UNDERSTANDING THE YIELD CURVE
UNDERSTANDING THE YIELD CURVE1
Sunday Oladunni 2
SECTION ONE
Introduction
Yield is a major characteristic of fixed income securities/bonds in addition to
maturity, risk, coupon, tax characteristics and embedded options. Bond issuers,
investors and other market participants often pay close attention to yields on
debt securities or bonds for several reasons, including price determination,
portfolio selection, profit expectations, cost considerations and value
maximizations, amongst others. Investors consider specific bond yield and the
general market yield dynamics when carrying out analysis to guide their decisions
on which bond is worth their funds. The yield curve contains information about
risk/return characteristics of specific bonds, and this allows investors to align such
characteristics with their individual risk/return appetites or profiles. Thus, investors
are guided by the yield curve to take decisions on which end of the curve they
would want to play. The yield on an investment can be expressed as the discount
rate that ensures the present value of its cash flows equal to its initial price. The
yield on an investment, usually denoted by r, is the interest rate by which the
bond price equation is satisfied. It is expressed as follows:
N
Cn
M

n
1  r n
n 1 1  r 
P
Where r = yield or interest rate
P = price of the bond
Cn = the coupon payment
M = maturity value or redemption value
n = maturity (life of the bond expressed in terms of months, years etc.)
1+r = discount factor
1
This publication is not a product of vigorous empirical research. It is designed specifically
as an educational material for enlightenment on the monetary policy of the Bank.
Consequently, the Central Bank of Nigeria (CBN) does not take responsibility for the
accuracy of the contents of this publication as it does not represent the official views or
position of the Bank on the subject matter.
2
Sunday Oladunni is an Economist in the Monetary Policy Department, Central Bank of
Nigeria.
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UNDERSTANDING THE YIELD CURVE
1.1
Definition of Basic Concepts
1.1.1 Par Value
The par value of a bond is also known as principal or face value. It is the amount
that the bondholder gets at maturity. Par value is the amount payable to the
bondholder upon maturity. A N1,000.00 par value bond will be worth N1,000.00
when it matures. If yields rise above the rate of a bond’s coupon, the bond will
sell at a price below its par value (at a discount). Conversely, should interest rates
decline; the bond will sell above its par value (at a premium).
1.1.2 Coupon
Coupon is the rate of interest on a bond. It is called the coupon rate. The rate
does not change over the life of the bond, except for bonds which have variable
interest rate associated with an external index.
1.1.3 Maturity
Maturity is the period between when a bond is issued and when the par value of
the bond is returned to the bond investor. The maturity of a bond spans through
the entire life of the bond. It may be 3, 5, 7, 10, 15, 20, 25 years or more. At
maturity, the bond investor or holder gets back the par value or the redemption
or maturity value of the bond. At this point, the issuer’s obligations to the
bondholder terminates as all transactions due to the bond becomes
extinguished.
1.2
Yield
Yield refers to the interest earning that the investor receives on a bond till
maturity. Yield on debt security is the return that investors earn from committing
funds to purchasing the security. It is the annual rate of return on investment in a
particular fixed income security. To an issuer or seller, it represents the periodic
interest payments made to bondholders throughout the life of the bond. Yield on
government bonds are key market interest rates, which influence the cost of
borrowing in the rest of the domestic and international market. For investors and
issuers, bond yields are very useful in the derivation of interest rates employed to
value securities. Often, they serve as benchmarks for establishing the minimum
yields that investors would require in order to invest in non-guilt edged securities.
The bond interest rate fixed at issuance is known as coupon yield, while the
current yield refers to the bond interest rate expressed as a percentage of the
current price of the bond. Yield to maturity represent the estimate of returns that
an investor receives, if the bond is held to maturity.
