The term structure of the interest rate has become in the past few years an overwhelming fertile
grounds which includes a lot of research into the effects or influence of the various macro-
economic variables such as inflation, income and the what snots .in this chapter, we shall delve
into the theoretical and empirical analysis on how the yield spread future change in real interest
rate as well as the yield spread future change in the inflation relationships is made. Some other
general studies or inquires related to this study will be made.
2.1 The Theoretical Literature
A simple study of the theoretical aspects of the research will be made known as well as some
theories of some prominent economists will be put forward so as to make known what the yield
curves and its related aspects are all about. We shall also discuss the nature and the character of
the yield curves and the rationale for the link between the yield spread and real interest rate as
well as inflation changes
2.1.1 Definitions of the term structure of interest rate.
According to Mishkin (2010), term structure of interest rate is the relationship among interest
rate of bond and their term to maturities. He talks about characteristics of bonds that influence
interest rates leading to the discussion about the default risk which occurs when the issuer of the
bond refuses or is unwilling to make interest payments or pay off face value when the maturity
of the bond is due.
2.1.2 Definition of Yield Curve
The yield curve has been described in diverse ways by various authors and economic scholars.
According to Nawalkha and Soto (2009), the term structure of interest rates, also referred to as
yield curve, is defined as a correlation between the investment yield and the investment maturity
period. Various literature use the yield curve and the term structure of interest rates
interchangeably. Mishkin (2010) pointed out that, a bond’ term to maturity also affects its
interest rate and the relationship among interest rates on bonds with different terms to maturity is
called the term structure of interest rates. He further defines the yield curve as the ‘description of
the term structure of interest rates’ and thus uses the yield curve and term structure of interest
rates interchangeably. To Martelli, Priaulet and Priaulet (2003), Bond yield or Term Structure of
Interest Rate (TSIR) is a series of interest rates ordered according to a certain due period. The
value and condition of the interest rate will determine the value and condition of the time
structure, which will finally result in yield curve. According to Jhinghan’s study (as cited by
Dzigbede, 2003), the term structure can be referred to as the ‘time structure’ or ‘maturity
structure’ as he used them interchangeable. He also asserts that the yield curve is a graphical
depiction of the relationship between yield and maturities of the same type of debt security.
These various authors seem to be saying the same thing even though they say it differently. The
yield curve therefore basically is a line graph that shows the relationship between bond yields
2.1.3 Types of yield curves
There are three types of yield curves based on their shapes. The shapes is also determined by the
relationship between interest rate and the yield to maturity. Actually, the shape of the yield curve
tells us a story. That is, the shape of a yield curve provides valuable information to investors as
to what other investors believe will take place in the fixed income market in the future (Prudent
Investments).These three are; the normal yield curve, inverted yield curve and the flat yield
curve and humped yield curve.
• The normal yield curve
The normal yield curve is upward sloping. This means, all else being equal, a bond with a longer
maturity pays a higher yield than the same bond with a shorter maturity (Warring, 2015). The
reason this type of situation is considered normal is that generally, longer term securities bear the
greatest investment risks and, as a result, “should” offer higher interest rates. (Prudential
Investment). The implication of an upward sloping yield curve is that investors expect the
economy to grow in the future. It is also signals that investors expect the economy to expand.
According to Prudential Investments, normal yield curve typically occurs when central banks are
“easing” monetary policy, increasing the supply of money and the availability of credit in the
• Inverted yield curve
An inverted yield curve has a downward slope. It occurs when long-term yields fall below short-
term yields. An inverted yield curve gives a signal that investors would expect the economy to
slow or decline in the future, and this slower growth may lead to lower inflation and lower
interest rates for all maturities. According to Prudential Investments, an inverted yield curve
typically indicates that central banks are “tightening” monetary policy, limiting the money
supply and making credit less available. An inverted yield curve has often historically been a
harbinger of an economic recession. Investors are willing to accept a lower interest rate now in
return for being locked in for years to come. (Prudential Investment)
• Flat yield curve
According to (Warring, 2015) this situation occurs when the yield of all maturities are close to
one another. He further added that this happens when inflation expectations have decreased to
the point where investors are demanding no premium for ‘tying’ their money up for longer
periods of time. Whenever an economy experiences a flat yield curve, it is a signal of a pending
or ongoing economic slowdown.
