Introduction

In the current economic situation, where the interest-rates world-wide are at
historical lows, and due to a 2008 mortgage crisis, many investors switched from
debt derivatives into a government obligations, where the security provides a stable
fixed income return, compared to an equity market where the fluctuations of the
stock prices can be hardly predicted and the dividends payout are not stable. In
many cases investors require stable returns and looking at investment at the
government obligations, but there are many factors that have to be looked at and
there is a need of a bond yield factor analysis so that investors know at which
factors to look during the analysis of the opportunities (^{Diebold, Piazzesi and Rudebusch, 2005}). There are a plenty of
studies available that answers the questions on the presence of the factors that
influence the corporate bond yields (^{Israel,
Palhares, & Richardson, 2017}; ^{Bai,
Bali and Wen, 2019}), These study shows the factors that have a
significant influence on the government obligations yields. Financial institutions
have sufficient resources to hire the analyst that can perform investment analysis
on the government obligations, where the private investors are not possessing with
such funds. This study provides the factors and magnitudes with which the bond
characteristics contribute to the yield to maturity, which can be used in the
investment analysis by private investors and institutional at the same time.

In many papers the key topic of the research is focused on corporate bonds, but not
to much on government ones. Especially, when the obligations contribute to a large
proportion of investors' portfolios (^{Bai, Bali and
Wen, 2016}; ^{Vukovic et al., 2020a};
Moinak et al., 2020b). What makes a research based on government obligations to be
an interesting topic, especially in the current market conditions? In Canada the
volume of quarterly bond outstanding has been growing over the period from 2009
until 2015, where the average volumes outstanding grew approximately on 50% over
this period, accounted to the 70 billion of Canadian dollars in government debt
placed on the market in 2015 (^{Fontaine, Garriott,
and Gray, 2016}). Where the convertible bonds are also popular and the
amount outstanding increased almost three times over the period of 2012-2015,
accounting to 157 billion Euros. The current market situation makes the topic of
government obligations to be a very important, as many funds are poured into this
asset, as bank deposits are at its lows and the stock returns are under a great
uncertainty due to an unpredictable behavior.

Due to a crisis many investors suffered from illiquidity during the pick of it, so
that liquidity risk started to be one of the key aspects in investment analysis and
also can provide a significant level of returns (^{Huang, Huang and Oxman, 2015}). In many cases the government obligations
are bought not only by institutional investors and financial institutions, but also
purchased by the central banks world-wide. In 2012 the European Central Bank
possessed 17% (42.7 bln. Euros) of the total amount outstanding of the Greek
government obligations available (^{Trebesch and
Zettelmeyer, 2018}). Many researchers focus on the liquidity factor
exclusively, where this paper takes into account the existing work on the liquidity
premiums and adds an understanding of other factors that are significant in
determination of the bond returns, providing the breakdown of yield to maturity
composition.

There are a plenty of bond characteristics such as: coupon payments, coupon
frequencies, amount outstanding, credit ratings, liquidity, maturity and the issuer
country. The term structure of interest rates provides a theory of the about the
maturity premiums, which explains that investors obtain an extra return for
possessing the risk during a longer period of time (^{Bodie et al., 2013}).

Many of the existing studies analyze the effect of the changes in the agency ratings
and the possible concerns in the financial markets about the reliability and the
significance of the credit ratings (^{Cooke, &
Bailey, 2015}; ^{Baum, Schafer and Stephan,
2016}) what became an important topic which is highly discussed, due to a
major failure in 2008 during the mortgage crisis. However, the actual magnitude of
the affect that the credit rating premium brings to investors is not analyzed. The
market players are left only with the theoretical approach without possessing the
average market behavior which can greatly simplify the investment analysis. Also, as
there has been a major financial recession worldwide, the current state of the
financial market is under the great concern and the study explains the current
behavior of the bond returns providing an inside in the relation of the credit
ratings and bond yields.

This paper provides an OLS regression (based on the cross sectional data at the current period of time) of bonds yield to maturity and the macroeconomic factors, which provide the coefficients that explain the effect of each significant indicator on the yield to maturity of the government obligation in United States (US) and European Union (EU). This could be used to explain the interrelation between the characteristics and the returns and show which premiums are higher, what makes it important to pay attention to them making the investments. Also, as there always a risk-return trade-off, the coeffect in the model represent the higher risk associated with the premium impaled in the yields; as well as, checking the difference in the debt markets between the US and EU markets. As the popularity of the government obligations investment is growing, both in the private and institutional divisions, as the bank deposits are losing its attractiveness due to a lower return. The factor analysis of the bond yields is useful for investors by providing the simple method of investment analysis to obtain a desired level of return. Also, financial markets worldwide have changed significantly due to a couple of the financial crises and increasing political tensions, makes it important to check the current composition of the bond yields and the method which is used hear can be applied when the current results are outdates. Regression model which is used in this study has a good fit with the data, what shows that the method can be implied to other economies and can implied during the investment opportunity analysis and portfolio composition to check the premiums implied in the bond returns.

