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?

2

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

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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

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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

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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, eπ :

eri π=− (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.

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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.

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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

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3. Pricing and Structure of Swedish Nominal and Inflation-Linked bonds4 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:

nytm

n

tt

ytm

tt i

Mi

CP

)1()1(1 ++

+= ∑

=

(3.1)

tP 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)

9

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

base index .

datesettlementRatioIndex = CPIBaseCPIDaily 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 1st 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 2.−mCPI 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:

=refCPIDaily +−3mCPI (30

1−n ) [ 32. −− − mm CPICPI ] (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 1st December or 1st 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 x360

)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.

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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 inflation eπ

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:

The Fisher Equation12: )1()1()1( eri π++=+ ⇒ 111

−++

ri eπ= (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.

11

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 , whereδ denotes

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:

ib

iii I

IC δ⋅∑ (4.2)

)1( CCn += (4.3)

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

10 )1( II =+π , 22 )1( II =+ π (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)

=⋅⋅++⋅⋅+⋅⋅= nbase

n

basebase IIC

IIC

IICP δδδ .......2

21

1

12

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).

13

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

Source: Reuters and own calculations

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:

=tS [ ]CPIBase

CPIDailyAccIntP treference

tt ⋅+ (4.5)

tS is the settlement amount today, tP is 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, ( )fS should match this

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.

14

360, )1(

tf

fttf rSS−

+⋅= (4.6)

In the equation above ftr , equals 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:

=fS [ fP fft AccIntRC ++ , ] CPIBase

CPIDailyfreference

⋅ (4.7)

Indeed, the accrued interest fAccInt and the potential coupon paid during the agreement period

RecCoupon ft , are deterministic and are known at date t.

However, the forward Daily CPI fref, may not be known at date t but the 2 to 3 months inflation

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,

fP = fS freferenceCPIDaily

CPIBase⋅ - fAccInt - ftRC , (4.8)

From the forward clean price the yield is calculated and the carry is obtained by subtracting the

current yield to maturity, tytm from the forward yield, .fytm

Carry = Implied tf ytmytm − (4.9)

16 In 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.

15

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.

16

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

17

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 DecSource: Statstics Sweden and Reuters EcoWin

% MoM Average montlhly change Jan-00 to Nov-07

18

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

19

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 that deviate 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

20

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)

21

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.

Let∧

x denote the forecast, in this case the unadjusted or adjusted BEI inflation series and x is the

survey based observation and n is the number of observations/surveys.

n

xxMSE

tt∑∧

−=

2)( (4.11)

MSERMSE = (4.12)

nxx

MEtt∑

∧

−=

)( (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.

22

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

23

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

Source: Reuters and ow n calculations

%

0

50

100

150

200

250bp

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>

24

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

Source: Reuters and own calculations

bp

15y Cashflow Adjusted BEI15y 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.

25

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.

26

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 BEICashflow 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

Source: Reuters and own calcualtions

bp

15y Generic BEICashflow and 1m fwd Carry Adjusted BEICashflow 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.

27

Figure 5.9 5y BEI Inflation Indexation lag and Carry Distortion

-30

-20

-10

0

10

20

30

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

Source: Reuters and own calculations

bp

-80

-60

-40

-20

0

20

40

60

80bp

1m fw d BEI Carry Distortion3m 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 Distortion3m 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.

28

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 BEICashflow 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

Source: Reuters and own calcualtions

bp

15y Generic BEICashflow and 1m fwd Carry Adjusted BEICashflow 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.

29

5.12 5y Seasonality Adjusted fwd BEI carry BEI

-20

-15

-10

-5

0

5

10

15

20

25

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

30

Figure 5.14 5y BEI Forward Seasonality Component

-30

-25

-20

-15

-10

-5

0

5

10

15

20

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

Source: Reuters and own calculations

bp

-40

-30

-20

-10

0

10

20

30

40bp

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

Figure 5.15 15y BEI Forward Seasonality Component

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

Source: Reuters and own calculations

bp

-15

-10

-5

0

5

10

15

1m fwd BEI Seasonality Distortion3m 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.

