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Yield curves and break even inflation

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TheMotorcycleBoy
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Yield curves and break even inflation

#441641

Postby TheMotorcycleBoy » September 12th, 2021, 2:29 pm

Hi folks

Following from recent posts from over here in which GS and dealtn, discussed Break even inflation I decided to spend some more time researching what this means. I imagine that I have got the wrong end of the stick, since I don't really have any decent books on this subject and all I know so far is from attempting to interpret the above two fools' posts and internet reads.

dealtn wrote:By comparing the nominal yield and the real yield of conventional gilts and index linked gilts you get an approximate market based inflation rate. It's approximate for a number of reasons. Firstly it is unusual to get exact matches of redemption dates on the gilts, so the simply derived difference lacks accuracy. Secondly you need to adjust for the credit curve of the issuer, which is usually negligible, but even for the UK government is non-zero. Thirdly the "yield" on index linked gilts does have some assumptions in its calculation (which aren't strictly speaking comparable between

So I decided to get some more information from the BoEs yield curve webpage by downloading the "latest yield curve data". This was a zip with the following contents:

'BLC Nominal daily data current month.xlsx'
'GLC Inflation daily data current month.xlsx'
'GLC Nominal daily data current month.xlsx'
'GLC Real daily data current month.xlsx'
'OIS daily data current month.xlsx'

Being slightly bewildered I took guess and looked at the 9/9/2021 figures from 'GLC Nominal daily data current month.xlsx' and 'GLC Real daily data current month.xlsx'. (Am I in the right ball park there?).

Since the earliest common data samples found in the above related to the periods 2.17 - 5.0 years maturity that was what I graphed using this formula for BE inflation, as below:

EDIT: I obtained my "nominal yield of conventional gilts" from the 'GLC Nominal daily data current month.xlsx' and "real yield of ILGs" from 'GLC Real daily data current month.xlsx.

Image

So is what I have done above remotely correct? I read the BoE speil, i.e. that the datas are zero coupon rates (YTMs) and I used the short end spot prices. Hence between 3.8 - 4.0% in the BE inflation curve. I didn't know the difference between BLC, GLC and OIS xlsx files, alas.

old style 8 month lagged linkers and new style 3 month lagged linked linkers).

Nor this, unfortunately.

Importantly though, if you want to look at inflation expectations for future time periods (rather than the average over the time up to that period) which is more useful), you need to analyse the future inflation curve, not the breakeven curve itself.

Would that be found in the 'GLC Inflation daily data current month.xlsx' spreadsheet?

thanks, Matt

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Re: Yield curves and break even inflation

#441731

Postby GoSeigen » September 12th, 2021, 9:50 pm

I must say I'm equally baffled by dealtn's interventions on the other thread and would welcome any explanation he has. All I can make of it is that dealtn believes the market is correct both in pricing gilts at their current level AND pricing the breakeven where it is. Perhaps he holds an EMH-type belief that all securities are correctly priced by the market at any particular time. If so then I'm happy for people to see my view is a rejection of that: i.e. I believe that markets often misprice securities, and in particular, I see no sense in the current pricing of gilts, either IL or fixed. That's not to say someone cannot buy gilts and achieve their aim in holding them -- I just think there is much better value elsewhere and especially I think gilts are mispriced for any significant inflation scenario. [And my view may change as the markets or wider economic situation changes BTW.]


Regards calculating breakevens, I've never bothered myself (that I can remember); I thought this link you posted earlier was a perfectly adequate source for UK breakevens:

https://www.macronomics.no/fixed-income ... ven-rates/

It's pretty easy to find similar for US markets.


GS

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Re: Yield curves and break even inflation

#441773

Postby dealtn » September 13th, 2021, 8:02 am

GoSeigen wrote:I must say I'm equally baffled by dealtn's interventions on the other thread and would welcome any explanation he has.




Here's your explanation then.

You said.

GoSeigen wrote:So I stick to my view that no inflation being priced in whatsoever.


To which I pointed out the market was pricing in a degree of inflation. It is easily verifiable the market is indeed pricing in a non-zero inflation expectation all along the inflation curve. I gave 2 sources of inflation pricing to look at, Gilt breakevens, derived from the pricing in the Gilt market, and inflation pricing derived from the derivative inflation swap market.

You then appeared to change your view from there being no inflation being priced in to admitting the market was pricing in some inflation.

At no point did I say I agreed with the markets view, nor that I am an adherent to EMH. Indeed I gave several examples why the Gilt market in particular is inefficient.

What is baffling?