Literature review

In the past years the financial situation in the world has changed dramatically and
the investors a constantly seeking for the low-risk stable investments. Due to the
changes in the economic situation there is a need to examine the key factors that
affect the returns on such investments. As many studies propose, in the period of
declining interest rates, even negative in some cases, the investors are constantly
looking for opportunities to perform a yield pick-up on the foreign markets, despite
the fact that the higher yields provides often more risk; or investors choose to go
for longer duration investments that reward its holders for a longer period of
exposed risk (^{Ammer et al., 2018}). Recently,
there has been a work done with the help of time-series analysis that contributed to
the research of the liquidity risk on the high-yield bonds affect before and after
the crisis period, where the results showed that liquidity risk is crucial
especially in the bond pricings (^{Zeng, 2018}).
In many cases, the investors that choose to pursue with the government obligations
in portfolio, tend to hold to a maturity, as there is almost twice the number of buy
orders on the debt market compared to a sell orders (^{Schultz, 2001}). There has been a research in the sphere of searching the
factors that responsible for the bond returns (^{Driessen, Nijman,. and Melenberg 2000}) have proposed a multi-country
model that takes into a currency hedged returns, where the key factors that were
included is the risk measures. The topic of the rating agencies announcements and
issuer grading especially the way it affects the prices on both the stock market and
debt market. ^{Hite and Warga (1997)}, carried
out a research on the correlation between the changes in the agency gradings and the
bond prices, where the key results showed that the there is a response of the prices
especially when the grades drop down to a non-investment grade. In many cases,
researches have tried to provide an alternative measure of stock or bond liquidity,
at the same time checking the relationship between the liquidity measures and
returns or prices of assets. One of the proposed measures is a "latent
liquidity" which provides a possibility of forecasting a trading cost, volume
and other paraments associated with the asset. To be able to construct such index,
authors used not only a classic measures of trading prices, but also included
parameters such as: volume, amount outstanding, age, ratings and interest coupon
payments. (^{Mahanti et al., 2008})

As recent research shows, investments in government obligations can bring a higher
return than ordinary bank deposit. However, still investments in government
obligations will be stable and secure, especially when choosing the countries with a
high agency rating (^{Vukovic and Prosin,
2018}). In another study, done by ^{Choi and
Kronlund (2018)}, at the current low-risk environment many funds are in
the consideration of choosing the higher yield investments in the era of low
interest on the markets compared to their general standards of investment risk, and
could suffer from a lower liquidity and greater associated risk with the investment.
Due to these facts, there is a need to analyze the factors that affect the bond
returns, especially yield to maturity and which factors affect the returns the most;
so that investors can pay a great attention when they analyze the investment
opportunity in the government obligations. In many insurance companies, asset
managers are focusing on returns higher than a standard benchmark making them
hunting for yields and composing their portfolio with higher rate obligations
compared to the stable high rating investments, the common risk measure is an agency
rating of the obligation which are used to compare the safety of different issuers,
and they are not affected by liquidity and market conditions what explains the
stability and the returns on the government bond (^{Becker and Ivashina, 2015}). In the research done by ^{Burger and Warnock's (2018)}, the analysis of
investors preference in the choosing of government debt securities is done, where it
has been compared the percentages of the different currency securities in portfolios
and the results showed that the investors focus not only on the local bonds, but
also prefer to include the foreign investments in to portfolios. These investor
preferences can be supported by adding extra factors that will support the better
investment analysis, which will contribute to a higher return. There is a good proxy
for analysis of the general activity on the debt market where the amount outstanding
of the government obligations (^{Aggarwal, Bai and
Laeven,2018}).

To be able to pursue a high-quality investment analysis, investor has to obtain
high-quality information about the future investment. In the case of the of the
government debt securities, one of the crucial information parameters is default
risk. The common risk characteristic of the issuers is the agency rating which
provides a grade of the stability of the company or an organization (^{Faerber, 2001}). The agency rating grades affect
both stock and bond returns, where the low-bond rating provides an insight into
instability of the issuer and shows that the issuer with a high probability of
default; and if there was a change in the rating grade the market will react by the
changes in prices and yields of the changed issuer. During the 2008 world financial
crisis, many institutions and private investors suffered from unreliable information
that caused the world crisis to begin, which had a great effect on all economies
worldwide (^{Sinclair and Timothy, 2010}).
Despite, the nature of the rating grades during 2008, the stock and bond returns are
still having a significant correlation between the grades (^{Sehgal and Mathur, 2013}).

Robin ^{Greenwood and Dimitri Vayanos (2014)}
proposed that with increased supply of the long-term obligations, the price of the
security falls die to a decrease in overall demand, what can make a plausible factor
in the determination of the factors affecting the bond returns. The bond convexity
is another crucial factor that relates the bond prices and interest rates. It is a
crucial, as its duration makes the bond with a greater sensitivity of the debt
instrument prices to a change in interest rates (^{Malkhozov et al., 2016}). In another study, the relationship between the
bid-ask spread and the earning announcements on the equity market were done by the
^{Acker, Stalker and Tonks (2001)}. The
following relation was found that on the day of earnings announcements the bid-ask
spread is falling and volumes and return rises as follow. As the bid-ask spread can
largely affect the returns on the stock market, this relation has to be checked on
the debt market to study how the bid-ask spread can contribute to the returns and to
what extent.

The existing research suggests that the returns on obligations do not follow a simple
monotonic function, but rather have a pick at certain maturities (^{Fama, 1984}). This proposes that the yield to
maturity doesn't grow at the steady rate. However, it has picks at certain
maturities what shows a necessity to evaluate factors that affect the yield to
maturity. This will propose a clear investment analysis factors to maximize the
investors returns. Also, in the work done by ^{Hopewell and Kaufman (1973)}, the general rule is that for the longer
maturities .the changes in the obligation prices are larger if there is a change in
yields; however, there are some anomalies where the longer term maturities affected
less than the shorter maturities. Despite the anomalies mentioned by the previous
study, in the article by ^{Litterman and Schenkman
(1991)} three factors were proposed that explain the returns on the
government bonds, this factor are as follow: level, steepness and curvature; where
these factors are particularly useful for the choosing the hedging strategies
especially in the different market segments and instruments. The yield curve has a
major dependence on the coupon payment, if the coupon payments is changed by the
duration of the obligation, what affects the yield to maturity (^{Cumming, Fleming and Liu, 2015}). Also, yield to
maturity assumes that all coupon payments are paid at the set constant time and
evaluates the present value of all cash flows till the maturity (^{Asonuma, Niepelt and Rancière, 2019}).

