Master-thesis

Mikael Jordal Skjellerd 0953540
Kalaitheepan Krishnarajah 0895114
BI Norwegian Business School
Estimating term premiums in nominal and
inflation-indexed bonds.
Examination code and name:
GRA-19003 Master Thesis
Hand-in date:
25.08.2015
Campus:
BI Nydalen Oslo
Supervisor:
Geir Høidal Bjønnes
Program:
MSc. Financial Economics
MSc. Business Major in Finance
This thesis is a part of the MSc programme at BI Norwegian Business School. The school takes no
responsibility for the methods used, results found and conclusions drawn.

GRA 19003 – Master Thesis 25.08.2015
Side 1
Table of Contents
ABSTRACT..................................................................................................................................... 3
LIST OF FIGURES ........................................................................................................................... 4
LIST OF TABLES ............................................................................................................................ 4
LIST OF ABBREVIATIONS............................................................................................................... 5
Variable Abbreviations............................................................................................................ 5
1.0 INTRODUCTION..................................................................................................................... 6
1.1 STRUCTURE............................................................................................................................. 7
2.0: BACKGROUND AND LITERARY REVIEW..................................................................... 8
2.1 BACKGROUND AND INSTITUTIONAL DETAILS .......................................................................... 8
2.1.1 Inflation .......................................................................................................................... 8
2.1.2 Index linked bonds and its reasons for existing.............................................................. 9
2.2 THEORY ................................................................................................................................ 10
2.2.1 Term structure and interest rates ................................................................................. 10
2.3 LITERATURE REVIEW............................................................................................................. 12
2.3.1 Cochrane and Piazessi (2005)...................................................................................... 14
3.0 EMPIRICAL METHODOLOGY ......................................................................................... 15
3.1 TERM PREMIUM ESTIMATION................................................................................................. 16
3.2 ARE INTEREST RATES STATIONARY, NEAR UNIT ROOT OR CLEAR UNIT ROOT PROCESSES?..... 18
3.3 THE MODEL IN 1ST
DIFFERENCE.............................................................................................. 20
3.4 OTHER STATISTICAL WORRIES............................................................................................... 20
3.4.1 Structural breaks .......................................................................................................... 20
3.4.2 Autocorrelation in the standard errors......................................................................... 21
3.4.3 Multicollinearity........................................................................................................... 21
4.0 DATA....................................................................................................................................... 22
4.1 UK GILT/IL GILT................................................................................................................ 22
4.2 US TREASURY BONDS/TIPS .................................................................................................. 24
5.0 RESULTS ................................................................................................................................ 25
5.1 DESCRIPTIVES ....................................................................................................................... 25
5.1.1 United Kingdom ........................................................................................................... 25
5.1.2 United States................................................................................................................. 27
5.2 TERM PREMIUM ESTIMATIONS............................................................................................... 27

Side 2
5.2.1 United Kingdom ........................................................................................................... 29
5.2.2 United States................................................................................................................. 32
5.3 TERM PREMIUM MODELING AND EVALUATION ...................................................................... 35
5.3.1 United Kingdom ........................................................................................................... 35
5.3.2 United States................................................................................................................. 36
6.0 DISCUSSION .......................................................................................................................... 37
6.1 TERM PREMIUM ESTIMATIONS............................................................................................... 37
6.2 COCHRANE AND PIAZZESI METHOD’S SHORTCOMINGS.......................................................... 50
6.2.1 The volatility of the estimated term premium and the downward bias of out-of-sample
forecasts. ............................................................................................................................... 50
6.2.2 The expectations hypothesis and the presence of multicollinearity.............................. 51
6.2.3 The high R2
and presence of non-stationarity. ............................................................. 52
7.0 CONCLUSION ....................................................................................................................... 54
8.0 BIBLIOGRAPHY................................................................................................................... 56
INTERNET SOURCES..................................................................................................................... 61
DATA SOURCES ........................................................................................................................... 61
EXCEL SHEETS ............................................................................................................................ 61
9.0 APPENDICES......................................................................................................................... 62
APPENDIX A: KEY FEATURES OF INFLATION-INDEXED BOND MARKETS...................................... 62
APPENDIX B: YIELD CURVE FITTING ........................................................................................... 63
APPENDIX C: TABLES AND TESTS................................................................................................ 65
Appendix C1: Summary statistics and normality tests........................................................... 65
Appendix C2: Stationarity- tests............................................................................................ 68
Appendix C3: Term premium regressions............................................................................. 70
Appendix C4: Correlation tables........................................................................................... 74
Appendix C5: Parameter stability tests................................................................................. 75
Appendix C6: Forecasting results......................................................................................... 76
APPENDIX D: ADDITIONAL GRAPHS ............................................................................................ 77
10.0 PRELIMINARY THESIS REPORT……...……………………………………………….82

Side 3
Abstract
We use and assess Cochrane and Piazzesi’s (2005) method to estimate the term
premium in nominal and inflation-linked bonds in the United States and United
Kingdom. We estimate a model in both levels and 1st
difference due to
stationarity-issues.
We find that even though our RHS-variables are non-stationary, the model in
levels is superior to the model in 1st
difference, both in-sample and out-of-sample.
We find a highly varying and countercyclical term premium. Periods of negative
term premium coincide with some combination of pension plan reforms,
increasing value of using government bonds as a hedge, and possibly a flight to
quality during an impending recession. We find that the inflation component of
the term premium has significantly decreased due to less inflation forecast
dispersion.

Side 4
List of Figures
FIGURE I GROWTH OF THE INFLATION-INDEXED BOIND MARKET
FIGURE II US EX-POST REAL INTEREST RATE AND REGIME SPECIFIC MEANS
1953:Q1-2007:Q2
FIGURE III ACTUALIZED AVERAGE EXCESS RETURNS FOR UK GOVERNMENT
BONDS
FIGURE IV REGRESSION COEFFICIENTS OF ONE-YEAR EXCESS RETURNS ON
FORWARDS RATES
FIGURE V GRAPHICAL REPRESENTATION OF THE FIRST STAGE REGRESSION
PARAMETERS IN UNITED KINGDOM.
FIGURE VI IN-SAMPLE ESTIMATIONS OF THE 7-YEAR REAL TERM PREMIUM UK
1992-2008
FIGURE VII IN-SAMPLE ESTIMATIONS OF THE 5-YEAR NOMINAL TERM
PREMIUM UK 1992-2008
FIGURE VIII IN-SAMPLE ESTIMATIONS OF THE TERM PREMIUMS ON 5-YEAR
NOMINAL GILTS AND INDEX LINKED GILTS 1992-2014
FIGURE IX THE BOND YIELD CONUNDRUM IN UNITED STATES 2004-2008
FIGURE X IN-SAMPLE ESTIMATIONS OF THE 5-YEAR NOMINAL TERM
PREMIUM US 2004-2008
FIGURE XI IN-SAMPLE ESTIMATIONS OF THE 6-YEAR REAL TERM PREMIUM US
2004 - 2009
FIGURE XII OUT-OF-SAMPLE ESTIMATIONS OF 5-YEAR NOMINAL TERM
PREMIUM UK 2010-2015
FIGURE XIII OUT-OF-SAMPLE ESTIMATIONS OF 7-YEAR REAL TERM PREMIUM
UK 2010-2015
FIGURE XIV OUT-OF-SAMPLE ESTIMATIONS OF 5-YEAR NOMINAL TERM
PREMIUM US 2012-2015
FIGURE XV OUT-OF-SAMPLE ESTIMATIONS OF 6-YEAR TERM PREMIUM US 2012-
2015
List of Tables
TABLE I ESTIMATES OF THE SINGLE FACTOR MODEL UK
TABLE II RESULTS OF REGRESSIONS ON INDIVIDUAL BOND EXCESS
RETURNS UK
TABLE III ESTIMATES OF THE SINGLE FACTOR MODEL US
TABLE IV RESULTS OF REGRESSIONS ON INDIVIDUAL BOND EXCESS
RETURNS US

Side 5
List of Abbreviations
REAL Real interest rate, real yield or to denote data gathered from the indexed linked
bond sample.
IIB Inflation indexed bonds or inflation linked bonds.
IL GILT Index Linked UK government bonds
Variable Abbreviations
Due to the use of abbreviations to denote variables while working in Excel and Eviews we offer a
short list of those used here. We have also used the same abbreviations when creating tables, so a
thorough read-trough is advised. The variables are computed as stated in the main text section
3.1. Short-term yields are obtained directly from the yield curves in the dataset, which we describe
in chapter 4. Short-term real yield for the UK is 3-year yields, annualized and continuously
compounded. Short term real yield for the US sample is 2-year yields, annualized and
continuously compounded.
AERR AVERAGE EXECESS RETURN REAL
YR SHORT TERM REAL YIELD
ER3R EXCESS RETURN OBTAINED FROM IIB WITH 3 YEARS TO MATURITY
F3R 2- TO 3-YEAR REAL FORWARD RATE
AER AVERAGE EXCESS RETURN
Y1 SHORT TERM NOMINAL YIELD (1-year)
ER2 NOMINAL EXCESS RETURN ON 2-YEAR BONDS
F2 1- TO 2-YEAR NOMINAL FORWARD RATE

Side 6
1.0 Introduction
Understanding bond yields is of great importance to finance, economics and
macroeconomics. Firstly, when setting monetary policy, central banks are able to
move short-term yields. However, what matters for aggregate demand are long
term yields, emphasizing the need for understanding of how long-term yields are
determined. Secondly, government’s debt policy is affected by interpretation of
the yield curve. Governments need to decide at what maturity they should issue
new debt, a decision involving numerous tradeoffs. (Piazzesi 2010). Thirdly, the
risk free rate is included as a variable in the majority of asset pricing models.
Finally, the yields obtained from long-maturity bonds are the average of expected
future short-term yields after adjustment for risk. This implies the yield curve
contains information about the future path of the economy. The forward spread of
government bonds has been found to be a factor in predicting recessions. (Estrella
and Mishkin 1998; Wright 2006) Yield spreads have been useful in forecasting
future short yields (Campbell and Shiller 1991, Fama and Bliss 1987), real
activity (Ang et al. 2006), and inflation (Fama 1990; Mishkin 1990), emphasizing
the need for correctly deducing the level of long-term yields. A widely used
method in finance to predict inflation is measuring the term spread in nominal
bonds in the form of Mishkin (1990) and break-even inflation in the form of
Deacon and Derry (1994). Modern research has used the yields of nominal and
inflation linked default-free bonds as proxies for the nominal and real interest
rates.
Campbell and Shiller (1991) find that an increasing term spread is usually
followed by a decrease in long-term interest rates and an increase in spot rates.
They credit this to the term premium, underlining the importance of a solid
method to estimate it in order to interpret the yield curve correctly. There have
been several major breakthroughs in estimating the term premium, with
McCulloch (1975), Fama and Bliss (1987), Campbell and Shiller (1991) and
Cochrane and Piazzesi (2005) as the most notable.

