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Final Paper.lyx
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#LyX 2.3 created this file. For more info see http://www.lyx.org/
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\begin_document
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\begin_body
\begin_layout Title
Term Spread Combinations: Its ability to Span different Macro-economic variables
and explain their future movements.
\end_layout
\begin_layout Author
Abdul Tawab Ajmal Safi
\end_layout
\begin_layout Abstract
In this paper, I show how different combinations and components of term
spread have varying shapes, which can be analyzed in order to understand
movements in the economy.
Calculating term spread dispersion can help us better price risk in the
bond market.
Term spread combinations have varying power in explaining future movements
in macro variable.
It shows that the spanning hypothesis of the term spread against a macro
variable might hold true depending on the combination and component of
term spread that we are taking into consideration.
This paper provides a mechanism through which we can identify the best
combination of a term spread for creating an efficient macro finance model.
\end_layout
\begin_layout Abstract
\begin_inset Newpage pagebreak
\end_inset
\end_layout
\begin_layout Section
Introduction
\end_layout
\begin_layout Subsection
What is the Term Spread?
\end_layout
\begin_layout Standard
\series bold
\color black
\begin_inset Formula
\[
Term\thinspace Spread=Long\thinspace Term\thinspace Interest\thinspace Rate\thinspace\thinspace-\thinspace\thinspace Short\thinspace Term\thinspace Interest\thinspace Rate
\]
\end_inset
\end_layout
\begin_layout Standard
Term Spread comprises of the difference between the long term and short
term yield curve.
The short term yield is the interest paid by the government on its bonds
over a short horizon.
It is a monetary policy tool used by the government to achieve its macro
economic objectives of price stability, full employment, and economic growth.
It short term usually ranges from 1 month [
\begin_inset Formula $y_{t}^{1m}$
\end_inset
] up until 18 months [
\begin_inset Formula $y_{t}^{18m}$
\end_inset
].
\end_layout
\begin_layout Standard
The long run yield curve, on the other hand, constitutes of two parts: the
expectation component and the term premium component.
\end_layout
\begin_layout Standard
\color black
\begin_inset Formula
\[
y_{t}^{10y}=\frac{1}{10y}\sum_{i=0}^{10y-1}E\left[y_{t+i}^{1m}\right]+TP_{t}^{10Y}
\]
\end_inset
\end_layout
\begin_layout Standard
As shown in the above equation, the 10 year long run yield curve comprises
of the expectation of the short run interest rate over the 10 year horizon
plus the term premium component.
The government cannot control the long run interest rate as it is determined
by people's expectation about the future of the economy and the bond risk
premium that they require in order to compensate for it.
\end_layout
\begin_layout Standard
The difference between the long and short run yield curve holds valuable
information about macro economic and financial variables in the economy.
In the United States, the 10 year minus 3 months term spread has been a
great indicator of future recession in the economy.
Throughout history, the term spread inversion forecasted 7 recessions in
the US economy out of which 6 were true.
This indicates that the term spread holds valuable information about the
economy.
For years, economists have been researching on the potential of term spread
in understanding the economy.
This led to the development of various complex term spread models such
as the expectation component term spread and the term premium component
term spread.
The expectation component term spread comprises of the difference between
the expectation of the long run and short run interest rate, while the
term premium component comprises of the difference between the long run
and the short run term premium.
\end_layout
\begin_layout Standard
Different components and combinations of term spreads have had varying power
in explaining movements in the economy..
In this paper, I intend to explore a mechanism through which we can identify
the best combination and component that can be used to develop a term spread
in order to better understand movements in macro economic variables.
\begin_inset Newpage pagebreak
\end_inset
\end_layout
\begin_layout Subsection
Different Combinations of Long Run and Short Run Yield Curve result in varying
Term Spreads
\begin_inset VSpace 1cm
\end_inset
\end_layout
\begin_layout Standard
The shape of the yield curve tend to change depending on the long run and
short run yield curve that we use to construct it.
It appears that the further apart the long term and short term yield curves
are the wider the term spread gets.
The volatility of the term spread also reduces or increases based on the
combination that we take.
All of this indicates that different combinations might be useful in explaining
different macro economic and financial variables.
\begin_inset VSpace 1cm
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Float figure
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\begin_inset Graphics
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\end_inset
\end_layout
\begin_layout Standard
As we can see in the graphs above, the 2.5 years minus 3 months term spread
appears to be more volatile than the 10 year minus 1 year term spread.
The percentage difference also appears to vary across the term spreads.
This varying shape of the term spreads is what motivated me to develop
a model that looks at all possible combinations of a term spread in order
to identify the best possible combination.