• The humped yield curve
The yield curve is said to be humped when short and long term rates are closer to each other than
with medium term rates (Warring, 2015). According to him, this generally happens there is either
an increase in demand, or decrease in supply of longer term bonds. The humped yield curve
indicates an expectation of higher rates in the middle of the maturity periods covered, perhaps
reflecting investor uncertainty about specific economic policies or conditions, or it may reflect a
transition of the yield curve from a normal to inverted, or vice versa. (Prudential Investment).
2.1.4 Factors that determine the yield curve
According to Culbertson (1957), there are four major factors that underlie the market’s relative
valuation of short-term and long-term debt. These are:
(1) The liquidity difference between long-term and short-term debt;
(2) The attractiveness of debts of different maturities on the basis of expected future changes in
(3) short-run effects of changes in the maturity structure of supply of debt coupled with rigidities
in the maturity structure of demand for it
(4) Differences in lending costs related to debt maturity.
Generally, most researchers agree that short-term bond is more liquid that long term bonds. This
fact compels some lenders to choose short-term debt, and induces others to prefer it. According
to Culbertson (1957), if there are limitations on the ability or willingness of debtors to do their
borrowing by short-term debt, this factor can thus result in a marginal lender preference for, and
lower yields on, short-term debt. In fact, it is clear that the ability of private borrowers to finance
their activities by short-term borrowing is subject to limitations (Culbertson, 1957). Long term
bonds thus have higher yield to maturity since it is relatively less liquid than short term bond
thus holder of long term, bonds have to be compensated with a premium called liquidity
premium( Mishkin, 2010). In effect, long term bonds would generally have a higher yield than
short term bonds causing the yield curve to be upward sloping.
Secondly, expectations of lenders and borrowers regarding future changes in interest rates, where
these exist, evidently must affect inducements to hold and to issue debt of different maturities
(Culbertson, 1957). Thus if people expect the yield to maturity of bonds to increase in the future,
they will generally prefer to hold long term bonds and if they expect it to fall in the future, they
will prefer to hold short term bonds. Culbertson (1957) however argued that, the behavior of
most borrowers and lenders is not ordinarily governed by such expectations. To Culbertson
(1957), other factors like the nature of their planning periods, characteristic timing of operations,
and other such details, as well as upon the interrelationship among individual patterns of activity
come into play.
In relation to third factor, Culbertson (1957) explained that, changes in the maturity structure of
supply of bonds, coupled with imperfect elasticity of demand for particular types of debt, must
have an effect on the term structure of rates, creating a structure different from that which would
exist with the same pattern of available bonds if a longer period of time were allowed for
With the last point Culbertson (1957) said that costs of acquiring and administering debt may
bear some systematic relationship to its maturity thus this would have to be a part of the theory
of the term structure of rates. Therefore if there are differences in lenders’ costs of evaluating,
acquiring, administering, and liquidating debt of different types, they must affect their net
returns, and thus should be reflected in the normal market structure of (gross) interest rates
2.1.5 Theories of Yield Curve
there are many theories to explain the nature and character of the yield curves and the influence
of certain macro-economic variables on the movements and shapes of these yield curves. The
expectation, segmented markets, liquidity premium and preferred market habitat theories have
single handedly tried to explain the behavior of the yield curve
There are some basic facts that term structure of interest rate must endeavor to explain as
revealed by Mishkin (2010). These facts are;
1. Interest rates on bonds of different maturities move together over time.
2. When short-term interest rates are low, yield curves are more likely to have an upward
slope; when short-term interest rates are high, yield curves are more likely to slope
downward and be inverted.
3. Yield curves almost always slope upward.
According to Mishkin (2010), the expectations theory has the ability to explain the first two
theories very well but falls short in explaining the third. The third fact is better explained by the
segmented markets theory despite its not been able to explain the first two facts. The liquidity
premium theory however has the ability to explain all three facts adequately since it is actually a
combination of the expectations and segmented markets theories.
