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

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**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

and maturities.

**2.1.3 Types of yield curves **

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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

economy.

• **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 **

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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

debt prices.

(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

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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

adjustment

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

(Culbertson, 1957)

**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

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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).

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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

the theory.

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

liquidity.

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

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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;

*I**nt **=( i**t**+i**t*^{e}*+1**+i*^{e}*t+2**+…+i*^{e}*t+(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

slop