\begin_inset Newpage pagebreak
\end_inset
\end_layout
\begin_layout Subsection
Paper Structure
\begin_inset VSpace 1cm
\end_inset
\end_layout
\begin_layout Standard
This paper consists of five major sections each of which looks at a different
research question that can be used to understand the effectiveness of term
spread combinations in explaining macro variables and movements in the
economy.
\end_layout
\begin_layout Standard
Research Questions:
\end_layout
\begin_layout Enumerate
Does it matter what short term and long term yield curve combinations we
use to calculate the term spread?
\begin_inset VSpace 1cm
\end_inset
\end_layout
\begin_layout Enumerate
Does the dispersion of spreads have any explanatory power for understanding
the Term Premium term spread?
\begin_inset VSpace 1cm
\end_inset
\end_layout
\begin_layout Enumerate
Are Macro economic variables captured in all different combinations of term
spread?
\begin_inset VSpace 1cm
\end_inset
\end_layout
\begin_layout Enumerate
Can different term spread combinations be used to explain future movements
in macro variables?
\begin_inset VSpace 1cm
\end_inset
\end_layout
\begin_layout Enumerate
Can the 1st Principle Component Analysis of all different combinations of
term spread give us the best possible term spread model?
\begin_inset Newpage pagebreak
\end_inset
\end_layout
\begin_layout Section
Does it matter what short term and long term yield curve combinations we
use to calculate the term spread?
\begin_inset CommandInset label
LatexCommand label
name "2nd Section"
\end_inset
\end_layout
\begin_layout Subsection
Term Spread Model Setup
\end_layout
\begin_layout Standard
\color black
\begin_inset Formula
\[
TS_{t}^{i}=y_{t}^{Long\thinspace Run}\thinspace-\thinspace y_{t}^{Short\thinspace Run}
\]
\end_inset
\end_layout
\begin_layout Standard
To construct all possible different combinations of term spread the following
set up was used:
\end_layout
\begin_layout Itemize
\series bold
Long Run
\series default
is assumed to range from 24 months
\series bold
to
\series default
120 months which is 97 different long term values.
\begin_inset VSpace 0.8cm
\end_inset
\end_layout
\begin_layout Itemize
\series bold
Short Run
\series default
is assumed to range from 2 months
\series bold
to
\series default
18 months which is 17 different short term values.
\begin_inset VSpace 0.8cm
\end_inset
\end_layout
\begin_layout Itemize
\series bold
i
\series default
indicates all 1649 different possible combinations of Term Spread.
\begin_inset VSpace 0.8cm
\end_inset
\end_layout
\begin_layout Itemize
\series bold
t
\series default
indicates monthly data which ranges from 1995-01-30
\series bold
to
\series default
2018-10-31 which is 286 observations for every single combination of term
spread.
\begin_inset VSpace 0.8cm
\end_inset
\end_layout
\begin_layout Itemize
The same model was used to construct three different types of term spread:
\end_layout
\begin_deeper
\begin_layout Itemize
Yield Curve Term Spread
\end_layout
\begin_layout Itemize
Expectation Component Term Spread
\end_layout
\begin_layout Itemize
Term Premium Component Term Spread
\end_layout
\end_deeper
\begin_layout Standard
\begin_inset Newpage pagebreak
\end_inset
\end_layout
\begin_layout Subsection
Major Results
\begin_inset CommandInset label
LatexCommand label
name "2nd Section Major Results"
\end_inset
\end_layout
\begin_layout Subsubsection
Yield Curve Term Spread
\color black
\begin_inset Formula
\[
TS_{t}^{i}=y_{t}^{Long\thinspace Run}\thinspace-\thinspace y_{t}^{Short\thinspace Run}
\]
\end_inset
\color inherit
\begin_inset VSpace 0.8cm
\end_inset
\end_layout
\begin_layout Standard
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rotateOrigin rightTop
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\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Subsubsection
Expectation Component Term Spread
\color black
\begin_inset Formula
\[
TS_{t}^{i}=EXP_{t}^{Long\thinspace Run}\thinspace-\thinspace EXP_{t}^{Short\thinspace Run}
\]
\end_inset
\color inherit
\begin_inset VSpace 0.8cm
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\end_inset
\end_layout
\begin_layout Subsubsection
Term Premium Component Term Spread
\color black
\begin_inset Formula
\[
TS_{t}^{i}=TP_{t}^{Long\thinspace Run}\thinspace-\thinspace TP_{t}^{Short\thinspace Run}
\]
\end_inset
\color inherit
\begin_inset VSpace 0.8cm
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\end_layout
\begin_layout Subsection
Analyzing the Results
\end_layout
\begin_layout Subsubsection
Interpretation
\end_layout
\begin_layout Standard
In the results above, The x-axis indicates the time horizon which ranges
from 1995 to 2015, the y-axis indicates the long and short run combination
being considered, and the z-axis indicates the term spread coefficient.