• The Expectations Theory
Several scholarly works have been produced and published in the field of economics to
determine the underlying variables of the term structure of interest rates and yet, no consensus
has been reached (Van der Merwe & Molletze, 2013). The expectations theory is one of the
theories that attempt to explain the relationship between interest rates of different maturities.
According to Mishkin (2010), the commonsense proposition of the expectations theory is that,
the interest rate on a long-term bond will equal an average of short-term interest rates that people
expect to occur over the life of the long term bond. Long term rates are, therefore, the average of
the current and expected short term interest rates (Modena, 2008). Therefore, an increase or
decrease in yield represents an increase or decrease in short-term interest rates (Martelli, Priaulet
and Priaulet, 2003). In other words, short term interest rates shape the term structure of long
interest rates (Beechey et al., 2008).
John R. Hicks (1939) and Friedrich A. Lutz (1940) who developed the expectation theory argues
that the interest rate on a long-term debt tends to equal the average of short-term rates expected
over the duration of the long-term debt ( Culbertson, 1957). For example, if people expect that
the average short term interest rate for the next five years would be say 15%, according to the
expectations theory, the interest rate on bonds with five years maturity would also be 15%.
According to Cox, Ingersoll and Ross (1985), the expectation theory has been hypothesizes in
various versions but then in its simplest form, the expectations hypothesis postulates that bonds
are priced so that the implied forward rates are equal to the expected spot rates. Generally, this
approach is characterized by the following propositions (Cox, Ingersoll and Ross, 1985):
(a)The return on holding a long-term bond to maturity is equal to the expected return on repeated
investment in a series of the short-term bonds, or (b) the expected rate of return over the next
holding period is the same for bonds of all maturities.
Jhinghan’s study as cited by Dzigbede (2003) outlined the following assumptions as underlining
1. All investors have definite expectations with respect to future short term interest rates and
these expectations are held with complete confidence. All investors hold with certainty
the same expectations of how future rates are going to behave.
2. The objective of investors is to maximize expected profits and they are prepared to
transfer funds freely from one maturity to another in order to achieve this objective.
3. There are no costs associated with investment and disinvestments insecurities, meaning
there are no transactions costs.
4. The short-term and long term rates are adjusted for any differences due to risk and
5. Safe securities of various maturities are perfect substitutes in the portfolios of investors.
6. Investors are profit maximizes who hold such financial asset in their portfolios, which
maximize returns over the period they are held.
Mishkin(2010) describes the point on bonds of different maturities being perfect substitutes as
the key assumption behind this theory. This means an investor is often indifferent in choosing
long-term bonds or short-term bonds. Thus the expected returns for both short and long term
bonds must be equal.
According to Mishkin(2010) the expectations theory is explained by the expression below;
Int =( it+ite+1+iet+2+…+iet+(n-1) ) ÷n
That is, the interest rate of the interest rate of int on an n-period bond must equal the above
equation at time t. Mishkin(2010) further explains that in a more precise terms, the n-period
interest rate equals the average of the one period interest rates expected to occur over the n–
period life of the bond.
The expectations theory does quite a good job in explaining facts 1 that interest rates on bonds
with different maturities move together over time. Mishkin (2010) states that historically, short-
term interest rates have had the characteristic that if they increase today, they will tend to be
higher in the future. This means that when short-term rates rises people’s expectations of future
short-term rates will also rise. Because long-term rates are the average of expected future short-
term rates, a rise in short-term rates will also raise long-term rates, causing short and long-term
rates to move together (Mishkin 2010).
The expectations theory also explains fact 2 that yield curves tend to have an upward slope when
short-term interest rates are low and have a downward slope when short-term rates are high.
When the short-term interest rate is low, we will expect the next period interest rate to be high
thus the average of the two terms’ rates (that is, the current short term and the next period rates)
will be high relative to the current short term rate. In effect, long-term interest rates will be
substantially above current short-term rates, and the yield curve would then have an upward
slope. In the same way, if short-term rates are high, we will expect them to fall in the next term.
The average of the two terms’ rates (that is, the current short term and the next period rates) will
be low relative to the current short term rate. In effect, long-term interest rates will be
substantially below current short-term rates, and the yield curve would then have a downward