Why does a drop in rates cause bond portfolio durations to fall?

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Virus4762
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Why does a drop in rates cause bond portfolio durations to fall?

Post by Virus4762 »

The reasoning goes that a drop in rates increases the rate of mortgage refinancing which in turn reduces the duration of the portfolios holding these mortgages which causes them to add duration to their portfolio by buying more bonds, leading to a further decrease in yields.


The part that throws me off though is the concept of mortgage refinancing reducing duration of a bond portfolio. If someone had 10 years on their mortgage remaining and they refinanced that mortgage to 30 years, it seems like that would that increase, not decrease, the duration of the portfolio holding that mortgage.


Does anyone have any understanding of this? Why do refinancings cause a decrease in bond portfolio duration?
SteadyOne
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by SteadyOne »

Virus4762 wrote: Wed Jun 16, 2021 11:04 am The reasoning goes that a drop in rates increases the rate of mortgage refinancing which in turn reduces the duration of the portfolios holding these mortgages which causes them to add duration to their portfolio by buying more bonds, leading to a further decrease in yields.


The part that throws me off though is the concept of mortgage refinancing reducing duration of a bond portfolio. If someone had 10 years on their mortgage remaining and they refinanced that mortgage to 30 years, it seems like that would that increase, not decrease, the duration of the portfolio holding that mortgage.


Does anyone have any understanding of this? Why do refinancings cause a decrease in bond portfolio duration?
This is about refinance RISK. This risk is inherent to mortgages so mortgage based securities are priced differently from ordinary bonds (lower).
“Every de­duc­tion is al­lowed as a mat­ter of leg­isla­tive grace.” US Federal Court
Explorer
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by Explorer »

Virus4762 wrote: Wed Jun 16, 2021 11:04 am The reasoning goes that a drop in rates increases the rate of mortgage refinancing which in turn reduces the duration of the portfolios holding these mortgages which causes them to add duration to their portfolio by buying more bonds, leading to a further decrease in yields.


The part that throws me off though is the concept of mortgage refinancing reducing duration of a bond portfolio. If someone had 10 years on their mortgage remaining and they refinanced that mortgage to 30 years, it seems like that would that increase, not decrease, the duration of the portfolio holding that mortgage.


Does anyone have any understanding of this? Why do refinancings cause a decrease in bond portfolio duration?
I tend to agree with your supposition that the mortgage bond fund duration should increase as more refinancing occurs (majority of people refinancing like to extend term).
SteadyOne
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by SteadyOne »

Explorer wrote: Wed Jun 16, 2021 11:22 am
Virus4762 wrote: Wed Jun 16, 2021 11:04 am The reasoning goes that a drop in rates increases the rate of mortgage refinancing which in turn reduces the duration of the portfolios holding these mortgages which causes them to add duration to their portfolio by buying more bonds, leading to a further decrease in yields.


The part that throws me off though is the concept of mortgage refinancing reducing duration of a bond portfolio. If someone had 10 years on their mortgage remaining and they refinanced that mortgage to 30 years, it seems like that would that increase, not decrease, the duration of the portfolio holding that mortgage.


Does anyone have any understanding of this? Why do refinancings cause a decrease in bond portfolio duration?
I tend to agree with your supposition that the mortgage bond fund duration should increase as more refinancing occurs (majority of people refinancing like to extend term).
Once the mortgage is refinanced it is no longer within the bond (mortgage based security MBS) so the number of mortgages underlying the bond are getting increasingly smaller as more and more underlying mortgages are basically disappear from within the bond. MBS shrinks and may become a shadow of it former self as more and more people refi.

If you refinance this is a new mortgage and it becomes a part of a new bond which has nothing to do with MBS bond within which the old mortgage at this particular house was written.
“Every de­duc­tion is al­lowed as a mat­ter of leg­isla­tive grace.” US Federal Court
alex_686
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by alex_686 »

SteadyOne wrote: Wed Jun 16, 2021 11:19 am This is about refinance RISK. This risk is inherent to mortgages so mortgage based securities are priced differently from ordinary bonds (lower).
I will agree with the first part but not the second.

Duration is a risk measure. You are measuring the same portfolio at 2 different times. So essentially, 2 different portfolio since they are holding 2 different sets of bonds. So duration, a risk measure, is going to change over time.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
SteadyOne
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by SteadyOne »

alex_686 wrote: Wed Jun 16, 2021 2:09 pm
SteadyOne wrote: Wed Jun 16, 2021 11:19 am This is about refinance RISK. This risk is inherent to mortgages so mortgage based securities are priced differently from ordinary bonds (lower).
I will agree with the first part but not the second.

Duration is a risk measure. You are measuring the same portfolio at 2 different times. So essentially, 2 different portfolio since they are holding 2 different sets of bonds. So duration, a risk measure, is going to change over time.
If you taking about portfolio containing multiple MBS, being bought and sold then yes.
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Thesaints
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by Thesaints »

That's only true for mortgage bonds. If rates drop, people refinance lowering the average maturity, since they would not take a new mortgage with the same residual maturity. Think of it: for an equal monthly payment they could shorten the maturity of their outstanding debt.