The change in color from purple to yellow of the term spread shows the
increase in the term spread coefficient.
\end_layout
\begin_layout Itemize
\series bold
Yield Curve term spread,
\series default
shows how the term spread changes not only across time but also across
the long and short run combination being considered.
Almost all term spread combinations appears to invert before the early
2000s recession and 2008 financial crisis.
As we start taking values for short and long run yield curve that are further
apart the term spread shape appears to change by becoming wider.
\end_layout
\begin_layout Itemize
\series bold
Expectation component term spread,
\series default
shows similar results in that the term spread changes not only across time
but also across the long and short run combination being considered.
It appears to fall below -0.5 before 2000s recession and 2008 financial
crisis.
In the case of the expectation component, the wideness between the term
spread based on the short and long term combination appears to change over
time.
During 1995 combinations were not as wide as those after the 2015.
This might be because increase in technology for sharing and analyzing
information might have allowed people to better formulate expectations
about the long run interest rate compared to short run interest rate.
\end_layout
\begin_layout Itemize
\series bold
Term Premium component term spread,
\series default
shows similar results in that the term spread changes not only across time
but also across the long and short run combination being considered.
It does not appear to have any major indication before the 2000s recession
and 2008 financial crisis.
In the case of the term premium component, the wideness between the term
spread based on the short and long term combination appears to reduce over
time and invert after almost 2012.
This might be because after 2012, bond risk premium on long term yield
started to reduce as people started to expect stable inflation and economic
growth over the long run.
\end_layout
\begin_layout Subsubsection
Major Takeaway
\end_layout
\begin_layout Standard
The Term spread shape appears to change across different combinations of
short and long run horizon.
This indicates that the different combinations would have varying explanatory
power in describing movements in the economy.
\begin_inset Newpage pagebreak
\end_inset
\end_layout
\begin_layout Section
Does the dispersion of spreads have any explanatory power for understanding
the Term Premium Term Spread?
\end_layout
\begin_layout Subsection
Spread Dispersion Model Setup
\end_layout
\begin_layout Standard
\color black
\begin_inset Formula
\[
Dispersion_{t}^{i}=TS_{t}^{i}\thinspace-\thinspace TS_{t}^{10y\thinspace3m}
\]
\end_inset
\end_layout
\begin_layout Standard
\color black
\begin_inset Formula
\[
TP\_TS_{t}^{i}\thinspace=\thinspace\alpha^{(i)}\thinspace+\thinspace\beta^{(i)}Dispersion{}_{t}^{i}\thinspace+\thinspace\varepsilon_{t}^{(i)}
\]
\end_inset
\end_layout
\begin_layout Standard
This model calculates the dispersion of all possible yield curve term spreads
from the 10 year minus 3 months term spread.
The 10 year minus 3 months term spread is the most widely used term spread.
I hypothesized that dispersion of all other term spread combinations from
this standard term spread might have explanatory power for understanding
movements in the term premium term spread.
This is because dispersion of the term spread might influence the bond
risk premium resulting or term premium resulting in an affect on the term
premium term spread.
\end_layout
\begin_layout Itemize
\series bold
i:
\series default
{1,1649}
\begin_inset VSpace 0.8cm
\end_inset
\end_layout
\begin_layout Itemize
\begin_inset Formula $TP\_TS_{t}^{i}$
\end_inset
indicates the Term Premium Term Spread
\begin_inset VSpace 0.8cm
\end_inset
\end_layout
\begin_layout Itemize
\series bold
t
\series default
indicates monthly data which ranges from 1995-01-30
\series bold
to
\series default
2018-10-31 which is 286 observations for every single combination of term
spread.
\end_layout
\begin_layout Standard
\begin_inset Newpage pagebreak
\end_inset
\end_layout
\begin_layout Subsection
Major Results
\end_layout
\begin_layout Subsubsection
Regression of Term Premium term spread against Dispersion and EXP
\color black
\begin_inset Formula
\[
TP\_TS_{t}^{i}\thinspace=\thinspace\alpha^{(i)}\thinspace+\thinspace\beta_{1}^{(i)}Dispersion{}_{t}^{i}\thinspace+\thinspace\beta_{2}^{(i)}EXP\_TS{}_{t}^{i}\thinspace+\thinspace\varepsilon_{t}^{(i)}
\]
\end_inset
\color inherit
\begin_inset VSpace -0.9cm
\end_inset
\end_layout
\begin_layout Standard
\series bold
\size scriptsize
\lang british
\begin_inset ERT
status open
\begin_layout Plain Layout
% Table created by stargazer v.5.2.2 by Marek Hlavac, Harvard University.
E-mail: hlavac at fas.harvard.edu % Date and time: Fri, Apr 12, 2019 - 4:12:30
PM
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