31

6.1 The 5y BEI – Short Term Inflation Expectations

When examining the RMSEs and the MEs for the 5y adjusted BEI-rates, it is obvious that

distortions were present over the sample period. It is also certain that the BEI as a predictor of

inflation expectations has generally improved from year 2000. From Primary Dealers turnover

figures we could find that the amount of Swedish IL-bonds traded every year as a ratio of the

total outstanding amount has increased substantially between year 2000 and 2007. As a result,

this improvement in liquidity implies a declining liquidity risk premium during the sample

period. The relatively high Swedish real rates and thus low BEI especially in the beginning of the

sample period also confirms such a state. The very high deviation between surveys and the

different BEI-rates in the early part of the sample also helps to confirm the existence of liquidity

risk premiums. However, this paper does not quantify this premium.

Between year 2000 and 2003, the Yield-toYield BEI was a better predictor than any other of the

adjusted BEI rates with an RMSE of 36.2. The second best was the cash flow adjusted BEI with

an RMSE of 39.4. In terms of MEs, the direction of the forecast error is obvious. For all the

adjusted and unadjusted BEI series, the observations significantly undershoot the survey based

expectations. MEs of around + 30bp are consequently reported for this period. The plain cash

flow adjusted BEI compared to the carry and seasonally adjusted BEIs correct some bias but it is

noticeable that there is no strong evidence of that carry and seasonality adjustment improve the

predictability. The other way around, according to RMSE and ME, the fully adjusted 3m carry

cash flow and seasonality adjusted BEI-rate seems to be the poorest indicator of inflation

expectations!

In the following period, 2004-2007, a somewhat different picture emerges, the lowest RMSE

values are found in the 1 and 3m carry adjusted and the 1m carry and seasonally adjusted BEIs

(RMSEs of 11.6, 11.2 and 11.0 respectively). Looking at RMSEs and MEs the improvements

compared to the other adjusted series are not strongly pronounced but there is evidence of that

carry adjustment does matter! A fair explanation is that the market in recent years has been more

efficient in pricing already published CPI figures. In all investment decisions there is a balance

of when to buy or sell an inflation security at the right time in order to gain as much carry as

possible before the actual inflation compensation is finally filtered through to the index ratio.

Market participants would however argue that a greater level of such sophistication has taken

place in recent years. This is also confirmed by an interesting observation in the sub-sample

2006-2007. The cash flow, seasonality and 1m carry adjusted BEI appears to be the best

32

predictor! RMSE is down to 7.6 and the ME is only -2.6. This is significantly lower than the

Yield-toYield BEI which holds a RMSE of 12.8 and a ME of -8.1. This observation confirms the

last two years market-focus on handling the impact due to seasonality in CPI. For instance, in

September 2005 the SNDO issued loan 3106, maturing the 1st April 2012. Before the bond was

brought to the market, analysts argued about its correct pricing since an April maturity bond’s

final accruing CPI figure will be a January CPI figure instead of a December figure. In other

words, as shown in section 3, since the January CPI figure tends to be negative while the

September CPI tends to be sharply positive, the investor would miss a significant amount of

inflation compensation if the new April maturity bond would be priced as a December maturity

bond. In addition, the SNDO would be the winner, making a seasonality arbitrage31.

One way of evaluating the BEI-rates predictability is to study the changes in BEI and survey

observations from survey-to-survey. The analysis notices that the BEI-rates generally seem to

catch changes in survey inflation expectations relatively well.

Table 6.1

5y BEI and Prospera MMP Survey

RMSE / ME

Period BEI: Yield-to-Yield Cash flow Carry 1m / 3m Seasonality & Carry 1m / 3m 2000-2007: 27.0 / 9.4 28.4 / 11.6 29.3 / 12.8 30.2 /13.9 28.2 / 12.2 32.3 / 7.9 2000-2003: 36.2 / 28 39.4 / 32.1 41.2 / 34.5 42.7 / 34.3 39.7 / 32.6 44.6 / 33.8 2004-2007: 15.3 / -8.7 13.1 / -4.5 11.6 / -4.4 11.1 / -3.2 11.0 / -4.1 14.9 / -9.0 2006-2007: 12.8 / -8.1 10.5 / -4.8 10.5 / -3.8 11.1 / -3.4 7.6 / -2.6 11.9 / -7.0

6.2 The 15y BEI – Long Term Inflation Expectations

Section 5 clearly illustrates that the distortions caused by carry and seasonality is significantly

lower in the 15y sample. Since long dated IL-bonds and BEI-rates, relative to its short dated

correspondents are less CPI sensitive, the difference in RMSEs when adjusting for carry and

seasonality is less in the 15y comparison than in the 5y case. Also, this explains the smaller

variation in RMSEs across all sample periods for the other carry and/or seasonality adjusted BEI-

rates. Analysing MEs, a similar pattern to the 5yr samples is observed. During the first part of the

31 1st of December matures all other outstanding Swedish IL-bond benchmark issues.