Side 7
We use data from the Treasury bond market due to the negligible default risk that
comes from the government’s ability to collect taxes in order to pay bondholders.
Most previous research has focused on the term premium of nominal bonds due to
the short history of inflation-linked bond issues and their low overall liquidity. We
extend previous research by using the Cochrane and Piazzesi’s (2005)-
methodology on both nominal and inflation-indexed bonds in UK and US.
Furthermore, we try to estimate a model in 1st
difference due to forward rates
exhibiting non-stationary properties. We interpret the evolution of the term
premium based on previous research and find out whether the assumption of
stationary interest rates is sound.
I) How large is term premiums in the markets we research?
i) Do they differ significantly between markets?
ii) What is the background for the changes in term premiums?
II) Is the Cochrane and Piazzesi single factor model adequate in
estimating the term premium?
i) Does it transfer well between different types of datasets?
ii) Is the assumption of interest rates and forward rates only being
near unit root realistic?
1.1 Structure
This thesis is structured into 5 main chapters and a conclusion. Chapter 2 goes
further into the background and the elementary theory of our research and bond
markets. We highlight the importance of inflation for asset returns, discuss the
term structure of interest rates and describe the institutional details of the index
linked bond market. We conclude the section by doing a literary review of the
major breakthroughs in term premium estimations, with a greater focus on
Cochrane and Piazzesi’s paper. Chapter 3 includes a description of the empirical
methods we use in answering our research questions while chapter 4 is an
overview of the data analyzed. Chapter 5 contains a discussion of our main
results. Chapter 6 involves an analysis and discussion of our findings, wherein we

Side 8
try to explain the change of the term premium. The conclusion and implications
of our results can be found in chapter 7.
2.0: Background and literary review
2.1 Background and institutional details
2.1.1 Inflation
Inflation affects investors’ purchasing power and the real returns of their
investments. The risk of loss in purchasing power is augmented as inflation has a
high autocorrelation, meaning shocks lead to a more volatile future inflation
(Cecchetti et al. 2007). Since investors are assumed to be risk averse they demand
a risk premium due to future uncertainty regarding the future level of inflation.
Mishkin (1992) states that the classic Fisher equation is decomposed in a nominal
interest rate of a given maturity, a real rate, and an inflation expectations
component1
. If expectations are rational, expected inflation will differ from actual
inflation by an unpredictable noise term. In addition to the expected inflation
factor, breakeven inflation estimation is depending on the risk premium embedded
in bond yields. The nominal risk premium includes both a liquidity factor and
inflation and interest rate risk factor. Investors want to be compensated for
holding this type of risk. Investors in inflation-indexed bonds are willing to pay
for protection against the uncertainty of future inflation but require higher yields
for holding less liquid inflation protected bonds. (Deacon and Derry 1994) This
makes the break-even inflation highly sensitive to correctly estimating the term
premium. The inflation and liquidity component of the term premium varies over
time and often in offsetting ways, which makes it difficult to capture the residual
expectations component of the breakeven inflation rate. (Christensen and Gillan
2011) Due to this there has been a surge in empirical research of the term
1
Irving Fisher (1930) modified this to ex-ante use where superscript e means
expectation. We use continuously compounded yields in our thesis that in effect makes the
approximation an equality due to its additive properties. Including the term premium in the Fisher
equation makes ( ) ( )

Side 9
premium in the 21st
century, however, this have often focused on the nominal term
premium. We expand upon previous research by trying to estimate the term
premium on inflation-indexed bonds.
2.1.2 Index linked bonds and its reasons for existing
In the context of the discussion above investors adjust their returns for inflation
and are aiming to maximize their real returns. This has led to asset pricing models
focusing on maximizing consumption, with the most noteworthy being the
CCAPM. (Breeden 1979) In contrast to conventional bonds, inflation-indexed
bonds (IIB) adjust the intermediate and principal payments to reduce the volatility
of investors’ real returns. (Veronesi 2010) The payments are indexed to a
domestic consumer or retail price index with a pre-specified lag. The lag
represents a basis risk in an inflation hedge that may be large in hyperinflation
periods. (Laatsch 2013) IIBs usually have maturities of 5 years or longer at
issuance. (Deacon, Derry and Mirfendereski 2004)
IIB represent a less risky class of assets as they have lower correlation with other
risky assets, making them a valuable hedge in portfolio optimization. At the same
time they represent an even less volatile investment opportunity than conventional
treasury bonds as real rates have less volatility than nominal rates. A factor that
can deter investors from purchasing inflation-indexed bonds is their tax treatment.
Many tax regimes effectively treat the inflation uplift on IIBs principal payments
as income, which could reduce overall demand except for a narrow sector of
investors that are exempt from taxes, such as pension funds. (Deacon, Derry and
Mirfendereski 2004) Studies find that inflation-indexed bonds are largely held by
“buy-and-hold”-investors. (ibid.) This is likely to reduce the attractiveness to
investors who value this trait and hence reduce liquidity in the secondary market.
There are several countries that issue IIBs, where the largest markets are for the
US TIPS, UK IL GILTS and French OATI. Even tough they are large in
denomination and can comprise of around 20% of national debt outstanding, they
are usually much less liquid than conventional bonds. (Campbell, Shiller and

Side 10
Viceira 2009; Deacon, Derry and Mirfendereski 2004) This is illustrated by the
turnover-ratio of UK conventional and inflation-indexed bonds. Based on
2002/2003-data from the UK debt management office UK conventional bonds had
a 20 times larger turnover ratio than their index linked counterparts. (ibid.) The
history of government IIBs is short but the IIB-markets have nonetheless grown
immensely in the last twenty years. (Joyce et.al. 2009)
The development can be seen in Figure
I. Appendix A show further
institutional details like names,
outstanding value, lag and if they have
floor protections. Floor protection is if
they have a floor against deflation and
hence a guarantee to pay the coupon
and principal in full.
Governments and treasuries have been
hesitant in complying with the demand
for inflation-indexed securities, even though the less risky nature of the return
reduces ex-ante inflation risk premiums and hence the borrowing costs. However,
investors may require a liquidity premium to hold indexed bonds because of its
liquidity issues, thus increasing the cost to issuers. The existence of indexed debt
removes one of the main incentives for a government to adopt inflationary
policies, i.e. the opportunity to reduce the real value of its outstanding liabilities.
This may lead to a reduction in the inflation risk premium paid on subsequent
issues of conventional debt. (Deacon, Derry and Mirfendereski 2004)
2.2 Theory
2.2.1 Term structure and interest rates
The term structure of interest rate tells us the implied yields on zero coupon bonds
for every possible maturity and is represented by the yield curve. The yield
FIGURE I – GROWTH OF THE INFLATION-
INDEXED BOIND MARKET (Krämer 2013)

Side 11
curves’ shape is one of the key concerns of fixed-income securities investors.2
(Bodie, Kane and Marcus 2014). By the pure expectations hypothesis the forward
rate is the markets expectations of the future spot rate. An upward sloping yield
curve is usually interpreted as a coming expansion in the economy as the market
expects higher inflation and future contractionary monetary policy to slow down
the economic activity. Similarly an inverted yield curve is interpreted as a sign of
an impending recession. The pure expectations hypothesis was disproven already
in the late 1930s (Keynes 1936; Lutz 1940) with the arrival of the liquidity
preference theory.
The liquidity preference theory uses the preferred habitat theory to discern
whether there is a premium on long-term bonds. Short-term investors are exposed
to the interest rate risk of long-term bonds, while long-term investors are exposed
to the reinvestment risk of short-term bonds. Hence, short-term investors prefer
short-term bonds while long-term investors prefer long-term bonds. Corollary,
short-term investors demand a premium on long-term bonds. There is often
assumed that there is a greater quantity of short-term investors in the market.
(Bodie, Kane and Marcus 2014) Both index linked and nominal term premiums
are likely to include a liquidity factor, either with a positive or negative sign.
Pflueger and Viceira (2011) find that there is an overall liquidity premium on US
TIPS. There is empirical support for a “flight to liquidity” effect preceding a
financial crisis, as investors want to invest in more liquid securities due to the risk
of a liquidity crisis, as seen during the great recession of 2008. (Beber, Brandt and
Kavajecz 2008) As mentioned previously, inflation linked bonds are mostly held
by buy-and-hold investors and one would expect that the liquidity component of
the term premium on indexed bonds, when measured as excess return of a long-
maturity bond over a short-maturity bond, would be either negligible or negative.
2
The yields, which are the geometric average of expected future spot rates, are the based on
discount factors implied in bond prices. The discount factors represent the time value of money,
which is defined as today’s price of a unit of currency today received at some point in the future.
(Veronesi 2010)

Side 12
Due to Irving Fisher (1896) we can decompose the nominal risk free interest rate
into a real interest rate and expected inflation factor. Hence nominal bonds are
exposed to uncertainty regarding the level of the real interest rate, unexpected
inflation and liquidity. The index linked bonds under perfect indexation are
supposed to only be exposed to real interest-rate risk and liquidity risk. Hence we
have theoretically decomposed the term premium into a liquidity component, real
interest rate component and inflation risk component.
2.3 Literature review
Excess returns on longer maturity bonds over short maturity bonds have been
researched comprehensively since the early seventies. We will review some of the
most noteworthy papers in the last 4 decades involving the term premium. We
will discuss further the paper of Cochrane and Piazessi (2005) as they apply
several methodologies in order to estimate the term premium, where their single-
factor model is going to be used in our thesis.
McCulloch (1975) researched the term premium with the assumption that today’s
forecast of some future value must be an unbiased estimator of all future forecasts
of that value. Hence the term premium is the spread between the forward rate and
the subsequent actualized spot rate.
( , ) = ( , ) + ( ) (EQ. 2.2)
In the period of 1951-1966 he found a fairly constant liquidity premium and could
not find any evidence of it depending on either time or level of interest rate. The
size increases with maturity and stabilizes for maturities longer than 5 years.
Fama (1976) found that once US Treasury Bills were adjusted for variation in
expected premiums, the forward rates contains predictions of future spot rates that
are likely to be as good as those based on a time series of past spot rates. The
premium was measured as the difference in the return at t+1 between two bills,
where the first is a longer-term treasury bill, and the second a one-month bill. His
results indicate, in contrast to McCulloch (1975), that the premium tends to vary.
Fama concludes that the premium consists of inflation uncertainty. When

