Why do POs exhibit negative convexity at low interest rates? I would think that since PO prices are negatively related with rates (i.e. lower rates increase PO value due to higher prepmts) they would respond very positively to decreases in rates not just marginally as negative convexity would suggest.
at low interest rate - wouldn’t the PO piece get prepaid? so it will be reduced very rapidly to 0?
i’m not really sure but could it be because they’re essentially callable?
“at low interest rate - wouldn’t the PO piece get prepaid? so it will be reduced very rapidly to 0?” Yes, at lower rates the refinancing activity increases which prepays your PO faster and makes it more valuable.
A lot like a callable bond. CFAI text has a graph for callable bond convexity that illustrates this pretty nicely. Sorry, I don’t have the page #. All I’ve got with me are CorpFin and Drv/PM
and isn’t that the definition of neg. convexity? I hope I am right!!!
BTW, negative convexity doesn’t mean that POs only respond “marginally” to decreases in rates - it simply means that the positive response to decreases in rates is not as great as the negative response to an increase in rates, but generally only marginally so. So if rates go up 1%, the PO drops 10 points, and if rates go down 1%, the PO “only” goes up 9 points.
^exactly - this is what I learnt in L1. Perfect.
“Why do POs exhibit negative convexity at low interest rates?” Because the refinancing option to the borrower makes them, as SSS said, “essentially callable”.
Yea I know how negative convexity works for callable bonds and I know the exact graph you are referring to in the book, which is exactly what I am going off of when I say that as rates drop negative convexity would result in a marginal increase in price whereas normal convexity would result in a larger increase in price. If you have the L1 curriculum for 2008 the graph is in volume 5 on page 485. And it shows that for a callable bond as rates fall the price increase is smaller than for otherwise similar non-callable bonds. So I understand that for a PO prepmts obviously increase as rates fall but everywhere I have read that this is a positive feature for the PO holders, i.e. they want fast prepmts, and if thats the case then faster prepmts should be valuable meaning the PO price should increase quicker if anything as rates drop as opposed to slower as negative convexity would seem to imply. Thoughts?? Perhaps a numerical example would help if anyone is that venturesome.
adavydov7 Wrote: ------------------------------------------------------- > Yea I know how negative convexity works for > callable bonds and I know the exact graph you are > referring to in the book, which is exactly what I > am going off of when I say that as rates drop > negative convexity would result in a marginal > increase in price whereas normal convexity would > result in a larger increase in price. > > If you have the L1 curriculum for 2008 the graph > is in volume 5 on page 485. And it shows that for > a callable bond as rates fall the price increase > is smaller than for otherwise similar non-callable > bonds. > > So I understand that for a PO prepmts obviously > increase as rates fall but everywhere I have read > that this is a positive feature for the PO > holders, i.e. they want fast prepmts, and if thats > the case then faster prepmts should be valuable > meaning the PO price should increase quicker if > anything as rates drop as opposed to slower as > negative convexity would seem to imply. Thoughts?? > Perhaps a numerical example would help if anyone > is that venturesome. I’m not sure if it is related, but is negative convexity because of re-financing burnout ? As the rates go down, prepayments will increase, but beyond a point as they go down further nothing is left to prepay and the price of PO does not rise as much. EDIT : Ohh refinancing burn out was already considered. Never mind. I don’t have more to add
hmm yeah i’m a little confused now http://www.analy$tnotes.com/notes/los_detail.php?id=2390 [replace $ with s] “If interest rates fall, prepayments increase, and CMOs contract: * IO securities plummet in value, because their projected cash flows disappear. * PO securities skyrocket in value, because all of their projected cash flows are received much earlier than anticipated. This is the direct influence of the time value of money.” i guess it’s possible for them to rapidly increase in value and still have negative convexity. out of curiosity, can you point me to where in the textbook it talks about PO strips convexity?
@super: this was actually on Exam 3 in Book 6, question 28. And i’m with everyone here, I get that because the principal holder has the option to prepay makes the bond callalbe at his will making it exhibit negative convexity. However, this negative convexity issue comes about for whole bonds (i.e. those with both an interest and coupon components), and is primarily due to the higher interest component that the bond pays going away in favor of a lower one once the bond/home owner refinances.
At low interest rates, the chance of prepayment / refinance increases. Since PO is principle only, they would face increasing contraction risk. This is like a bond getting called and so the convexity is negative.
@elita: yes we have already covered this, the problem is that contraction risk is good for PO strips. PO holders are worried about extension risk.
“At low interest rates, the chance of prepayment / refinance increases.” To a point - if you look at graphs of POs run at varying prepayment speeds, you’ll see that refinancing burnout actually causes refinancings to hit a virtual “wall” at some interest rate - for example, the prevailing rate at the time the PO was issued was 6%, and now rates have decreased to 5%, and lots of borrowers refi. Now rates have fallen to 4%, and (possibly) even more borrowers refi. Rates now drop to 3%, and not as many people refi as would be predicted if there was a direct linear relationship between rates and refinancing, and at 2% these same people who didn’t refi at 5,4, or 3% are still too lazy/bored/apathetic to refinance at 2%, then there’s the same story at 1%, et cetera. Sorry if that went off on a bit of a tangent, but the fact that, even at 0% interest rates there would still be people who would not pay off their POs makes them not perfectly linearly inversely related (mouthful) to interest rates, which is where the negative convexity comes into play. That’s my final answer.
PO is meant for investors who are concerned about extension risk. Problem is, PO (on its own) has little protection against contraction risk and must often rely on support tranches. Unlike PAC, it doesn’t have an interest rate collar to control the prepayment rate. That’s why the contraction risk is still there and should be a concern to the investor if it goes out of control, as investors would face increasing reinvestment risk as interest rate goes down.
@skillionaire: this explanation is the only one I have thought about that makes any sense at all as a potential explanation for negative convexity of POs (the burnout effect). However, this explanation is something that is not espoused at all in any of the books (CFAI or Schweser, which in fact only talk about how POs benefit from lower rates because prepmts speed up). I guess the POs would have negative convexity which would be: a) very slight compared to the regular curve, and b) this negative convexity would only appear at very low rates What I think is important to learn from this is that POs exhibit negative convexity for a reason other than everyone has espoused here (i.e. because they are callable, in fact this feature is valuable to POs) but rather because of prepayment burnout! @eltia: no, PO holders like contraction risk, they want high prempts they benefit from this.
PO holders *expect* contraction risk. But if the contraction exceeds their expectation, their exposure reinvestment risk exceed the benefit of the contraction risk they are exposed to.
@elita: reference please? would be great.