Swedish Breakeven Inflation (BEI) - a market based measure of inflation expectations?

UPPSALA UNIVERSITY Department of Economics Msc. Thesis

Autumn 2007

Author: Jonas Calmvik Supervisor: Bengt Assarsson

Swedish Breakeven Inflation (BEI) - a market

based measure of inflation expectations?

Abstract

The Fisher Equation suggests that the spread between nominal and real interest rates is equal to the inflation expectations. In Sweden, where both nominal and inflation linked bonds exist the fisher equation implies that the yield spread could provide investors and policymakers with important information about markets inflation expectations. The aim of this thesis is therefore to estimate whether the yield spread between Swedish nominal and real interest rates - widely referred to as the Breakeven Inflation (BEI) - is a market based measure of inflation expectations. A sample based on historical bond prices between year 2000 and 2007 is used and adjusted for 3 distortions: i) The mismatch in cash flow structure arising from different bond characteristics. ii) The inflation indexation and bond finance implications (carry). iii) The seasonality in Consumer Price Index (CPI). In the absence of “true” inflation expectations, the benchmark used for the evaluation and comparison of the unadjusted and adjusted BEI series is the survey based, Prospera Money Market Players inflationary expectations, i.e. professional forecasters. The evaluation uses two statistical measures to estimate the errors, the Root Mean Squared Error (RMSE) to estimate the size of the forecast error and the Mean Error (ME) to measure the bias or the tendency for the forecast error to point in a particular direction. The general conclusion of the study is that both the unadjusted and the adjusted BEI series have improved significantly throughout the sample period as predictors of inflation expectations.

Further, in the first half of the sample, the MEs show that the BEI tends to underestimate inflation expectations, while in the second part of the sample the direction of the errors are less univocal. However, the carry adjusted and in some extent the carry and seasonality adjusted BEI seem to improve the BEI somewhat, although the conclusions are not very convincing. When using BEI to measure inflation expectations the conclusions should also be balanced against the possible bias associated with survey based expectations.

Keywords: Inflation-Linked Bonds, Index Linked, Swedish Bonds, Carry, CPI Seasonality, Sveriges Riksbank, SNDO, Prospera, Inflation Expectations.

Please submit your thoughts and comments to:

calmvik@hotmail.com

Table of Contents

Abstract

1. Introduction 5

2. Previous Research 7

3. Pricing and Structure of Swedish Nominal and Inflation-Linked bonds 8

3.1 The Index Ratio 8

3.2 Interest Payments and Accrued Interest 9

4

.

Methodology - The Breakeven Inflation, its Distortions and the Comparison 10

4.1 Maturity and Cash Flow Mismatch Explained 10

4.2 Maturity and Cash Flow Mismatch Derived 11

4.3 Inflation Indexation implications and Carry Explained 12

4.3.1 The Repo Market 12

4.4 Carry of Inflation Linked Bonds Derived 13

4.5 Consumer Price Index (CPI) Seasonality Explained 15

4.6 Consumer Price Index (CPI) Seasonality Derived 15

4.6.1 The Seasonality Adjustment Method 16

4.6.2 What drives Seasonality? 16

4.6.3 How long History should be used? 17

4.7 Liquidity Premium Explained 18

4.8 Inflation Risk Premium and Bond Convexity 18

4.9 Survey Data 19

4.9.1 Prospera – Inflationary Expectations for Sweden 20

4.10 The Comparison – An Overview 20

4.11 The 5y Short dated BEI – the Comparison Explained 21

4.12 The 15y Long dated BEI – the Comparison Explained 22

5. Swedish Breakeven Inflation Rates – Empirical findings 22

5.1 Real and Nominal Yields during the Sample 22

5.2 The Cash Flow Adjustment 23

5.2.1 The Size of the Cash Flow Distortions 24

5.3 Inflation Indexation and Carry Adjustments 25

5.3.1 The Size of Carry and Inflation Indexation Distortions 26

5.4 Seasonality Adjustment 27

5.5 The Size of the Carry when adjusted for Seasonality 28

5.6 BEI Seasonality Distortion 29

6. Inflation Expectations 30

6.1 The 5y BEI – Short term Inflation Expectations 31

6.2 The 15y BEI – Long term Inflation Expectations 32

6.3 Inflation Expectations – A Summary 34

7. Conclusions and Discussions 35

References Appendices

1. Introduction

The Fisher Equation shows that the difference between the nominal interest rate, n and the real interest rate, r is the expected rate of inflation, π^e:

i − r =

π

^e (1.1) This implies, in countries where both nominal and inflation-linked (IL forthcoming) bonds exist,

the spread between the nominal and real yields may carry valuable information about inflation expectations. In the financial markets, this yield-spread is widely referred to as the Breakeven Inflation (BEI forthcoming) since it is roughly the inflation level that equates the “net return” of the bonds involved.

In 1994 the Swedish National Debt Office (SNDO) began issuing SEK denominated inflation- linked bonds on behalf of the Swedish Government. These bonds are often referred to as

“linkers” since all cash flows (coupon and principal payments) are linked to the Swedish Consumer Price Index (CPI). The major reason behind the SNDO’s decision to launch their inaugural index linked bond-issuance, was to provide policy makers and investors with a means of estimating market inflation expectations¹. Timely evaluation of the markets credibility to price stability, compared alternative methods such as surveys or econometric analysis, are making these price observations attractive for monetary authorities and investors.

Inflation-linked bonds issuance is globally a relatively new phenomenon, where the Swedish Government was among the very first countries to bring this asset class to the market. However, in the United Kingdom “Index Linked Gilts” were tradable already in 1982. Many countries have issued since, US and France are today among the largest issuers and came to the market as late as 1997 and 1998 respectively. Germany decided as late as in 2006 to join the other G7 countries in inflation-linked bond issuance and in 2007 Turkey decided, in an attempt to raise credibility in price stability policies, to re-enter the inflation-linked market. In the coming years it is reasonable to suggest, that inflation market development will be largely driven by changes in the regulations concerning life-insurers and pension-funds, with regards to their liability matching needs. In Sweden, the implementation of the “Traffic Light Model” regarding life insurers caused significant volatility in the Swedish index-linked and nominal bond markets during 2005.

1 Other reasons were to reduce funding costs, broaden the range of available investment options and to enhance the credibility of monetary policy.