Side 13
incorporating the expected premium into the forward rate (i.e. subtracting the
premium), he finds that forward rates are as good at predicting future interest rates
as an advanced autoregressive model based on previous spot-rates.
According to Shiller (1979) a time-varying risk premium implies the variance of
spot rates is higher than the variance of forward rates. He finds that there is a
significant term premium for 2-month forecasts up 12 months ahead ranging from
0.28% to 1.34%. He finds that the term premium explains from 36.3% to 69.4% in
the deviations between forward rates and the expected spot rate. This implies that
the term premium is an important factor in the excess returns on longer-term
bonds. He conclude that the term premium exist, is time varying, and increases
with forecast horizons up to 12 months.
Fama and Bliss (1987) test if forward rates can predict 1- to 5-year interest rates.
They find the expected term premium, measured as the net of 1-year expected
returns on a 5-year bond and a 1-year bond is significantly different from zero and
time-varying. The premium also tends to vary with business cycles - i.e. mostly
positive during good business cycles, and mostly negative during recessions. This
is inconsistent with the liquidity preference theory that says the term premium is
always increasing with maturity. Campbell and Shiller (1991) conclude that
contrary to the expectations theory a high forward spread leads to falling long-
rates and rising short-rates. This is consistent with term-premium theory, i.e. the
yield curve is better at predicting long run changes in short rates than short run
changes in long rates.
During the last 15 years there has been an increase in term premium research. Kim
and Orphanides (2007) find that they are counter-cyclical, meaning they tend to
fall in expansions and increase in recessions. Several argue that the term premium
in nominal bonds mainly reflects uncertainty about future inflation. (Rudebusch
and Swanson 2008) Gil-Alana and Moreno (2012) expand upon the finding by
Cochrane and Piazzesi (2008) that the term premium in long-term bonds depends
upon the order of integration assumed for short-term interest rates. Hence the

Side 14
more persistent short rate shocks are, the higher the term premiums. They also
show that unemployment rate is significantly correlated with the term premium
and can arguably be defined as a driver for the term premium. The rationale is that
higher unemployment signals uncertainty about the state of the economy. They
find that higher output growth lowers the expected future term premium and that
high term premiums predict significant declines in future inflation, money growth
and equity returns. Wright (2006) that find that Cochrane and Piazzesi (2005)
single factor excess return coefficient to be significantly negative in predicting
recessions six quarters ahead.
A large part of the research post 2005 uses the Cochrane and Piazzesi single factor
model in some variation. We will next outline their assumptions and findings in
the Cochrane and Piazessi (2005)-paper. In chapter 3 we outline their
methodology and how ours differs. The assumptions will be further discussed in
chapter 6.
2.3.1 Cochrane and Piazessi (2005)
Cochrane and Piazessi find that a single tent-shaped linear combination of forward
rates predicts excess returns on one- to five-year maturity bonds with a high
degree of precision. The excess return is measured as the annualized holding
period return of a portfolio consisting of a long n+m maturity bond and a short n-
maturity bond. The portfolio is closed the following month by buying a n+m-1
bond. The use of term structure models to forecast future excess returns are based
on the tent shaped linear combination of forward rates. The premise is that even
though the term structure is only a tiny factor for yields, it provides much
information on expected returns on all bonds, and hence should also be able to
explain a lot of the movements in the excess return. They then imply that the
coefficients on the excess returns should follow the same tent-shaped pattern as
the forward rates.

Side 15
They used the Fama & Bliss dataset from CRSP3
. It consists of monthly
unsmoothed zero coupon prices of US government nominal bonds from 1964-
2003. By using a two-stage single factor model they obtain R2
up to 35% and
reject the expectations hypothesis. They update the Fama-Bliss (1987) regression
to include data up to 2003. They find that their model significantly outperforms
Fama and Bliss with higher X2
rejections and more than double the R2
. They run
several robustness tests and find that their model significantly outperforms both a
factor model consisting of the first three factors4
, and the Campbell-Shiller (1991)
regressions. The single factor model also seems fairly robust to adding RHS-
variables as the tent-shaped factor only slowly diminishes.
Furthermore they ran regressions on individual excess returns using lags of the
forecasting factor. Spuriously high prices at t will erroneously indicate poor
returns at t+1. If the errors have no autocorrelation, then using lags would
eliminate any measurement errors. At the 1st
and 2nd
lag they find that the tent-
shape is unaltered. This result implies that measurement error is not the reason for
the validity of the predicting factor. When they add lags of the single factor they
increase their R2
and obtain up to 44% fit for the bond excess returns. However,
they find the single factor model is rejected in favor of the unrestricted model.5
3.0 Empirical methodology
In this chapter the focus is to define the variables, illustrate the methodology and
discuss statistical worries. 3.1 will outline the Cochrane and Piazzesi method of
estimating the term premium. 3.2 contain a discussion of whether interest rates are
stationary and the results from the stationarity-tests we have performed. 3.3
contain a slight extension of the Cochrane and Piazzesi methodology, due to the
unit-root issue we discussed in 3.1. 3.4 will explain some further statistical
caveats.
3
Center for Research in Security Prices
4
The three factors are referring to level, slope and curvature.
5
For information regarding testing methodology we refer to Cochrane and Piazzesi (2005) and
their online Appendix.

Side 16
3.1 Term premium estimation
As mentioned in the literary review the term premium is the excess return of
holding a longer-term bond over holding several shorter-term bonds. We follow
Cochrane and Piazzesi very closely in their methodology. First a short set of
definitions and notations.
( )
is defined as the continuously compounded yield attained from the yield curve
with n years to maturity. Cochrane and Piazzesi define the log yield as
( )
=
( )
. Contrarily to Cochrane and Piazzesi we already have continuously
compounded yields from our source and not zero coupon prices making this step
unnecessary. The price of a zero coupon bond with n years to maturity is defined
as
= 100 ( ( ) )
. (EQ. 3.1)
The log price of n-year discount bond at time t is defined as
( )
= ln( ). (EQ. 3.2)
Log forward rate at time t
( )
=
( ) ( )
. (EQ. 3.3)
Holding period return (HPR), i.e. the yield gained from selling a n-1-year bond at
t+1 after buying the n-year bond at t is mathematically defined as
( )
=
( ) ( )
. (EQ. 3.4)
The definition of log excess returns gained for buying the n-year bond rather than
buying the one year bond and rolling over is stated as
( )
=
( ) ( )
. (EQ. 3.5)
For the inflation indexed bonds it will become
( )
=
( )
for the UK IL
GILT sample and
( )
=
( )
for the US TIPS sample due to data
limitations.
We then get the excess return vectors: = ( ) ( ) ( ) ( )
.

Side 17
Its real counterpart is defined as = ( ) ( ) ( ) ( )
.
For the excess returns n is defined as 4 year excess returns in the IL GILT sample
and 3 year excess returns for the US TIPS sample. As explanatory variables we
get the = 1 ( ) ( ) ( ) ( ) ( )
and its real counterpart =
1
( ) ( ) ( ) ( ) ( )
. In the UK IL GILT sample n is
defined as 3 years to maturity, for the US TIPS sample n is defined as 2 years to
maturity.
Using matrix notation the first stage regression is done on;
= + . (EQ. 3.6)
The overhead bar indicates the average excess returns for all maturities for that
period and is mathematically defined as
= . (EQ. 3.7)
Equation 3.6 would be equal to the following representation of the 1st
stage
regression.
= +
( )
+
( )
+
( )
+
( )
+
( )
+ (EQ. 3.8)
From the 1st
stage regression we obtain the state variable, which we then regress
on every individual excess return.
( )
= ( ) +
( )
(EQ. 3.9)
For nominal estimations it would be for n=2,3,4,5 for UK real n=4,5,6,7 and US
real n=3,4,5,6. The second stage regression is restricted, and its coefficient should
average to 1.6
Even though we do not show the results in the main text, we also
estimate the unrestricted model.
( )
= +
( )
(EQ. 3.10)
for n=2,3,4,5 (nominal) and n=4,5,6,7 (real). The measures of fit obtained from
these regressions are shown in Appendix C3.
6
i.e. 1
4 = 1

Side 18
We follow Cochrane and Piazzesi by using Wald-statistics for statistical inference
of whether the expectations hypothesis holds. If the expectations hypothesis is
true, the yield curve should have no explanatory power in predicting the excess
returns, hence implying that the coefficients should be jointly zero.
3.2 Are interest rates stationary, near unit root or clear unit root processes?
Interest rates are often modeled as a mean reverting “brownian motion” or
“Vasicek”-model. (Veronesi 2010) By definition a mean reverting process is
stationary. Interest rates may drift a long way from its mean and exhibits slow
mean reversion, hence we suspect that interest rate series contain a unit root.
Jardet, Monfort and Pegorari (2009) argue the presence of unit roots in interest
rates is spurious. Whenever an interest rate shock occurs, the interest rates are
highly persistent for a prolonged period of time. Hence the mean changes and we
obtain what is called the discontinuity problem. A representation of the
discontinuity problem is illustrated in the figure below. If we classify the periods
before and after a shock as different interest rate regimes, the interest rate series
may exhibit stationary properties within each regime. For an overall sample it
would follow the series exhibiting a unit root.
FIGURE II – US EX-POST REAL INTEREST RATE AND REGIME SPECIFIC MEANS 1953:Q1-2007:Q2
Note: The figure plots the US ex-post real interest rate and means for the different regimes defined by structural breaks
estimated using the Bai and Perron (1998) methodology. This graph show the implied ex-post real interest rate based on
nominal interest rates and CPI levels, available from St.Louis Fed’s FRED database. Neely and Rapach (2008)