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Re: Yield curves and break even inflation

#441870

Postby TheMotorcycleBoy » September 13th, 2021, 1:33 pm

GoSeigen wrote:Regards calculating breakevens, I've never bothered myself (that I can remember); I thought this link you posted earlier was a perfectly adequate source for UK breakevens:

https://www.macronomics.no/fixed-income ... ven-rates/

Thanks,

Yes that says 3.76% at 10/9/2021 using the 10yr maturity spot rate, which is in very good agreement with my calc/graph using the 5yr spot.

I also opened the file 'GLC Inflation daily data current month.xlsx' from the BoEs zip and it contains identical figures to my Break even inflation figures that I calculated with my spreadsheet :)

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Re: Yield curves and break even inflation

#441874

Postby TheMotorcycleBoy » September 13th, 2021, 1:39 pm

dealtn wrote:I gave 2 sources of inflation pricing to look at, Gilt breakevens, derived from the pricing in the Gilt market

Hi dealtn,

What is the significance of 5yr maturity spots calculating 3.78% and 10 yr spots calculating 3.76% ?

I assume the answer is "None, since this is all just an abstraction based attempting to use the Gilt market to estimate *expected* inflation. All that it's really saying is that market participants are anticipating an annualised rate of roughly that figure over the near term". Does that sound about right?

and inflation pricing derived from the derivative inflation swap market.

If you have time can you walk me through how this calculation is made, and if at all possible with links to figures similar to those that I downloaded from the BoE site yesterday?

thanks again,
Matt

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Re: Yield curves and break even inflation

#441891

Postby Alaric » September 13th, 2021, 2:34 pm

TheMotorcycleBoy wrote: All that it's really saying is that market participants are anticipating an annualised rate of roughly that figure over the near term".


Recent issues of inflation linked bonds have had an almost zero coupon. That means that buyers of the bonds have to look to the revaluation through indexation and thus the protected maturity amount to see a return. A comparison to other risk free assets such as conventional Gilts can give an insight as to what rate of indexation gives equivalent monetary outcomes.

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Re: Yield curves and break even inflation

#441895

Postby dealtn » September 13th, 2021, 2:50 pm

Alaric wrote:
TheMotorcycleBoy wrote: All that it's really saying is that market participants are anticipating an annualised rate of roughly that figure over the near term".


Recent issues of inflation linked bonds have had an almost zero coupon. That means that buyers of the bonds have to look to the revaluation through indexation and thus the protected maturity amount to see a return. A comparison to other risk free assets such as conventional Gilts can give an insight as to what rate of indexation gives equivalent monetary outcomes.


Check what price they have been issued at to see how "protected" that maturity amount is though. Buying something issued at 200 that redeems at 100 isn't much protection - unless you consider getting half your money back as it being protected.

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Re: Yield curves and break even inflation

#441990

Postby GoSeigen » September 13th, 2021, 9:04 pm

dealtn wrote:
GoSeigen wrote:I must say I'm equally baffled by dealtn's interventions on the other thread and would welcome any explanation he has.




Here's your explanation then.

You said.

GoSeigen wrote:So I stick to my view that no inflation being priced in whatsoever.


To which I pointed out the market was pricing in a degree of inflation. It is easily verifiable the market is indeed pricing in a non-zero inflation expectation all along the inflation curve. I gave 2 sources of inflation pricing to look at, Gilt breakevens, derived from the pricing in the Gilt market, and inflation pricing derived from the derivative inflation swap market.

You then appeared to change your view from there being no inflation being priced in to admitting the market was pricing in some inflation.

Well, I accepted that the breakeven figures are in line with where they have been for some 20 years, a period of the lowest inflation and gilt yields for generations or perhaps centuries. I'd like to think that that period was one of low inflation, not high inflation -- though I may be completely wrong of course.

Perhaps I'm going to be a bit heretical too, by saying I don't believe the breakeven is the "market's pricing of inflation". People claim that is what it is, but to me it is only a measure of pricing of one type of security in relation to another type, both of whose prices could be suspect. The fact that the calculation "looks" like an estimate of inflation is just a supposition, a kind of mathematical analogy -- I'm struggling to come up with the right term here; "myth" perhaps?

What the breakeven actually expresses, UIAVMM is the inflation rate above which linkers outperform fixed gilts. That doesn't mean it's a measure of inflation expectations. The more telling figure to me, is that at the point where linkers outperform fixed gilts, inflation is at 3.7% (or so) and yet fixed 10yr gilts yield around 0.75% nominal! That to me is insane. How is that in any sense "pricing in an inflation rate of 3.7%"? Sure, index linkers would "win" but would that not be one of the most pyrrhic of victories?


At no point did I say I agreed with the markets view, nor that I am an adherent to EMH. Indeed I gave several examples why the Gilt market in particular is inefficient.

What is baffling?