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UNDERSTANDING THE YIELD CURVE
1.3
Yield Curve
Yield curve was defined by Mishkin (2010) as “a plot of yields on bonds with
differing term to maturity but the same risk, liquidity and tax considerations”. A
yield curve is a chart, graph or table of figures that shows the yield on bonds of
the same credit risk with different maturities. It is a description of the relationship
between yield on short term bond usually referred to as short end of the yield and
long term bond also referred to as long end of the yield. “In other words, it is a
snapshot of the current level of yields in the market, and not a historical graph”
(Choudhry, 2006). It indicates whether, and by how much, yields on long-dated
securities differ from the yields on short-dated securities. It is the graphical
depiction of the relationship between bonds of the same or similar credit quality
and their respective term to maturity. The yield curve is different from the term
structure of interest rates. The term structure is the relationship between the
annual interest rates on pure discount securities or zero coupon bonds and their
respective terms to maturity. The yield curve provides information on where the
bond market is trading at a current time and reflects the perception of investors
about the future. The yield curve is known to be a good indicator of the future
level of the market; thus, acting as an indicator of future yields.
The yield curve is usually constructed from a table of yields on bonds of the same
credit rating with their respective term to maturity. Table 1 represents the yield
table of FGN bonds as at December 31, 2013. It shows the period of time
remaining for each bond to the redemption date, and the prevailing yields (or
interest rates) at which the bonds traded as at December 31, 2013.
Table 1. A Typical Federal Government of Nigeria (FGN) Bond Yield Table as
December 31, 2013
FGN Bond Yield Table: Dec. 31, 2013
Term to Maturity (TTM)
0.22
0.25
0.5
0.74
1.31
2.63
3.32
3.58
3.67
4.42
5.5
5.81
8.08
14.91
15.39
15.89
16.57
Yield (%)
12.13
12.20
12.70
12.43
13.40
13.10
13.05
13.07
13.07
13.06
13.06
13.09
13.20
13.22
13.22
13.22
13.22
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UNDERSTANDING THE YIELD CURVE
As evident in table 1 and figure 1.1, bonds with closer redemption dates have
lower yields; while bonds that are far from their maturity dates as at the date of
trading, tend to assume higher interest rates.
Figure 1.1: Federal Government Bond Yield Curve as at December 31, 2013
The yield curve, usually, reveals the range of returns in form of returns that bond
investors may expect on their investments over different spectrum of maturity
terms. The normal shape of the yield curve is generally known to be upward
sloping; indicating the relatively higher yields that investors in long term bonds
would generally expect to earn as a compensation for parting with liquidity for
longer period of time. The higher yield associated with the longer end of the yield
curve, is expected to compensate bond investors for the risks and uncertainty
that tend to intensify, as maturities go further into the future. This risk reflects
concerns about interest rates movements, inflation environment, exchange rate
volatility, government policy and other socio-economic and political eventualities
that are increasingly difficult to predict, as the time horizon extends into the
future.
A yield curve for government bonds equates that of risk-free investments. A zerocoupon yield refers to the interest rate or yield on a bond that does attract
coupon payment. Examples of pure discount securities or zero coupon bonds
include the Nigerian Treasury Bills (NTBs) issued by the CBN, on behalf of the
Federal Government of Nigeria (FGN) and the Open Market Operation (OMO)
bills used by the CBN, for liquidity management purposes.
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UNDERSTANDING THE YIELD CURVE
1.4
Types of Yield Curves
Generally, four types of yield curves can be identified in most bond markets. Each
yield curve type captures the sentiments of investors about key macroeconomic
variables such as interest rates movements, inflation and issuer’s credit ratings,
among others. The information content of each yield type reflects risk perception
along the entire maturity spectrum of the bonds.
1.4.1 The Normal Yield Curve
A normal yield curve rises as it moves to the right from left. With the normal yield
curve, longer maturity bonds attract higher interest rates while bonds with shorter
maturity term attract low interest rates because of risks perception and
considerations peculiar to the time horizon. As shown in figure 1.2, a normal yield
curve depicts a situation in which the longer the maturity of a particular bond,
the higher the yield required by investors. The curve is derived when investors are
rewarded for holding longer maturity bonds in the form of higher potential yield.
