Okay… who wants to give me a primer on this topic… For whatever reason, really struggling with this topic which floors me! I understand how MBS’s have negative convexity because of the pre-payment option by homeowners. When rates drop, they are more likely to exercise their option and pay off their mortgage. So as I understand it… when interest rates fall, MBS’s will rise but not as much as other non-callable or bullet bonds because the prepayment option has value. Hope I got that right. Now what about when interest rates rise? Do MBS’s decrease in value more than non-callable or bullet bonds because of negative convexity? until it reaches a point where the prepayment option is far out of the money and then it acts like a regular positive convexity bond? Lastly… someone please save me from the misery of trying to understand the hedging aspect of this section. I can’t for the life of me wrap my head around the value of the hedge relative to the MBS and vice versa… Any extended comments on this topic would be very much appreciated. PJStyles
Securities with call options: -will underperform non-callables when rates fall because of the negative convexity. -when rates are rising, but are still below the coupon callables will overperform non callables, because the negative convexity makes them less sensitive to interest rate changes. -when rates are relatively high, the options have little to no value thus will move in sync with non callables. That hedging stuff in there is tough 
hey, if no one will answer, i will do a write up when i will get to work. -csk
Big Babbu Wrote: ------------------------------------------------------- > Securities with call options: > -when rates are rising, but are still below the > coupon callables will overperform non callables, > because the negative convexity makes them less > sensitive to interest rate changes. If they are less sensitive to int. rate changes, why would they overperform non callable bonds? You also talk about callable bonds but aren’t MBS different from Callable bonds? I get that MBS are callable by the homeowner but aren’t they treated slightly different or is it exactly the same concept? Would still love it if someone provided a very good detailed response on MBS and the effect of convexity, int. rate changes, when are they most responsive (ie: above par, below par) and what about the hedge’s convexity and/or duration etc… Thanks guys…
As rates rise, the bond prices decline. As callables are less sensitive to int rates they decline less while non callables decline more. Hence callable outperform non callables.
PJStyles Wrote: ------------------------------------------------------- > Big Babbu Wrote: > -------------------------------------------------- > ----- > > Securities with call options: > > -when rates are rising, but are still below the > > coupon callables will overperform non > callables, > > because the negative convexity makes them less > > sensitive to interest rate changes. > > If they are less sensitive to int. rate changes, > why would they overperform non callable bonds? > You also talk about callable bonds but aren’t MBS > different from Callable bonds? I get that MBS are > callable by the homeowner but aren’t they treated > slightly different or is it exactly the same > concept? > > Would still love it if someone provided a very > good detailed response on MBS and the effect of > convexity, int. rate changes, when are they most > responsive (ie: above par, below par) and what > about the hedge’s convexity and/or duration > etc… > > Thanks guys… Ok, so here is a couple of concepts that might clarify MBS and other Callable/Putable bonds 1) Convexity Negative vs Positive. Negative convexity has negative second derivative Positive convexity has positive second derivative What is second derivative? You can think of it as accelartion. It is the rate of change of the speed versus time. Velocity is the first derivatives as it is a rate of change of distance versus time So for MBS, when interest rates fall below coupon, it starts exhibit negative convexity. It means that duration is increasing (velocity is still positive) but speed of increase is decelerating (acceleration is negative). You can also think of it as a slope of tangent line (that is what the first derivative is), the slop starts to decrease. What happens with regular bond (which exhibits positive convexity?) duration will increase as interest rates start to fall (velocity is positive) and speed of increase will accelerate (accelration is positive). You can also think of it as a slope of tangent line which increase. Now if interest rates is above coupon for MBS and it starts to fall, you can work backwards and see that MBS will be less sensetive (as velocity is less because it was decelerating as interest rates passed coupon) Ok i hope that makes some sense, but understanding first and second derivatvies will clarify SOO mcuh for Bonds and Options
That helps quite a bit… F-up question… so what happens when interest rates fall below the coupon rate on the MBS, does the MBS price increase still but just by a lesser amount than non-callable bonds? or does the actual MBS price fall because pre-payment is imminent?