The liquidity is a key concept in evaluation of investments in affecting the returns,
as also has a crucial aspect when the investor tries to sell the asset. However,
there is a crucial difference between the liquidity and liquidity risk. The
liquidity determines the possibility of a holder to sell a big volume of assets on
the market with low transaction costs and in short period of time, where the
liquidity risk refers to the relationship between the liquidity of the asset and its
expected return (^{Ng, 2011}). According to
^{Lin, Wang and Wu (2011)}, the liquidity
risk is not situation where investors will not be able to sell the obligation on the
market, but rather due to a low demand, they will suffer from a loss in prices due
to a lower demand, which follows by the lower prices on the market. The theory shows
that, the investor should be rewarded by a greater overall for choosing the asset
with lower liquidity compared to the more liquid assets. The liquidity premium is a
key determinant in the prices and returns not only on fixed-income markets, but also
on the money market. ^{Pástor and Stambaught
(2003)} have analyzed the relationship between the liquidity risk and the
expected stock returns and proposed, that if the asset is under a strong influence
of liquidity risk, it provides a higher returns for its investors; as well as,
proposed to check if such a behavior holds for other markets including the debt
market. Despite the fact the equity market tends to be more liquid than the debt
market, the liquidity factor in returns still plays a crucial role that needs to be
taken into account (^{Lin, Wang and Wu, 2013}).
^{Joslin and Konchitchki (2018)} proposed a
research that analyzed four factors that influence the term structure which included
the price of risk on the market, macroeconomic situation, volatility and
convexity.

The study of the bond agency ratings was discussed for a vast period of time, many
studies searched the effects of the bond ratings (^{Vukovic, Lapshina, & Maiti, 2019}) changes announcements on the stock
and bond returns. In 1977, Hite and Warga have discussed the results of the
downgrade of the ratings and its response to the market characteristics. ^{Chen, Lesmond and Wei (2007)} carried out the
research that cheeked couple of the liquidity measures which supported that the
liquidity is key factor on the yield-spreads, which are suitable not only for a
high-grade security but also for speculative level ones. The agency ratings play an
important role in the bond returns, with increasing grade level investors are faced
with less credit risk what lowers the premium on the investment (^{Spiegel, and Starks, 2016}). ^{Amihud and Mendelson (1986)}, argued that
liquidity is highly correlated with equity return, where the measure of liquidity
was proposed the bid-ask spread. The higher bid-ask spread shows that the asset
suffers from the liquidity problems and there should be a liquidity premium on this
asset (^{Wulandari, Schhfer, Andreas, and Sun,
2018}). In some cases, if there has been a downgrade of the country credit
rating, players on the market can start speculating on the fundamental information
regarding the country currency, what will force largely affect the bond returns as
well (Baum, Schafer and Stephan, 2014).

Despite the bond characteristics as major effect on their yields, there is also a
significant influence from the macroeconomic environment on the bond market. Many
researchers try to decompose the risk premiums in to specific categories. The topic
of government obligations and macro factors has been in particular interest in the
financial sphere, especially due to a couple of the severe financial crisis (^{Aguiar and Gopinath, 2004}). In many studies,
researchers test the methods of (^{Vukovic et al.,
2020b}, ^{Maiti et al, 2020a}) the
interest rates and the yield curve forecasting, what makes the interest rates to be
one of the key factors in the bond returns (^{Diebold
and Li, 2006}). Interest rates have a major effect on the bond yields,
which capture an extra return for the interest rate risk and that can be a good
factor in forecasting the bond returns (^{Ferson and
Harvey, 1991}). Central banks have regulatory instrument interest rates,
where the economies money supply can be controlled. By changing the interest rates,
countries adjust the cost of borrowings for firms and investors what reduces the
spending in the economy, while increasing the attractiveness of savings
(particularly the deposits and investments in bonds). This shifts the demand for
investment instruments (^{Engel, 2016}). In many
cases the interest rates is a good benchmark for the expected bond returns. With
increasing interest rates, yield to maturity of the government obligations grows by
dropping the prices due to a decreased demand for the government obligations and the
bank deposits become more attractive due to a higher interest rates paid on them
(^{Cox, Ingersoll and Ross, 2005}; ^{Lustig, Stathopoulos & Verdelhan, 2016}).
However, some countries implied negative interest rates in the economy. This measure
was implied to control the inflation in the economy and to increase the holdings of
the government obligations by the Central banks to keep the money supply constant in
the economy (^{Bech and Malkhozov, 2016}).

The country growth rate also has a significant influence on the bond returns (^{Ang and Piazzesi, 2000}). Economic growth has a
direct relation to the bond yields, with increasing economic prospective in the
economy, the stock investments are increasing its attractiveness due to an increased
return. Bond yields are also increasing, as the investors are switching from the
low-risk stable investments to a equity investments. Such situation forces the bond
yields to go up as well as demand is falling down and forces the prices to lower as
well (^{Nakamura, Sergeyev and Steinsson,
2017}). In some other studies, researchers proposed and successfully checked
that the behavior of the bond yield premiums has a significant predictive power of
the future economic growth and shows that there is a significant relation between
the economic growth and bond returns (^{Bleaney, Mizen
and Veleanu, 2016}).

Debt to GDP ratio is another commonly known macroeconomic factor that has a major
effect on the bond yields with a positive correlation (^{Lemmen, 1999}). With increasing debt burden by the government,
the investors that possess the state debt securities are subject to a higher default
risk as the government has a higher default and credit risk for which the investors
have to be rewarded (^{Blanchard, Mauro and Acalin,
2019}). As the current study suggests, with increasing debt to GDP in the
country, the government obligation returns increase in both long and short run
perspectives (^{Poghosyan, 2014}). From other
side, there are studies where the opposite economic theory is proposed, as the debt
to GDP increases the uncertainty in the economy increases as well, what shifts the
demand to the stable debt instruments increasing its prices what forces the returns
on the government to go down (^{Bernoth, von Hagen and
Schuknecht, 2012}).

