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MBS: Impact of negative convexity at higher yields

Roshan Ramdas

Active Member
Hi David,

Need your help with the below question please (from the BT 2010 mock). I've copied out 2 passages which have conflicting opinions about the impact of higher interest rates on MBS investors.

Passage 1 seems to suggest that investors are benefitted by prepayment at higher interest rates on account of better reinvestment income potential.
Passage 2 seems to indicate that investors do not benefit at high and low yields.

Question - How does the embedded option in the mortgage pass-through impact the price-yield curve at HIGHER yields (think of the answer to 8.2)?

Passage 1 (from the mock pdf itself)

As Tuckman explains, “this phenomenon [higher price than noncallable equivalent at higher yields] is due to the fact that housing turnover, defaults, and disasters generate prepayments even when rates are relatively high. And when rates are high relative to the existing mortgage rate, prepayments benefit investors in the pass-through: A below-market fixed income investment is returned to these investors at par.” To summarize 8.3 and 8.4, the embedded call in the mortgage pass-through creates negative convexity at low yields (a generic feature of the embedded call) AND increases the price (relative to a nonprepayable mortgage) at higher yields (a specific feature of mortgagor dynamics).


Passage 2 (from BT question bank)

D. Negative convexity is unfavorable to the long at both low and high yields. (and so the investor is compensated with a higher yield, ceteris paribus) Fabozzi: "It is important to understand how changes in prepayment rates impact the performance of mortgages and MBS. Since prepayments increase as bond prices rise and market yields are declining, mortgages shorten in average life and duration when the bond markets rally, constraining their price appreciation. Conversely, rising yields cause prepayments to slow and bond durations to extend, resulting in a greater drop in price than experienced by more traditional (i.e., option-free) fixed income products. As a result, the price performance of mortgages and MBS tends to lag that of comparable fixed maturity instruments (such as Treasury notes) when the prevailing level of yields increases. This phenomenon is generically described as “negative convexity.” The effect of changing prepayment speeds on mortgage durations, based on movements in interest rates, is precisely the opposite of what a bondholder would desire. (Fixed income portfolio managers, for example, extend durations as rates decline, and shorten them when rates rise.) The price performance of mortgages and MBS is, therefore, decidedly nonlinear in nature, and the product will underperform assets that do not exhibit negatively convex behavior as rates decline."

Thank you
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @Roshan Ramdas

Great observation. Candidly, it reflects the difference (progression) in the assigned readings (specifically, Tuckman from 2nd to 3rd edition, but also the addition of Veronesi and the addition of Fabozzi). Tuckman 2nd edition says "And when rates are
high relative to the existing mortgage rate, prepayments benefit investors in the pass-through: A below-market fixed income investment is returned to these investors at par. Therefore, these seemingly suboptimal prepayments raise the price of a pass-through relative to the price of a nonprepayable mortgage." (Tuckman page 471, 2nd edition) but this is replaced in Tuckman 3rd with a more nuanced explanation at higher yields.

Veronesi (for sure) and Fabozzi (I think) both illustrate negative convexity at high yields, as the base case). But they make a key assumption that PSA is consistently decreasing with yield (i.e., a consistent function of higher PSA at lower rates).

Even in the current syllabus, I think it's fair to say that Tuckman (3rd edition) still has a base case of positive convexity at high yields but Veronesi has negative convexity throughout. But their PSA assumptions vary, is why! I don't actually think these two statements contradict because the first ("And when rates are high relative to the existing mortgage rate, prepayments benefit investors in the pass-through") must be true about loans that are prepaid, while the second concerns the convexity implied by the proportion (constant? varying) that are prepaid as rates increase. Strictly, I can reconcile ....

But I think the more helpful point is, to be candid, I learned something as the syllabus progressed. Previously I thought (per Tuckman 2nd) that, for a pass thru, negative convexity was only a feature at lower rates while positive convexity was likely at higher yields (consistent with viewing the prepayment option as a call option on the bond, that had diminishing influence at higher rates: when viewed only as an embedded option, or where the financial optionality dominates the sub-optimal turnover, the positive convexity ought to restore at higher rates!), but now I understand better:
  1. Let's not forget the key point: negative convexity as low yields is the defining characteristic of pass-thru MBS (as prepayment is a defining risk). Nothing above has changed the low yield statement!
  2. At higher yields, it depends on the PSA assumption. As Tuckman shows, PSA can be constant but is more likely an incentive function. I hope that explains, great observation!
 