Perhaps we agree but just assign subtly different meanings to the term "pricing in". My interpretation of that term is that if I price in an inflationary outcome, then I buy my securities at a price which will grow those assets at a rate greater than inflation in the event that consumer prices accelerate significantly.

The other possibility is that I don't understand something about the gilt markets, but as an investor in that market for some 15 years I must admit it would be pretty galling to find that I've misunderstood and important aspect of it!


GS

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Re: Yield curves and break even inflation

#442793

Postby TheMotorcycleBoy » September 16th, 2021, 3:47 pm

dealtn wrote:
TheMotorcycleBoy wrote:
dealtn wrote:A noticeable rise in reported inflation day, and the trigger for the Bank of England to explain its thinking.

https://www.bbc.co.uk/news/business-58563417

Whilst the rate isn't that far above the top of the Bank's target, nor significantly high by historical standards, it does mark the steepest monthly increase since comparable records began in 1997.

So that's (3.2%) about 0.6% less than the value predicted by Gilts vs ILGs (3.8ish%).

Help me out and show how me to derive inflation forecasts from the inflation swap curves. ;)

Matt


Firstly the Index Linked Gilts all reference RPI, not CPI. RPI is 4.8% according to todays announcement.

Secondly the breakeven calculation from the Gilts market is complicated. I didn't read your BofE numbers from the other day but I think they were 3.5%ish across the curve. What's important to note though is this is a "spot" curve not a "forward" curve so it isn't intuitively obvious what the predicted rate of inflation is.

In simple terms if 1 year "spot" inflation is priced at 3.5% and 2 year inflation is also priced at 3.5%, then the 1 year inflation rate in a years time is also priced at 3.5%. The 2 year rate is the average, and since we know the 1 year rate is also 3.5%, then the second year must also be 3.5%.

Were spot prices such that 1 year was 2% and 2 year was 3% then we can infer that (approximately) the 1 year rate starting in 1 years time is 4% (since 1 year at 2% followed by 1 year at 4% gives a 2 year average of 3%). This is called "bootstrapping" where you can construct the forward implied rate (be that inflation, or interest, or FX etc.) from all known spot prices along a curve to derive successive unknown future points in between.

In the example above we knew the 1 year and 2 year rates to get the unknown 1 year rate starting in 1 years time. With a 3 year spot rate (and a 1 year and 2 year and the 1 year in 1 years time rate) we can calculate the 1 year rate starting in 2 years time. With a 4 year (knowing the 1 year, 2 year, 3 year, 1 year 1 year forward, 1 year 2 years forward) you can know calculate the 1 year 3 years forward rate etc.

In practice you will have a pricing model more complicated than this and can derive all sorts of more complicated future rates of multiple periods, and create zero coupon real and nominal interest rates for any future date to use to discount any predicted cashflows back to their net present values (NPV) etc.

I hope I didn't lose you.

Don't worry regarding forward and spot rates, I'm not in the least bit confused. But what I find puzzling at the moment, is that as you mentioned forward rates, I referred back to those xlsx files which I downloaded from the BoEs site, and attempted to make sense their declaration of fwds, short end tab. Below is an image depicted a small part of this:

Image

So whilst I understand the maturity (helpfully presented in months and years!) what really I losing me currently are those figures because they are devoid of any notation by which I understand forward rates, i.e.

FyMy where the F=length of the forward period, M is the underlying period. As is mentioned here for example.

In other words: 0y5y, 0.08y5y, 0.16y5y. So perhaps you did lose me, since I was expecting to see this in the BoEs yield data.

Matt

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Re: Yield curves and break even inflation

#442795

Postby dealtn » September 16th, 2021, 3:59 pm

TheMotorcycleBoy wrote:So whilst I understand the maturity (helpfully presented in months and years!) what really I losing me currently are those figures because they are devoid of any notation by which I understand forward rates, i.e.

FyMy where the F=length of the forward period, M is the underlying period. As is mentioned here for example.

In other words: 0y5y, 0.08y5y, 0.16y5y. So perhaps you did lose me, since I was expecting to see this in the BoEs yield data.

Matt


Does this help?

https://www.bankofengland.co.uk/statist ... d-concepts

The data you are showing are the "instantaenous" forward rates, or roughly equivalent to what the 1 day rate will be in the market at that forward date.

So on 9th September 21 the nominal overnight rate in one years time (9th September 2022) according to market pricing is 0.17% (cell M11 - assuming "Maturity" sits in cell A1).

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Re: Yield curves and break even inflation

#443342

Postby TheMotorcycleBoy » September 18th, 2021, 4:52 pm

dealtn wrote:
TheMotorcycleBoy wrote:So whilst I understand the maturity (helpfully presented in months and years!) what really I losing me currently are those figures because they are devoid of any notation by which I understand forward rates, i.e.