Higher yield on longer maturities indicates compensation for playing on the
longer end of the curve, and an extra inducement for investors to commit funds
to longer term investments.
Figure 1.2: Normal Yield Curve
Normal
(Positively Sloped)
Yield
Maturity
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UNDERSTANDING THE YIELD CURVE
An example of the series of interest rates on bonds with their respective term to
maturity is shown in table 2 below:
Table 2: Bonds’ Term to Maturity and their respective yields
Schedule of a Normal Yield Curve
Term to Maturity
Yields (%)
1 month
9.89
2 months
9.94
3 months
9.98
6 months
10.00
1 year
10.21
2 years
10.25
3 years
10.29
5 years
10.89
7 years
11.00
9 years
11.25
10 years
11.95
13 years
12.08
15 years
12.92
17 years
13.25
20 years
13.55
From table 2, lower yields are matched with bonds with lower term to maturity,
while higher yields are associated with bonds with longer term to maturity;
indicating that yields on bonds are ceteris paribus an increasing function of
respective maturities.
1.4.2 The Inverted Yield Curve
An inverted yield curve declines as it moves to the right from left. The curve
reflects an interest rate environment in which debt instruments with long term
maturity, have yields lower than those on debt instruments with short term
maturity but are of similar or same credit rating. It is sometimes referred to as
negative yield curve. The information content of the inverted yield curve is such
that it has often been seen as a predictor of an imminent downturn in economic
activities. In an environment where short-tenured bonds attract higher interest
rates compared to long-tenured bonds, investors’ sentiments tend to indicate a
pessimistic long-term stance, and that the yields associated with long-term bonds
will maintain a downward trend. When long-term yields fall below short-term
yields; investors effectively anticipate that the economy would slow down in the
future, and this lower growth may result in lower inflation expectations, hence
lower interest rates for all maturities.
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UNDERSTANDING THE YIELD CURVE
Figure 1.3: Inverted Yield Curve
Inverted
(Negatively Sloped)
Yield
Maturity
However, it has been argued that it is the law of demand and supply, rather than
imminent economic downturn, which makes borrowers attract lenders without
paying more attractive interest rates on the longer end of the yield curve. In
essence, when the demand for debt instruments increases, the price would rise
and the debtor would offer lower interest rates.
1.4.3 The Flat Yield Curve
This is obtained when yields of different maturities are the same or close to one
another. The flat yield curve seems almost like a straight line curve, in which yields
on long- and short-term bonds are almost similar. A flat yield curve indicates a
near-zero interest rates sensitivity to respective terms to maturity for bonds of
similar or same credit rating. The main feature of the flat yield curve, is that there
are no interest rates differentials between bonds on the short and long ends of
the yield curve.
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UNDERSTANDING THE YIELD CURVE
Figure 1.4: Flat Yield Curve
Yield
Flat
Maturity
The condition obtains when inflation expectations have become lowered to the
point where investors require no premium for committing funds for longer term. As
it is with the inverted yield curve, when the yield curve changes from normal to
flat, it depicts generally a sign of an impending or ongoing recession in the
economy.
1.4.4 The Humped Yield Curve
This yield curve shape results when yields on long- and short-term bonds are
somewhat similar, while yields on medium-term bonds are high. This forms a hump
shape. A humped yield curve initially rises, but then falls for longer maturities. It
tends to indicate investors’ sentiments or expectation of higher interest rates
around the middle of the maturity periods under consideration. This could be a
reflection of investor uncertainty about specific macroeconomic variables or it
may connote a movement of the yield curve from a normal to inverted, or vice
versa.
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UNDERSTANDING THE YIELD CURVE
Figure 1.5: Humped Yield Curve
Yield
Humped
Maturity
1.5
Other Types of Yield Curve
1.5.1 Yield-to-Maturity Yield Curve
This type of yield curve is derived by plotting the yield to maturity against the
respective term to maturity for a group of bonds that are usually of the same
class. This type of yield curve is based on the assumption of a constant rate for
coupons in the life of the bond at the redemption yield level. The assumption is
considered however, unrealistic since most market rates fluctuate over time. Thus,
it would be impossible to guarantee zero re-investment risk, as it is common with
zero-coupon bonds.