Side 19
By doing several unit-root tests Jardet, Monfort and Pegoraro (2012) find that
both short and long nominal rates in the United States are confirmed as a unit-root
series. Rapach and Weber (2004) responds to the controversial paper of Rose
(1988) who concludes real interest rates are I(1). Rose (1988) find that nominal
interest rates are I(1) and inflation rates are I(0) in 18 OECD-countries. By the
assumption that errors in inflation expectations are stationary he concludes that
real interest rates are non-stationary. Rapach and Weber (2004) use the Ng and
Perron-test (2001) obtaining results indicating non-stationary real interest rates for
four countries, and stationary real interest rates for two countries. For the ten
remaining countries in their study they do cointegration-tests, resulting in no
robust rejections of real interest rates being I(1).
We test for non-stationarity using the Augmented Dickey Fuller- (ADF) test
allowing for both an intercept and deterministic trend, with number of lags chosen
by the Aikake Information Criterion.7
The null hypothesis is that the series is I(1),
hence non-stationary. As the power of ADF-test regarding near unit root problems
is low, we are also to use the KPSS-test for confirmatory evidence, in which the
null hypothesis is that the series is I(0). The table of our results is in Appendix C2
Table 1 to 4. It shows that all of the UK real interest and forward rates are non-
stationary. The UK nominal interest rate and forward rates are either near unit
root-processes or I(1). The nominal US interest rates are all I(1), while the real
interest rates are in general stationary. The UK excess returns are I(0), but the US
are mainly non-stationary.
Cochrane and Piazzesi do not report any results from stationarity-tests but
acknowledge near-unit root problems by running a 12-lag VAR that imposes a
single unit root and four co-integrating vectors. They then update results by
gathering the t-statistics from these regressions. We will not perform this
procedure due to its complexity, and the small sample T-stats would have to be
estimated through extensive simulations. In Cochrane and Piazzesi (2008) they
7
We chose the AIC because, even tough it is not consistent (on average it gives a too large model),
it is efficient. (Brooks 2008)

Side 20
use the term spread to get around the non-stationarity issue. We find by
preliminary research, that some of the term spreads are also I(1). The most used
remedy for unit root is to difference the series (Brooks 2008) as most series are at
most I(1). Due to this we extend the Cochrane and Piazzesi-model and estimate a
model in 1st
difference. The model will be represented in 3.3. We use RMSE to
analyze the out-of-sample performance and to decide which model we use in our
discussion part.
3.3 The model in 1st
difference
The Cochrane and Piazzesi method assumes that interest rates and forward rates
are only near unit root processes, rather than clear unit root processes. We have
shown that this assumption is too strong and run the regressions in both levels and
in 1st
difference. The first stage regression in 1st
difference would thus be
= + (EQ. 3.11)
is then modeled as
( ) = + .8
(EQ. 3.12)
The start value was the average excess return at our first observation. We found
that ( ) was also non-stationary. Hence we had to estimate the second stage
regression as
( )
= ( ) +
( )
(EQ. 3.13)
3.4 Other statistical worries
We have already discussed the issue of unit root in interest rate series. In this
chapter we focus on other statistical issues we encounter.
3.4.1 Structural breaks
A second type of non-stationarity is structural breaks. As the data generating
processes within macroeconomics are influenced by exogenous shocks, the
coefficients obtained in regression analysis may not be unbiased. (Stock and
Watson 2011) We test this by using the Quandt-Andrews test with 15% trimming
implemented in Eviews. Quandt-Andrews test the null hypothesis of stable
8
We denote Forecasts with a capital F to avoid confusion with the forward vector.

Side 21
coefficients against the alternative hypothesis of an unknown breakpoint. The
results are shown in Appendix C5 Table 1 to 4. We trim the sample to avoid the
structural breaks; however we are not able to trim the sample at every breakpoint
as we would be left with a too small sample. A clearer representation of the
sample used is described in 4.1 and 4.2.
3.4.2 Autocorrelation in the standard errors
When doing multi-period regressions with overlapping data we obtain serial
correlations in the standard errors. Consider a forecast of one year excess return,
where there is an exogenous event that occurs in one of the following months. The
prediction would not include this event. It would then follow that the next month’s
prediction would also include the same prediction error unless the event occurred
in the succeeding month. This leads to the errors being serially correlated, which
is inconsistent with OLS-assumptions. (ibid.) As we use monthly data our
standard errors would exhibit an MA(12)-structure. This is confirmed by Durbin
Watson-tests and Box Jenkins-tests (not shown). This would depress the standard
errors in our regressions and make the Wald-test for joint significance rather
challenging, as we would get spuriously high results.
Cochrane and Piazzesi use Newey West Heteroskedasticity and Autocorrelation
Consistent (HAC) standard errors with 18 lags to give it a greater chance to
correct for the MA(12)-structure created by the monthly data. We will follow their
example and do the same. We use weekly data for the US-sample, and hence our
predictions could include an even higher order of MA-structure. It turns out when
adding more than about 26 lags the Newey-West covariance matrix reaches near-
singularity, hence we continue with 18 lags. We have in mind that these standard
errors may be depressed.
3.4.3 Multicollinearity
Our right hand side variables exhibit near multicollinearity. Multicollinearity is
imposed when the right-hand-side variables are highly correlated. Near perfect
multicollinearity lead OLS to not being able to separate each variable’s effect on

Side 22
the dependent variable, hence inflate the standard errors. There are no obvious
solutions for near multicollinearity except to exclude an independent variable.
However, if this is not supported by theory, it could lead to omitted variable bias.
(Brooks 2008)
We search for multicollinearity by looking at correlation tables, which are
attached in Appendix C5. We find the forward rates are highly correlated within
the UK sample with correlation values of between 0.9 and 1.0. Within the US
sample the correlation is not as high but still such that we have to take it into
account. For the TIPS sample the 4-, 5- and 6-year forwards have correlations
within the interval of 0.9 and 1.0. For the nominal sample none of correlations are
within the interval of 0.9 and 1.0. The differencing does not significantly affect
the correlations, even though they are somewhat decreased.
4.0 Data
Cochrane and Piazzesi (2005) used the Fama and Bliss dataset from CRSP,
consisting of monthly non smoothed zero coupon yields for the period of 1964 to
2003. The dataset at CRSP is regularly updated but using this would be, in our
opinion, of limited interest. As we wanted to extend previous research by using
the Cochrane and Piazzesi method on indexed bonds we had to look outside the
scope of United States due to the TIPS’ short history. Furthermore we wanted to
use smoothed datasets due to critique formed by Dai, Singleton and Yang (2004).
In their paper they got a wave-shaped pattern rather than a tent-shaped pattern in
the first stage regression coefficients. Due to availability of reliable data we use
the UK Gilt/Index linked Gilt-market. To do some comparative analysis we also
chose to use the US treasury bond/TIPS-market.
4.1 UK GILT/IL GILT
The UK government started to issue indexed GILT’s linked to the RPI (Retail
Price Index) in 1981. Beside the freeze in issuance between 1988 and 19919
the IL
9
This is outside our prediction period due to parameter stability tests.

Side 23
GILT has seldom been part of any buy-back programs, and the UK government
has been active doing liquidity-enhancing operations on the IL GILTs behalf. The
indexation lag used is 8 months with 2 months used to compute the change in RPI.
In April 2005 they changed the lag to 3 months. (dmo.gov.uk) We use the yield
curve attained from Bank of England such that the indexation lag would not
warrant any extra considerations in this case. (Anderson and Sleath 2001)
We obtain end-of-month yield curves from the Bank of England. The nominal
yield curves are available from January 1979, and the real yield curves are
available from January 1985. There is a considerable amount of missing data at
the short end of the real curve. Consequently we use 3 years to maturity as the
short-term yield. There are still 2 periods of missing data in the relevant sample, a
13-month period starting December 1996 and ending December 1997. The other
is a 6-month period starting March 2005 and ending August 2005. As re-
estimation of the yield curve would be too time-consuming we are opting to not
re-estimate the whole of the yield curve. Additionally, there has been little
previous research into possible issues with smoothing an already smoothed curve
with another smoothing technique than originally used. Instead we solve this issue
by using a logarithmic interpolation technique.
= where = . (EQ. 4.1)
a is defined as the number of observations from the known value up to x, which is
the value we want to estimate. b is the number of observations from x to the next
known value. (Deserno 2004)
The yields are annualized and continuously compounded. The government
liability nominal yield curves are derived from UK GILT prices and General
Collateral repo rates on the short end. The real yield curves are derived from UK
index-linked bond prices. The yields that have been quoted are derived from a
fitted curve using the VRP-model10
. Due to the parameter stability tests done in
10
We elaborate on yield curve fitting in Appendix B.

Side 24
chapter 3.2 our UK sample consists of 190 observations, from end of March 1992
until end of November 2007.
4.2 US treasury bonds/TIPS
The US government issued the first US Treasury Inflation Protected Securities
(TIPS) in January 1997 after the market expressed a strong demand in the
inflation-indexed asset class. The principal of TIPS is linked to non-seasonally
adjusted CPI given by the Bureau of Labor Statistics. TIPS are currently issued in
terms of 5, 10, and 30 years, and pays interest semiannually at a fixed rate with a
3-month indexation lag.
The US TIPS data consists of continuously compounded daily yields from
01.04.1999 to 20.04.2015 and is constructed by the extended Nelson Siegel-
model. This data was provided by Barclays Capital Markets to the Division of
Research & Statistics and Monetary Affairs Federal Reserve Bond, Washington
DC, which is published and continuously updated along with the working paper
by Gürkaynak, Sack and Wright (2006). The nominal curve is going to be attained
from the series of zero coupon continuously compounded yields obtained from
Datastream. How this is fitted is unclear, but Datastream use the Federal Reserve
as their source, hence we expect the yield curve is fitted according to the Nelson
Siegel-model. Our work with the nominal interest rate-series confirms our belief
that this is a smoothed yield-curve series. We have no missing data in either of
these samples.
There was a trade-off between using daily, weekly and monthly data. Monthly
data was excluded quickly due to the low amount of observations it would deliver.
We were hesitant to use daily data, as we were unsure of the source of the
Datastream-series. If the yields gathered from there were unsmoothed it would be
noisy and depending on trades for every maturity on every date, hence we chose
to use weekly data. As Datastream gives mid-week data, we cleaned the daily real
yield curve dataset to obtain mid-week observations.