In the Monetary Policy Report (MPR) the Swedish Riksbank’s is often using the BEI as a “rough measure” of market inflation expectations. This measure is, apart from survey based expectations such as Prospera and NIER, continuously priced and accessible in the financial markets. Yet a number of obstacles still arise. Differences in liquidity between nominal and inflation-linked bonds, the inflation risk premium, imperfect indexation, CPI seasonality and difference in cash flow structure, are a number of distortions that may cause errors in the measure of inflation expectations.

The aim of this thesis is therefore to evaluate whether the Swedish Breakeven Inflation (BEI), adjusted for distortions, is an improved measure of the market’s inflation expectations. More specifically, this paper seeks to analyse the yield spread between Swedish Inflation Linked and nominal bonds for the years 2000 to 2007, adjusted for 3 distortions².

i) The mismatch in cash flow structure arising from different bond characteristics ii) The inflation indexation and bond finance implications, i.e. carry

iii) Consumer Price Index (CPI) seasonality

Two additional distortions: the inflation and liquidity risk premiums are discussed frequently in closely related research. To quantify these premiums extensive research is required. In order to limit the extent of this paper, the inflation and liquidity risk premiums are therefore only described and discussed briefly. They are not closely quantified.

The structure of this paper is the following: Section 2 presents previous research conducted in this area, in order to put the present paper in context. Section 3 describes the structure of the inflation linked and nominal bonds, followed by section 4 which provides the methodology and technical framework behind the distortions of the Swedish BEI. The empirical section 5 contains the BEI analysis and its results. Section 6 presents and compares the outcomes of the adjusted BEI and the unadjusted BEI, (the nominal and real yield spread), with the survey based inflation expectations. Finally, section 7 provides a concluding summary with discussions.

2 In accordance with the views of many researchers and market participants, these are the most significant distortions.

2. Previous Research

The most widely used measure to forecast and estimate inflation expectations is derived from bond and interest rate derivatives prices. It is primarily the yield spread between the real and the nominal rates, a measure that has attracted a great deal of attention from researchers. More sophisticated methods to estimate inflation expectations have appeared in the recent literature.

Sack (2000) derives a model for inflation expectations which he calls, inflation compensation measure, using yields of Treasury Inflation Indexed Securities³ (TIPS) and a constructed portfolio of US Treasury nominal rates. The constructed portfolio has the advantage of matching the increasing payment structure of the indexed security and having similar level of liquidity.

Sack finds this measure to be a reliable proxy for inflation expectations if the inflation risk premium is small and the expected path of inflation does not fluctuate too much. Sack also finds the inflation expectations using this measure to be more time varying than that expected from survey measures. In the UK, studies using prices of indexed gilts show that Deacon and Derry and Mirfendereski (2004) overcome some of the problems with the bias derived from the characteristic 8 months indexation lag in the UK, when deriving an Inflation Term Structure.

Alonso, Blanco and Rio (2001) analyse the 10-year French government indexed bond and nominal bonds and find that the French BEI is only an unbiased estimator of inflation expectations under very restrictive assumptions, which in practice, are not fulfilled. The inflation indexation lag, inflation risk, liquidity premium and different cash flow structures are important sources of distortions. However, Alonso, Blanco and Rio also apply Sacks, inflation compensation measure and with a few modifications correct some of the bias.

Christensen, Dion and Reid (2004) examine Canadian nominal and Real Return Bonds. They examine whether risk premiums and distortions can account for what they found, a BEI higher and more variable than survey measures.

Andersson and Degrér (2001) use a forward interest rate method based on the Fisher’s identity to derive a measure for the Swedish BEI and experience a similar outcome to that obtained in surveys, although with a greater variation over time. However, the authors conclude that, as this measure can be produced continuously, there is good reason to use this as a complement to the surveys.

3 Inflation Indexed Bonds issued by the US Treasury

3. Pricing and Structure of Swedish Nominal and Inflation-Linked bonds

⁴

The value of a bond at any time during its life is equal to the sum of the present values of all its future cash flows and its principal. An inflation-linked bond is simply a nominal bond linked to an index factor in order to adjust the real coupon rate and the principal for the realised inflation.

More precisely, the nominal yield to maturity, ytm and for the inflation linked bond, the real yield to maturity, is obtained implicitly using the following expression:

n ytm n

t t

ytm t

t i

M i

P C

) 1 ( ) 1

1( + +

=

∑

+

=

(3.1)

Pt equals the price of a bond maturing at par (M=100) in n years, and paying an annual coupon of C. For inflation-linked bonds, the price needs to be adjusted for realised inflation. This is done by applying an index ratio⁵.

In Sweden, there are 3 different existing versions of inflation-linked bonds totalling a market value (including accrued inflation compensation) of SEK 212bn, or 25% of the total debt⁶:

• Zero-Coupon bonds

• Coupon bonds with deflation protection

• Coupon bonds with no deflation protection

Today, the SNDO primarily issues the coupon bearing “capital-indexed bond”. This structure is the most widespread form of inflation linked bond and issued by a number of governments, for example Canada, UK, US and France. These bonds pay an annual coupon and an inflation adjusted principal is repaid at maturity.

3.1 The Index Ratio

The index ratio expresses the change in the consumer price index and is applied to calculate the nominal coupon payments and the final inflation adjusted redemption amount. The inflation linked bond carries a base index (a historical CPI index at the time of issuance) and the index

4 Official Swedish calculation standards can be found in the document “Calculation principles for the Swedish Money- and Bond market” published by the Swedish Securities Dealers Association.

5 Swedish inflation-linked bonds cash-prices obtained in the market include the accrued inflation. This is not the case for euro-denominated inflation-linked bonds.

6 The Swedish Central Government Debt, SNDO, No. 802, (2007)

ratio for a given settlement date⁷ is defined as the ratio of an interpolated reference CPI and the base index.