1.5.2
The Par Yield Curve
Par yield is the coupon rates for bonds that are priced near par or at par. The par
yield curve, therefore, represents the plot of yields to maturity against their
respective terms to maturity for current bonds trading at par. It is not usually
applicable in secondary market trading, but enjoys the patronage of corporate
bonds issuers and others, in the primary market.
1.5.3 Zero Coupon Yield Curve
The zero coupon yield curve depicts graphically, the interest rates (or rate of
return) on bonds with zero coupon and different maturity periods. The zero
coupon yield curve is used as a simple tool for arriving at the price of many fixed
income bonds. Whereas, the zero coupon bond does not pay interest, it
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UNDERSTANDING THE YIELD CURVE
however, has a discount to its face value. The investor receives one payment to
cover the face value of the bond at its maturity, which sums up to the principal
invested and the interest over the life of the bond. The bond yield might be
computed based on the amount of discount and time to maturity.
1.6
Information Content of the Yield Curve
1.6.1 Flattening Yield Curve
The yield curve is said to be flattening when interest rates on instruments with
longer term to maturity are falling, while yields on instruments with lower term to
maturity are either unchanged or are rising. A flattening yield curve indicates
decrease in the gap between yields on short-term bonds and yields on long-term
bonds. This makes the curve become less steep. Also, the contracting gap shows
that yields on long-term bonds are declining faster than yields on short-term
bonds. For instance, if on February 1, the 3-year bond is at 8.0% and the 10-year
at 10.0%; on March 1, the 2-year bond yields 8.1% while the 10-year yields is 10.5%.
The gap reduced from 210 basis points to 50 basis points, resulting in a flatter yield
curve.
A flattening yield curve provides indication about expectations on future inflation
trend. It suggests that economic agents expect inflation rate to decelerate in
future. In a high inflation environment, investors ask for higher long-term yields to
compensate for the possible reduction in the value of their assets; given that
inflation reduces the future value of an investment. The premium narrows when
the concern about inflation is benign. Also, a flattening yield curve may occur if
investors anticipate a slower economic growth in the future. The yield curve may
also flatten when short-term interest rates rise, in anticipation that the Central
Bank will raise the benchmark interest rate, or pursue a policy stance that would
induce a general rise in interest rates.
1.6.2 Inverted Yield Curve
If the yield curve flattens to the extent that short-term interest rates exceed long
term interest rates, the curve is said to have become “inverted.” Inverted curve is
a common predictor or precursor of a recessive period. If investors believe that
interest rates are going to fall in future, they may be prepared to tolerate low
rates now, in order to avoid further decline in the interest rate structure in the
economy. In the case of the United States, more than 2/3 of the time, the
economy has slid into a recession within two years following the onset of an
inverted yield curve. Inversion in the yield curve impacts greatly on fixed-income
investors. Ordinarily, long-term investments tend to attract higher yields; owing to
the fact that investors risk their funds for longer time period, they receive higher
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UNDERSTANDING THE YIELD CURVE
payouts. The implications of inverted yield curve on various stakeholders are as
follows:
1.6.2.1 Investors
Yield curve inversion removes the risk premium for long-term investments,
conferring higher returns on investors in short-term investments. When the spread
between Government bond and risky alternative investment vehicles has fallen
to its lows, it is usually easier to invest in lower-risk investment vehicles. In such
cases, investing in government bonds attracts a yield similar to the yield on junks
and other debt instruments, but devoid of the risk inherent in these investment
vehicles. Money market instruments and funds placements may also be
attractive; particularly when they are paying yields comparable to those on a
long tenured government bonds.
