THE TREASURY BREAKE

INFLATION CURVE 

James A. Girola 

U.S. Department of the Treasury 

March 26, 2019 
Introduction 

● This presentation describes the Treasury Breakeven 

(TBI) Curve, which provides breakeven inflation ratefrom nominal Treasury notes and bonds and TIPS. 

● Breakeven inflation rates are future inflation rates e

the Treasury securities market. Breakeven rates perinflation of the (not seasonally adjusted) Consumer Pfor All Urban Consumers (CPI-U). 

● The Treasury TBI curve uses methodology that overc

deficiencies in other approaches. 
Introduction 

● Although TBI rates can be influenced by a variety of 

factors, on balance over time they are reliable indicatmarket expectations for future inflation. Therefore, tused to compute projections of inflation into the futurin accord with markets. 

● Inflation projections have many uses, including econo

forecasting, pension trust funds, and conversion of funominal cash flows to real payments, as in the BlendRetirement System. 

● Moreover, when combined with projected real interes

based on the structure of the economy, projected inflaforecast future nominal interest rates. 
Treasury Yield Curves 

● The TBI curve is one of a set of yield curves done by T

Data generated by these curves are already used by tDepartment. 

● The first Treasury curve is the Treasury Nominal Co

(TNC) Yield Curve, which pertains to Treasury nominissues. 

● The second is the Treasury Real Coupon-Issue (TRC) 

for Treasury Inflation-Protected Securities (also know

● And the third is the High Quality Market (HQM) Cor

Yield Curve, which pertains to U.S. high quality corp

● The following discussion summarizes these curves an

methodology. The last slide contains links for more in
The HQM Yield Curve 

● The HQM corporate bond yield curve is produced as m

the Pension Protection Act of 2006 (PPA). This curve high quality corporate bonds, that is, bonds in the top qualities AAA, AA, and A. 

● To meet the requirements of the PPA, it was necessar

a new yield curve methodology at Treasury for the HQThe methodology is sketched out below. 

● The HQM curve data are disseminated by IRS and by 

Treasury Office of Economic Policy, and include spot rrelated yields that are used by single-employer pensidiscount future liabilities. HQM yield curve data are back through 1984. 

● The HQM yield curve is also used in the Blended Ret

System. 
The TNC Yield Curve 

● The HQM methodology was subsequently applied to 

market to produce the TNC yield curve, which pertaiTreasury nominal coupon issues, both notes and bond

● The TNC curve includes both on-the-run issues (secu

recently issued of each maturity) and older off-the-ruHowever, in this presentation the focus is on spot ratthe-run issues. 

● The initial application of the TNC yield curve was to 

future liabilities of various federal agencies including Defense Department, such as pension and other postliabilities, for the agencies’ audited financial statemethe annual Financial Report of the U.S. Government

● The TNC curve goes back through 1976, and is the m

extensive Treasury yield curve dataset currently ava
The TRC Yield Curve 

● The HQM and TNC methodology was subsequently u

produce the TRC yield curve. The TRC yield curve is yield curve derived from Treasury Inflation-Protected or TIPS, and includes both real notes and real bonds. 

● And the nominal TNC and real TRC yield curves are 

derive the Treasury Breakeven Inflation (TBI) Curve

● The TRC yield curve and the TBI curve are both avai

through 2003. 
Yield Curve Data 

● These yield curves each provide several sets of d

including spot rates, selected par yields, and forwThe TNC curve provides off-the-run and on-the-

● The curves are calculated late in the day on each 

day, and the results are disseminated each montspot rate data, which are of particular interest fobreakeven inflation, include monthly averages orates, as well as end of month spot rates from thTRC curves and the TBI curve as a combination 
Yield Curve Data, continued 

● Spot rates are available for each maturity at hal

intervals starting at 1⁄2 year up through 100 yeartotal of 200 maturities. Rates beyond 30 years mare projected as described below. 

● All spot rates are semiannually compounded, ex

following convention, TBI rates are annually com
Yield Curves for January 2019 

● Slide 12 contains the average TNC, TRC, and HQM s

curves for January plus the TBI breakeven curve. Alprojected out through100 years maturity. 

● The HQM spot rate is 4.58 percent at 30 years matur

compared to 3.16 percent and 1.22 percent for the TNspot rates, respectively. The TBI rate is 1.95 percent maturity. 