Side 25
The maturities we use are 2-6 years, constraining the possible sample from
07.01.2004 until 29.04.2015. Due to the parameter stability tests mentioned in
section 3.2 the estimation sample for the nominal data consists of 211
observations from 09.01.2004 until 09.01.2008. The TIPS sample consists of 279
mid-week observations from 09.01.2004 until 29.04.2009.
5.0 Results
We have gone trough the preliminary diagnostic tests and how we resolve these
issues. Next we describe the descriptive statistics of the variables used. After that
we show and discuss the results for both level and differenced regressions using
the Cochrane and Piazzesi (2005) model. In the end of this section we forecast the
term premium, both in-sample and out-of-sample and shortly discuss which model
performs best.
5.1 Descriptives
We add to the information given in chapter 3.2 and chapter 4 to give the reader a
clear overview of our dataset. Table of summary statistics is shown in the
Appendix C1, Table 1 to 8.
5.1.1 United Kingdom
The average excess returns used as the dependent variable in the 1st
stage
regressions are highly varying within the UK estimation period. In Figure III we
see the cyclicality in the average excess return, from which we obtain the state
variable to predict the individual term premiums. The average of the mean excess
return is 58 basis points (bp) for the nominal bonds and 4.8 bp for the indexed
bonds. We infer that the mean does not adequately explain the excess returns. We
see both series are highly volatile, hence showing large standard deviations of
respectively 1.13% and 1.23% for the nominal and real bonds.

Side 26
FIGURE III – ACTUALIZED AVERAGE EXCESS RETURNS FOR UK GOVERNMENT BONDS (31.03.1992-
30.11.2007)
Note: The graph shows the level of the nominal and real average excess return, computed as = for the
period of 03.1992-11.2007 in UK. The average excess return is the dependent variable in the first stage regression.
The individual excess returns for the nominal bonds are logarithmically increasing
with maturity, implying that the term premium for bonds with longer maturities
than 5 years may not be substantially larger than the 5-year term premium. The
individual excess returns for the nominal bonds have means between 37 and 70
bp. They exhibit substantial volatility with standard deviations roughly twice their
means. The first moment of the individual real excess returns have more of a
convex shape with means ranging between 7.9 and 5.3 bp. Their standard
deviations are in the size of between 100 and 140 basis points.
The nominal yield curve is upward sloping on average with the 1-year yield
averaging at 5,5%. They yields and forward rates have all standard deviations in
the size of about 1,5%, indicating stable short rates. It is worth mentioning that the
1-year yield exhibit high leptokurtosis in the mean so that severely low and high
spot rates are more likely than a normal distribution implies. This is a
consequence of the aforementioned discontinuity problem. The real yield curve is
fairly flat on average with only basis points differencing the mean between the 3-
year yield and the forward rates. Their means are in the size of 2,6%. They all
exhibit severely low standard deviations ranging from 75 basis points to 98 basis
points, consistent with previous research that short-term real interest rates exhibits
low volatility and are stable. (Nelson and Schwert 1977; Garcia and Perron 1996)
-6,0 %
-4,0 %
-2,0 %
0,0 %
2,0 %
4,0 %
6,0 %
Size
Date
Nominal average excess return Real average excess return

Side 27
5.1.2 United States
The average excess return for the nominal bonds is 48 bp with a standard
deviation of 98 bp. The individual excess returns exhibits the same dynamics with
means increasing from 19 basis points to 80 basis points with maturity, however
with a more linear increase than for the GILT’s. Their standard deviations are
between 56 and 134 basis points, making them slightly less volatile than the UK
sample. This is probably due to the shorter estimation period and the shorter time
increments used. Also in US, the yield curve is upward sloping on average with
short rates between 3.73% and 4.52%. The estimation period coincides with the
start of contractionary monetary policy, in which the Federal Reserve increased
the short-term interest rates, making the short-term interest rates negatively
skewed. However, as we discuss further in chapter 6, the long-term interest rates
did not increase parallel to the increase in short term interest rates. Corollary, the
four and five year forward rate is not negatively skewed.
The average real excess return has much higher mean in for the TIPS than IL
GILT with a mean of 55.6 bp and standard deviation of 115 bp. This could be due
the period of negative or near zero excess returns are much shorter in the US
estimations sample rather than the UK estimation sample. All the excess return
series exhibits fat tails and highly negative third moments. This indicates there has
been a regime switch in the excess returns series with no stable period of excess
returns. The real yield curve is upward sloping on average with short rates being
in the range of 1.4% and 2.25% on average. The standard deviations are also here
substantially low, in the size of about 30 to 55 bp for the forward rates and 120 bp
for the 2-year real rate.
5.2 Term premium estimations
The motivation behind the 1st
stage regression is to estimate the return-forecasting
factor, also called the state variable, obtained from the term structure of interest
rates. According to Cochrane and Piazzesi (2005) this should be a symmetric, tent
shaped linear combinations of yields and forward rates.

Side 28
FIGURE IV - REGRESSION COEFFICIENTS OF ONE-YEAR EXCESS RETURNS ON FORWARDS RATES
Note: Cochrane and Piazzesi’s (2005) coefficient values from the unrestricted regressions above. Below are their first stage
regression results. They use the unsmoothed Fama and Bliss dataset from the CRSP-database.
Their theoretical framework implies that our results should show the same
structure in the first stage regression parameters. In order to solve for the issue of
non-stationarity we regress the model in 1st
difference and compare the measures
of fit and out-of-sample performance between the models. As the two models are
almost identical in regard to sample period and data used, we see comparisons of
R2
as an appropriate measure of fit. The next stage involves running both a
restricted regression using the state variable as the independent variable on the
individual excess returns and an unrestricted regression where the term structure is
the independent variable. In the restricted regression we see the information
extracted from the yield curve as a single state factor by imposing the
restriction = . As a result of the restriction, 1
4 = 1. We expect the
coefficient to increase with time to maturity of the underlying long-term bond. We
will also run an unrestricted model where the coefficients from the whole term
structure may vary for the various maturities on the excess returns. We will not
discuss this, but we will present their R2
and unadjusted X2
-statistics in Appendix
C3.
We are differing from Cochrane and Piazzesi (2005) by selecting different
markets and sample periods meaning that a direct comparison of R2
-statistics is
not appropriate. We expect to have highly significant X2
test statistics. The X2
test
is a robustness test for checking the joint hypothesis that all parameters may be
zero. If this is rejected we would obtain the same conclusion as previous research
(Fama and Bliss 1987; Cochrane and Piazzesi 2005), which is that the
expectations hypothesis is rejected by the data. More precisely, accepting H0

Side 29
indicates that the term structure tells us nothing about the excess returns. The
implication of this results is that excess returns are totally random i.e. no term
premium. We reject the null if the X2
test statistic exceeds the critical value at the
5% level. The X2
test statistic may be inflated due to the MA(12)-structure
induced by the overlapping data and near singularity. We will furthermore do the
same solution for the apparent X2
-inflation as Cochrane and Piazzesi did by
calculating the sum of squared t-statistics. The adjusted test-statistic is vulnerable
to multicollinearity, as it would be deflated due to the inflated standard errors it
imposes.
Table I shows the results from the first stage regression. We obtain R2
statistics of
45.68% for the real regression in levels and 65.61% for the nominal ones. For the
1st
difference regressions we obtain an R2
of 44.87% and 43.44 % for the nominal
and real sample respectively. If the relationship between the excess returns and the
term structure were to be spurious, the R2
should have dropped significantly when
estimating the model in 1st
difference. Our results indicate that the relationship
still holds, and the term structure is in fact a reliable factor in predicting the excess
returns.
We show here only the adjusted X2
statistic11
, which rejects the expectations
hypothesis at the 5% level for both methods and samples. The rejection is not
strong for the nominal sample in the 1st
difference model, but we are attributing
this to the near multicollinearity as we will discuss further below.
11
The full X2
-statistic is shown along the tables in Appendix C3 Table 1-8.

Side 30
TABLE I - ESTIMATES OF THE SINGLE FACTOR MODEL UK
Panel A. Estimates of the return-forecasting factor, +1 = t
ft + t+1
Nominal 0 1 2 3 4 5 R2
X2
*
OLS estimates -0,0103a
-0,6696a
1,4738 -5,2841a
7,2236a
-2,5298a
0,6561 67,45a
Newey-West (18) (0,0038) (0,1245) (1,1056) (2,5980) (2,2278) (0,6590)
Real
-0,8023a
0,2698a
-0,8948 4,4407a
-2,7895a
0,4568 189,39a
Newey-West (18) (0,0013) (0,0687) (0,0661) (0,9638) (1,6694) (0,8107)
Panel B. Estimates of the return-forecasting factor, +1 = t
t + t+1
Nominal 0 1 2 3 4 5 R2
X2
*
OLS estimates 0,0005a
0,3096 1,5609 -4,0445 5,1839 -0,7506 0,4487 16,46a
Newey-West (18) (0,0002) (0,3791) (1,3054) (3,1224) (4,1229) (2,1174)
Real
OLS estimates 0,0005a
1,8059a
1,0518a
0,5336 2,2315 -1,7138 0,4333 109,91a
Newey-West (18) (0,0002) (0,2172) (0,1812) (0,5859) (1,9718) (1,6498)
Notes: The regressions are estimated as described within the table. Panel A shows the estimated coefficients from the first
stage regressions in levels. Panel B shows the estimated coefficients from the first stage regressions in 1st
difference.
Nominal and Real denotes that the sample used is respectively the nominal sample or the inflation indexed sample. The
sample-period used for estimation is 03.1992-11.2007. The standard errors shown are Newey-West HAC standard errors
computed with 18 lags using the Bartlett Kernel in Eviews. Superscript “a” denotes that the coefficients are significantly
away from zero at the 5% level or greater. The R2
shown is the unadjusted R2
. The X2
-statistic shown is the adjusted X2
and
is computed as ( ) . The critical values for X2
with 6 degrees of freedom are respectively 12.592, 14.499 and 16.812 at the
10, 5 and 1% level.
The coefficients have no explicit economic meaning; however, there should be a
tent-shaped structure in the coefficients for the 1st
stage regression. Our sample
exhibits more of a waveform in the coefficients for both the samples and methods.
This is consistent with Dai, Singleton and Yang’s (2004) results from using
smoothed datasets. The reason for the wave-shaped structure is multicollinearity,
which we will discuss further later.
FIGURE V – GRAPHICAL REPRESENTATION OF THE FIRST STAGE REGRESSION PARAMETERS IN UK.
Note: This is a graphical representation of the coefficients obtained from the results of our first stage regressions in Table I.
0 is excluded. Real denotes the indexed term premium regressions, while
nominal denotes the nominal term premium regressions. Levels denote the model in level, while 1st
diff. denotes the
coefficient values from the regressions in 1st
difference.
-10
-5
0
5
10
1 2 3 4 5
CoefficientValue
Coefficient number
Real (Levels)
Nominal (Levels)
Nominal (1st. Diff.)
Real (1st. Diff.)