If rates increase, instead, the number of people who would have prepaid their debt becomes smaller, thus increasing the fund's average maturity.

For non mortgage backed bonds instead the story is different. Everything else being equal, a bond with lower yield has a longer duration. Therefore, lower rates tend to push up average durations, but this is not an effect as big as it is (in the opposite direction) for mortgage backed bonds.
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by Explorer »

SteadyOne wrote: Wed Jun 16, 2021 2:05 pm
Explorer wrote: Wed Jun 16, 2021 11:22 am
Virus4762 wrote: Wed Jun 16, 2021 11:04 am The reasoning goes that a drop in rates increases the rate of mortgage refinancing which in turn reduces the duration of the portfolios holding these mortgages which causes them to add duration to their portfolio by buying more bonds, leading to a further decrease in yields.


The part that throws me off though is the concept of mortgage refinancing reducing duration of a bond portfolio. If someone had 10 years on their mortgage remaining and they refinanced that mortgage to 30 years, it seems like that would that increase, not decrease, the duration of the portfolio holding that mortgage.


Does anyone have any understanding of this? Why do refinancings cause a decrease in bond portfolio duration?
I tend to agree with your supposition that the mortgage bond fund duration should increase as more refinancing occurs (majority of people refinancing like to extend term).
Once the mortgage is refinanced it is no longer within the bond (mortgage based security MBS) so the number of mortgages underlying the bond are getting increasingly smaller as more and more underlying mortgages are basically disappear from within the bond. MBS shrinks and may become a shadow of it former self as more and more people refi.

If you refinance this is a new mortgage and it becomes a part of a new bond which has nothing to do with MBS bond within which the old mortgage at this particular house was written.
Wouldn't new MBS with newly refinanced mortgages get bought by the fund -- which would have longer duration?
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by Thesaints »

Explorer wrote: Wed Jun 16, 2021 3:39 pm Wouldn't new MBS with newly refinanced mortgages get bought by the fund -- which would have longer duration?
Some people refinance to lower their monthly rate, but others refinance to decrease their residual maturity. On average, the new mortgages tend to be shorter dated.
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by SteadyOne »

Explorer wrote: Wed Jun 16, 2021 3:39 pm
SteadyOne wrote: Wed Jun 16, 2021 2:05 pm
Explorer wrote: Wed Jun 16, 2021 11:22 am
Virus4762 wrote: Wed Jun 16, 2021 11:04 am The reasoning goes that a drop in rates increases the rate of mortgage refinancing which in turn reduces the duration of the portfolios holding these mortgages which causes them to add duration to their portfolio by buying more bonds, leading to a further decrease in yields.


The part that throws me off though is the concept of mortgage refinancing reducing duration of a bond portfolio. If someone had 10 years on their mortgage remaining and they refinanced that mortgage to 30 years, it seems like that would that increase, not decrease, the duration of the portfolio holding that mortgage.


Does anyone have any understanding of this? Why do refinancings cause a decrease in bond portfolio duration?
I tend to agree with your supposition that the mortgage bond fund duration should increase as more refinancing occurs (majority of people refinancing like to extend term).
Once the mortgage is refinanced it is no longer within the bond (mortgage based security MBS) so the number of mortgages underlying the bond are getting increasingly smaller as more and more underlying mortgages are basically disappear from within the bond. MBS shrinks and may become a shadow of it former self as more and more people refi.

If you refinance this is a new mortgage and it becomes a part of a new bond which has nothing to do with MBS bond within which the old mortgage at this particular house was written.
Wouldn't new MBS with newly refinanced mortgages get bought by the fund -- which would have longer duration?
New mortgages might be securitized into new MBS and those will have lower coupon. Or banks might keep mortgages in their own portfolios. It still happens. The former may be assumed to have longer duration IF rates go higher. If rates still go lower people will refi again and cycle repeats. That’s why Ginnie Maes have worse performance than many other government guaranteed obligations. If rates go up up people will be stuck with lower mortgages reluctant to move and unable to refi. And investors will be stuck with lower coupons or capital losses.

Also, people who are unable to refi even when rates are lower usually have lower credit and prone to default. Government will pay investors principal since GSEs guarantee it, but then they have to refinance cash at a lower rates
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by Stinky »

Thesaints wrote: Wed Jun 16, 2021 3:18 pm That's only true for mortgage bonds. If rates drop, people refinance lowering the average maturity, since they would not take a new mortgage with the same residual maturity. Think of it: for an equal monthly payment they could shorten the maturity of their outstanding debt.

If rates increase, instead, the number of people who would have prepaid their debt becomes smaller, thus increasing the fund's average maturity.

For non mortgage backed bonds instead the story is different. Everything else being equal, a bond with lower yield has a longer duration. Therefore, lower rates tend to push up average durations, but this is not an effect as big as it is (in the opposite direction) for mortgage backed bonds.
This is a good summary.