IndexRatio_{settlementdate} =

CPI Base

CPI Daily _ref

(3.2)

The reference CPI equals the CPI for the calendar month falling three months earlier⁸. This implies that inflation-linked bonds traded for settlement the 1^st of January, reference CPI corresponds to the CPI for October. The reference CPI for any other day in the month m is calculated by linear interpolation between the adjacent monthly CPI numbers. Interpolation is possible since CPI_m.−2 is published before month end⁹. All months are considered to have duration of 30 days and n is the number of days since the start of the month:

DailyCPI_ref =CPI_m−3+( 30

−1

n ) [CPI_m.−2 −CPI_m−3] (3.3)

3.2 Interest Payments and Accrued Interest

For inflation linked bonds, the coupon to be paid out, in nominal terms, is calculated by multiplying the real coupon of the bond with the index ratio¹⁰. This occurs on an annual basis, on either the 1^st December or 1^st April¹¹. These dates are also the maturity dates.

Nominal Coupon_t = Real Coupon ^x Index Ratio_t (3.4)

Further, a Swedish IL-bond, with annual coupon payments, the received/paid accrued interest is simply:

Accrued interest_t = Real Coupon ^x Index Ratio_{t x} 360

) 360

( −d

(3.5)

To calculate the actual amount, the accrued interest above is multiplied by the notional amount.

Similarly, at maturity, the redemption amount bond holders receive (excluding the final coupon), is calculated as the notional amount multiplied by the index ratio. Both loan 3104 maturing

7 Settlement occurs three business days after the trade date.

8 Swedish Inflation-linked bonds follow a 3 months indexation lag. This is also the convention used in Canada, France, Eurozone and the US. United Kingdom is using an 8 months lag. However, as of Sep 2005 all primary market UK-issuance follows the 3mths indexation lag, often referred to as the “Canadian model”.

9 In Sweden, the consumer price index (CPI) survey is conducted and published by Statistics Sweden:

http://www.scb.se

10 For Zero-Coupon bonds the only cash flow that occurs is on the maturity date.

11 Differences between April and December maturity are discussed later with regards to seasonality in CPI.

December 2028, and loan 3105 maturing 2015, are deflation protected; e.g. the index ratio on the maturity date can not be less than one and the par value is guaranteed by the SNDO.

4. Methodology - The Breakeven Inflation, its Distortions and the Comparison

Estimating market based inflation expectations in a simple world would be to pick a nominal and an inflation-linked bond with the same maturity. Assuming risk neutral investors, efficient markets and ignoring any distortions, the difference in yields between the nominal and the inflation-linked bond would produce an estimate of the average expected rate of inflationπ ^e from today until the maturity of the bonds. In this simple world, the Fisher Hypothesis must hold and the nominal rate is equal to the real rate adjusted for expected inflation:

TheFisher Equation¹²: (1+i)=(1+r)(1+π^e) ⇒ 1 1

1 −

+ + r

i =πe (4.1)

The calculated expected inflation rate above is the rate of inflation that equalises the total return on an inflation-linked bond with that on a nominal bond. Under a number of assumptions this is an unbiased estimator of the average inflation expectations. In the real world however, the BEI may contain distortions that both vary over time and affect the absolute level of the BEI.

4.1 Maturity and Cash Flow Mismatch Explained

There are obviously some shortcomings with the real and nominal yield-to-yield bond spreads, those easily obtained in the market. It can be difficult to find a nominal and an inflation-linked bond with exactly the same maturity dates. In the inflation market, the nominal bond in the BEI- spread is usually the nominal bond that is closest in maturity to the IL-bond. This may cause a curve effect depending on the slope of the yield curve but does not necessarily need to have a major negative impact when analysing the BEI. However, the shape of the yield curve, an extremely steep or sharply inverted yield curve could result in, despite a minimum difference in maturity, significantly different yields. This is directly affecting the yield spread, i.e. the BEI and has nothing to do with market’s inflation expectations. Further, any difference in coupon structure complicates the comparison between the bonds. The index ratio implies that the IL- bond coupon payments accumulate and rise with inflation while nominal bond coupon payments are constant over time, thus a mismatch may occur.

12 This equation was derived by Irwing Fisher and is a better approximation of inflation expectations than equation 1.1.

4.2 Maturity and Cash Flow Mismatch Derived

In order to take the first step in estimating the adjusted breakeven and to address some of the issues raised above, this section derives a BEI using a nominal benchmark that more effectively matches the payment stream of the IL-bond. Since the yield-to-yield difference between the nominal and the real bond do not match in terms of maturity and could create a mismatch, a few actions are needed to be undertaken. For a given level of inflation, the path of increasing coupon and principal payments of an IL-bond can be calculated. From the nominal yield curve we could extract a zero coupon curve that exactly matches the payment stream from the IL-bond. In other words, the easily obtained nominal government bond yields are recalculated to Zero Coupon yields¹³ exactly matching the cash flows of the IL-bond. Following the pricing structure of an inflation linked bond, the formula implies that the IL-bond contains an implicit valuation of the index factor, thus the expected inflation. By solving iteratively for the inflation rate that equates the market value of the relevant zero coupon rate the mismatch in maturity and coupon structure is accounted for, thus removing the distortion. At a given level of inflationπ, whereδdenotes the nominal discount factor, P is the price of an IL-bond, I the index ratio or base-index (equation 3.2) and C is the IL-bond coupon. The breakeven inflation would be given by:

i b i i

i I

C I δ

⋅

∑ (4.2)

C_n =(1+C) (4.3)

Thus, the Breakeven Inflation, BEI, is then obtained by solving for the expected inflation,π

I₀ (1+π )=I₁ , I₂ (1+π )=I₂ (4.4)

4.3 Inflation Indexation implications and Carry Explained

The analysis of IL-bond yields are complicated by the inflation indexation lag since the IL- payments are indexed to the CPI 2 to 3 months earlier. As a result, spot market prices contain information of already published inflation figures that are filtered through to the IL-bond via the index factor. Also, both IL and the nominal bonds are affected by bond finance implications in the repurchase market, generally referred to simply as the repo market. The combined effect –

13 For Zero-Coupon rates and different bond structures, see Cuthbertson (1999)

=

⋅

⋅ + +

⋅

⋅ +

⋅

⋅

= _n

base n base

base I

C I I

C I I

C I

P ¹ δ₁ ² δ_{2 .......} δ

for linkers the inflation indexation lag plus the cost of financing the bond and for nominal bonds the latter alone – this effect is often referred to as “carry”. For policy makers and investors it is therefore more interesting to analyse the carry adjusted yields. To make a relevant comparison, the carry is calculated for both the IL and the nominal bond. As a result, for all daily BEI observations a carry in basis points is calculated. 1 month and 3 month forward carry is first calculated and later applied to the BEI-spread.