33

sample, the BEI-rates significantly underestimate the survey based expectations. In the latter part

of the sample the direction of the errors are more balanced, and they even tend to overshoot the

survey based expectations somewhat.

In the short term analysis above, the results show that distortions exist and vary over time.

However, a substantial improvement in RMSE throughout the entire sample period is

experienced. Since the improvement in liquidity has a similar impact across the entire real yield

curve it is fair to say that the liquidity risk premium also has declined in the 15y segment.

It is noticeable that the full sample, year 2000 to 2007, and in particular during the first part of

the sample, 2000-2003, a significant divergence exist between the Yield-to-Yield BEI and the

adjusted BEI series. A RMSE of 37 is recorded for this measure compared to roughly 30 for the

other adjusted series. As seen in section 5, this deviation is caused by the difference in maturity

in the underlying bond spread. A so called curve risk emerges. As one can see, the difference is

declining in the latter part of the sample when bonds with equally matched maturities are being

used in the Yield-to-Yield spread. This is showing the importance of cash flow and maturity

matching, in particular in an environment when yield curves are relatively steep. This was clearly

the case at the beginning of the decade.

In the sub sample, year 2006-2007, the 3m carry adjustment show a significantly low RMSE of

13.9. This should be compared to an RMSE of around 17 for the other series. The ME is also the

lowest for this BEI serie, printing only -4.4. Similar to the 5yr case, the reason behind the carry

adjusted BEI being somewhat a better predictor could be explained by markets ability to price in

carry and seasonality in a more sophisticated manner in recent years. However, this conclusion

should be balanced by the relatively limited CPI sensitivity that categorises the 15yr IL-rates!

Finally, similar to the 5y BEI series, the 15y samples are matching changes in survey based

expectations when analysing changes in survey-to-survey. This strengthens the BEI-rate as a

predictor of inflation expectations.

34

Table 6.2

15y BEI and Prospera MMP Survey

RMSE / ME: Period BEI: Yield-to-Yield Cash flow Carry 1m / 3m Seasonality & Carry 1m / 3m 2000-2007: 28.5 / 14.2 24.4 / 6.9 24.5 / 7.2 25.3 / 7.4 24.5 / 6.8 25.0 / 7.4 2000-2003: 37.0 / 29.6 30.0 / 19.2 30.0 / 19.9 31.7 / 20.8 29.7 / 19.1 30.1 / 20.8 2004-2007: 18.5 / -1.2 18.8 / -5.4 18.9 / -5.6 18.5 / -6.1 19.4 / -5.5 19.8 / -6.1 2006-2007: 18.8 / -8.6 16.9 / -6.9 16.9 / -5.0 13.9 / -5.0 18.0 / -4.4 15.3 / -5.2 6.3 Inflation Expectations – A Summary i) Both short term and long term BEI rates as predictors of inflation expectations have improved

significantly during the sample period. Without quantifying the size of the premium, the increase

in liquidity – based on primary dealer statistics – is behind the improvement. In turn,

continuously falling RMSEs across the samples confirm this. In terms of MEs, the BEI tended to

significantly undershoot the survey based expectations during the period 2000 to 2003. However,

in the latter part of the sample - 2004-2007 - the MEs show a much more balanced view although

it tends to overshoot the survey based expectations somewhat.

ii) The level of sophistication and pricing efficiency has increased, in particular between 2004

and 2007. For both the 5y and the 15y sample, lower RMSEs are obtained in the latter sample

when the 1 or 3 months carry adjustment and in some extent also seasonality adjustments are

implemented. This evidence confirms the markets ability to price in carry and seasonality in a

more efficient way today compared to the first part of the sample.

iii) Analysing “survey-to-survey” changes in expectations with the changes in BEI-rates an

interesting observation is made. For both the 5y and the 15y sample - to a relatively large extent -

changes in inflation expectations are caught in both surveys and BEI rates. Despite the size of the

RMSEs, this conclusion is highly valuable.