In general, the duration of bond funds increase when rates drop. An exception to the general rule is funds with significant amounts of MBS, whose duration may decrease because of refinancing.
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by grabiner »

The relevant factor is convexity. If a bond has positive convexity, its duration decreases when rates rise. If it has negative convexity, its duration increases when rates rise. (The term corresponds to the definition of convexity in calculus; convexity is the second derivative of price with respect to rates.)

Zero-coupon bonds have zero convexity (for Macaulay duration; it is very slightly positive for modified duration): a ten-year zero-coupon bond has a duration of ten years regardless of what happens to bond prices and interest rates.

Coupon bonds have slightly positive convexity. If rates rise, the present value of the later payments is discounted more, so more of the bond's value comes from its coupons.

Callable bonds, including mortgage-backed bonds (where a refinance of the mortgage works like a call) and most municipal bonds, have negative convexity. If rates fall, the bond is more likely to be called, so it behaves like a shorter-term bond. (This is why Vanguard's "long-term" muni funds have relatively short durations now; rates are so low that a 25-year muni callable in 5 years will probably be called.)
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by Doc »

grabiner wrote: Wed Jun 16, 2021 9:30 pm The relevant factor is convexity. If a bond has positive convexity, its duration decreases when rates rise. If it has negative convexity, its duration increases when rates rise. (The term corresponds to the definition of convexity in calculus; convexity is the second derivative of price with respect to rates.)

...

Callable bonds, including mortgage-backed bonds (where a refinance of the mortgage works like a call) and most municipal bonds, have negative convexity. If rates fall, the bond is more likely to be called, so it behaves like a shorter-term bond.
David lays out the major aspects of the negative convexity issue. The big difference is in the "call" issue. With normal Treasuries the call provision lies with the issuer. But "The Treasury has not issued callable securites since 1985. Larry Swedroe" The Only Guide to a Winning Investment Strategy You'll Ever Need: The Way Smart Money Invests Today" First Edition March 2006 p 156.

This is the major reason for MBS to yield more than nominal Treasuries. You "win" with the MBS as long as the rooster doesn't come home to roost. Since "bonds are for safety" I personally don't invest in MBS and therefore use a 1-10 Gov/credit index as my bond bogey instead of a Total Bond Market fund.

So in answer to the OP's question: To the extent that mortgage rates are declining many people with mortgages are refinancing and trading their high rate mortgages for cheaper ones which may actually have a higher expected duration than the original.

Aarrgghh.
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Virus4762
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by Virus4762 »

Thesaints wrote: Wed Jun 16, 2021 3:18 pm That's only true for mortgage bonds. If rates drop, people refinance lowering the average maturity, since they would not take a new mortgage with the same residual maturity. Think of it: for an equal monthly payment they could shorten the maturity of their outstanding debt.

If rates increase, instead, the number of people who would have prepaid their debt becomes smaller, thus increasing the fund's average maturity.

For non mortgage backed bonds instead the story is different. Everything else being equal, a bond with lower yield has a longer duration. Therefore, lower rates tend to push up average durations, but this is not an effect as big as it is (in the opposite direction) for mortgage backed bonds.
I don't understand. Don't longer duration bonds normally have higher yields (i.e. 10 year note has a longer duration than a 1 year bill)?


EDIT: Or are you referring to coupon payments?
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Re: Why does a drop in rates cause bond portfolio durations to fall?

Post by grabiner »

Virus4762 wrote: Mon Jun 21, 2021 10:19 pm
Thesaints wrote: Wed Jun 16, 2021 3:18 pm For non mortgage backed bonds instead the story is different. Everything else being equal, a bond with lower yield has a longer duration. Therefore, lower rates tend to push up average durations, but this is not an effect as big as it is (in the opposite direction) for mortgage backed bonds.
I don't understand. Don't longer duration bonds normally have higher yields (i.e. 10 year note has a longer duration than a 1 year bill)?

EDIT: Or are you referring to coupon payments?
The statement "everything else being equal" implies a comparison of identical bonds. Given two bonds with the same payment schedule, the bond with a higher yield will have a shorter duration. The reason is that Macaulay duration is the average of the time to all future payments, weighted by the present value of those payments. A higher yield has a greater reduction on the present value of payments farther in the future. The most extreme example is an infinite-maturity bond (or a preferred stock, which is equivalent to an infinite-maturity bond but does not guarantee payments); a preferred stock with a 4% yield has a 25-year duration, but if the yield rises to 5%, the duration declines to 20 years. But a long-term, high-yielding bond would behave similarly, because a relatively small part of its value is the repayment at maturity.

There is another effect if you use modified duration, which is the actual measure of interest-rate sensitivity; a bond with a modified duration of 10 years will have its value change by 10 times a small change in interest rates. Modified duration is equal to Macaulay duration divided by (1+interest rate). Thus the modified duration of even a zero-coupon bond decreases when rates increase. A 10-year zero-coupon bond has a Macaulay duration of 10 years regardless of interest rates, but its modified duration is 9.62 years at a rate of 4%, and 9.52 at a rate of 5%.

(As a separate point, given two bonds with the same yield, the one with the higher coupon payment will have a shorter duration, because less of its value is in the final payment at maturity.)
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