Duration of Pay Fixed, Receive Floating
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singlesong80
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- Jun 18, 2026
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Pay fixed, receive floating position should give a negative duration. So duraction should decrease.
3rdtimesacharm
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- Jun 18, 2026
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I did this last night.
Because a PAY FIXED position becomes more valuable as Interest rates increase ( paying lesser of a fixed rate is more valuable,) and as interest rates Increase, your LOAN VALUE Decreases, therefore negative duration
Right ?
Because a PAY FIXED position becomes more valuable as Interest rates increase ( paying lesser of a fixed rate is more valuable,) and as interest rates Increase, your LOAN VALUE Decreases, therefore negative duration
Right ?
duration decreases for pay fixed, receive floating swap. If I remember corectly its because you are esentially buying a florating rate asset that has a variable rate, hence lower duration than the fixed rate asset. its been months since I read this section, just wanted to pretend I knew something….
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I used study note of Schweser, 2009 version. On page 225, book 4, it reads as follows:
“Now we’ll assume management enters a pay-fixed, receive-floating swap to change the nature of a floating rate liability. For simplicity, we’ll assume the swap floating payments are the same as the floating rate liability payments so that they exactly offset one another. The result is that management has effectively changed the liability form floating to fixed without changing the firm’s assets.
Since fixed-rate instruments have a longer duration than floating-rate instruments, the addition of the swap has increased the duration of the firm’s liabilities and narrowed the difference between the asset and liability durations. The bottom line is that the firm’s equity, with a shortened duration, is now less sensitive to changes in interest rates than before management entered the swap. If rates rise, the value of the equity will fall less than before management entered the swap. If rates rise, the value of the equity will fall less than before managment used the swap. To protect against risign rates, management has sacrificed some of the upside potential from falling rates.”
“Now we’ll assume management enters a pay-fixed, receive-floating swap to change the nature of a floating rate liability. For simplicity, we’ll assume the swap floating payments are the same as the floating rate liability payments so that they exactly offset one another. The result is that management has effectively changed the liability form floating to fixed without changing the firm’s assets.
Since fixed-rate instruments have a longer duration than floating-rate instruments, the addition of the swap has increased the duration of the firm’s liabilities and narrowed the difference between the asset and liability durations. The bottom line is that the firm’s equity, with a shortened duration, is now less sensitive to changes in interest rates than before management entered the swap. If rates rise, the value of the equity will fall less than before management entered the swap. If rates rise, the value of the equity will fall less than before managment used the swap. To protect against risign rates, management has sacrificed some of the upside potential from falling rates.”
cfamania Wrote:
——————————————————-
> Does duration increase after adding pay fixed,
> receive floating position? If so, equity of such
> counterparty will be less sensitive to interest
> rate change as Equity Duration = Asset Duration -
> Liability Duration.
Equity Duration(ED)=Asset Duration(AD) - Liabilities Duration(LD).
Assumption - Assets are higher than liabilities (Equities is not zero)
D of Fixed leg (Pay or receive) will always be higher than the floating leg.
Receive(assets) fixed ….. Assets D increases…..Equity D increaese (ED=AD-LD)
Pay(liability) Fixed….Liabilities D increases…..Equity D decreases (ED=AD-LD)
Equities D …. +ve correlated with asset D & -ve correlated with Liabilities D.
Easy to remeber if you focus on fixed leg.
Therefore, sensitivity(Duration) of firm equity will increase/decrease depending upon whether firm has entered as fixed payer/reciever on swap.
——————————————————-
> Does duration increase after adding pay fixed,
> receive floating position? If so, equity of such
> counterparty will be less sensitive to interest
> rate change as Equity Duration = Asset Duration -
> Liability Duration.
Equity Duration(ED)=Asset Duration(AD) - Liabilities Duration(LD).
Assumption - Assets are higher than liabilities (Equities is not zero)
D of Fixed leg (Pay or receive) will always be higher than the floating leg.
Receive(assets) fixed ….. Assets D increases…..Equity D increaese (ED=AD-LD)
Pay(liability) Fixed….Liabilities D increases…..Equity D decreases (ED=AD-LD)
Equities D …. +ve correlated with asset D & -ve correlated with Liabilities D.
Easy to remeber if you focus on fixed leg.
Therefore, sensitivity(Duration) of firm equity will increase/decrease depending upon whether firm has entered as fixed payer/reciever on swap.
cfamania Wrote:
——————————————————-
> Does duration increase after adding pay fixed,
> receive floating position?
Incorrect bcos
Duration of Equity/portfolio decreases as pay fixed (liability) D increases (Inverse relationship)
Correct
If so, equity of such
> counterparty will be less sensitive to interest
> rate change as Equity Duration = Asset Duration -
> Liability Duration.
To be honest, this accounting equation is helping me to remember these relationships as I find it difficult to use the term negative duration (assets or liabilities prices are positively correlated with interest rates)
——————————————————-
> Does duration increase after adding pay fixed,
> receive floating position?