Methodology

*Data description and sample statistics*

The dataset consists of 175 observation, from US and EU debt markets with a
wide-range of maturities with current prices as on 3^{rd} April, 2019.
The criteria for selection countries in EU (out of US data) in dataset where EU
countries with the highest number of issued treasuries. Maturities range from 1
month up to 600 months (50 years), where there 37 short-term government
obligation (less than or equals to a year until maturity) and 138 maturities
with time to expiration over one-year period. Figure 1 shows that in most of the countries have the long-term debt
outstanding, with some countries possessing only the long-term debt on the
market (Finland, Croatia, Latvia); where Sweden, Hungary, Norway and Greece
possess more short-term government obligation than the long-term ones. This data
shows that most of the countries are focused on the long-term issues of
government obligations and try to spread its debt burden over the years, by
varying the maturity. For example, US and UK (for the UK, data were collected in
period before Brexit) have a 16 long-term bond traded on the market, Germany and
France have 11 of them, where the short term bonds currently traded on the
market are much lower in quantities: US and France have 5 b bonds each, UK had 4
bonds and Germany has 3 bonds.

Combining the obtained data from Figure 1 and Figure 2, countries with the highest debt outstanding, possess the highest number of long-term bonds available on the market. The US and UK take up in the lead across the highest owners of debt, with 803 bln. USD and 666 bln. USD respectively; and with the highest number of long-term bonds outstanding which account to 16 long-term bonds for both countries. When looking at the countries that have only the long-term bonds trading on the market, the total amount outstanding of the debt in these countries is one of the lowest analyzed in this research. Latvia has only 0.5 billion dollars outstanding and the highest out of the countries which have only the long term debt is Finland with 4 long term bonds trading, which account to 20.9 billion dollars outstanding. Countries like Sweden, Norway, Greece and Hungary focus more on issuance of the short-term obligations that are traded on the market at the current period of time.

Due to a fact that bonds that are trading on the market at the current period of
time are issued on different dates and years, that bonds from the sample have a
different economic conditions on the date of issue, what affects their interest
rate payments. Due to this nature, in many cases bonds with shorter maturities
can provide a higher coupon payment than a bond with a longer maturity in the
same country (as a paradox by interest rate theory). In US market, the 30 years
bond can provide 3% coupon payments where the 14 years government obligation can
provide in coupon 6.25% (see more about similar paradox cases in ^{Bodie et al., 2013}). The same situation can
be seen in UK where the 12-year bond can provide 4.75% coupon payment, and a
30-year bond only 1.5%. Due to financial crisis during which countries raised
the interest rates, during this period, bonds with a higher yield where issued.
Soon after the crisis, economies came back to a more stable growth rate, the
interest rate lowered and the coupon payments declined back to a before crisis
period.

In the chosen sample, the greatest number of bonds account to the AAA rating, as the US and EU markets are one of the most developed and include one of the most stable countries world-wide. The rating for this research were divided into three sub-categories. The data collected from the market (Figures 3 and 4), shows that the categories are not evenly distributed and most of the obligations analyzed fell into the highest rating criteria and shows that on the analyzed markets, issuers are graded as the upper investment grades, where the most of the issuers and its outstanding debt is subject to a low default risk, providing the investment to be stable and moderately risk-free.

*Models*

In many papers that exist in the sphere of finance research, the key concern, is the way liquidity affects returns or prices of assets. The assets that are mainly analyzed are corporate debt instruments or the stock market, while this research is focused on the government obligations, which can be affected by the common measures in a slightly different manner.

The population that this research can be extended to is all government obligations in United States and European union that are traded at the current period of time on the debt market. The research is based on the convenience sample, as there care certain difficulties in the data collection. As the market data was collected from the Thomson Reuters terminal, in the export files for a certain number of countries the data is missing, forcing this observation to be excluded from the sample. Where the research sample contains 175 observations, with US market and 19 European Union countries. Each observation consists of a government obligation, with different characteristics which include the following factors that are considered in the regression model.

The data available on Thomson Reuters is related to the current trading prices on
the market from different brokers, with different dates of issues, what makes
the interest rate payments on those bonds to be inconsistent, as they all were
issued at different economic environments. To stabilize the returns the market
adjusts the prices on the assets to keep the overall return consistent with the
general market tendency. The key aim of this research is to find the key factors
that can describe the yield to maturity (YTM) of the government obligations in
EU and US, where the dependent variable will be YTM. YTM is taken as it is one
of the common measures that is used to describe the total bond return if the
asset will be held to the end of maturity (^{Bodie
et al., 2013}). Where the YTM is calculated by the following
formula:

Where the following notation is used:

YTM: yield to maturity

C: coupon

FV: Face value of bond

P: price of bond

T: time to maturity in years

In many cases the coupon payment is handed out to the holders more than once a year, in this case YTM has to annualize to the frequency of coupon payments a year. Using the following formula:

Where the following notation is used:

Adj. YTM: annualized YTM to the frequency of coupon payments per year

n: frequency of coupon payments per year

One of the key factors that is considered in this research, is the liquidity factor which has a variety of the possible indexes used. In one of the recent papers, done by Vadim Konstantinovsky and Bruce Phelps, the directors of the Quantitative Portfolio Strategy Group of Barclays in New Your, proposed a measure of "Liquidity cost score (LCS)" that is used by the traders, and represents liquidity measure as a trading cost. The following formula is proposed for the Liquidity cost score calculation:

(^{Konstantinovsky and Phelps, 2016})

Were all the prices are taken from the market data from brokers.