● The HQM rate exceeds the TNC rate largely because 

bond default risk, and the TNC rate exceeds the TRC positive inflation. 
Yield Curves for January 2019, continue

● The spot yield curves rise gradually throughout the p

range from 30 years maturity through 100 years matis typical. At 100 years maturity, the HQM spot rate percent, the TNC rate is 3.33 percent, the TRC rate ipercent, and the TBI rate is 2.01 percent. 
••••••••••••••••••••••••••••••••••

• 

• • • • 

• • 

--  ·--·  - -  -  -  - .-•·-· 

SPOT YIELD CURVES 

January 2019, Percent 

10 20 30 40 50 60 70 80 90 

0 1 2 3 4 5 

Maturity 

HQM 

TNC 

TRC 

TBI 
Methodology Features 

The methodology used for the yield curves contains and capabilities that do not appear in other yield capproaches: ● The methodology makes use of established bond 

characteristics to generate a stable yield curve tcaptures market movements. 

● The methodology projects yields beyond 30 years● The methodology combines regression variables 

yield curve. 
Methodology Features, continued 

● The requirements of the PPA made necessary th

of this methodology, which is new and more exte

● In particular, this methodology is grounded in es

bond market characteristics, which generate and the mathematical form of the yield curve. 

The following slides summarize details of this met
Maturity Ranges 

● A central feature of the methodology is that it breaks 

curve into maturity ranges. 

● This is because trading in securities tends to divide in

ranges, such that the trading activity in each range oreflects similar purposes, similar views of risk, and siexpectations about securities in that range. 

● Because market views can be considered similar for s

the same range, yields in each maturity range are relother in a simple fashion. 

● Consequently, this methodology models yields, and in 

forward rates, in each maturity range as a smooth (cufunction, and joins the functions together smoothly a(as a cubic spline). 
Maturity Ranges, continued 

● At the present time five maturity ranges are used for 

curves, delineated by the maturity points 0, 1.5, 3, 7, years maturity. These points provide separate rangecritical maturities of 2 years, 5 years, the benchmark and 30 years. 

● The choice of fixed maturity ranges increases signific

stability of the yield curve estimates over time. 

● In addition, the methodology is statistically straightf

estimate, generating statistical equations that are weconditioned. 
The Long-Term Forward Rate 

● The methodology must also be able to project yields a

rates beyond 30 years maturity out through 100 year

● First of all, the long-term forward rate at and beyond 

maturity is set to a constant, because there are not ento estimate accurately movements in the forward ratyears maturity. 

● Then this constant is taken to be the average forward 

15- to 30-year maturity range. 

● Therefore, using the long-term forward rate, spot rat

projected beyond 30 years maturity out to 100 years mThe projected spot rates provide discount rates for loncash flows, and also enable projection of inflation 100 forward. 
Methodology: Regression Variables 

● This methodology also has the special capability of co

regression variables with the yield curve. The regresvariables adjust for various features of the market anattributes of individual securities. 

● The TNC and TRC yield curves use regression to mea

hump in yields that is sometimes seen around 20 yeaThe TNC curve also uses regression to measure price on-the-run securities. 

● The HQM yield curve uses regression variables to com

AA, and A rated bonds into a single average curve. 

● Given this summary of the yield curves, the next topi

definition and examination of breakeven inflation. 
Definition: Breakeven Inflation 

● The most useful way to define breakeven inflation is 

the breakeven inflation rate over a future period is tinflation rate during that period that, if realized, woufor the period the dollar return gotten from nominal securities and the dollar return gotten from TIPS. 

● Put another way, investing in nominal Treasury note

for a period, say 10 years, provides a future return in received at the end of the 10 years. Similarly, investprovides a real return after 10 years, which is then cdollars by the CPI-U. The breakeven inflation rate iinflation rate over the 10 years that, if realized, wouthese two returns equal. 
Definition: Breakeven Inflation, continu

● It follows from this definition that the breakeven infl

an indicator of inflation expectations by market partiexpectations were different, returns would not be equtraders would buy or sell securities to make them equ

● However, the use of breakeven inflation to show infla

expectations is subject to qualifications. First, the brrate must be derived from suitable data, and must be correctly. This is done for the TBI curve by using spothe TNC and TRC yield curves. 

