Do MBS have POSITIVE convexity when rates rise?

I understand what happens when rates fall. My old CFA readings seem to imply that when rates rise, MBS are positively convexed due to the decline of the prepay option. These are from 2013, FYI.

Is that right? My understanding is that when rates rise, prepayments slow. Pretty straightforward. But shouldn’t this cause the price to decline MORE than an option free bond of similar maturity? A potable bond would be positively conveyed when rates rise, not MBS?

MBS with the same maturity as option free bond should have lower price than option free bond in order to have higher yield as MBS has negative convex. When rates rise, MBS [Option Free Bond] has positive convex. For instance, MBS with 10yr maturity should decline more than 5yr option free bond when rates rise.

Not sure I agree with this. If rates rise and it declines MORE and if rates falls and it increases LESS, isn’t that negative convexity? For instance, think of a putable bond. If rates rise, it’s price will approach par. That’s positive convexity. For an option free bond, if rates rise it’s price will decline below par. If rates rise and an MBS’s price decline more than an option free bond’s price, how is that positive convexity?

I took a closer look at the readings. I think it depends on the bond’s coupon relative to market yields. If the coupon is less more than the market yield it will be negatively convexed (increase LESS than decrease when rates go down or decrease MORE than an option free when rates go up) because the call option is in the money i.e. borrowers refi activity is very sensitive to rates. However if the coupon is more less than market yield, like way more, than the MBS should behave like an option free bond since the call option is virtually worthless and the prepay activity will be very small.

Am I on the right track here? What do others think?

Yes you’re right. That was my typo.

However, at the higher yield for MBS, [I think] PSA assumption must be accounted.

P.S. Better wait for S2000 to come and illuminate us then

Thanks for clarifying. S2000 is still around? I remember him from back when I was preparing for Level 3.

I think so.

And you figured that I figured, "Well, Dan’s no longer here, so what’s the use?


At low yields, MBSs have negative convexity, just as callable bonds do. (A prepayment option is very much similar to a call option.)

At higher yields, the likelihood of prepayments diminishes sufficiently that the MBS will start to have positive convexity; again, just as callable bonds have. (In essence, when interest rates rise high enough, the prepayment option is out of the money.)

Whether the percentage price change on a 10-year MBS will be greater than or less than the percentage price change on a 5-year straight bond when interest rates increase depends on many factors; it’s impossible to formulate a general rule of “it will” or “it won’t”.

S2000 is legendary as always and thank for illuminating us. In addition to S2000’s awesome answer, I found this book on page 471 under the section Price - Rate Curve of a Mortgage Pass - Through that MBS can have positive convexity when rates rise. All in all, like S2000 said it all depends on the factors. No hard rule then!!

Thanks S2000! To clarify, low yields means higher coupon and vice versa? Higher coupon = higher yield on loans underlying the MBS = more likely to prepay i.e. options in the money. Why would a higher coupon bond have a lower yield? Sorry, it’s been a long couple of days for me and I’m having a moment…


Coupon and yield are independent of each other.

The coupon rate is what the issuer decides to pay. Yield is what the market decides it needs to receive. Price reconciles the two: for a fixed coupon, higher yield results in lower price and vice versa.

For example, a company can issue 10-year, semiannual-pay, $1,000 par bonds that pay coupon rates of 2% or 4% or 6%. If the market decides that it must earn a 5% yield on this company’s bonds, then the 2% bonds will sell for $766.16, the 4% bonds will sell for $922.05, and the 6% bonds will sell for $1,077.95.

If, instead, the market decides that it must earn a yield of 3%, then the bonds will sell for $914.16, $1,085.84, and $1,257.53, respectively.

Putable. Just sayin’…

Thanks and I understand that. I

My thinking is that a higher coupon MBS is more likely to preapy and exhibit negatively convexity than a lower coupon MBS all other things being equal. I never thought of it in terms of “yield” and that’s why I’m struggling a little bit with this concept. I do get the negative and positive convexity that can be exhibited by an MBS but I think of this in coupon versus yield. Maybe I’m overthininking this?

The key difference is that things like yield and price will capture effects missed by the coupon. For example, you just asked about higher coupon versus lower coupon. Sure if everything is exactly the same, higher coupon probably prepays faster. But that doesn’t really tell the full story. Maybe the collateral on a 5% coupon bond was previously HARP’d and therefore hard to refinance again. Maybe the loan balances are low enough that the pain in the ass factor of refinancing outweighs the financial benefits of refinancing. Maybe the collateral is really old and therefore likely burnt out on prepays. Maybe the borrowers have lower FICO scores and therefore can’t refinance. All of these factors will, to varying degrees, slow down prepayment speeds on higher coupon bonds compared to production coupon. And all of these effects will be captured in the price and therefore yield. Since, all else equal, slower prepays are generally better for MBS, these bonds will likely trade at higher prices than general TBAs and hence, all else equal, have lower yields. That’s the way to connect what S2K was saying before, and why it’s probably harder than you think to see the full convexity picture with just coupon.

Now two questions you should think about, just for your growth.

  1. I said slower prepays are generally good for MBS. Can you think of a situation with MBS where slow prepays are a bad thing?

  2. Since you wanted to think of convexity in terms of coupon, which coupons will you expect there to be negative convexity? And which should have positive? (Hint: think of an MBS as long a bond and short an American option).