Roshan Ramdas

Active Member
Hi @Roshan Ramdas

Great observation. Candidly, it reflects the difference (progression) in the assigned readings (specifically, Tuckman from 2nd to 3rd edition, but also the addition of Veronesi and the addition of Fabozzi). Tuckman 2nd edition says "And when rates are
high relative to the existing mortgage rate, prepayments benefit investors in the pass-through: A below-market fixed income investment is returned to these investors at par. Therefore, these seemingly suboptimal prepayments raise the price of a pass-through relative to the price of a nonprepayable mortgage." (Tuckman page 471, 2nd edition) but this is replaced in Tuckman 3rd with a more nuanced explanation at higher yields.

Veronesi (for sure) and Fabozzi (I think) both illustrate negative convexity at high yields, as the base case). But they make a key assumption that PSA is consistently decreasing with yield (i.e., a consistent function of higher PSA at lower rates).

Even in the current syllabus, I think it's fair to say that Tuckman (3rd edition) still has a base case of positive convexity at high yields but Veronesi has negative convexity throughout. But their PSA assumptions vary, is why! I don't actually think these two statements contradict because the first ("And when rates are high relative to the existing mortgage rate, prepayments benefit investors in the pass-through") must be true about loans that are prepaid, while the second concerns the convexity implied by the proportion (constant? varying) that are prepaid as rates increase. Strictly, I can reconcile ....

But I think the more helpful point is, to be candid, I learned something as the syllabus progressed. Previously I thought (per Tuckman 2nd) that, for a pass thru, negative convexity was only a feature at lower rates while positive convexity was likely at higher yields (consistent with viewing the prepayment option as a call option on the bond, that had diminishing influence at higher rates: when viewed only as an embedded option, or where the financial optionality dominates the sub-optimal turnover, the positive convexity ought to restore at higher rates!), but now I understand better:
  1. Let's not forget the key point: negative convexity as low yields is the defining characteristic of pass-thru MBS (as prepayment is a defining risk). Nothing above has changed the low yield statement!
  2. At higher yields, it depends on the PSA assumption. As Tuckman shows, PSA can be constant but is more likely an incentive function. I hope that explains, great observation!
Thank you David,....this helps !!
 

southeuro

Member
hi all,

sorry for the "very basic" question... but here's a statement:

"when the yield is higher than the coupon rate of an MBS, the MBS behaves similar to corporate bond as interest rates change" -- the statement is said to be true.
here the "yield" is used to mean "interest rate", correct? b/c if it is, then obviously, there's little incentive to prepay, hence no negative convexity, hence similar behavior to that of a corporate bond.

Thoughts? If you can include a diagram I think that'd help me understand better.

Thanks
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @southeuro

"Yield" refers to "yield to maturity" (YTM) which is a specific type of Interest Rate (others are spot and forward, e.g.), but in this context (i.e., Tuckman and Veronesi on MBS) yield is synonymous with rate. That's because we are generally here referring to the classic Price/Yield curve where the X axis is yield.

The statement refers to the ambiguity at the higher yield (rate) that I referred to above. To illustrate, see the chart below, which is Tuckman 20.5 but I added the blue line:
  • The solid line (i.e., S-Curve CPR) illustrates Tuckman's baseline. Notice it exhibits the classic negative convexity at low yields but, consistent with your quote, reverts to positive convexity at high yields (at high yield, it's matching the CPR=6% which is constant prepayment). The prepayment models (i.e, CPR=6% and S-Curve CPR) have a higher price, at the higher yield (rate), because prepayments are sub-optimal to the borrower and conversely advantageous to the investors: "the price of the pass-through is above that of the nonprepayable mortgage when rates are relatively high. This phenomenon is due to the fact that housing turnover, defaults, and disasters generate prepayments even when rates are relatively high. And when rates are high relative to the existing mortgage rate, prepayments benefit investors in the pass-through: A below-market fixed income investment is returned to these investors at par. Therefore, these seemingly suboptimal prepayments raise the price of a pass-through relative to the price of a nonprepayable mortgage. These prepayments are only seemingly suboptimal because it may very well be optimal for the homeowner to move. But, from the narrower perspective of interest rate mathematics and of investors in the MBS, turnover prepayments in a high-rate environment raise the value of mortgages." (Tuckman 2nd Edition, where he better explains it!)
  • The blue line represent Veronesi's baseline. What's the difference? Simply that his model assumes the PSA (and CPR) is decreasing throughout the curve as the rate increases. A decreasing CPR/PSA "keeps alive" the negative convexity (as opposed to the above Tuckman models which feather into a low but constant CPR at high rates). In this way, it depends on the prepayment (CPR) assumption used.
 
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