35

7. Conclusions and Discussions In this thesis, the Swedish Breakeven Inflation – the spread between the Swedish nominal and

real rates has been evaluated as a measure of short and long term inflation expectations.

The deviation measured in terms of Root Mean Squared Errors – RMSEs – indicate that between

adjusted or unadjusted BEI-rates and the Propsera survey based inflation expectations,

distortions exist and vary over time.

The cash flow mismatch should be the most obvious to quantify and an adjustment should

correct some of this bias, mainly caused by the difference in coupons and maturity.

Carry and seasonality adjustments make sense, especially for the more CPI sensitive short end of

the inflation yield curve. However, adjusting for these distortions do not improve the BEI rates

significantly. Nevertheless, RMSEs for the period 2004-2007 and in particular 2006-2007

indicate that the carry adjustments somewhat improves the BEI rates in both the 5y and the 15y

samples. In my view, the conclusions are not strong enough and should be interpreted carefully.

On the other hand, the evidence of improvement when adjusting for carry and / or seasonality

could be explained by a higher level of sophistication in terms the market’s ability to price in

carry and seasonality.

An interesting observation is made in the overall sample, a significant improvement in RMSEs in

the second half of the sample compared to the first period. Without further quantifying its size,

turnover statistics confirms a sharply declining liquidity risk premium throughout the sample

period. In addition, there is a decent level of matching between changes in BEI and changes in

survey-to-survey expectations. The match is not perfect, but it provides evidence of both survey

based and financial measures catch changes in inflation expectations.

As discussed in earlier sections, an obstacle when evaluating BEI rates is that there are no “true”

inflation expectations. The intention of this thesis is not to analyse the possible bias of existing

surveys but one could easily argue that there is massive bias in the survey based expectations.

From this perspective, the BEI-rates are much better and more reliable than the survey based

measures. The large number of investors and market participants behind the “pricing” of the

market based inflation expectations would create a balance and any “error” in expectations

36

would be an arbitrage opportunity for other investors. On the other hand, as discussed throughout

this paper, when using a market based measure there are a number of distortions that are

impossible to quantify and adjust for. This is causing the BEI to be volatile and more time

varying compared to the survey based measures. From this perspective, there is a risk that more

structural distortions consequently over or underestimate the “true” inflation expectations. In

addition, the survey based expectations remove uncertainty with regards to liquidity risk

premiums, which in this thesis explain the lower RMSEs in the latter part of the sample, a period

with more sufficient liquidity.

However, in an environment where spot inflation is within the Riksbank’s tolerance interval,

thus minimising the inflation risk premium and a decent liquidity risk premium as experienced in

the last couple of years, a short and long dated BEI would provide policy makers, monetary

authorities and investors with a sufficient measure of inflation expectations. If not used in

isolation, it should at least provide a highly valuable complement to existing survey based

measures.

The Riksbank is today using the BEI-rates as a “rough” estimate of the market’s inflation

expectations. That is fair, but the adjustments discussed in this paper might improve this “rough”

measure further or at least provide the Riksbank with some valuable comments.

Finally, the outlook for the Swedish Inflation Linked Bond market is today uncertain. The

Swedish National Debt office “struggles” with a massive surplus due to the very strong Swedish

economic growth. During the autumn 2007 the SNDO proposed a few guidelines with regards to

an overhaul of the outstanding inflation linked debt. A reduction in the number and size of bond

auctions, and a buy back program in order to reduce the cost of the outstanding debt is already

announced and partially implemented.

What might counteract the last couple of year’s improvement in the Swedish inflation linked

bond market could instead be a distortion in the form of a supply premium. This might push the

real rates to artificially low levels implying a lower BEI and, as a result, overstate the inflation

expectations.