Occasionally, the prices on the market for the short-term treasury securities (in this research, the short-term US government obligations) are quoted in terms of its discount rates, so to obtain a price the discount should be converted to a dollar value. For the conversion the following formula is used:

(^{Fool, 2019})

Where the following notation is used:

Price: the bid/ask price calculated from the market discount rates

FV: face value of a bond

maturity: the proportion of the year that is left until maturity (days/360)

To be able to find the factors that affect the bond yield, the regression analysis is used. The method is going to be an Ordinary least squares regression with a multi-factor characteristic of bonds available on the market at the current period of time, to capture the current situation of the market behavior. The regression equation fits the following form:

Where the following notation is used:

α:the y-intercept

β1,j:the regression coefficent of the factor

Government obligation charecteristic: independent variables

ε: error term

(^{Koijen, Lustig and Van Nieuwerburgh,
2017})

The key concept of this research is to provide the key factors that influence the bond returns on the market at the current state of the world-wide economic situation. The Government obligation characteristics for the regression are chosen to be the following:

Characteristic | Description | Independent variable (Notation used in the regression equation) |
---|---|---|

Coupon rate | Interest rate paid on the bond in decimals | Coupon |

Agency rating | Dummy variable for the
agency rating grade, the rating are pulled into groups with the following characteristic. Upper investment level (AAA, AA+, AA, AA-), medium investment grade (A+, A,A-) and all the other grades are left to a lower and speculative grade pool. (Fitchratings.com, 2019) |
Uinv Minv |

Amount outstanding | Total value of the bonds
released on the market; the value is turned into billions. |
Amoinbil |

Liquidity index | Liquidity cost score | Liquidaskbidbid |

Maturity | Maturity in years | Maturityinyears |

Issuer country | In to the regression the
US dummy is added, to analyze if there is a significant difference in the returns between the EU and US markets. |
USdami |

Coupon frequency | Frequency of the coupon payments per year | Couponfrequencyperyear |

Source: arranged by authors

The factors in the table 1 above are used to determine the factors that determine the adjusted yield to maturity of the bond and used as a bond characteristic for the regression model. The second regression model is done on the basis of the macroeconomic factors, to determine the key independent variables that affect the yield to maturity, with the following regression equitation:

Where the following notation is used:

α:the y-intercept

β_{1,j}: the regression coefficent of the factor

Macroeconimic charecteristic: independent variables

ε: error term

(^{Koijen, Lustig and Van Nieuwerburgh,
2017})

The second model represents the macroeconomic factors affecting the bond yield returns, with the following factors that are used in the regression model:

Characteristic | Description | Independent variable |
---|---|---|

Inflation | Inflation in the country of the issuer | Inflation |

Interest rates | Interest rates in the country of the issuer | Interest rates |

Country growth rates | Country growth rates in the country of the issuer | Country growth rates |

Debt to GDP ratio | Debt to GDP ratio in the country of the issuer | Debt GDP |

The factors that are mentioned in the table
2 above are used as the macroeconomic characteristic in the
regression model that determines the effects of on the yield to maturity of the
government obligations in the countries chosen for the analysis. To be able to
accept the model there following test should be carried out. Test for the
heteroscedasticity: Breusch-Pegan test is used for the heteroscedasticity test,
where the null hypothesis is that the variance is constant, where the absence of
the heteroskedasticity is one of the key assumptions underlying the OLS for the
coefficients of regression to be unbiased (^{Breusch and Pagan, 1979}). Test for the multicollinearity: Absence
multicollinearity is another assumption that has to be present for the OLS. The
independent variables should be free from perfect correlation. The test for the
multicollinearity is variance inflation factor, which is a common measure of the
magnitude that the variance of the regression coefficients obtained from the
regression is increased due to multicollinearity. The VIF factor should be less
than 10, to be able to prove that the model obtained is free from the
multicollinearity (^{Chatterjee and Hadi,
2012}; ^{Belsley, Kuh, & Welsch,
1980})

Results and Discussion

For the first regression all of the factors have been chosen that should influence the YTM. Despite the fact that the R2, is 0.7804, what represents a good quality description of the dependent variable by it regressors. However, amount outstanding in billions is not significant in the model providing the p(value) of 0.538. The amount outstanding is not significant in describing the Yield to maturity, due to a low relationship with the interest payments and transaction costs for both buyers and sellers.

As the amount outstanding is not significant in Table 3, this variable is removed from the model. The second variable which is not significant in the model is the coupon payments. This is due to multicollinearity between the independent variables. In Table 3, the coupon frequency and the coupon itself have a strong correlation, with the value of 0.5657. All of the other factors have a correlation less than the absolute value of 0.5, what shows that other factors are applicable for the regression.

YTMadjysted | Coef. | Std. Err. | t | P>t | [95% Conf. | Interval] |
---|---|---|---|---|---|---|

Liquidaskbidbid | 1.066858 | .3295158 | 3.24 | 0.001 | .4162763 | 1.717441 |

Uinv | -.0083878 | .0018524 | -4.53 | 0.000 | -.0120452 | -.0047304 |

Minv | -.0105864 | .0026612 | -3.98 | 0.000 | -.0158405 | -.0053323 |

Amoinbil | -8.84e-6 | .0000143 | -0.62 | 0.538 | -.0000371 | .0000194 |

Coupon | .0005973 | .0004856 | 1.23 | 0.220 | -.0003614 | .0015559 |

Maturityinyears | .0003028 | .0000899 | 3.37 | 0.001 | .0001253 | .0004803 |

USdami | .0359305 | .002349 | 15.30 | 0.000 | .0312928 | .0405682 |

Couponfrequencyperyear | .0087554 | .0012082 | 7.25 | 0.000 | .0063699 | .0111409 |

_cons | .0021722 | .0017883 | 1.21 | 0.226 | -.0013586 | .0057029 |

According to the Table 4, and high correlation between the two factors one of the factors should be dropped from the regression model. As one of the key cash-flows associated with the investment in bonds is coupon payments, what should be taken into account in the model.