1.6.2.2 Profit Margins of Companies
In an environment with an inverted yield curve, profit margins on corporations
that borrow cash at short term interest rates and lend at long term interest rates
fall. However, inversions in the yield curve tend to impact less on healthcare firms
and consumer staples, which do not depend on interest rate. The nexus is clearer
when an inverted yield curve happens in the run up to recession. This makes
investors prefer defensive stocks, such as those in the tobacco, oil and food
industries, which are usually less subject to economic downturns.
1.6.2.3 Consumers
An inverted yield curve affect consumers too, especially home buyers who
finance their assets with adjustable rate mortgages (ARMs), which have interest
rate structure that are periodically adjusted based on movements in the short
term rates. When short term rates are higher than long term rates, payments on
ARMs tend to trend upward. In this case, fixed-rate loans are deemed to be more
attractive than adjustable rate loans. In the same way, credit lines are affected.
These imply that consumers would have to commit a larger fraction of their
incomes to servicing existing debt obligations. This reduces disposable income,
impacts negatively on welfare and constrains economy as a whole.
1.6.2.4 Fixed-Income Investors
Inversion in the yield curve has profound impact on fixed-income or bond
investors. Ordinarily, long-term investments tend to attract higher yields; owing to
the fact that investors commit fund for longer time horizon, they are
compensated with higher returns. Inverted yield curve removes the premium on
risk associated with long term investments, thus ensuring that investors obtain
better returns with short term investments. When the spread between FGN bonds
(a Nigerian risk-free investment) and high-risk corporate bonds are at historical
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UNDERSTANDING THE YIELD CURVE
lows, it is often easier to invest in lower-risk investment vehicles. In such situations,
government securities offer yields typical of those on corporate bonds, junk
bonds and other debt instruments, but devoid of the risk associated with these
vehicles.
1.6.2.5 Equity Investors
When yield curve assumes an inverted shape, the profit margins of organizations
that lend at long term and borrow at short term rates declines. Also, hedge funds
are usually compelled to assume higher risk appetite for profit considerations.
Inversions in the yield curve tend to have less impact on healthcare firms and
staple products, which are not dependent on interest rate. This link is usually
made clear when yield curve inversion precedes a recession. Investors usually
respond to this by turning to defensive stocks in the tobacco, oil and food
industries that are often less affected by economic downturns.
1.6.3 Steepening of the Yield Curve
The yield curve is said to be steepening, when interest rates on instruments with
longer term to maturity are rising, while yields on instruments with lower term to
maturity are either unchanged or are declining. Rise in the gap between shortand long-term bonds shows that yields on long term bonds are surging faster than
those on short term bonds or, sometimes, that yields on short term bonds are
declining even as longer term yields are rising. For instance, if on April 1, the 7year bond yield is at 10.0% and the 10-year at 11.0%; on May 1, the 7-year bond
yields 10.1% while the 10-year yields 11.5%. The difference went from 10 basis
points to 50 basis points, leading to a steeper yield curve. Steepness in the yield
curve essentially reflects investor expectations about rising inflation and stronger
economic performance, given that the expectation about long term growth
tend to induce rise in the demand for longer term capital.
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UNDERSTANDING THE YIELD CURVE
SECTION TWO
Yield Curve Measures
The yield curve can be measured in several ways, including through the coupon
yield, yield to call, current yield, yield to maturity, yield to worst, yield to put, cash
flow yield, gross redemption yield and cost of borrowing to the issuer.
2.1
Coupon Yield
Coupon yield is the interest rate stated on a fixed income security or bond,
expressed as a fraction or percentage of the principal, face or redemption value.
It is also called coupon rate. For example, a N1,000 bond having a coupon yield
of 5 percent would pay N50 a year. A N1,000 bond with a coupon yield of 7 per
cent will pay N70 a year. Ordinarily, the N50 or N70 or any amount to be paid out
is made bi-annually on any particular bond.