● But even when this is done, there are short periods w

demand for nominal Treasuries vs TIPS is distorted bthat are more important than equating returns, such temporary movements in liquidity in times of econom

● The following slides discuss these issues. 
Use of Spot Rates 

● The biggest problem with most computations of break

inflation rates is that they use yields rather than spo

● Following the definition, breakeven rates are derived 

returns received at the end of future periods from nomTreasuries vs TIPS. The spot rate on securities, nomTIPS, gives the correct amount received at the end of 

● In contrast, yields do not give returns received at the 

periods because yields include streams of coupon payreceived throughout the periods before the end. Spot the same as zero coupon rates: that is, rates on securpay a single amount at the end of the investment per
Use of Spot Rates, continued 

● Consequently, use of yields significantly biases down 

calculation of breakeven inflation. Perhaps yields arused because many analysts do not have spot rates. curve uses spot rates from the TNC and TRC yield cu

● Another way to view the problem of yields is that at a

the duration of TIPS in nominal terms is longer than nominal Treasuries, with the result that the two typesecurities are mismatched for the purpose of calculatbreakeven rate. In contrast, for a given maturity, the nominal and TIPS spot rates are the same and equal maturity. 

● It should be noted that spot rates computed from the 

TRC yield curves are estimated from coupon-issue seTherefore, they may not match market returns exacttime. 
Liquidity Bias 

● The use of breakeven inflation for inflation expectatio

been questioned because it has been argued that nomTreasuries are more liquid than TIPS. If so, this impnominal Treasuries are more desirable and have lowewhich would bias down the calculation of breakeven i

● However, this argument typically assumes the use of 

the on-the-run, that is, the most recently issued, Treasecurities. In contrast, spot rates in the TBI curve peolder off-the-run nominal Treasuries whose liquidity closer to that of TIPS, thereby eliminating any such b
Additional Sources of Bias 

● Another source of bias in the usual computations of b

inflation rates comes from the fact that the rates are simply the subtraction of TIPS rates from nominal raAlthough not reproduced here, the correct formula emcompounding rather than subtraction, as done for TB

● In addition, breakeven computations often assume se

compounding as in the bond market. In contrast, infconventionally measured as annual, and consequentlare annual too. 

● All these biases need to be taken into account: if brea

inflation is under consideration for inflation projectio

has to be calculated correctly. 
Inflation Risk Premium 

● A final source of possible bias in breakeven inflation, 

thought to be the largest, is the inflation risk premiunominal Treasury notes and bonds. 

● Because future inflation is uncertain, there is a risk a

with real returns on nominal Treasuries that is not in compensate for this risk, holders of nominal Treasurito demand returns that are on average above the retuTIPS based on expected inflation. This pushes up thnominal Treasuries and thereby biases up the breakeinflation rate as an indicator of inflation expectations
Inflation Risk Premium, continued 

● Of course, just as future inflation may be unexpected

may also be unexpectedly low, thereby boosting real rnominal Treasuries. So the inflation risk premium arisk aversion by security holders toward inflation surmay not actually exist, especially for institutional inv

● The data in the rest of the slides provide evidence ab

inflation risk premium. The data are consistent with that the risk premium is small at most. 
Breakeven Inflation over Time 

● The following chart in slide 28 shows TBI breakeven 

selected maturities for January 2003 through Januar

● The breakeven rates in the chart are somewhat highe

maturities earlier in the period but not so much latelindicate that inflation expectations rose for more dist

periods, but it may also reflect some inflation risk pre

● It is not possible to assess the premium from these da

more data are considered in the following slides. 

● The chart also shows sharp declines in breakeven inf

crisis at the end of 2008. The declines came from higyields stemming largely from TIPS liquidity concernsdeclines show that over short periods, breakeven infl

influenced by special factors and may not be a good inexpected inflation. 
3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 

0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

-4 -3 -2 -1 

0 1 2 3 4 5 

2 Years 5 Years 10 Years 30 Years 

BREAKEVEN INFLATION RATES

 AT SELECTED MATURITIES 

Monthly, Percent 
Forward Breakeven Inflation 

● The chart in slide 30 shows selected forward bre

inflation rates, also for January 2003 through Ja2019. 

● Forward breakeven inflation is the inflation rate 

given horizon for a future time. It is computed fregular breakeven inflation rates. The series inthe chart are common measures of future inflatiexpectations. 

● All the breakeven rates converge near 2 percent 

similar to the breakeven rates on slide 28. 
••••• -··· 

i .. 

• + • ..."".' 