37

Referenser Alonso, F., R. Blanco and A. del Rio. (2001). “Estimating Inflation Expectations using French Government Inflation.Indexed Bonds”. Banco de Espana, Working Paper Series No.N.0111. Anderson, M. and H. Degrér. (2001). “A financial measure of inflation expectations”. Sveriges Riksbank, Economic Review 2001:3 Assarsson, B. (2007). “Riksbanks forecast of import prices and inflation”. Sveriges Riksbank, Economic Review 2007:3 Christensen, I., F. Dion, and C. Reid. (2004). “Real Return Bonds, Inflation Expectations, and the Break-Even Inflation Rate.” Bank of Canada, Working Paper. Cuthbertson, Keith. (1999), “Quantitative Financial Economics”, Wiley Finance Series Deacon M., Derry. A. and D. Mirfendereski. (2004), “Inflation-indexed Securities, Bonds, Swaps and Other Derivatives”. 2nd edition, Wiley Finance Series Sack, B. (2000). “Deriving Inflation Expectations from Nominal and Inflation-Indexed Treasury Yields”, Finance and Economics Discussion Series. Federal Reserve Board, 2000-33. Saragoussi, J. (2005). “UK 50Y Linker in the Spotlight”, Fixed Income Weekly. Deutsche Bank Group. Svensson, J. (2006). “Christmas Special – Convexity”, Rates Strategy. Handelsbanken Capital Markets. The Swedish Central Government Debt, SNDO, No. 802, (2007)

38

Appendix 1. Short Term Inflation Expectations – The 5y BEI / Survey Comparison (bp) Negative and Positive Mean Errors (MEs) for each sample are marked in red and blue respectively!

7.912.213.912.811.69.4ME (2000-2007):

32.328.230.229.328.427.0RMSE (2000-2007):

33.832.634.334.532.128.0ME (2000-2003):

44.639.742.741.239.436.2RMSE (2000-2003):

174.0164.7185.2170.4170.2170.3181.32000:1 (Jan 24 - Feb 04)

172.6165.1151.1157.2165.6168182.92000:2 (Apr 03 - Apr 13)

145.6144.5148.5155.2140.5144.1180.72000:3 (Aug 14 - Aug 28)

143.0147.5129.0130.3146.1146.9182.32000:4 (Oct 23 - Nov 02)

96.8102.1107.3111.6104.1104.7176.72001:1 (Jan 29 - Feb 12)

114.4148.9164.7137.4156.4156.7191.42001:2 (Apr 11 - Apr 25)

-------2001:3 (No survey conducted!)

153.8153.8152.1146.5150.0154.9217.62001:4 (Nov 05 - Nov 16)

179.5182.8177.0188.5182.4188.6227.32002:1 (Feb 18 - Feb 29)

208.4209.0200.4202.1211.3218.6241.22002:2 (Apr 29 - May 17)

166.3168.7157.2171.9168.5174.4215.52002:3 (Sep 16 - Sep 26)

175.1173.9172.2166.6175.3181.7202.42002:4 (Nov 04 - Nov 14)

174.1187.5174.6194.6196.5202.4215.52003:1 (Feb 10 - Feb 24)

199.6181.8190.7175.1174.7180.3202.52003:2 (May 05 - May 15)

184.6180.8174.6185.0179.2185.1194.42003:3 (Sep 15 - Sep 24)

212.3206.7208.2197.4204.5210.7195.62003:4 (Nov 03 - Nov 13)

-9.0-4.1-3.2-4.4-4.5-8.7ME (2004-2007):

14.911.011.211.613.115.3RMSE (2004-2007):

179.0170.4169.3176.3167.5173.2169.92004:1 (Mar 01 - Mar 11)

198.8190.4183.2180.4192.1198.4164.62004:2 (Apr 26 - May 06)

193.4191.9181.0197.0189.5195.4176.52004:3 (Sep 13 - Sep 27)

201.8188.4201.9180.3188.8194.4181.22004:4 (Nov 08 - Nov 22)

142.5136.7140.1148.4133.0138.3150.72005:1 (Feb 14 - Feb28)

129.4128.2128.3122.9123.9128.0137.22005:2 (May 23 - Jun 03)

169.2167.5151.4171.5171.5174.7154.42005:3 (Sep 19 - Oct 03)

182.5179.1178.9171.8178.3180.7175.62005:4 (Oct 31 - Nov 14)

-7.0-2.6-3.4-3.8-4.8-8.1ME (2006-2007):