Incorrect bcos
Duration of Equity/portfolio decreases as pay fixed (liability) D increases (Inverse relationship)
Correct
If so, equity of such
> counterparty will be less sensitive to interest
> rate change as Equity Duration = Asset Duration -
> Liability Duration.
To be honest, this accounting equation is helping me to remember these relationships as I find it difficult to use the term negative duration (assets or liabilities prices are positively correlated with interest rates)
yellayella
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- Jun 18, 2026
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sorry i am still confused here:
if i am a floating rate borrower and i enter into a pay fixed receive floating swap, my final position ends up being like a fixed rate loan.
does equity duration increase or decrease?
_> in the book p. 484, reading 38 it says it increases the risk of the companys market value
but acutally the duration of my liabiilites goes from -0.125 to -0.625
2) i am a fixed rate borrower and want to take advantage of sinking rates so i enter ito a pay floating receive fixed swap, making my loan floating.
what happens to the equity duration?
in another example there was a borrower, that converted its loan from fixed to floating and it said that the liabilites have no less duration (bc they are floating) and so the duration of the equity increases.
im not sure what the two effects are? both have negative impact on the equity?
is the confusion bc of the minus signs?
if i am a floating rate borrower and i enter into a pay fixed receive floating swap, my final position ends up being like a fixed rate loan.
does equity duration increase or decrease?
_> in the book p. 484, reading 38 it says it increases the risk of the companys market value
but acutally the duration of my liabiilites goes from -0.125 to -0.625
2) i am a fixed rate borrower and want to take advantage of sinking rates so i enter ito a pay floating receive fixed swap, making my loan floating.
what happens to the equity duration?
in another example there was a borrower, that converted its loan from fixed to floating and it said that the liabilites have no less duration (bc they are floating) and so the duration of the equity increases.
im not sure what the two effects are? both have negative impact on the equity?
is the confusion bc of the minus signs?
Duration increases by holding a position that movies inversely with rates. If rates go up, you’ll add a pay fixed, receive float.cfamania wroteoes duration increase after adding pay fixed, receive floating position? If so, equity of such counterparty will be less sensitive to interest rate change as Equity Duration = Asset Duration - Liability Duration. Do I understand correctly?
If rates are gonna go down, you’d pay float, receive fixed.
yellayella
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- Jun 18, 2026
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if i am a floating rate issuer and i add pay fixed received floating, i end up wiht more duration.
let’s say i was a floating rate issue, my duration was -0.25 (bc i am the issuer). now i enter into a pay fixed receive floating swap ( +0.25-0.75= -0.5 (assumin it is a 1 yrs swap with semi annual payment).
new duration is= -0.25 + -0.5 = -0.75
so sensitivity of equity goes up bc minus minus sign!
the duration of a issuer is minus.
please can somebody clearify!!
let’s say i was a floating rate issue, my duration was -0.25 (bc i am the issuer). now i enter into a pay fixed receive floating swap ( +0.25-0.75= -0.5 (assumin it is a 1 yrs swap with semi annual payment).
new duration is= -0.25 + -0.5 = -0.75
so sensitivity of equity goes up bc minus minus sign!
the duration of a issuer is minus.
please can somebody clearify!!
let’s say you’re paying fixed for 20 years, you have have negative duratione exposure. adding a pay float, received-fixed (+ duration) would reduce the liaiblity duration EXPOSURE if rates are going down.
duration of assets stay the same, so the duration of equities must increase to equalize (A = L goes down + E goes up).
duration of assets stay the same, so the duration of equities must increase to equalize (A = L goes down + E goes up).
yellayella
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- Jun 18, 2026
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ok agree makes sense, with numbers
we would say, if i am the fixed issuer, i have an initial duration of lets say (-0.75) + (0.5 (swap)) = - 0.25 (duration decreases in absolute terms)
Dur Assets - Dur Liab = Dur Equity
7 - - 0.75 = 7.75
7 - - 0.25 = 7.25
what is wrong here?
2nd case
what happens if i am floating rate issuer:
my duration of the issued bond: (-0.25) then i add adding a pay fixed , received-floating (- duration) would increase the liaiblity duration EXPOSURE
-0.25+ 0.5 = 0.25
7 - -0.25 = 7.25
7-0.25 = 6.75
i am also refering here to p. 484, reading 38 it says it increases the risk of the companys market value
we would say, if i am the fixed issuer, i have an initial duration of lets say (-0.75) + (0.5 (swap)) = - 0.25 (duration decreases in absolute terms)
Dur Assets - Dur Liab = Dur Equity
7 - - 0.75 = 7.75
7 - - 0.25 = 7.25
what is wrong here?