Side 31
In the level regression all the coefficients for the nominal sample is significant at
the 5% level or better except for the 2-year forward. The 3-year forward is the
only insignificant parameter in the real sample. We see quite another picture for
the regressions in 1st
difference. The nominal coefficients are all not statistically
significant except for the constant term. For the real regressions the constant term,
the 3-year yield and the 4-year forward are significant. The rest of the forward
rates have insignificant coefficient but we infer this is due to the multicollinearity,
even though the correlation tables show that the correlations are slightly
decreasing when differencing them. We run the same regressions while excluding
one of the forward rates. Whichever forward rate we exclude the rest of the
coefficients are statistically significant. Additionally we obtain the tent-shaped
structure and clear rejections of the expectations hypothesis. The R2
is declining
only slightly. We do not show these results, but this clearly implies that the
inconsistencies we obtain in contrast to Cochrane and Piazzesi is due to
multicollinearity. The background the imposed multicollinearity will be further
discussed in chapter 6.2.2.
Below are the results from the restricted second stage regressions. We see the
same dynamics as Cochrane and Piazzesi in our regressions. The loading of the
single factor is increasing with maturity and the coefficients are all statistically
significant. However, we obtain high and severely varying R2
-statistics. In the 1st
difference regressions the R2
are much less varying and range beyond 40 to 45 %.

Side 32
TABLE II.- RESULTS OF REGRESSIONS ON INDIVIDUAL BOND EXCESS RETURNS UK
Panel A: rx(n)
t+1 = bn
t
ft) (n)
t+1
n b2 b3 b4 b5
Nominal 0,63505a
0,97838a
1,14507a
1,24159a
SE (0,02032) (0,02546) (0,03604) (0,05554)
R2
0,74156 0,71248 0,62058 0,53022
Real 0,94539a
0,98483a
1,02882a
1,04096a
SE (0,04486) (0,05318) (0,08009) (0,11311)
R2
0,54161 0,47735 0,42121 0,3628
Panel B: rx(n)
t+1 = bn( t
t) + (n)
t+1
n b2 b3 b4 b5
Nominal 0,40245a
0,8024a
1,20164a
1,59352a
SE (0,01955) (0,0375) (0,06521) (0,1014)
R2
0,41532 0,42184 0,43787 0,4464
Real 0,74689a
0,93097a
1,09017a
1,23197a
SE (0,05967) (0,07139) (0,08341) (0,09543)
R2
0,42261 0,42663 0,42747 0,42186
Note: Table II show the results from the restricted second stage regressions. The regressions estimated is as described
within the table, where panel A show the results of the model in levels, while Panel B show the results of the model in 1st
difference. Nominal and Real denotes that the sample used is either the nominal sample or the inflation indexed sample
respectively. The sample-period used for estimation is 03.1992-11.2007. The subscripts in the n-row denote the maturity of
the nominal term premium. For the real term premium the maturity of the term premium is n+3. Superscript “a” denotes
significantly away from zero at the 5% level or greater. The standard errors shown are Newey-West HAC standard errors
computed with 18 lags using the Bartlett Kernel in Eviews. The R2
.
5.2.2 United States
The results for the US sample are quite similar to the results in the UK sample.
The results from the 1st
stage regressions are shown in the following table. The
HAC covariance matrix reaches near singularity at around 26 lags, so we chose to
continue with the 18 lags as previously. However it is important to mention that
this could lead to deflated standard errors. As this is a shorter sample with shorter
time increments the excess returns are less varying and contain fewer cycles,
which could lead to a better fit. Also as mentioned in chapter 4.2 we have a
slightly longer estimation period of the TIPS-series.
As shown in Table III we obtain extremely high R2
-statistics of 92% for the
nominal state variable and 71.56% for the state variable in the real sample when
regressing in levels. We also reject the expectations hypothesis in both samples

Side 33
based on the level regression. However, for the regressions in 1st
difference we
cannot reject the expectations hypothesis for the nominal government bond
market. The reason is near multicollinearity occurring in the independent
variables. We test this by running regressions where we exclude one of the most
correlated variables and are able to clearly reject the expectations hypothesis for
both datasets and models.
Even though the measure of fit obtained from the model in 1st
difference is
excellent compared to previous literature, there are two issues that need to be
addressed; the remarkably high R2
in the level regressions and the substantial drop
when differencing the series. We attribute the remarkable R2
to the low volatility
of the US excess returns and the short estimation period. We attribute the
unfortunate combination of insignificant RHS-variables and high R2
to
multicollinearity. The drop in R2
is harder to explain but the fit is still good in the
1st
difference regressions, making us unable to conclude whether this is a spurious
regression.
TABLE III - ESTIMATES OF THE SINGLE FACTOR MODEL US
Panel A. Estimates of the return-forecasting factor, rxt+1 = t
ft t+1
Nominal 0 1 2 3 4 5 R2
X2
*
-1,0948a
1,3719a
-2,2414 2,0203 0,1211 0,9178 312,85
Newey-West(18) (0,0025) (0,0640) (0,6597) (2,2921) (1,2791) (1,2791)
Real
OLS estimates -0,0032 -0,8963a
-1,3383a
6,8397a
-8,9644a
4,5194a
0,7156 1147,61
Newey-West (18) (0,0021) (0,0285) (0,1607) (1,0335) (1,8777) (1,0431)
Panel B. Estimates of the return- rxt+1 = t
t t+1
Nominal R2
X2
*
OLS estimates -0,00001 0,4993a
-0,1950 1,6766 1,0218 -0,4444 0,5516 5,60
Newey-West (18) (0,00038) (0,2268) (0,9960) (2,2579) (3,2231) (1,8516)
Real
OLS estimates -0,00001 0,7470a
1,8588a
-1,8314 6,5903a
-4,0058a
0,5395 180,70
Newey-West (18) (0,00030) (0,0658) (0,3494) (1,2107) (2,0047) (1,2461)
Notes: The regressions are estimated as described within the table. Panel A shows the estimated coefficients from the first
stage regressions in levels. Panel B shows the estimated coefficients from the first stage regressions in 1st
difference.
Nominal and Real denotes that the sample used is respectively the nominal sample or the inflation indexed sample. The
sample-period used for the nominal estimations is 09.01.2004-09.01.2008. The sample used for real estimations is
09.01.2004-29.04.2009. The standard errors shown are Newey-West HAC standard errors computed with 18 lags using the
Bartlett Kernel in Eviews. Superscript “a” denotes significant at the 5% level or better. The R2
.
The X2
-statistic shown is the adjusted X2
and is computed as ( ) . The critical values for X2
with 6 degrees of freedom are
respectively 12.592, 14.499 and 16.812 at the 10, 5 and 1% level.

Side 34
We see the same wave-shape occurring in these samples as well, which we by
now credit to the multicollinearity-problem. (Figure 1 in Appendix D) Most of the
coefficients in the level regressions are statistically significant except for the 3-
year nominal forward rate and the constant term in the real excess return
regression. For the regressions in 1st
difference we do not have such significant
coefficients. For the nominal sample only the 1-year yield is significant, while in
the real sample we have only two insignificant variables.
For the second stage regressions we find the same dynamics as with the UK-
results. The coefficient loadings are increasing with maturity and are all highly
statistically significant. The regressions in levels exhibit severely high R2
-
statistics.
TABLE IV - RESULTS OF REGRESSIONS ON INDIVIDUAL BOND EXCESS RETURNS US
Panel A: rx(n)
t+1 = bn
t
ft) (n)
t+1
n b2 b3 b4 b5
Nominal 0,527818a
0,895325a
1,17293a
1,403941a
SE (0,010685) (0,00954) (0,008119) (0,015924)
R2
0,873998 0,925503 0,903928 0,855781
Real 0,734361 0,951689 1,102297 1,211719
SE (0,045688) (0,021005) (0,069816) (0,114034)
R2
0,69005 0,734103 0,685722 0,611585
Panel B: rx(n)
t+1 = bn( t
t) + (n)
t+1
n b2 b3 b4 b5
Nominal 0,430863a
0,849273a
1,210678a
1,509186a
SE (0,024494) (0,05312) (0,06943) (0,070158)
R2
0,622523 0,567378 0,535192 0,50707
Real 0,539389a
0,89758a
1,81556a
1,381475a
SE (0,025737) (0,042072) (0,054706) (0,052655)
R2
0,349566 0,519363 0,564498 0,556848
Note: Table IV show the restricted second stage regressions The regression estimated is as described within the table,
where panel A show the results of the model in levels, while Panel B show the results of the model in 1st
difference. The
sample-period used for the nominal estimations is 09.01.2004-09.01.2008. The sample used for real estimations is
09.01.2004 -29.04.2009. Nominal denotes the nominal term premium coefficient estimates, while real denotes the real term
premium estimates. The subscripts in the n-row denote the maturity of the nominal term premium. For the real term
premium the maturity of the term premium is n+2. Superscript “a” denotes significant away from zero at the 5% level or
better. The standard errors shown are Newey-West HAC standard errors computed with 18 lags using the Bartlett Kernel in
Eviews. The R2
.