4.3.1 The Repo market

To provide a deeper understanding of how the cost of holding a bond influences an investor, this part describes the so called repo-market, which is the market place where bonds and other securities are financed through lending and borrowing activity¹⁴. A “repo” is an agreement for a spot “sale” in combination with a forward contract “purchase". A forward contract may be seen as a spot transaction with delayed payment where the forward price is determined on the basis of the spot price plus/minus the implicit repo-rate. The buying part of the repo transaction borrows the bond and simultaneously lends money plus receives compensation (interest) at the agreed forward date. This could also be interpreted as the investor borrows cash in the repo-market and by using the bonds as collateral, the investor finances the bond purchase. The interest, the difference measured in basis points, between the forward and the spot yield, is widely referred to as the carry. As stated earlier, when IL-bonds are involved in repo-markets the difference between the spot yield and the forward yield includes two components, the implicit repo-rate (interest) and the accrued inflation due to the indexation lag. All in all, the carry is indicating how much the bond yield needs to change to “break-even” in terms of financing costs and inflation compensation.

In addition, since the nominal bond is exempted from the inflation indexation lag, the nominal yield carry gradually changes in a more continuous fashion; more of a slowly changing function in line with the slope of the yield curve. See figure 4.1 below. Conversely, the short maturity IL- bonds have a significant CPI sensitivity and a relatively low interest rate risk, thus contributing to more volatile carry series. Most important, as carry differs between the bonds and moves continuously, a BEI analysis without adjusting for carry, i.e. inflation indexation and financing is, in my view, impaired by errors.

14 SNDO recently discussed the Swedish repo-market and its participants in “The Swedish Central Government Debt”, SNDO, No. 802, (2007).

Figure 4.1 Index Linked and Nominal carry

IL and Nominal Carry

-30 -20 -10 0 10 20 30

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 So urce: Reuters and own calculatio ns bp

1m fwd IL-Carry 1m Nominal Carry

4.4 Carry of Inflation Linked Bonds Derived

For typical nominal bonds, we know that the carry over a given period is simply the difference between the current market yield (spot yield) and the forward yield implied by the financing cost, the implicit repo-rate. For the IL bond, the interpretation is exactly the same but the inflation indexation, is needed to be taken into account urging for a technical explanation:

Step 1: Initially (date t), the investor borrows the following settlement (invoice) amount:

S_t =

[ ]

CPI Base

CPI Daily AccInt

P_t + _t ⋅ ^referencet (4.5)

St is the settlement amount today, P_tis the clean price¹⁵ and the ratio above is simply the Index ratio at t. During the repo-agreement period, the financing cost accrues in line with the implicit repo rate and all other bond related income during the period, accumulated coupon and inflation compensation.

Step 2: At the loan maturity date (date f) the bond is sold and the loan is repaid. The repayment amount is known today as the loan has a fixed rate. In a simple non-arbitrage world the amount that the investor expects to receive for the bond sale at maturity f, (S should match this _f) repayment amount:

15 In Sweden, the clean price usually includes inflation compensation. This is not regular market convention. but has been included to simplify the presentation above.

(1 _, )³⁶⁰

t f f t t

f S r

S

−

+

⋅

= (4.6)

In the equation above r_t,fequals the repo-rate for a loan starting in t and maturing in f and gives a forward clean price expected today, P_f implied by:

S_f = [P _f + RC_t,f + AccInt_f ]

CPI Base

CPI Daily _referencef

⋅ (4.7)

Indeed, the accrued interest AccInt and the potential coupon paid during the agreement period _f RecCoupon_t,f are deterministic and are known at date t.

However, the forward Daily CPIref, may not be known at date t but the 2 to 3 months inflation _f indexation lag and the mid-month CPI release date allow estimating the Index Ratio on a forward basis. Carry calculations over a longer period require assumptions to be made regarding the coming MoM inflation figures. As our model deals with historical data, there is no need to use any forecasted CPI figures¹⁶.

The reinvestment rates for any coupons are a minor issue and often easily obtained using money market forward rates.

We calculate the forward price from the previous equation,

P = _f S _f

referencef

CPI Daily

CPI

⋅ Base - AccInt - _f RC_t,f (4.8)

From the forward clean price the yield is calculated and the carry is obtained by subtracting the current yield to maturity,ytm from the forward yield,_t ytm_f.

Carry = Implied ytm_f − ytm_t (4.9)

16In the inflation markets, banks and other participants are basing buy and sell recommendations based on their own expected inflation paths. Forward looking periods longer than the inflation indexation period are used to motivate whether there is value in the index linked bond markets compared to current pricing.

A positive carry means that the yield to maturity today is lower than the implied forward yield to maturity, the bond is returning more than is needed to repay the loan so the ytm can rise (price can fall) to the implied forward ytm before the contract looses money. A negative carry means that the ytm has to decrease (price increases) for the contract to be in the money¹⁷.

Put simply, if the reference CPI rises by, say, 0.5% from one month to the next, then over the period over which that CPI increase accrues, all things being equal, the cash dirty price of the bond will rise by 0.5% of the nominal, creating a strong carry effect. The opposite is true when large MoM negative figures occur.

4.5 Consumer Price Index (CPI) Seasonality Explained

IL-bonds and derivatives are indexed to the unrevised seasonality unadjusted CPI. As the IL- market is maturing, recent year’s product developments, complex IL derivatives¹⁸ and bonds issued with different maturity months have increased attention to the analysis of seasonality when it comes to pricing IL-products correctly. This section is not for the purpose of evaluating historical CPI but the importance to take seasonality into account requires estimating seasonality factors for the Swedish CPI in order to adjust the relevant carry and, as a result, create a BEI- adjusted for seasonality. Indeed, the seasonality components estimated will be based on historical inflation behaviour.

In the final section when a comparison is made between the fully adjusted BEI and the survey based inflation expectations, seasonality is of highest importance. If we were to study a full 12 months of bond prices, the seasonality effect is netted and does not affect the BEI. Inflation expectation data taken from survey data is however obtained during certain dates. To make a relevant comparison between the survey data and the BEI, a seasonality adjustment is highly required. For the investor, ignoring seasonality would result in monetary losses.