Correlation | Liquid~d | Uinv | Minv | Amoinbil | Coupon | Matur~rs | USdami | Coupon~r |
---|---|---|---|---|---|---|---|---|

Liquidaskb~d | 1.0000 | |||||||

Uinv | 0.2219 | 1.0000 | ||||||

Minv | 0.0169 | 0.4936 | 1.0000 | |||||

Amoinbil | 0.4171 | 0.0086 | 0.1205 | 1.0000 | ||||

Coupon | 0.2419 | 0.0257 | 0.0944 | 0.1005 | 1.0000 | |||

Maturityi~rs | 0.1567 | 0.2373 | 0.0374 | 0.0187 | 0.3518 | 1.0000 | ||

USdami | 0.1936 | 0.2533 | 0.1250 | 0.0751 | 0.2101 | 0.1013 | 1.0000 | |

Couponfreq~r | 0.0962 | 0.1127 | 0.0762 | 0.0841 | 0.5657 | 0.4581 | 0.3106 | 1.0000 |

If the coupon frequency is eliminated from the model, the following results are obtained as shown in table 5.

YTMadjysted | Coef. | Std. Err. | t | P>t | [95% Conf. | Interval] |
---|---|---|---|---|---|---|

Coupon | .0022136 | .0004919 | 4.5 | 0.000 | .0012425 | .0031847 |

Maturityinyears | .0005268 | .0000956 | 5.51 | 0.000 | .0003381 | .0007155 |

Uinv | -.0092671 | .0021034 | -4.41 | 0.000 | -.0134197 | -.0051145 |

Minv | -.0129305 | .0030072 | -4.30 | 0.000 | -.0188673 | -.0069938 |

USdami | .0393692 | .0025882 | 15.21 | 0.000 | .0342596 | .0444789 |

Liquidaskbidbid | .8826693 | .336635 | 2.62 | 0.010 | .2180895 | 1.547249 |

_cons | .00608 | .0019374 | 3.14 | 0.002 | .0022553 | .0099047 |

To accept the model the test on the heteroskedasticity and multiclonality are carried out. Where the zero hypotheses implies the homogeneity of variance and the alternative hypothesis is that the model implies heteroscedasticity.

As Table 6 shows, that p value is high and much greater than 0.05, what shows that the standard deviations in the error terms are not changing are not related with the independent variables. The second very important test that has to be carried out is the test for the multi-collinearity of independent variables, in the good model there should be an absence of the perfect multicollinearity. If the multicollinearity is present, one of the independent variables can be expressed as the linear combination of the other independent variable (one explaining variable can be predicted by the means of the other one).

Table 7 shows, the variance inflation factors
of the independent variables in the model. The values of the VIF factor are
moderately low. The multicollinearity is confirmed if the variance inflation factor
exceeds 10 (^{Chatterjee and Hadi, 2012}). As
the values of the VIF for the model are in average, 1.33 with the highest value 1.61
and the lowest 1.18 what confirms that there is no multicollinearity in the
regression constructed.

Variable | VIF | 1/VIF |
---|---|---|

Uinv | 1.61 | 0.621497 |

Minv | 1.39 | 0.717030 |

Coupon | 1.30 | 0.770607 |

Maturityi~rs | 1.26 | 0.791279 |

Liquidaskb~d | 1.24 | 0.805241 |

USdami | 1.18 | 0.845846 |

Mean VIF | 1.33 |

As the model obtained is free from multicollinearity and homoscedastic the model can
be taken as a fair approximation of YTM. Table
3 shows the coefficients of the independent variables. The p(value) of
the factors in model are all significant at 5% significance level (less than 0.05),
and the R2 of this regression model is high and accounts to the 0.7109. LCS: Has one
of the strongest effects on the yield to maturity. If the LCS is increased by the 1
unit, the YTM increases approximately by the 0.88 units in YTM if the other factors
are kept constant. This shows that of the bid-ask spread is increasing investors are
rewarded for a less liquid investment what shows that there is a liquidity premium,
and investors are rewarded for taken a larger liquidity risk. As on average the
bid-ask spread in the sample 0.15% and the average adjusted YTM is 1.2%. The
regression coefficient shows that if the LCS is increased by the 0.01% the YTM
increases approximately by the 0.0088% if the other terms kept constant. The
regression model supports the literature review, which shows that at the current
state of the financial market liquidity plays a crucial role in the bond returns.
The investors have a choice between the assets with different level of liquidity,
and they have to choose higher returns with a greater liquidity risk or a lower
return but have a higher chance of selling the asset on the market if they have a
need to do so. The Liquidity Cost Score (^{Konstantinovsky and Phelps, 2016}) is a good measure of liquidity for the
bond prices and is applicable for the investment opportunity analysis on the debt
market. This factor in the regression model supports the theory of the liquidity
premiums and adds to the study done by Pastor and Stambaught (2001), which were
interested in the further research of the liquidity influence in the debt
market.

The bonds are pulled into three pools, and the default value in the regression is the
Lower investment grade pools. According to the coefficients in the regression the
Lower investment pools yields higher return than the Upper and Medium investment
grades. The medium investment grades bonds have a Yield to maturity lower by
approximately 1.3% (keeping all the other factors constant), what confirms that with
the lower grading, investors face higher default risks for which they have to be
rewarded with the higher returns. However, the upper investment grades have yields
lower than the lower investment grades by 0.93%, but the difference between the
upper and medium investment grades is opposite. The medium investment grade yield
lower than the upper investment grade by 0.37%. The regression model supports the
general behavior of the bond yields with respect to the different credit ratings,
the lower investment grade yields higher than medium investment grade (^{Spiegel, & Starks, 2016}), but results in
the obtained model show that upper investment grade provide a higher return than a
medium investment grade. One of the key reasons that could be associated with such
behavior, is if some of the countries in the Upper Investment grades should have
been lowered in the agency ratings that is why the return for them is higher, but
there is often a delay in the updates of the ratings grades what could cause the
upper investment grade to yield higher than the medium grade if the other factors
are constant (^{Broto and Molina, 2014}). Also,
the American government obligations have yields significantly greater than the EU
market, and America is graded as the AAA, what can be the cause of the higher
returns in the Upper investment grade pool.