Side 35
For the 1st
difference regression we see that the restriction still holds and the
coefficients average to 1. The R2
have dropped significantly, which confirms our
belief that the R2
for the model in levels are somewhat dubious.
5.3 Term premium modeling and evaluation
We model the term premium by using the standard OLS equation framework. A
capital F is used for forecasted value to avoid confusion with the forward-vector.
Furthermore we had to make a choice of which value we used as the initial
forecast when forecasting the model in 1st
difference. We chose to use
accompanying for each series as the initial value. The evaluation criteria used
is the RMSE and Correct sign.
Root Mean Squared error is calculated as
= ( ) . (EQ. 5.1)
It has the following desirable properties that negative and positive errors do not
cancel each other out. Additionally it punishes large errors more than small errors.
The last evaluation criteria we show is the correct sign percentage because
interpretation of the term premium would differ significantly when predicting the
incorrect sign. The correct sign prediction is measured as:
Correct Sign % = , (EQ. 5.2)
where = 1 if > 0 and 0 if not.
We expect the differenced model to perform better out-of-sample due to the non-
stationarity in the level-regressions, and the original Cochrane and Piazzesi-model
performing better in the estimation sample.
We were able to estimate the excess return with a quite high precision when using
the term premiums obtained in the level regressions. The results are attached in
Appendix C6 Table 1. For the nominal GILTS we have RMSE-errors in the sizes

Side 36
of basis points both for the estimation sample, and the out-of-sample period. For
the indexed GILTS we have higher errors than in the nominal sample on average
but still quite adequate. The errors in the estimation period are around 1%, while
the errors in the out-of-sample period range between 1% and 2%. There is clearer
evidence of unit root behavior in the real forward vector than in the nominal
vector, as can be seen by test statistics in Table 1 and 2 in Appendix C2. If this is
the reason for the real series performing worse out-of-sample relative to in-sample
or if there is simply a change in the data-generating process is unknown. We
expected to get better predictions for the 1st
difference method, especially in the
out-of-sample forecasts. We see the 1st
difference estimations perform
significantly worse with errors in the size of economic importance.
Furthermore we see the level estimations give correct signs for the excess return
between 75% and 89% of the time for the in-sample observations. However, the
occurrence of the correct sign decreases significantly for the nominal excess
return, and actually increases for the indexed excess returns in the out-of-sample
period. This is probably because the nominal excess returns change sign more
often than the real excess returns. For the model in 1st
difference we obtain better
out-of-sample sign predictions for the nominal estimations, but worse for the real
estimations. The overall results for the UK sample seems to indicate the original
Cochrane and Piazzesi model perform better both in the estimation sample and
out-of-sample. This is puzzling since the RHS-variables exhibit non-stationary
properties.
5.3.2 United States
In the US-dataset we obtain errors consistently in the size of basis points both in
the estimation period and out-of-sample. The exceptions are the nominal 2-year
excess returns and the 5-year excess returns, both slightly above 1%. We are able
to predict the correct sign a substantial amount of the time for the level
regressions, both in the estimation sample and in the out-of-sample period. For the
regressions in 1st
difference we are actually able to predict the correct sign more

Side 37
often out-of-sample than in-sample. We credit the apparent better performance in
the US sample to less variability in the excess returns in the out-of-sample period.
As we see in Appendix C6 Table 2, the term premiums estimated through the
regressions in levels seem to clearly outperform the model in 1st
difference for the
estimation period. For the out-of-sample period the conclusion is not that clear,
but our results seem to indicate the model in levels also here outperforms the
differenced model.
We conclude that the best model to capture the excess returns is the original
Cochrane and Piazzesi-model. This could be due to us excluding the financial
crisis in the out-of-sample period and may be seen as data mining. However,
almost no model could predict even normally extremely liquid markets like the
mortgage-backed-securities market or the equity markets during the great
recession. Hence, we use the predictions from the level estimations in our
discussion chapter. We will discuss why we believe the estimations in 1st
difference perform sub-par in chapter 6.2.1.
6.0 Discussion
In this section we discuss the estimated term premium. Afterwards we discuss the
shortcomings of the Cochrane and Piazzesi-model.
6.1 Term premium estimations
We model the term premium in the way we mentioned in section 5.3. We will not
show and discuss the term premium at all maturities, but rather focus on the
longest maturity term premiums for each type of bond.
In Figure VI and VII we see the estimated term premium for the longest maturity
UK indexed and nominal bonds in the estimation period. The excess returns for
nominal and indexed bonds follow the same cycles.

Side 38
FIGURE VI – IN-SAMPLE ESTIMATIONS OF THE 7-YEAR REAL TERM PREMIUM UK 1992-2007
Note: The sample consists of the period of 03.1992-11.2007 for the IL GILTS with 7 years to maturity issued by Bank of
England.. The Actualized excess returns is computed as EQ 3.5 while the forecasted excess return is computed as
(
( )
) = ( ).
As mentioned in 2.2 the interest rate risk component of nominal bonds can be
decomposed into a real interest rate component and an inflation-rate uncertainty
component. If there were no inflation uncertainties, it would follow from the
Fisher equation that uncertainty regarding future nominal interest rates is the same
as the uncertainty regarding future real interest rates. This argument comes from
basic statistics as Var(x)=Var(x+c).
FIGURE VII - IN-SAMPLE ESTIMATIONS OF THE 5-YEAR NOMINAL TERM PREMUM UK 1992-2007
Note: The sample consists of the period of 03.1992-11.2007 for GILTS with 5 years to maturity issued by Bank of
England.. The Actualized excess returns is computed as EQ 3.5 while the forecasted excess return is computed as
(
( )
) = ( ).
1992-1997
We see the term premium of the inflation indexed GILTS stayed somewhat
constant at about 1% from 1992 to 1997. A positive term premium relating to
-6,0 %
-4,0 %
-2,0 %
0,0 %
2,0 %
4,0 %
6,0 %
8,0 %
Size
Date
Actualized Excess Return Estimated Term Premium
-4,0 %
-2,0 %
0,0 %
2,0 %
4,0 %
6,0 %
8,0 %
Size
Date
Actualized excess return Estimated Term Premium

Side 39
liquidity in indexed bonds is quite puzzling intuitively. There should be a liquidity
premium to hold inflation-indexed bonds relative to other more liquid asset
classes. However, the buy-and-hold nature of the indexed bondholders, should
lead to low or negative liquidity term premiums. Thereby the term premium
should be either constant over maturities or lower for long-term bonds in relative
to short-term bonds. If we had reliable liquidity data for the period we could
estimate the part of the term premium owing to liquidity. Our results imply that
the real term premium is relatively stable and we infer this is due to uncertainty
regarding future real interest rates, rather than liquidity.
We see the term premiums on the nominal longer-term bonds are higher and more
volatile than the term premium of inflation linked bonds. This period coincided
with the aftermath of the Maastricht treaty, the high inflation period of the 1980’s
in the UK and Black Wednesday. In 1988 UK started to shadow the Deutsche
Mark (DRM), which was made official when UK agreed to join the ERM in 1990.
Due to this they had to adhere to follow the DRM within a bound. Due to the high
inflation the UK was experiencing at the time, this led to severely high interest
rates of up to 15% to control inflation and stay within the bounds. (Budd 2004)
George Soros of Quantum Fund didn’t think that the UK could uphold its high
interest rates as it was in a mild recession, and took huge short positions in the
UK-pound. This led to something we like to call an exchange rate war that
ultimately led to the UK withdrawing from the ERM. (Drobny 2013) The ERM
deal was practically a deal to lower inflation, and hence inflation uncertainty
became increased in the aftermath. In October 1992, then Chancellor of
Exchequer Norman Lamont established the first direct inflation target. The target
was to lie in-between the range of 1-4% for annual RPIX inflation. (Benati 2007)
Macroeconomic theory says the best solution for lowering inflation is
contractionary monetary policy, i.e. setting up interest rates. However, in a
country where there had recently been a mild recession one would need to lower
interest rates in order to increase economic activity. (Chamberlin 2010) Hence the
market got conflicting signals and we believe there was low confidence in the

Side 40
United Kingdom being able to reach its inflationary targets, leading to the high
nominal term premiums in the early 1990’s.
1997-2004
The excess returns declined to negative levels in end of 1997 and stayed low until
the end of 2001. This coincided with two major happenings in UK monetary and
political climate: The election where UK got a Labour-government for the first
time since 1979, and the Bank of England being granted operational independence
in setting monetary policy.
Lower term premiums and negative excess returns may indicate a coming
recession. (Wright 2006) Negative excess return means that long-term yields are
lower than expected future short rates. This would be due to excess demand for
long maturity bonds. The nominal forward rates did decrease extensively in the
period when the Bank of England got granted their independence in setting the
monetary policy. This led to lower expected inflation and inflation risk premiums.
(Joyce et.al. 2009) We believe the Bank of England’s independence may have
given a signal of more freedom in setting monetary policy such that they were
better able to follow the mandate of stable inflation. The combination of relatively
stable inflation in the mid-nineties and the credibility of the signal given by Bank
of England’s independence may have reduced the inflation component of the term
premium. (Benati 2007) Even though is rational for the term premium to decline,
we fail to see why the term premium should be negative. It could be due to high
short-term uncertainty regarding inflation or real interest rates, but this does not
seem likely due to the UK economy being stable in the late 1990’s. However, as
we are to mention there was an influx of long term investors in the government
bond who would require a risk premium on the short-term bonds rather than the
long-term bonds.
As the real term premium also decreased, we could infer that this as well was due
to the independence of Bank of England, however Joyce et.al. (2009) mention
several other reasons that are more likely. The Minimum Funding Requirement of

Side 41
95 came into effect in April 1997. This led to pension funds increasing their
demand for index linked bonds, and safe government bonds in general. The
consequence was reductions in long-term yields, and consequently decreases in
both the real and nominal term premium. This also rationalizes the negative sign
of the term premium, as pension funds are generally long term investors and
therefore prefer long-term bonds. Other reasons could be the LTCM collapse and
the Asian crises in 1997 and 1998 leading to a flight to quality, meaning investors
preferred less risky government bonds. The third reason they mention is the
evolution of the global index-linked bond markets, with the TIPS being
introduced in 1997. This led to overall reductions in the liquidity premium of
index-linked bonds as an asset class. These low term premiums continued until
the end of 2000, where they again rose to positive levels. The average size of the
real term premium was about 50 basis points and of the nominal term premium of
90 to 100 basis points.
The nominal/real term premium puzzle
The arguments above do not explain what we name the nominal/real term
premium puzzle. There is natural high correlation between excess returns on
different maturities. As we decomposed the different term premiums components
above, we saw that they differ slightly in definition. Both the nominal and real
term premium is subject to real interest rate risk, but the liquidity and inflation
component should differ. Due to these facts there would be some correlation
between term premiums on nominal and real bonds. However, the correlation
occurring between nominal and real term premium after the Bank of England got
their independence needs further discussion.