11.97.611.110.510.512.8RMSE (2006-2007):

187.0180.6194.5184.6181.4183.6176.62006:1 (Jan 23 - Feb 03)

185.6184.5180.4180.6187.4191.1190.52006:2 (May 15 - May 29)

200.4193.3189.8193.8193.5196.5198.82006:3 (Sep 25 - Oct 09)

192.9195.9195.9192.0191.9194.8191.72006:4 (Nov 13 - Nov 27)

188.2186.4199.5190.7188.0191.4189.02007:1 (Jan 15 - Jan 29)

219.5214.9214.2209.6217.6221.3199.82007:2 (May 09 - May 28)

237.1224.3211.1237.6235.5240.2215.62007:3 (Sep24 - Oct 08)

& Carry 3m fwd& Carry 1m fwd3m fwd BEI1m fwd BEIAdjusted BEIYield-to-Yield BEI Survey Mean (bp) Prospera MMP

Seasonal AdjustedSeasonal AdjustedCarry AdjustedCarry AdjustedCashflow

7.912.213.912.811.69.4ME (2000-2007):

32.328.230.229.328.427.0RMSE (2000-2007):

33.832.634.334.532.128.0ME (2000-2003):

44.639.742.741.239.436.2RMSE (2000-2003):

174.0164.7185.2170.4170.2170.3181.32000:1 (Jan 24 - Feb 04)

172.6165.1151.1157.2165.6168182.92000:2 (Apr 03 - Apr 13)

145.6144.5148.5155.2140.5144.1180.72000:3 (Aug 14 - Aug 28)

143.0147.5129.0130.3146.1146.9182.32000:4 (Oct 23 - Nov 02)

96.8102.1107.3111.6104.1104.7176.72001:1 (Jan 29 - Feb 12)

114.4148.9164.7137.4156.4156.7191.42001:2 (Apr 11 - Apr 25)

-------2001:3 (No survey conducted!)

153.8153.8152.1146.5150.0154.9217.62001:4 (Nov 05 - Nov 16)

179.5182.8177.0188.5182.4188.6227.32002:1 (Feb 18 - Feb 29)

208.4209.0200.4202.1211.3218.6241.22002:2 (Apr 29 - May 17)

166.3168.7157.2171.9168.5174.4215.52002:3 (Sep 16 - Sep 26)

175.1173.9172.2166.6175.3181.7202.42002:4 (Nov 04 - Nov 14)

174.1187.5174.6194.6196.5202.4215.52003:1 (Feb 10 - Feb 24)

199.6181.8190.7175.1174.7180.3202.52003:2 (May 05 - May 15)

184.6180.8174.6185.0179.2185.1194.42003:3 (Sep 15 - Sep 24)

212.3206.7208.2197.4204.5210.7195.62003:4 (Nov 03 - Nov 13)

-9.0-4.1-3.2-4.4-4.5-8.7ME (2004-2007):

14.911.011.211.613.115.3RMSE (2004-2007):

179.0170.4169.3176.3167.5173.2169.92004:1 (Mar 01 - Mar 11)

198.8190.4183.2180.4192.1198.4164.62004:2 (Apr 26 - May 06)

193.4191.9181.0197.0189.5195.4176.52004:3 (Sep 13 - Sep 27)

201.8188.4201.9180.3188.8194.4181.22004:4 (Nov 08 - Nov 22)

142.5136.7140.1148.4133.0138.3150.72005:1 (Feb 14 - Feb28)

129.4128.2128.3122.9123.9128.0137.22005:2 (May 23 - Jun 03)

169.2167.5151.4171.5171.5174.7154.42005:3 (Sep 19 - Oct 03)

182.5179.1178.9171.8178.3180.7175.62005:4 (Oct 31 - Nov 14)

-7.0-2.6-3.4-3.8-4.8-8.1ME (2006-2007):

11.97.611.110.510.512.8RMSE (2006-2007):

187.0180.6194.5184.6181.4183.6176.62006:1 (Jan 23 - Feb 03)

185.6184.5180.4180.6187.4191.1190.52006:2 (May 15 - May 29)

200.4193.3189.8193.8193.5196.5198.82006:3 (Sep 25 - Oct 09)

192.9195.9195.9192.0191.9194.8191.72006:4 (Nov 13 - Nov 27)