• 

3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 

0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

-1 

0 1 2 3 4 5 

2-Year Forward 2-Year 5-Year Forward 5-Year 

10-Year Forward 10-Year 30-Year Forward 1-Year 

SELECTED FORWARD 

BREAKEVEN INFLATION RATES 

Monthly, Percent 
10-Year CPI Inflation Forecasts 

● The next charts compare TBI 10-year forecasts t

10-year forecasts and actual inflation over 10 ye16 years 2003-2018. 

● The chart on slide 32 has the quarterly 10-year 

from the Survey of Professional Forecasters at thReserve Bank of Philadelphia and the semiannuforecast from the long-range consensus in Blue CEconomic Indicators (derived the successive 5-yeforecasts). 

● The two forecasts vary little throughout the peri

also very close to each other. They both start ou2.5 percent and end around 2.2 percent in 2018. 
--

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10-YEAR INFLATION: 

FORECAST AND ACTUAL 

5 4 3 2 1 0 

Quarterly, Percent 

Philadelphia Blue Chip 

1993 1998 2003 2008 2013 20
10-Year CPI Inflation Forecasts, continu

● The chart on slide 34 adds the TBI 10-year forec

(quarterly averages) to the survey forecasts. 

● The TBI forecast is near both survey forecasts (a

the drop in the financial crisis) but there are diffthe TBI forecast starts somewhat higher than that the beginning and then falls below them at th

● However, the important point to note in this cha

there is no evidence of any bias in the TBI forecaparticular, there is no evidence that the TBI ratebiased up by a risk premium. 
--

10-YEAR INFLATION: 

FORECAST AND ACTUAL 

5 4 3 2 1 0 

Quarterly, Percent 

TBI Philadelphia Blue Chip 

1993 1998 2003 2008 2013 20
10-Year CPI Inflation Forecasts, continu

● The chart on slide 36 removes the TBI line but a

actual average CPI inflation rate 10 years back quarter (inflation rates are computed by log regrtime trends which smoothly depict underlying in

● Actual 10-year inflation rates accelerated to 2.78 

2008 and then showed steady deceleration to the falling to around 1.64 percent by the end of 2018

● The survey forecasts did not pick up the inflatio

in advance. In particular, except for a belated smdecline the last few years, these forecasts missed deceleration in inflation. 
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I I I I I I I I I I I I I I I I I I I I 

10-YEAR INFLATION: 

FORECAST AND ACTUAL 

5 4 3 2 1 0 

Quarterly, Percent 

Actual Philadelphia Blue Chip 

1993 1998 2003 2008 2013 20
10-Year CPI Inflation Forecasts, continu

● The last chart on slide 38 adds back the TBI line 

survey forecasts and actual 10-year inflation. 

● The chart shows that the TBI forecasts do better 

survey forecasts. The higher TBI rates in 2004-up the ensuing inflation acceleration, while the rates in 2015-2018 track the inflation deceleratimuch better than the surveys which moved little period. 

● Nevertheless, TBI forecasts were still very slow 

changes in actual inflation: they did not foresee years in advance and they mostly moved simultawith actual inflation. 
--

• 

10-YEAR INFLATION: 

FORECAST AND ACTUAL 

5 4 3 2 1 0 

Quarterly, Percent 

Actual TBI Philadelphia Blue Chip 

1993 1998 2003 2008 2013 20
5-Year CPI Inflation Forecasts 

● The chart on slide 40 is the same as slide 38 exc

done for 5-year periods. 

● This chart confirms the same conclusions: there 

in TBI rates and no noticeable inflation risk preTBI forecasts do better than surveys in capturinchanges in inflation, although they are still very foreseeing such changes in advance. 
• 

--

5-YEAR INFLATION: 

FORECAST AND ACTUAL 

Quarterly, Percent 

-1 

0 1 2 3 4 5 

Actual TBI Philadelphia Blue Chip 

1993 1998 2003 2008 2013 20
1-Year CPI Inflation Forecasts 

● Finally, the chart on slide 42 shows 1-year TBI i

forecasts compared with 1-year back inflation ra

● This chart indicates that 1-year TBI forecasts tr

inflation, with some evidence that the forecasts 1-year inflation changes. 

● It is notable that the big dip in the 1-year TBI fo

2008 was followed shortly by a dip in actual 1-yeinflation. This indicates that the TBI dip was inboth by liquidity concerns in the crisis and by anof actual deflation in the CPI over 1-year period
• 

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11\ 

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1-YEAR TBI INFLATION FORECAST 

-6 -4 -2 

0 2 4 6 

Actual TBI 

Quarterly, Percent 

1993 1998 2003 2008 2013 20
Alternative TBI Projections 

● The next step is to use the TBI rates to project e

future inflation. 