4.6 Consumer Price Index (CPI) Seasonality Derived

Assuming a linear increase of the CPI during each year would be an approximation but is far from correct as the monthly inflation figures can be positive or negative. This assumption would consequently under- or overestimate the monthly changes due to the seasonality because the CPI accumulates differently during the year. Luckily, it is widely known that the CPI moves in a seasonal fashion due to its structure, i.e. the same months every year show, basically, a

17 In The Money = a positive monetary state or outcome.

18 In Sweden, the inflation derivatives market is still relatively limited.

recognisable pattern. January and July are, in Sweden and many other countries, seen to experience low inflation due to sales periods. By evaluating and quantifying the seasonal factors, we could adjust the monthly CPI figures and by incorporating these seasonal adjusted figures in our breakeven model our adjusted BEI will take the relevant seasonality into account when making comparisons between the adjusted BEI and the survey based expectations.

4.6.1 The Seasonality Adjustment Method

We choose to apply a multiplicative model to the decomposition of the CPI series:

y(t)=Trend(t)ּ Cycle(t)ּ Season(t)ּ Noise(t) (4.10)

The model first eliminates the season and noise by smoothing the series with a centered moving average. The smoothed series is then simply identified as the trend. The model merges the trend and the cycle into one component. Since CPI figures are released monthly, as a result, the length of the centred moving average is 12. For example the seasonal factor for January will be calculated from all January observations in the sample. The model eliminates the noise terms and normalises the seasonal factors to make the average of the seasonal factors equal to one.

Why this method? The model is taken from Reuters EcoWin. This method is widely used among analysts and researchers in the financial industry. Other models frequently used within this field are X-11, ARIMA X12 and TRAMO-SEATS. The methods might generate somewhat different results to the Reuters EcoWin method. However, that is beyond the scope of this paper.

4.6.2 What drives Seasonality?

Seasonal factors can be driven by calendar effects such as Christmas holidays, social traditions like winter and summer sales, natural factors e.g. fresh food prices, or due to tax-related payments or changes in legislation. Noise is unpredictable in terms of timing, direction or magnitude. Strikes, disasters, extreme weather conditions or non-standard sales periods are all examples impossible to foresee. When measuring seasonality it could be difficult to separate between seasonality and noise. The oil or energy prices for instance. Some parts of oil price are seasonal but it is often overtaken by large volatility in oil prices driven by other factors than seasonality. The challenge is to produce an adjustment with none or at least minimal residual effect, only trend and noise. It is also important that the seasonality factors need to be revised

constantly as new data becomes available but these revisions should be very small unless there is a major change of the CPI calculation method or substantial changes in consumer behaviour.

4.6.3 How long History should be used?

It is arguable that consumer spending patterns continuously change between years so a long history is not necessarily a better history. Questions arise whether history will repeat itself in the future. However, when estimating seasonal components a decision must be made of how far back one should go with data. There is a trade off between using a large enough sample to mitigate the effects of outliers whilst simultaneously considering that a sample must be compact enough to be representative of the present situation. For instance, it is worth considering whether the seasonality effects in the mid 90’s when oil was stable at a fifth of today’s price is a reasonable approximation of current seasonality effects. Furthermore some shocks need to be taken into account, especially one-off tax or fiscal effects. It is more difficult to strip out shocks due to oil price, energy or fresh food price behaviour, as a decision will need to be made as to whether it is the result of noise or seasonal factors. Also, it is worth considering that seasonal effects can be amplified at any given point by the introduction of a shock. The oil price is once again a good example and could significantly amplify the effect of seasonal trends in inflation through secondary effects of fuel consumption impacts. Importantly, the seasonal factors are estimates based on past experiences and may not show the same pattern in coming years. Regardless of the approach, it will be more accurate to include seasonality than to ignore it. In this paper, Swedish headline CPI figures running from January 1998 are used when estimating the seasonality factors. Why start in 1998? The Riksbank inflation target was introduced in 1993. Using data from 1998 is suitable since it is reasonable to assume that it takes some years to establish such a target. On the other hand, a sample less than 10 years would not produce sufficient data.

Figure: 4.2 The Seasonality monthly changes in Swedish CPI

Seasonal monthly changes for Swedish Headline CPI

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Source: Statstics Sweden and Reuters EcoWin

% MoM

Average montlhly change Jan-00 to Nov-07

4.7 Liquidity Premium Explained

The global inflation-linked bond and derivatives markets are steadily growing. Inflation itself is often today considered as a commodity, attracting hedge funds and speculative money. In addition, an IL-product friendly regulatory framework has in many countries forced pension funds and insurance companies to match their outstanding (real) liabilities. All these different types of investors have contributed to sharply improve the liquidity in IL-markets.

In several academic papers on the IL-market the liquidity premium or liquidity risk is often discussed and considered very hard to estimate. The premium originates from the risk the investor faces from not being able to sell the asset without creating large costs or disproportionate market fluctuations. This theoretically leads to a higher real yield, lowering the BEI, and in turn increases the issuers cost of borrowing. As the IL-market matures, the size of the premium is declining. The obstacle is more to quantify it and then observe whether it varies over time. For certain, the liquidity premium reduces demand, primarily from speculative investors such as hedge funds and other important liquidity providers. However, long-term investors (buy and hold investors) are less vulnerable to weaker liquidity since they trade only on an occasional basis.

4.8 Inflation Risk Premium and Bond Convexity

As the liquidity premium results in higher real rates, the inflation risk premium offsets and affects the nominal rate investor. As described above, by investing in an IL-asset the investor is compensated for the entire realised inflation. The issuer retains the inflation risk. However, the nominal bond investor is facing a problem if the realised inflation during the holding period significantly exceeds the inflation expected at the time of the investment. This could erode the value of the nominal investment dramatically, deteriorating the real rate of return. To compensate the investor nominal bonds carry an inflation risk premium, leading to higher nominal rates, thus widening the BEI. The size of this risk premium depends primarily on the investors risk aversion and the future inflation uncertainty. If uncertainty varies, the size of the premium changes and assuming that inflation uncertainty is positively correlated with actual inflation and inflation expectations, the BEI will rise to a larger extent than the inflation

expectations. In order to get the full picture it is needed to broaden the discussion to Jensen’s inequality¹⁹ and convexity.

