------------------------------------------------- > > that’s why my head hurts. “Positive” means “like > straight bonds” (which are mathematicaly negatve > yield/price relationsihp). “Negative” actually > means “the opposite of positive bond duration > convention” (so “Negative” actually is > mathematically positive yield/price relationship) > Thanks CP and AMA. So, our understanding is fine as to why POs will behave like a regular bond and IOs will behave opposite. Only thing is what we were terming as ‘Negative’ duration, is by convention termed as a ‘Positive’ one. Makes things clear now. Or does it

Negative slope = Pos Duration Positive Slope = Neg Duration Duration, I thought you were cool!

AMA Wrote: ------------------------------------------------------- > It shall be price-yield curve I remember from Level II, there was a line graph with the POs (negative slope) and IOs positive slope using the Price on Y axis and Interest Rates on X axis.

Thanks everyone! I have checked with the FI gurus at work and they too explained to me that positive duration is “normal” and implies rising PO prices when yields fall, while negative duration just means that prices (in this case IO prices) rise when yields rise. Very confusing though!