● The projection can be done from a single recent m

data such as in slide 12, but as has been shown, can be distorted by special factors over short perTherefore, the projection should use averages of 

over a span of time. 

● In particular, because the focus is on inflation ov

long-term, market expectations averaged over loperiods provide settled market views about the las opposed to shorter periods which may be influrecent inflation behavior. 
Alternative TBI Projections, continued 

● The chart on slide 45 shows TBI rates averaged 

various time spans. For each projection, the valmaturity is the projected average inflation rate fpresent through that maturity. 

● The chart includes the 2-year average, analogou

segment rates in the Pension Protection Act, as 5-year and 7-year averages, and the 10-year aveis used by government agencies including Defendiscount rates for future liabilities. 

● The chart shows that the averages are close, esp

shorter maturities. Therefore, the expected futuof inflation has been stable over the last decade. 
I I 

••••••• 

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-~ -·~ • •-----==-=-= - 1 ... - - - - - --==•----- --------= ~- .~ -.. I.I u ... u -

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ALTERNATIVE TBI PROJECTIONS 

5 4 3 2 1 0 

Annual, Percent 

2-Year 5-Year 7-Year 10-Year 

Maturity 

1 10 20 30 40 50 60 70 80 
TBI Inflation Projection 

● In view of this stability, the full 10-year average 

projection that captures recent market views, eslong-term inflation, and minimizes the influenceterm effects. However, the 10-year average exteinto the recession period, which may affect the rTherefore, the average chosen is the 115 months first month of recovery July 2009 through Janua

● The projection using this average is depicted in 

on slide 47. The chart shows that average inflatfrom values around 1-1/2 percent to 2.09 percent years maturity, 2.33 percent at 30 years, 2.38 peyears, and 2.41 percent at 100 years maturity. 
--

I 

TBI INFLATION PROJECTION 

Annual, Percent 

5 

Maturity 

4 3 2 1 0 

1 10 20 30 40 50 60 70 80 
Yearly Inflation 

● The projection in the previous chart provides av

inflation over increasingly long time spans. The on slide 49 converts this to projected inflation rayear for the 100 years 2019 – 2118, and adds the yearly CPI inflation rates for the 98 years 1921 – (Actual rates are calculated from January of eacthrough January of the following year using log on time.) 
j M 

~" - \~ j• ~r • 

, ' ' 

1950 

2000 2010 

2030 

2050 

2070 

2080 

25 20 15 10 

5 0 

-5 

-10 

1

9

20 

1

9

30 

1

9

40 

1

9

60 

1

9

70 

1

9

80 

1

9

90 

2

0

20 

2

0

40 

2

0

60 

2

0

90 

Historical Projected 

Annual, Percent 

YEARLY INFLATION 
Yearly Inflation, continued 

● The historical line shows the movement of inflat

the last century. The line illustrates the sharp dthe Great Depression and the surge in inflation War II, followed by a period of stability. Inflatio

accelerated in the 1960s with the Vietnamese Wcontinued to rise in the 1970s, reaching a peak opercent in 1979. The ensuing monetary tightnesinflation down, and for the last 30 years, inflatiorelatively stable around 2.40 percent. 

● The projection line shows that inflation is expect

accelerate from its current rate of 1.41 percent, asome variation, reach a steady rate of 2.44 perce2050. Therefore, the inflation rate is projected to down in the future to the same rate as it has beelast several decades. 
Yearly Inflation, continued 

● It is clear from all these charts that the TBI curv

much more information for inflation projections sources. Survey data are not nearly rich enough kinds of projection computations, and even thoupossible crudely to extrapolate past inflation ratthe results are not nearly as refined as are gotterates. Therefore, the TBI curve provides an impsource for projecting inflation. 
For More Information 

● Data and documentation for the TNC and TRC yield 

available on the Treasury Economic Policy website at

https://www.treasury.gov/resource-center/economic-policy/corp

yield/Pages/TNC-YC.aspx 

● The HQM corporate bond yield curve for the PPA is p

the IRS each month. Data and documentation are alon the Treasury Office of Economic Policy website at: 

https://www.treasury.gov/resource-center/economic-policy/corp

yield/Pages/Corp-Yield-Bond-Curve-Papers.aspx 

● Previous applications of the methodology presented h

yield curves can be found in papers 0601 and 0501 in Economic Policy Research Paper Series on the Office Policy website.