The bond price equation is a convex function of interest rates. Jensen’s inequality could therefore be applied and, for the same expected interest rate over the lifetime of a bond, the convexity produces a larger price of a bond than in a convexity free world. In other words, an investor taking convexity into account would demand a lower yield. From a nominal bond perspective, Jensen’s inequality implies that, if investors are risk neutral, the yield spread between real and nominal bonds will underestimate inflation expectations. From the nominal bond perspective, the inflation rate risk premium and the convexity will bias the BEI in the opposite direction. In other words, assuming no difference in convexity between the nominal and the real bonds, it is reasonable to assume that the net impact of the BEI is solely an inflation risk premium²⁰.

4.9 Survey Data

The traditional way of obtaining inflation expectations is simply to question households and money market participants. In Sweden, Prospera and NIER²¹ are conducting surveys on a regular basis. This thesis does not examine the bias of such surveys but it is important to understand that in the absence of “true” expectations, survey measures are the most reliable source when later comparing our estimated market based BEI. A disadvantage of survey based measures is that respondents are weighted equally or have no incentive to reveal private information. It is also fair to say that many households lack the ability to give a balanced view of inflation 2 or 5 years ahead. Studying professional forecasters, there are other problems to address. Theoretically, these forecasters may behave strategically and rather than revealing their true forecast they stick to what is market consensus. Or the other way round, making forecasts thatdeviate sharply from consensus in order to attract more attention. Interest market position taking might also, theoretically, affect professional respondents. On the other hand, an advantage of survey based measures is that they do not include the liquidity risk premiums and similar bias.

19 For a more analytically description of the problems caused by the inflation risk premium and the convexity of the bond price equation see Deacon, Derry and Mirfendereski (2004).

20 In a recent article by Svensson, J. (2006) there is no significant convexity premium in the Swedish Inflation Linked Bond curve. This is primarily due to the relatively limited duration of the Swedish IL-bond curve. (The longest bond, loan 3104 matures in 2028). Svensson concludes that transaction costs would erode the return from convexity. However, according to a study by Saragoussi, J (2005) convexity in the UK inflation linked bond curve is decisive when analysing returns on ultra long bonds. The UK curve is stretching out to year 2055 in terms of maturity and a substantial impact on returns from convexity appears when maturity is exceeding 30 years.

21 National Institute of Economic Research

4.9.1 Prospera – Inflationary Expectations for Sweden

Prospera has been commissioned by Sveriges Riksbank²² to undertake surveys four times a year aiming at mapping inflationary and wage increase expectations in Sweden among labour market parties, purchasing managers and money market players.

The Prospera Inflationary expectations are reported for individual years, i.e. for the next coming year²³ (months 0-12), the second year from now (month 12-24) and the fifth year from now (months 48-60)²⁴. Since BEI is simply interpreted as the yearly average expected inflation, it is important to use the average Prospera inflationary expectation figures in order to make all figures comparable.

4.10 The Comparison – An overview

This section describes the comparison between the survey based measure and the BEI of which the market based BEI is divided into two buckets. A short dated BEI and a long dated BEI. The BEI samples starts in January year 2000. The reason behind this is simple, the Swedish inflation market was then considered to have reached a critical level of maturity. Further, the relevant survey figures are then compared to a number of different BEI-rates. The simple yield-to-yield unadjusted BEI, i.e. the yield spread between the IL-bond and the nominal bond directly traded in the market. A number of comparisons follow to adjust for the distortions discussed throughout this paper. A cash flow matched BEI and a BEI calculated for both 1 and 3 months forward carry. A CPI seasonally adjusted BEI and finally a fully adjusted BEI, including all distortions above in this section. As mentioned in chapter one, the liquidity and inflation risk premiums are not quantified in this paper. However, there are several reasons for reverting to these distortions in the final discussion. Finally, the survey based inflationary expectations used in the BEI-survey comparisons are the so called “Prospera Money Market Players”, i.e. professional forecasters and the choice of BEI maturity dates in the comparison described in detail below.

The evaluation uses two standard statistical measures²⁵ to estimate the size and the bias of the unadjusted and the adjusted BEI-series divergence from the “true” Prospera survey based inflationary expectations. The Root Mean Squared Error - RMSE - estimates the size of the

22 Central Bank of Sweden

23 Year-over-Year, change compared to previous year.

24 This method of reporting has not always been the case. During the period 1995-2001 inflation and wage increase expectations were, on request, reported as averages for the respective forecast periods (1, 2 and 5 years). However, these averages were calculated on data for the individual years.

25 See for instance Sveriges Riksbank, Economic Review 3/2007 (Assarsson)

forecast error and the Mean Error - ME - measures the bias or the tendency for a forecast error to point in a particular direction. A negative ME means overestimations of the variable.

Letx^∧ denote the forecast, in this case the unadjusted or adjusted BEI inflation series andx is the survey based observation and n is the number of observations/surveys.

n x

MSE ₌

∑

⁽x^{t − ∧t)2} (4.11)

MSE

RMSE = (4.12)

n x

ME ₌

∑

⁽x^{t − ∧t)} (4.13)

4.11 The 5y Short dated BEI – the Comparison Explained

In the 5y case, the Prospera survey based inflationary expectations for year 1 and year 2, a yearly average is calculated for all quarterly surveys. This figure is then compared to a BEI holding approximately 5 years in maturity. This might appear to be a bit strange!? Why would we compare a short dated survey based inflation expected figure with a 5yr BEI rather than the 1 or 2yr BEI-rate? This is simply because of the market-participants way of interpreting short term BEI. The 5yr BEI is among investors and analysts considered to be the relevant benchmark when dealing in short-term inflation expectations²⁵. A shorter BEI, for instance 1 or 2 years in maturity, tends to trade in line with direct changes in spot inflation and does not provide any information about short term inflation expectations. In addition, SNDO usually introduces buy back programs in both IL and nominal bonds when just a few years remains until maturity, thus draining the liquidity.

Finally, by arranging the comparison as described above, one finds whether the unadjusted or fully adjusted BEI is a good measure of the “true” survey based inflation expectations. In turn, this would also help us in evaluating the Riksbank’s ability to achieve their short term inflation target.