FyMy where the F=length of the forward period, M is the underlying period. As is mentioned here for example.

In other words: 0y5y, 0.08y5y, 0.16y5y. So perhaps you did lose me, since I was expecting to see this in the BoEs yield data.

Matt


Does this help?

https://www.bankofengland.co.uk/statist ... d-concepts

The data you are showing are the "instantaenous" forward rates, or roughly equivalent to what the 1 day rate will be in the market at that forward date.

So on 9th September 21 the nominal overnight rate in one years time (9th September 2022) according to market pricing is 0.17% (cell M11 - assuming "Maturity" sits in cell A1).

Sort of - thanks.

But surely in this context, an instantaneous forward rate is not strictly speaking instantaneous, since that would imply that the loan's period is zero units of time [1], would it not?

So, please correct me if I'm wrong, but these figures, i.e. the 0.17% are rates for which one can borrow for a 24 hour period. Am I right?

thanks Matt

[1] And presumably zero risk, therefore rate=0.0%

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Re: Yield curves and break even inflation

#443346

Postby TheMotorcycleBoy » September 18th, 2021, 5:02 pm

So if my last post was right, does this imply that if I wanted to borrow £1000 on 9th September 2022 for 24 hours, I have to repay the hypothetical lender £1001.70 at the same time on 10th September 2022?

thanks again,
Matt

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Re: Yield curves and break even inflation

#443378

Postby GoSeigen » September 18th, 2021, 6:41 pm

TheMotorcycleBoy wrote:So if my last post was right, does this imply that if I wanted to borrow £1000 on 9th September 2022 for 24 hours, I have to repay the hypothetical lender £1001.70 at the same time on 10th September 2022?

thanks again,
Matt


No! It's an annualised rate!

GS

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Re: Yield curves and break even inflation

#443400

Postby TheMotorcycleBoy » September 18th, 2021, 8:52 pm

GoSeigen wrote:
TheMotorcycleBoy wrote:So if my last post was right, does this imply that if I wanted to borrow £1000 on 9th September 2022 for 24 hours, I have to repay the hypothetical lender £1001.70 at the same time on 10th September 2022?

thanks again,
Matt


No! It's an annualised rate!

GS

Ok. But the hypothetical life time of the loan is 24 hours, correct?

So the *daily* rate is 0.17/365 percent, right?

I was more attempting to get my head around the concept of it being called an instantaneous fwd rate. Check out the post I made immediately prior to the one youve just replied to i.e.

https://lemonfool.co.uk/viewtopic.php?p=443342#p443342

Matt

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Re: Yield curves and break even inflation

#443581

Postby GoSeigen » September 19th, 2021, 2:24 pm

TheMotorcycleBoy wrote:
GoSeigen wrote:
TheMotorcycleBoy wrote:So if my last post was right, does this imply that if I wanted to borrow £1000 on 9th September 2022 for 24 hours, I have to repay the hypothetical lender £1001.70 at the same time on 10th September 2022?

thanks again,
Matt


No! It's an annualised rate!

GS

Ok. But the hypothetical life time of the loan is 24 hours, correct?

So the *daily* rate is 0.17/365 percent, right?

If the rate were equal throughout the period it would be 0.17^(1/365), but in practice the rate is a non-linear curve hence:

I was more attempting to get my head around the concept of it being called an instantaneous fwd rate. Check out the post I made immediately prior to the one youve just replied to i.e.

https://lemonfool.co.uk/viewtopic.php?p=443342#p443342

Matt



... the instantaneous rate can be considered an interpolation of other known rates. There's a decent explanation here:

https://quant.stackexchange.com/questio ... rward-mean


GS
[@not a quant or any sort of expert on this subject]

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Re: Yield curves and break even inflation

#447417

Postby TheMotorcycleBoy » October 3rd, 2021, 10:24 am

GoSeigen wrote:
... the instantaneous rate can be considered an interpolation of other known rates. There's a decent explanation here:

https://quant.stackexchange.com/questio ... rward-mean


GS
[@not a quant or any sort of expert on this subject]

Thanks GS,

I eventually got there. Have been busy with a lot of other stuff it's taken a while for the penny to drop. I spent a while fooling myself that is was a day rate being considered here, hence all the silly division by 365 stuff.

It was in the BoEs page all the time https://www.bankofengland.co.uk/statist ... d-concepts !

In the limit, as the period of the loan considered tends to zero, we arrive at the instantaneous forward rate. Instantaneous forward rates are a stylised concept that corresponds to the notion of continuous compounding, and are commonly used measures in financial markets. Instantaneous forward rates are the building block of our estimated yield curves, from which other representations can be uniquely derived.

Matt


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