2.2
Nominal Yield
The Nominal yield is the (annualized) amount of the coupon, which is a fixed
percentage of the par value. Nominal yield represent the interest rate that an
issuer pays to par value. This rate is fixed, and only paid to par. Unlike current
yield, it does not vary with the market price of the security. Nominal yield may
equal total net rate of return or may not. Assume a fixed income security (bond)
was bought above par or at a premium; the entire yield to maturity will be lower
than the stated coupon rate. If a bond has an 8.0% nominal yield or coupon and
was purchased at a premium of N103 (N1030), then the yield-to-maturity (YTM)
will be lower, because the 8.0% interest is only paid to the N1000 par. The N30
premium does not attract interest and cannot be redeemed at par. So, an 8.0%
bond at a premium does not really "yield" 8.0% in the given example. A bond
bought at a discount will have the reverse effect on yield. The yield-to-maturity is
higher for a discount bond, given that the investor earns interest on par even if
the investor paid under par.
2.3
Current Yield
Current yield can be derived by dividing bond’s coupon yield by the price of the
bond. Assuming an investor had a bond worth N1,000 face value with a coupon
rate of 5 percent, which would equate to N50 a year. If the bond sells now for 98
(at a discount for N980), the current yield would be N50 divided by N980 = 5.10
percent. If that same bond’s price rises to a premium of 103 (selling for N1,030),
the current yield is N50 divided by N1,030 = 4.85 percent.
The current yield provides rough and possibly entirely inaccurate estimate of the
return that can be earned on a bond over the coming months. For example,
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UNDERSTANDING THE YIELD CURVE
today’s current yield multiplied by 30 will not provide a good estimate of how
much income a bond will generate in the next month. This is because of the
volatility associated with the current yield at any point in time.
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UNDERSTANDING THE YIELD CURVE
SECTION THREE
Theories of Yield Curve
The yield curve is affected by a host of factors. These include factors such as
monetary policy stance, inflation concerns, liquidity preference, money and
capital market conditions as well as economy-wide fundamentals. Three theories
are known to have provided explanations for the major yield curve dynamics.
3.1
The Expectations Theory
This hypothesis posits that bond investors’ expectations define the course of future
interest rates. It holds that, the yield curve shape derives from market participants’
expectations about interest rate. The expectation of increasing short term interest
rates in the future is a reason for a rising yield curve, while the expectation of
declining short term interest rates in future will cause long term rates to lie below
current short term rates and yield curve will decline. According to the theory, long
term interest rate is a representation of the geometric mean of present and future
interest rates that should prevail over the bond’s maturity. Two main versions of
the expectations hypothesis exist. These include: (a) the local expectations
hypothesis; and (b) the unbiased expectations hypothesis.
3.1.1 The Local Expectations Hypothesis
The local expectations hypothesis posits that bonds of the same class and
different terms to maturity will have the same expected holding period rate of
return. By this postulate, a 6-month bond and a 20-year bond will yield the same
rate of return, on average, over a given holding period. Thus, if an investor intends
to hold a bond for six months, he will receive the same return irrespective of the
specific bond he purchased. Generally, yields on bonds with longer tenor are on
average higher than those with short tenor. Longer-dated bonds are expected to
offer higher yields to provide compensation for the higher price volatility (risk)
associated with them. The local expectations hypothesis is in contrast with the
conventional notion that (risk averse) investors require higher returns as a
compensation for assuming higher risk. The local expectation hypothesis does not
offer any explanation on the shape of the yield curve.
3.1.2 The Unbiased Expectations Hypothesis
The unbiased or pure expectations hypothesis explains that present (current)
implied forward rates are good predictors (or unbiased estimators) of future spot
interest rates. The assumption underlying the hypothesis holds that investors
behave in a manner that removes any advantage of holding instruments of a
particular maturity. With a normal yield curve, the hypothesis holds that the
market expects spot interest rates to increase. Also, an inverted yield curve
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UNDERSTANDING THE YIELD CURVE
indicates that spot rates are expected to decline. If short term rates are expected
to increase, then longer yields would be higher than shorter ones to reflect this.
However, if the case was different, investors would only purchase the shorter
dated bonds and roll over the investments upon maturity. Also, if rates are
expected to decline, longer yields should be lower than short yields.