25 After discussions with interest rate strategists Kaplan, P. and H. Eriksson at Handelsbanken.Capital Markets I find support in this way of interpreting the different BEI maturities.

4.12 The 15y Long dated BEI – the Comparison Explained

In the evaluation of long dated inflation expectations, the Prospera 5 year survey based inflation expectation figure is compared to a BEI-rate that holds 15yr maturity. This might trigger the same type of question as above. Why on earth would we compare a 5yr survey based measure to a 15yr BEI-rate? Similar to the 5yr BEI comparison described above, the 15yr BEI-rate is among investors and analysts interpreted as a measure of long term inflation expectations²⁶. The same goes for the 5yr Prospera inflation expectation figure. Both figures are used for measuring the expected long term inflation. In turn, this would also provide some information about the markets belief of the Riksbank to maintain a long term monetary credibility.

5. Swedish Breakeven Inflation Rates – Empirical findings

At this stage, it is widely accepted that the simple Yield-to-Yield BEI traded in the market and directly obtained from market quotes contains a number of distortions. These distortions cause the BEI to fluctuate and have nothing to do with changes in inflation expectations. To illustrate how the BEI samples and the distortions vary over time and have developed since year 2000, this section illustrates the time series covering the unadjusted and adjusted BEI samples for the two maturities, the “short dated” 5 year BEI rate and the “long dated” 15y BEI-rate.

5.1 Real and Nominal Yields during the sample period

In Sweden, during the period years 2000 to 2007 the Swedish Riksbank, as with many other central banks, delivered a large number of rate cuts. The burst of the IT bubble, falling domestic and international corporate profits as well as the 11 September event changed the domestic and international economic outlook drastically.

In 2005, previous repo-rate cuts combined with low imported inflation and the Riksbank struggled against extremely low spot inflation. A surprisingly low GDP figure released early in 2005²⁷ forced the Riksbank to deliver a final 50bp rate cut. The Riksbank has been on a hiking path since and today it paints a mixed picture of the economic outlook. High spot inflation driven by a recent surge in food and soft commodity prices are balanced by recession fears following the housing market crisis in the United States.

However, today as in the beginning of the decade, high volatility and lower equity market prices are increasing the focus on fixed income products and in particular, real assets such as IL-

26 After discussions with interest rate strategists Kaplan, P. and H. Eriksson at Handelsbanken.Capital Markets I find support in this way of interpreting the different BEI maturities.

27 This GDP figure was later revised upwards

products. In the early days of the Swedish IL-market when the investor base consisted mainly of buy-and-hold investors²⁸ the liquidity was relatively poor. This explains the high outright real yields in Sweden as late as the beginning of the decade, thus relatively low Breakeven Inflation rates. Figures 5.1 and 5.2 illustrate the development in real and nominal yield for the 5y and 15y maturities.

Figure 5.1 5y “Yield-to-Yield" BEI, Nominal and Real Generic Yields

0 50 100 150 200 250

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 Source: Reuters and ow n calculations bp

0 1 2 3 4 5 6 7

%

5y Yield-to-Yield BEI (lhs) 5y Generic Nominal Yield (rhs) 5y Generic Real Yield (rhs)

Figure 5.2 15y “Yield-to-Yield" BEI, Nominal and Real Generic Yields

0 1 2 3 4 5 6 7

okt-07 okt-06 okt-05 okt-04 okt-03 okt-02 okt-01 okt-00

Source: Reuters and ow n calculations

%

0 50 100 150 200 250 bp

15y Generic Nominal Yield (rhs) 15y Generic Real Yield (rhs) 15y Yield-to-Yield BEI (lhs)

5.2 The Cash Flow Adjustment

Figures 5.3 and 5.4 plot the 5y and 15y BEI-rates adjusted and unadjusted for the difference in coupon structure and maturity, i.e. the cash flow mismatch. The differences between the unadjusted and adjusted series are not huge. However, generic time series with different underlying bonds during the samples result in distortions that can be entirely accounted for by the cash flow adjustment.

28 Annual reports and bond holding search on Bloomberg PHDC <GO>

Figure 5.3 5y “Yield-to-Yield" vs. Cash flow Adjusted BEI

0 50 100 150 200 250 300

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 Source: Reuters and ow n calculations bp

5y BEI Yield-to-Yield 5y Cashflow Adjusted BEI

Figure 5.4 15y “Yield-to-Yield" vs. Cash flow Adjusted BEI

0 50 100 150 200 250 300

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 So urce: Reuters and o wn calculatio ns bp

15y Cashflow Adjusted BEI 15y Yield-to-Yield BEI

5.2.1 The Size of the Cash Flow Distortions

The 5yr BEI cash flow distortion appears to be relatively contained. The steepness of the yield curve, in particular during 2001 distorts the BEI as little as 7.5bp. Further, the curve flattening, in some extent driven by LDI²⁹ related flows have in recent years offset the distortion and balanced the BEI.

The long end of the curve, the 15y BEI, shows an even more pronounced pattern due to the cash flow mismatch. The first part of the sample uses a nominal bond that differs 1.5 years in maturity to the IL-bond. This causes a mismatch of 25-30bp during late 2001. Since 2005, the sample uses a nominal bond that matures on exactly the same date as the underlying IL-bond. As could be seen below, the difference declines and the remaining distortion could be explained by the difference in coupon structure. Figures 5.5 and 5.6 illustrate the distortions for the 5y and 15y BEI-rates.

29 Liability Driven Investment, mainly liability matching flows from lifers and pension insurers.

Figure 5.5 5y BEI Cashflow Distortion

-2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 Source: Reuters and ow n calculations bp

5y Cashflow Distortion

Figure 5.6 15y BEI Cashflow Distortion

-30 -25 -20 -15 -10 -5 0 5 10

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 Source: Reuters and ow n calculations bp

15y Cashflow Distortion

5.3 Inflation Indexation and Carry Adjustments

Taking the analysis a step further, an adjustment for the IL-bond inflation indexation lag and for both the IL and the nominal bond (because of the bond finance issues) requires some attention.

This thesis is adjusting for 2 types of indexation and carry distortions. The 1 month forward and the 3 months forward. The different carry adjustment periods are entirely chosen due to the length of the indexation lag, discussed in section 3. In addition, the periods are chosen since they are often the standard periods referred to among inflation linked product analysts. Figure 5.7 and 5.8 illustrate the BEI-rates under these adjustments.