188.2186.4199.5190.7188.0191.4189.02007:1 (Jan 15 - Jan 29)

219.5214.9214.2209.6217.6221.3199.82007:2 (May 09 - May 28)

237.1224.3211.1237.6235.5240.2215.62007:3 (Sep24 - Oct 08)

& Carry 3m fwd& Carry 1m fwd3m fwd BEI1m fwd BEIAdjusted BEIYield-to-Yield BEI Survey Mean (bp) Prospera MMP

Seasonal AdjustedSeasonal AdjustedCarry AdjustedCarry AdjustedCashflow

39

Appendix 2. Long Term Inflation Expectations – The 15y BEI / Survey Comparison (bp) Negative and Positive Mean Errors (MEs) for each sample are marked in red and blue respectively

7.46.87.47.26.914.2ME (2000-2007):

25.024.525.324.524.428.5RMSE (2000-2007):

20.819.120.819.919.229.6ME (2000-2003):

30.129.731.730.030.037.0RMSE (2000-2003):

187.6183.8190.8185.0184.2183.1192.42000:1 (Jan 24 - Feb 04)

153.5150.5146.7148.6151.2151.9188.02000:2 (Apr 03 - Apr 13)

143.4142.5143.8145.7141.2138.0202.02000:3 (Aug 14 - Aug 28)

148.3150.4145.4145.2149.7146.3196.62000:4 (Oct 23 - Nov 02)

153.5154.8155.9156.2153.8139.6192.02001:1 (Jan 29 - Feb 12)

171.6179.8164.8176.4180.9165.2199.72001:2 (Apr 11 - Apr 25)

-----2001:3 (No survey conducted!)

167.8166.8167.6163.6165.9150.0213.72001:4 (Nov 05 - Nov 16)

191.7192.2191.1196.2192.9185.3211.92002:1 (Feb 18 - Feb 29)

219.9218.8215.3215.7220.4212.3218.82002:2 (Apr 29 - May 17)

189.7190.4184.8192.0190.1178.7211.82002:3 (Sep 16 - Sep 26)

209.6209.7209.0205.6209.8189.8208.42002:4 (Nov 04 - Nov 14)

204.0211.2204.6214.0214.7200.7213.22003:1 (Feb 10 - Feb 24)

217.8207.9213.2205.2204.8188.6208.92003:2 (May 05 - May 15)

208.9206.0204.0207.8204.6191.6211.72003:3 (Sep 15 - Sep 24)

232.0229.3231.1224.9227.7214.6211.12003:4 (Nov 03 - Nov 13)

-6.1-5.5-6.1-5.6-5.4-1.2ME (2004-2007):

19.819.418.518.918.818.5RMSE (2004-2007):

220.7215.3217.3219.0214.5197.9202.22004:1 (Mar 01 - Mar 11)

236.9231.3230.1227.2231.5215.6202.22004:2 (Apr 26 - May 06)

228.7226.2223.5228.4224.6212.7198.92004:3 (Sep 13 - Sep 27)

233.2227.3234.0224.0226.6215.0199.52004:4 (Nov 08 - Nov 22)

200.0197.0199.8201.3194.5182.1196.52005:1 (Feb 14 - Feb 28)

168.4166.8167.4164.4164.3152.2186.62005:2 (May 23 - Jun 03)

176.4174.6170.3175.7176.0169.6193.22005:3 (Sep 19 - Oct 03)

191.5190.5190.4186.5189.8190.8198.92005:4 (Oct 31 - Nov 14)

-5.2-4.4-5.2-5.0-6.9-8.6ME (2006-2007):

15.318.013.916.916.918.8RMSE (2006-2007):

184.7181.1187.9183.0181.4183.4191.92006:1 (Jan 23 - Feb 03)

191.1182.0189.1188.1191.4193.5199.72006:2 (May 15 - May 29)

199.2195.9194.3196.0195.8198.6200.92006:3 (Sep 25 - Oct 09)

198.9200.5200.6198.7198.6201.7198.82006:4 (Nov 13 - Nov 27)

203.1202.3206.7202.6201.3205.1194.72007:1 (Jan 15 - Jan 29)

222.7220.4220.0217.9221.3225.7203.92007:2 (May 09 - May 28)