Side 42
FIGURE VIII – IN-SAMPLE ESTIMATIONS OF THE TERM PREMIUMS ON 5-YEAR NOMINAL GILTS AND 5-
YEAR INDEX LINKED GILTS 1992-2014
Note: The sample consists of the period of 03.1992-11.2007 for the IL GILTS and the nominal GILTS, both with 5 years to
maturity issued by Bank of England. The forecasted excess return is computed as (
( )
) = ( ). The graph also
includes the out-of-sample forecast for the period of 01.2010-03.2015, explaining the straight line between 11.2007 and
01.2010.
In the period from January 1997 until the end of the out-of-sample period we find
a correlation-coefficient of 0,67. The correlation from january 2001 is almost
0,88. We obtain approximately the same level of correlation between the 4-year
nominal and real term premium as well. In a complete inflation certainty scenario
this could be seen as reasonable, as in this case the only uncertainty would be the
level of real interest rates and the liquidity.
Christensen et.al (2010) find that the inflation risk premium was very low in the
US in the early 2000s which is probably the reason for the similar correlation
between the excess returns of the two asset classes in the United States. Benati
(2007) mentions that UK has experienced low and stable inflation since the
exchange rate crisis and good macroeconomic performance. This accompanied by
the lower standard deviation of Bank of Englands short rate and inflation forecasts
have probably led to low inflation uncertainty.
As mentioned we see a similar correlation for the US bonds, but the nominal term
premium spikes at relatively even intervals. (Figure 6 in Appendix D) The
increases in the term premium coincides with Federal Reserves reports to
congress, in which they report “the conduct of monetary policy and economic
-3,0 %
-2,0 %
-1,0 %
0,0 %
1,0 %
2,0 %
3,0 %
4,0 %
5,0 %
Size
Date
Estimated 5 year Nominal Term Premium Estimated 5 year Real Term Premium

Side 43
developments and prospects for the future.” However, if this is due to more trades
in short term nominal bonds relative to long-term bonds, or higher inflation
uncertainty is ambiguous. This warrants further research into how the bond
market reacts to central bank reports.
2004-2007, The bond yield conundrum and the financial crisis
After 9/11 the Federal Reserve decreased interest rates to increase economic
activity as the equity market experienced a small shock. From June 2004 to June
2006 the Fed gradually raised the short term interest rates from 1% and up to
above 5%. Expectations hypothesis and liquidity preference theory states that the
yield curve should show an upward shift. However, long-term rates stayed
constant leading to a significantly decreased yield spread. Ben Bernanke and other
academics called this the bond yield conundrum.
“To the extent that the decline in forward rates can be traced to a decline in
the term premium, . . . the effect is financially stimulative and argues for greater
monetary policy restraint, all else being equal. Specifically, if spending depends
on long-term interest rates, special factors that lower the spread between short
term and long-term rates will stimulate aggregate demand. Thus, when the term
premium declines, a higher short-term rate is required to obtain the long-term
rate and the overall mix of financial conditions consistent with maximum
sustainable employment and stable prices.”
-Ben Bernanke Federal Reserve Chairman 2006
(Paraphrasing from Rudebusch, Sack and Swanson 2006)
This was not confined to the US. The Bank of England raised short term interest
rates as well, with the consequence that the forward curve stayed relatively flat in
stead of increasing. We also attribute this to a decrease in the term premium. The
purpose of increasing the short-term interest rate is to decrease economic activity
and inflation. However, the public does not react as strongly to short term interest
rates as long-term interest rates. The whole of the yield curve needs to shift, either
upwards or downwards, for monetary policy to be effective.

Side 44
FIGURE IX - THE BOND YIELD CONUNDRUM IN UNITED STATES 2004-2008
Note: The sample consists of the period of 09.01.2004-09.01.2008. The estimated nominal term premium is the forecast
computed as (
( )
) = ( ) for nominal US government bonds with 5 years to maturity. The 1 and 5-year yield is
the annual continuously compounded yields for the bonds with 1 and 5 years to maturity.
The estimated nominal term premium declined substantially, making the yield
curve flat. Backus and Wright (2007) discuss several events that may have
contributed to the low term premium. Firstly, the countercyclical behavior of the
term premium suggests that the US economy was in a boom. However, this is
inconsistent with Wright’s (2006) results that lower term premiums increase the
probability of an impending recession. We believe the truth is somewhere in-
between. The term premium is declining in booms as the risk averseness of
investors decreases. Referring to Ludvigson and Ng (2009) Figure 8 we see the
moving average risk premium of 5-year nominal bonds have often decreased
before recessions, and increasing while in recession. As we further can deduce
from their Figure is that a low or negative term premium may not necessarily
mean that a recession will occur. This issue forms the question of why the term
premium is low or negative. A negative term premium would imply that investor
requires excess returns to invest in short term securities. The latter argument is
consistent with flight to quality-theory that under uncertain market conditions,
investors demand safe long-term government bonds due to the reinvestment risk
and credit risk. An answer to this question could lead to more accurate predictions
of recessions.
-2,0 %
-1,0 %
0,0 %
1,0 %
2,0 %
3,0 %
4,0 %
5,0 %
6,0 %
Size
Date
1 year yield 5 year yield Estimated Nominal Term Premium

Side 45
Secondly, there was a general decline in asset price volatility that also led to a
decline in the term premium (Backus and Wright 2007; Rudebusch, Swanson, and
Wu 2006). According to surveys the dispersion of long run macroeconomic
expectations and especially their long-run inflation expectations tightened. The
reason for this could be a more credible and transparent monetary policy created
by the publication of their reports to congress. Thirdly, it could be due to more
integrated financial markets. This could reduce the potential short-term gains from
any country adopting inflationary policies and hence making commitments to a
low inflation policy more credible. Finally, demand for longer-duration securities
may have increased due to the possibility of corporate pension reforms that might
lead to funds increase the duration in their portfolio. However, the development in
pension schemes has proceeded slowly in the US making the last argument less
plausible for the US markets.
FIGURE X – IN-SAMPLE ESTIMATIONS OF THE 5-YEAR NOMINAL TERM PREMIUM US 2004-2008
Note: The sample consists of the period of 09.01.2004-09.01.2008. The estimated nominal term premium is the forecast
computed as (
( )
) = ( ) for nominal US government bonds with 5 years to maturity. The Actualized excess
returns are computed as in EQ 3.5.
Low inflation uncertainty certainly explains a declining term premium, but it does
not explain the negative level of the term premium, especially in the index-linked
markets. Furthermore the decline in asset price volatility should give a lower term
premium overall, but we fail to see why this would imply a negative level.
Bernanke (2013) used the safe-haven position of treasury bonds in his reasoning
for why the term premium may be negative. He also mentions the fact that
treasury bonds have lately been more popular as a hedge in portfolios, making the
-2,0 %
-1,0 %
0,0 %
1,0 %
2,0 %
3,0 %
4,0 %
5,0 %
Size
Date

Side 46
overall term premium lower, and if popular enough may lead to a negative term
premium.
FIGURE XI – IN-SAMPLE ESTIMATIONS OF THE 6-YEAR REAL TERM PREMIUM US 2004 - 2009
Note: The sample consists of the period of 09.01.2004-29.04.2008. The estimated term premium is the forecast computed
as (
( )
) = ( ) for US TIPS with 6 years to maturity. The Actualized excess returns are computed as in EQ 3.5.
In the prelude of the financial crisis the US nominal term premium increased,
while the real term premium decreased. The increase in the nominal term
premium is consistent with previous research in the behavior of the term premium
during financial crises. The market expects lower future interest rates in order to
increase economic activity, hence also increasing the output gap and inflation.
This leads to higher uncertainty regarding the future inflation, thereby increasing
the inflation risk premium. Regarding the decrease in the real term premium, we
attribute this to the flight-to-quality theory, as a financial crisis was inevitable.
Financial intermediaries had large investments in asset-backed securities and used
them as collateral in order to obtain repo financing. (Krishnamurthy 2010) When
the subprime mortgage crisis started at the end of 2007, the financial
intermediaries began to demand safe long term government bonds in order to
reduce the haircut they had to pay for the short term financing. The real term
premium increased in the end of 2008, probably due to the overall liquidity crisis
in the economy.
2010-2015 The out-of-sample period
As mentioned in 5.3.1 the prediction errors of the UK nominal excess returns were
small in the out-of-sample estimations. However, as we see in Figure XII our
-8,0 %
-6,0 %
-4,0 %
-2,0 %
0,0 %
2,0 %
4,0 %
6,0 %
Size
Date

Side 47
nominal estimations have an upward bias. Secondly, our estimations seem more
volatile. The size of the estimated term premium is varying between 150 and -20
basis points, while the size of the actualized excess returns have a much tighter
range of 50 to 0 basis points for the out-of-sample period.
FIGURE XII- OUT-OF-SAMPLE ESTIMATIONS OF 5-YEAR NOMINAL TERM PREMIUM UK 2010-2015
Note: The sample consists of the period of 01.2010-03.2015 for the nominal GILTS with 5 years to maturity issued by
Bank of England. The forecasted excess return is computed as (
( )
) = ( ) while the actualized excess returns
are computed as in EQ 3.5.
FIGURE XIII– OUT-OF-SAMPLE ESTIMATIONS OF 7-YEAR REAL TERM PREMIUM UK 2010-2015
Note: The sample consists of the period of 01.2010-03.2015 for the IL GILTS with 7 years to maturity issued by Bank of
England. The forecasted excess return is computed as (
( )
) = ( ) while the actualized excess returns are
computed as in EQ 3.5.
The forecast excess return on the index-linked GILTS seems to be much more
constant and downward biased relative to its ex-post actualized values. The
forecast real term premium was about 1% in 2010 and 2011, while dropping down
to around zero in the period of 2012 and 2013 which were considered times of
hardship in the UK economy. The GDP-growth after the financial crisis had been
-1,0 %
-0,5 %
0,0 %
0,5 %
1,0 %
1,5 %
2,0 %
Size
Date
Actualized Excess Returns Estimated Term Premium
-4,0 %
-2,0 %
0,0 %
2,0 %
4,0 %
6,0 %
8,0 %
Size
Date

Side 48
low with 1.9% in 2010, 1.7% in 2011 and 0.7 % in 2012. (data.worldbank.com)
Basic macroeconomic policy is to lower interest rates when GDP growth is slow.
Hence, more demand of long-term bonds with slightly higher yields could lead to
lower term premiums in 2012.
For the US we have clear downward bias both for the nominal government bond
series and TIPS series. Hence any inferences from the curves should be taken with
great care. Even though there seem to be a downward bias, we find that they
follow each other well. Either way we see it, the nominal excess return have
increased through our out-of-sample forecasts. Estimated term premiums range
between 0% and 1% during 2012 and increase to between 1% and 2 % from mid
2013 and onwards. This implies higher uncertainty of the future inflation, but we
have to take into account the real term premium also increased to the same levels
in this period. (Figure XV) This indicates that the inflation component of the term
premium is relatively small.
FIGURE XIV – OUT-OF-SAMPLE ESTIMATIONS OF 5-YEAR NOMINAL TERM PREMIUM US 2012-2015
Note: For the out-of-sample forecasts we start our forecasts for US nominal and real bonds mid-week first week of 2012
and end at 15th
of April 2015. The estimated nominal term premium is the forecast computed as (
( )
) = ( ) for
nominal US government bonds with 5 years to maturity. The Actualized excess returns are computed as in EQ 3.5.
-1,0 %
0,0 %
1,0 %
2,0 %
3,0 %
4,0 %
5,0 %
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