MBS price will still increase but by the smaller amount because of call option ( i think, i am not 100% sure on how exactly prepayment option is priced)
MBS will Outperform when Interest Rates increase b/c the Prepayment Option will Decrease as the Bond Price Decreases which gives the MBS security an Extra Bump in return (Prepayment option is a Negative, so a Negative of a Negative is a Positive). So think about it. If Treasuries decrease by 5% and teh Prepayment Option goes from I dont know 2 to 1, than thats a +50% gain on the prepayment option, so then depending on the overall weight of the prepayment option to the overall MBS say 1% teh overall return on the MBS might be -4.5% vs -5% for the same interest rate increase on the Treasury…
willy, that is the reason for negative convexity - optionality.
Its also the reason why MBS’s Outperform in a Increasing Interest Rate Environment… Reread my post, I was referring to Itnerest Rates increasing not Decreasing… If they were Decreasing my MBS would Underperform b/c of the Prepayment Option, but when they are Increasing my MBS will Outperform b/c of the Prepayment Option… Remember… MBS = Treasury - Prepayment Option So When The prepayment is “Decreasing” its actually a positive boost.
I guess the part I’m struggling with is that the advantage of positive convexity is that the bond will react more to decreases in interest rates than it will to increases in interest rates. So for a non-callable bond, a rate drop will cause the price to increase more than the decrease in the bond price if interest rates had increased. My understanding of negative convexity is that it’s the opposite effect. The fixed income security will react more to increases in interest rates as opposed to decreases in interest rates. So when I translate this back to the MBS topic: - An increase in interest rates will cause the MBS to fall by more than a non-callable bond because of negative convexity… BUT, this doesn’t seem to be the case because you gain on the value drop of the pre-payment option. Frig… time to go back and re-read this area from the beginning… grrr… Crazy thing is I had this material down cold a few months back when I went over it the first time!
BigBadBadri Wrote: ------------------------------------------------------- > As rates rise, the bond prices decline. As > callables are less sensitive to int rates they > decline less while non callables decline more. > Hence callable outperform non callables. In re-reading this I’m not sure I agree with this. Callable bonds have negative convexity, which implies that it will be more sensitive to interest rate increases than it will for interest rate decreases. So if rates drop, Non-Callable bonds will perform better than Callable Bonds because of the risk that the Callable bond will be called by the issuing firm, particularly when it’s close to the call price. On the flip side, if the call option is far out of the money ie: Rates are extremely high, then the callable bond would act like a regular bond and exhibit positive convexity. Am I wrong on this assessement?
Remember the bond only exhibits negative convexity when Interest rates are low. When Interest rates are high, I believe it exhibits a more Positive convexity than a non-callable… until I guess the prepayment option reaches 0.
Right…when interest rates are really high, it exhibits positive convexity when rates subsequently drop. However, your statement said that as rates rise, callable bonds will outperform non-callable bonds… is that true?
Yes, I believe so. I’m no FI expert thoguh.
bigwilly Wrote: ------------------------------------------------------- Prepayment Option… > > Remember… MBS = Treasury - Prepayment Option > So When The prepayment is “Decreasing” its > actually a positive boost. I like this… make sense. I guess I’m just trying to wrap my head around the little details like “if interest rates are far above or below the coupon rate, or if the bond is priced far away from it’s par value etc etc…” See a lot of questions worded like that.
bigwilly Wrote: ------------------------------------------------------- > Remember the bond only exhibits negative convexity > when Interest rates are low. When Interest rates > are high, I believe it exhibits a more Positive > convexity than a non-callable… until I guess the > prepayment option reaches 0. how can it expereince a more ‘positive convexity’?
think about it. You have different levels of convexity. CSK you’re the Math genius of the bunch you should know this 
Convexity >0 is a positive.
I think what he meant to say wasn’t that it exhibits “MORE” positive convexity than a non-callable bond but rather that the further out of the money the pre-payment option is, the more it acts like a non-callable bond with positive convexity. The last question I have on this topic before I go back and review this because I’m a little messed up right now on this simple topic is this: “If the pre-payment option is currently in the money ie: int. rates are low and interest rates subsequently rise, which bond performs best, a Callable Bond or a Non-Callable Bond” The reason I ask this is recall that a non-callable bond has positive convexity so that it responds more to int. rate drops than it does to int. rate increases. The MBS is displaying negative convexity when interest rates are low ie: rate is < coupon rate. So which bond is better to hold in this scenario. On the one hand I see the value of the pre-payment option falling which is positive for the MBS holder, but how does the MBS price react compared to that of a non-callable bond?