233.0238.5227.7238.6237.9242.0199.92007:3 (Sep24 - Oct 08)

& Carry 3m fwd& Carry 1m fwd3m fwd BEI1m fwd BEIAdjusted BEIYield-to-Yield BEI Survey Mean (bp) Prospera MMP

Seasonal AdjustedSeasonal AdjustedCarry AdjustedCarry AdjustedCashflow

7.46.87.47.26.914.2ME (2000-2007):

25.024.525.324.524.428.5RMSE (2000-2007):

20.819.120.819.919.229.6ME (2000-2003):

30.129.731.730.030.037.0RMSE (2000-2003):

187.6183.8190.8185.0184.2183.1192.42000:1 (Jan 24 - Feb 04)

153.5150.5146.7148.6151.2151.9188.02000:2 (Apr 03 - Apr 13)

143.4142.5143.8145.7141.2138.0202.02000:3 (Aug 14 - Aug 28)

148.3150.4145.4145.2149.7146.3196.62000:4 (Oct 23 - Nov 02)

153.5154.8155.9156.2153.8139.6192.02001:1 (Jan 29 - Feb 12)

171.6179.8164.8176.4180.9165.2199.72001:2 (Apr 11 - Apr 25)

-----2001:3 (No survey conducted!)

167.8166.8167.6163.6165.9150.0213.72001:4 (Nov 05 - Nov 16)

191.7192.2191.1196.2192.9185.3211.92002:1 (Feb 18 - Feb 29)

219.9218.8215.3215.7220.4212.3218.82002:2 (Apr 29 - May 17)

189.7190.4184.8192.0190.1178.7211.82002:3 (Sep 16 - Sep 26)

209.6209.7209.0205.6209.8189.8208.42002:4 (Nov 04 - Nov 14)

204.0211.2204.6214.0214.7200.7213.22003:1 (Feb 10 - Feb 24)

217.8207.9213.2205.2204.8188.6208.92003:2 (May 05 - May 15)

208.9206.0204.0207.8204.6191.6211.72003:3 (Sep 15 - Sep 24)

232.0229.3231.1224.9227.7214.6211.12003:4 (Nov 03 - Nov 13)

-6.1-5.5-6.1-5.6-5.4-1.2ME (2004-2007):

19.819.418.518.918.818.5RMSE (2004-2007):

220.7215.3217.3219.0214.5197.9202.22004:1 (Mar 01 - Mar 11)

236.9231.3230.1227.2231.5215.6202.22004:2 (Apr 26 - May 06)

228.7226.2223.5228.4224.6212.7198.92004:3 (Sep 13 - Sep 27)

233.2227.3234.0224.0226.6215.0199.52004:4 (Nov 08 - Nov 22)

200.0197.0199.8201.3194.5182.1196.52005:1 (Feb 14 - Feb 28)

168.4166.8167.4164.4164.3152.2186.62005:2 (May 23 - Jun 03)

176.4174.6170.3175.7176.0169.6193.22005:3 (Sep 19 - Oct 03)

191.5190.5190.4186.5189.8190.8198.92005:4 (Oct 31 - Nov 14)

-5.2-4.4-5.2-5.0-6.9-8.6ME (2006-2007):

15.318.013.916.916.918.8RMSE (2006-2007):

184.7181.1187.9183.0181.4183.4191.92006:1 (Jan 23 - Feb 03)

191.1182.0189.1188.1191.4193.5199.72006:2 (May 15 - May 29)

199.2195.9194.3196.0195.8198.6200.92006:3 (Sep 25 - Oct 09)

198.9200.5200.6198.7198.6201.7198.82006:4 (Nov 13 - Nov 27)

203.1202.3206.7202.6201.3205.1194.72007:1 (Jan 15 - Jan 29)

222.7220.4220.0217.9221.3225.7203.92007:2 (May 09 - May 28)

233.0238.5227.7238.6237.9242.0199.92007:3 (Sep24 - Oct 08)

& Carry 3m fwd& Carry 1m fwd3m fwd BEI1m fwd BEIAdjusted BEIYield-to-Yield BEI Survey Mean (bp) Prospera MMP

Seasonal AdjustedSeasonal AdjustedCarry AdjustedCarry AdjustedCashflow