The coupon payment is one of the key factors that affect the yield to maturity, as the YTM adjusted calculates the compounding of the coupon payments and takes into account all of the reinvestments of the coupon payments. According to the model, if the coupon payment for the bond with all of the other factors the same by 1% the YTM increases by approximately 0.22%. Coupon payment is one of the key contributors in the yield to maturity which plays a role of the stable regular cash flow and contributes to the investors return. The literature review supports these findings and the results contributes to the studies, by providing the magnitude of the influence, at which the coupon payments affects the bond yields in the US an EU markets.

Maturity factor in the regression has the lowest standard error and supports the
maturity premium concept. As the maturity of the bond increases by 1 year, the YTM
increases by 0.05%, if the other factors are kept constant. The maturity premium is
paid to the investor as the default risk of the investment in government obligation
is exposed for a longer period of time and this risk should be rewarded with a
greater return. This is a general tendency in the economic theory, and supports the
term structure of interest rates, what shows that the maturity premium is one of the
crucial aspects in the bond returns. The risk associated with the longer holding of
the asset, is rewarded by the maturity premium which goes in line with the theory
proposed by the ^{Williamson (2016)}.

The American market has one of the highest returns among the top-rated countries.
Average YTM on the American bond market in the sample is 4.7% where on the European
market countries in the Upper investment grade yield only 0.55%, as many countries
in the EU have a negative yield. The regression coefficient on the US dummy confirms
that, on average if the other factors are kept the same, US government obligations
have a YTM higher by 3.9% compared to the EU securities. There is a significant
difference in the economic situation in the US market and on the EU. US government
has plans to increase the interest rates, decreases the buyout of the government
obligations, decrease its holdings of quantitative easing and raise more funding for
investments. Where the EU is under the pressure of low and negative interest rates,
large quantitative easing which force down the interest rates decreasing the money
supply, stable low-inflation and low growth rate (^{Ashworth, 2019}).

As the regression in Table 3, shows the bond characteristics factors that affect the yield to maturity of the government obligations. However, there are still macroeconomics factors that affect the bond returns, which are strongly related to the yields. The key macroeconomic conditions that affect the returns are inflation rate, country interest rates, country growth rates and percentage of debt with respect to the GDP. Constructing the regression with four factors mentioned (Table 8).

YTMadjysted | Coef. | Std. Err. | t | P>t | [95% Conf. | Interval] |
---|---|---|---|---|---|---|

Inflation | .0009366 | .0015055 | 0.62 | 0.535 | -.0020352 | .0039084 |

Interestrates | .0131431 | .0012884 | 10.20 | 0.000 | .0105997 | .0156865 |

Countrygrowthrate | .0038117 | .0016745 | 2.28 | 0.024 | .0005063 | .0071171 |

DebtGDP | .000139 | .000032 | 4.34 | 0.000 | .0000758 | .0002022 |

_cons | -.0112351 | .004666 | -2.41 | 0.017 | -.020446 | -.0020243 |

The results show that the inflation factor is not significant with a high p(value) of
0.535. The R^{2} coefficient is 0.694 what shows that the proposed
regression model is suitable and explains the yield behavior well. As the factor of
inflation is not significant, it is removed from the model.

YTMadjysted | Coef. | Std. Err. | t | P>t | [95% Conf. | Interval] |
---|---|---|---|---|---|---|

Interestrates | .0135181 | .0011367 | 11.89 | 0.000 | .0112744 | .0157618 |

Countrygrowthrate | .0036334 | .0016468 | 2.21 | 0.029 | .0003828 | .006884 |

DebtGDP | .0001254 | .0000233 | 5.37 | 0.000 | .0000793 | .0001715 |

_cons | -.0086808 | .002213 | -3.92 | 0.000 | -.013049 | -.0043126 |

Removing the insignificant factor form the regression, doesn't affect the R2 coefficient significantly, and the new value is 0.6933. All of the independent variables in the model are significant. However, test for the heteroskedasticity test (table 10), shows that the model obeys the homoskedasticity required for the OLS.

As the model doesn't go through the test for heteroskedasticity, to obtain unbiased standard errors of the Ordinary Least Squares coefficients for the model is to add the option robust to the model.

As the model in the table 11 is suitable for
the yield to maturity description with the chosen macroeconomic factors, in the
table 11 the following regression
coefficients are obtained. The regression model with the robust standard error,
shows a good with a high significance level of the factors. There is only one factor
that is on the boundary if significance, which is country growth rate and it is
p(value) in the model 5.5%. This p(value) is slightly greater that the general
accepted significance level of 5%, which for this model can be extended to 7.5% to
decrease a probability of the type 1 error, as the coefficient is significant of the
robust option is not implements. The country growth rate is commonly known for its
strong influence on the government obligations returns, what supports the use of the
factor in the model (^{Poghosyan, 2014}). The
last test that has to be carried out is the test for the multicollinearity (table 12), to be able to accept the model.