2nd case
what happens if i am floating rate issuer:
my duration of the issued bond: (-0.25) then i add adding a pay fixed , received-floating (- duration) would increase the liaiblity duration EXPOSURE
-0.25+ 0.5 = 0.25
7 - -0.25 = 7.25
7-0.25 = 6.75
i am also refering here to p. 484, reading 38 it says it increases the risk of the companys market value
yellayella
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- Jun 18, 2026
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please…
hezagenius
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- Jun 18, 2026
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Adding a pay fixed/receive floating swap decreases duration regardless of duration sign. If your duration is already negative, the pay fixed/receive floating swap will make it more negative and thus more sensitive to interest rate changes.
Let’s say you just purchased a fixed bond and you have no debt. Let’s assume that the duration of the bonds you bought is 5 years. Your Equity Duration = Asset Duration - Liability Duration. In this case, your AD is 5 and your LD is 0 so your ED = 5 - 0 = 5. If you want to reduce your sensitivity to interest rate changes, you need to find a way to reduce your duration.
The receive side of a swap is the asset side and the pay side is the liability side. The duration of a pay fixed/receive floating swap = Duration of receive floating - Duration of pay fixed. The duration of a floating rate instrument will usually be much shorter than the duration of a fixed rate instrument. Let’s say the duration of the floating side is 0.25 and the duration of the fixed side is 3. That means the duration of the pay fixed/receive floating swap is 0.25 - 3 = -2.75.
So your portfolio currently has a duration of 5 and you want to reduce your sensitivity to interest rate changes by lowering your duration. That means you need to add a swap that has a negative duration so you want to add a pay fixed/receive floating swap. This reduces your duration from 5 to 2.25 (5 + -2.75). Your sensitivity has been reduced.
Now, let’s say you issued the same bonds from the first example and you don’t have any assets (yes this is hypothetical). So your ED = AD - LD = 0 - 5 = -5. You think, I know, I will add a pay fixed/receive floating swap to reduce my duration! Your new duration would be -5 + -2.75 = -7.75. Your duration went from -5 to -7.75 so you actually increased your sensitivity to interest rate changes!
Keep in mind that duration can be positive or negative and the greater the absolute value of the duration, the greater the sensitivity to interest rate changes.
If you have a positive duration and want to reduce your sensitivity, you need to add a swap with negative duration (pay fixed/receive floating) to get you closer to a duration of 0. If you have a negative duration, you would want to add a swap with positive duration (pay float/receive fixed) to get you closer to 0.
Let’s say you just purchased a fixed bond and you have no debt. Let’s assume that the duration of the bonds you bought is 5 years. Your Equity Duration = Asset Duration - Liability Duration. In this case, your AD is 5 and your LD is 0 so your ED = 5 - 0 = 5. If you want to reduce your sensitivity to interest rate changes, you need to find a way to reduce your duration.
The receive side of a swap is the asset side and the pay side is the liability side. The duration of a pay fixed/receive floating swap = Duration of receive floating - Duration of pay fixed. The duration of a floating rate instrument will usually be much shorter than the duration of a fixed rate instrument. Let’s say the duration of the floating side is 0.25 and the duration of the fixed side is 3. That means the duration of the pay fixed/receive floating swap is 0.25 - 3 = -2.75.
So your portfolio currently has a duration of 5 and you want to reduce your sensitivity to interest rate changes by lowering your duration. That means you need to add a swap that has a negative duration so you want to add a pay fixed/receive floating swap. This reduces your duration from 5 to 2.25 (5 + -2.75). Your sensitivity has been reduced.
Now, let’s say you issued the same bonds from the first example and you don’t have any assets (yes this is hypothetical). So your ED = AD - LD = 0 - 5 = -5. You think, I know, I will add a pay fixed/receive floating swap to reduce my duration! Your new duration would be -5 + -2.75 = -7.75. Your duration went from -5 to -7.75 so you actually increased your sensitivity to interest rate changes!
Keep in mind that duration can be positive or negative and the greater the absolute value of the duration, the greater the sensitivity to interest rate changes.
If you have a positive duration and want to reduce your sensitivity, you need to add a swap with negative duration (pay fixed/receive floating) to get you closer to a duration of 0. If you have a negative duration, you would want to add a swap with positive duration (pay float/receive fixed) to get you closer to 0.
yellayella
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- Jun 18, 2026
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thanks this all makes sense, thank you.
all i want to know what happens to duration of equity when
(i)converting floating loan to fixed (w/ pay fixed receive floating swap) does duration of equity increase or decrease?
ii) converting fixed to floating (w/ receive fixed pay floating swap) does duration of equity increase or decrease?
please make an example wiht numbers, as it is still not clear to me!
all i want to know what happens to duration of equity when
(i)converting floating loan to fixed (w/ pay fixed receive floating swap) does duration of equity increase or decrease?
ii) converting fixed to floating (w/ receive fixed pay floating swap) does duration of equity increase or decrease?
please make an example wiht numbers, as it is still not clear to me!
yellayella
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- Jun 18, 2026
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duration of assets - duration of liabilites = duration of equity, please see also the cfai textbook where it is explicitly mentioned and also exam schweser exams 2011 exam 3PM (question 17.2)