Figure 5.5 5y Cash flow and Carry Adjusted BEI

0 50 100 150 200 250 300

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 Source: Reuters and ow n calculations bp

5y Cashflow matched BEI

Cashflow and 1m fwd Carry Adjusted BEI Cashflow and 3m fwd Carry Adjusted BEI

Figure 5.8 15y Cash flow and Carry Adjusted BEI

50 100 150 200 250 300

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 So urce: Reuters and o wn calcualtions bp

15y Generic BEI

Cashflow and 1m fwd Carry Adjusted BEI Cashflow and 3m fwd Carry Adjusted BEI

5.3.1 The Size of Carry and Inflation Indexation Distortions

It is interesting to see the importance of carry adjustment, in particular for short maturity BEI- series. The shorter the BEI, the larger is the CPI impact. This causes a more volatile and time varying BEI for shorter maturities. And, when analysing the level of the BEI at a certain time, i.e. a specific month or week, the carry is considered to be distorted, and adjustments are highly required. See graphs 5.9 and 5.10 below for the 1 and 3 months carry components.

Figure 5.9 5y BEI Inflation Indexation lag and Carry Distortion

-30 -20 -10 0 10 20 30

okt-07 jan-07 maj-06 aug-05 nov-04 mar-04 jun-03 sep-02 jan-02 apr-01 jul-00

Source: Reuters and own calculations bp

-80 -60 -40 -20 0 20 40 60 80 bp

1m fw d BEI Carry Distortion 3m fw d BEI Carry Distortion

Figure 5.10 15y BEI Inflation Indexation lag and Carry Distortion

-25 -20 -15 -10 -5 0 5 10 15 20

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 Source: Reuters and own calculations bp

1m fwd BEI Carry Distortion 3m fwd BEI Carry Distortion

5.4 Seasonality Adjustment

Maintaining the cash flow adjustment and substituting the CPI figures with the seasonally adjusted CPI numbers, graphs 5.10 and 5.11 are display seasonally adjusted BEI series.

Figure 5.10 5y Carry and Seasonality Adjusted BEI

0 50 100 150 200 250 300

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 Source: Reuters and ow n calculations bp

5y Cashflow matched BEI

Cashflow and 1m fwd Carry Adjusted BEI Cashflow and 3m fwd Carry Adjusted BEI

Figure 5.11 15y Carry and Seasonality Adjusted BEI

50 100 150 200 250 300

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07

So urce: Reuters and o wn calcualtio ns

bp

15y Generic BEI

Cashflow and 1m fwd Carry Adjusted BEI Cashflow and 3m fwd Carry Adjusted BEI

5.5 The Size of the Carry when adjusted for Seasonality

By applying seasonality adjusted CPI figures instead of the actual published CPI figures an interesting view appears. The estimations remove the seasonality and smooth the 1 and 3 months carry series. We could distinguish 2 extremely volatile carry periods. During year 2001 the

“mad-cow” disease resulted in a shock to food prices sending inflation figures temporarily upwards. A similar shock occurred during 2003 when a cold winter and empty water reservoirs sharply boosted electricity prices. The shock was so pronounced that the Riksbank, for a certain period of time, was “forced” to evaluate monetary policy based on the underlying inflation (UND1X³⁰) excluding energy. Despite the removal of seasonality, the graphs below highlight that carry is needed to be taken into account. It exists, moves and reshapes the BEI-rates. Figure 5.12 and 5.13 describe the seasonality adjusted carry movements.

30 In 2007, KPIX has replaced UND1X to denote the underlying inflation.

5.12 5y Seasonality Adjusted fwd BEI carry BEI

-20 -15 -10 -5 0 5 10 15 20 25

okt-07 jan-07 maj-06 aug-05 nov-04 mar-04 jun-03 sep-02 jan-02 apr-01 jul-00

Source: Reuters and own calculations bp

-40 -30 -20 -10 0 10 20 30 40 50bp

Seasonality Adjusted 1m fwd BEI Carry (rhs) Seasonality Adjusted 3m fwd BEI Carry (lhs)

s

Figure 5.13 15y Carry and Seasonality Adjusted BEI

-15 -10 -5 0 5 10 15

jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 Source: Reuters and own calculations bp

Seasonality Adjusted 1m fwd BEI Carry Seasonality Adjusted 3m fwd BEI Carry

5.6 BEI Seasonality Distortion

This is the essence! By subtracting the cash flow and carry adjusted BEI series from the corresponding seasonality adjusted BEI-rates, presented above, we receive the CPI Seasonality components on a forward basis expressed in basis points! Graphs 5.14 and 5.15 are plotting the seasonality components measures in basis points.

Figure 5.14 5y BEI Forward Seasonality Component

-30 -25 -20 -15 -10 -5 0 5 10 15 20

okt-07 jan-07 maj-06 aug-05 nov-04 mar-04 jun-03 sep-02 jan-02 apr-01 jul-00

Source: Reuters and own calculations bp

-40 -30 -20 -10 0 10 20 30 40 bp

1m fwd BEI Seasonality Distortion (rhs) 3m fwd BEI Seasonality Distortion (lhs)

Figure 5.15 15y BEI Forward Seasonality Component

jan-07 maj-06 aug-05 nov-04 mar-04 jun-03 sep-02 jan-02 apr-01 jul-00

Source: Reuters and own calculations bp

-15 -10 -5 0 5 10 15

1m fwd BEI Seasonality Distortion 3m fwd BEI Seasonality Distortion

6. Inflation Expectations

In section 5, we illustrated graphically and commented on the evidence of distortions in the Swedish 5y and 15y BEI-rates. To answer the question whether these BEI-rates are a market based measure of inflation expectations, a comparison to a relevant benchmark is required. In the absence of “true” inflation expectations the most reliable figures to use are the survey based expectations. As described earlier, the benchmark chosen when comparing the adjusted and unadjusted BEI rates is the Prospera “Money Market Players” (MMP) Inflationary Expectations.

The statistical measures are the Root Mean Squared Error (RMSE) and the Mean Error (ME). In addition, Appendix 1 and 2 show all MEs marked in relevant colours - negative or positive - on both subsample and aggregated levels! RMSEs, individual BEI rates and survey observations are displayed as well.