YTMadjysted | Coef. | Robust Std. Err. | t | P>t | [95% Conf. | Interval] |
---|---|---|---|---|---|---|

Interestrates | .0135181 | .001135 | 11.91 | 0.000 | .0112776 | .0157586 |

Countrygrowthrate | .0036334 | .0018782 | 1.93 | 0.055 | -.0000741 | .0073409 |

DebtGDP | .0001254 | .0000246 | 5.11 | 0.000 | .0000769 | .0001738 |

_cons | -.0086808 | .0019762 | -4.39 | 0.000 | -.0125817 | -.0047799 |

Variable | VIF | 1/VIF |
---|---|---|

Countrygro~e | 1.99 | 0.502003 |

Interestra~s | 1.98 | 0.504869 |

DebtGDP | 1.01 | 0.991264 |

Mean VIF | 1.66 |

Table 12 suggest that the constructed
regression model is free from the multicollinearity as all of the individual VIF are
less than 10 (^{Chatterjee and Hadi, 2012};
^{Belsley, Kuh, & Welsch, 1980}), and
the mean VIF of all of the independent variables is less than 10 consequently. What
shows that the model is suitable in describing the macroeconomic factors affecting
the yield to maturity of the government obligations in US and EU.

Country growth rate is strongly significant as the p(value) is 0 and has the highest
value of the t-statistic. The coefficient of the regression represents that country
with increased economic growth by 1% keeping the other entire factors constant, the
yield to maturity increases by approximately 1.35%. The coefficient represents that
countries that have a higher growth rate have a higher return on government
obligations. This result suggests that countries with higher growth rates attract
investors for its government obligations by increased returns. What also supports
the economic theory: if the economy is growing, more money is required to keep the
economic growth and a demand for the money is high, the funds are attracted form the
debt market to keep the economic growth (^{Nakamura,
Sergeyev and Steinsson, 2017}; ^{Bleaney,
Mizen and Veleanu, 2016}). Also, if the country is growing the returns on
equities are increasing and other assets look more attractive, demand from bonds is
shifted away and the prices are falling, what increases the YTM.

Interest rates are one of the key determinants in the bond yields, despite the fact
that the p(value) is higher than 5%, and so the implied assumption of the of the
7.5% significance level. The coefficient in the model shows that if the interest
rates in the country are higher by 1% with all of the other factors kept constant,
the YTM is increased by 0.36%. This nature is due to the fact, that when the
government is lowering down the interest to bust up the spending in the economy,
reducing the attractiveness of savings and busting up the spending in the economy.
What proposes to lower down the retunes on government obligations, and vise versa.
When the economy is growing rapidly and government needs to slow down and control
the stable growth, raised interest rates increases savings in the economy,
population uses deposits and debt instruments as the new conditions in the economy
provides higher returns. The results obtained from the model support the literature
review and economic theory (Cox, Ingersoll and Ross, 1985; ^{Lustig, Stathopoulos & Verdelhan, 2016}).

Debt to GDP ratio is also significant factor with a p(value) of 0 in the regression
model. If the Debt to GDP ratio increases by 1% the YTM increases by 0.0125%. With
increasing Debt to GDP government relies more on the debt finance and increases its
debt burden, to attract investors and as the government possess a higher debt
burden, the default and credit risks are increasing, for which the investors are
rewarded with the higher returns. With higher debt countries increase the
uncertainty in the economy and increase inflation rates, what bust up the country
risk premiums on the government obligations. Despite the general nature, if the debt
to GDP ratio increases the bond prices go up due to a higher demand on the market.
Demand grows due to a higher uncertainty in the economy and the stock investment
decrease its returns with increased risk, investors tend to shift to the fixed
income investments, what forces the yield to maturity to go down. In the sample
collected, US has one of the major parts and one of the highest yields to maturity
among the collected data, while possessing highest debt to GDP ratio, what provides
a controversial result to the general economic theory. What can be explained by the
changing economic environment and countries are just starting to recover from the
financial crisis possessing a high debt burden but already provide a higher bond
yield. That nature is due to fact that investors have to obtain a premium for
holding the government obligations of the country, which posses' higher debt burden
(especially in the cases when the debt is higher than GDP) what imposes risk such
investments. The results obtained disagree with the theory provided by the ^{Bernoth, von Hagen and Schuknecht (2012)} where
the debt to GDP negatively affects the yield to maturity; on the other hand, it
supports the theory provided by the ^{Blanchard, Mauro
and Acalin, (2019)} and ^{Poghosyan
(2014)}.

Conclusion

This paper contributes to the existing research, by adding the analysis on the current state of the economy to the prior research on the government debt instruments. The study provides an insight into the yield to maturity factors of the EU and US markets that compose the returns.

There are many factors for which the investors are rewarded with premiums to compensate for the risk that they are taking on investing in the government obligations. There are two main types of factor that are examined, which are the bond characteristics itself and the macroeconomic factors in the issuer country. The bond characteristic factors play a crucial role on the bond yields, as each factor is rewarded with a premium for the risk taken on by the investor. The contribution of this paper for financial players is that during the investment opportunity analysis, investors can decide which factors they want to focus to maximize its yield to maturity. One of the key factors is the liquidity, which plays a crucial role, and has a highest premium for taking the risk of illiquidity. Another major finding is that the upper investment level bonds provide a higher return than a medium investment level, what makes it attractive for the investor to choose the higher return but be exposed to a lower level of risk. Also, according to the analysis, the US provides a much higher return than in European zone, despite the fact that US is graded at a top credit rating. The best choice for the investor is to focus on the US government debt, which provides a highest yield, one of the highest liquidities and a wide range of maturities. Professional investors can consider their future returns in relation to portfolio diversification, and especially in relation to international investments (due to the reason that US bonds generated more returns in comparing with the EU bonds).

Policy maker can use models and results to predict their policy on interest rate. As a good addition to the study, the historical periods can be analyzed to track the trends and changes on the debt market. Also, this work only concentrates on the bonds returns, and doesn't quantify the risk associated with each premium that the model represents. The risk measure could be a good addition as the investors will be able to analyze factors not only on desired return, but rather on the risk-return trade off.