3.1.3 The Naïve Expectation or Globally Equal Holding Period Return
This naïve expectation hypothesis states that the expected return from any
strategy for any holding period are equal.
3.1.4 The Return to Maturity Expectation
It states that the expected return of holding any zero coupon bond, has to be
equal to the expected return obtainable by running over a sequence of single
period bonds, over the same horizon.
3.2
Market Segmentation Theory (MST)
The MST states that bond investors and issuers tend to reflect preferences for
specific maturity terms in their decisions on investments in fixed income securities.
The theory states that, based on the preferences, the financial markets are
divided into a number of smaller markets, with market dynamics unique to each
segment determining the equilibrium yields for each segment. The main factors
that determine yield for a maturity segment are the market interplay, reflected in
the demand and supply conditions characterizing the segment. For instance, a
high grade corporate bond yield curve could be segmented into three markets,
namely: short term, medium term and long term. The companies’ demand for
short-term assets such as inventories and accounts receivables determines the
supply of short term corporate bonds like commercial paper, while the demand
for short term corporate bonds would emanate from investors in search of short
term investment opportunities. The demand for short term bonds by investors and
the supply of such bonds by companies would ultimately determine the rate on
short term corporate bonds. In the same vein, the supply of medium term and
long term bonds would come from companies wanting to finance their medium
term and long term assets such as equipment purchases, acquisitions and plant
expansion, while the demand for such bonds would come from establishments
such as insurance companies, pension funds and mutual funds who have long
term liabilities. Similarly, the demand and supply of intermediate funds and long
term debts determines their respective equilibrium interest rates.
The Market Segmentation theory emphasizes the uniqueness of markets, noting
that the rates determined in one maturity segment of the bonds market, do not
influence the other maturity segments of the market. Thus, the medium and long
term bonds markets do not affect short term market and vice versa. The
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UNDERSTANDING THE YIELD CURVE
assumption of independence in the different maturity segments of the market is
based on the premise that investors and borrowers are desirous of matching the
maturities of their assets and liabilities. In addition, bond holders and issuers’ desire
to dodge market risk, result in hedging activities that leads to bonds market
segmentation along maturity spectrum.
3.3
Liquidity Preference Theory
The theory posits, fundamentally, that most investors or lenders express
preference for short term bonds over long term bonds, and for short term liquidity
compared to long term return, owing to concerns about high price and yields
volatility that abounds in the longer time horizons. The liquidity preference theory,
otherwise known as the liquidity premium theory, stresses that long-term interest
rates do not only reflect investors’ perceptions about future interest rates, but also
include a premium for holding long-term bonds referred to as the liquidity
premium. The premium provides compensation for the added risk undertaken by
bonds investors in parting with their money for a longer period and the greater
price uncertainty associated with longer maturities. Consequently, owing to the
term premium, long dated bonds yields tend to be higher than short dated yields,
and the yield curve slopes upward. According to the theory, long term yields are
higher to compensate for both liquidity and risk premia associated with holding a
security over the long term.
In addition, yields on long term bonds are usually higher, because prices of short
term bonds tend to oscillate less in response to interest rates variations than do
the prices of long term securities. If interest rates rise during the life of a bond and
a lender has to liquidate it before it matures, the capital loss on a short-term bond
will be much less compared to that on a long-term bond. Consequently, bonds
with shorter maturity tenors tend to attract larger quantum of investible funds and
are usually associated with lower yields. On the other hand, bonds with longer
maturity tenors tend to attract smaller supply of loanable funds and are usually
associated with higher yields. To encourage long term lending, borrowers must
offer higher rates, which represent the liquidity premium needed to overcome
lenders’ preference for liquidity. The condition of inverted yield curve is not
explained in the theory.
3.4
Preferred Habitat Theory
The preferred habitat theory incorporates features of the other three theories of
yield curve. It connotes that market participants with their individual investment
orientations exhibit interest in specific areas of the yield curve and that, they can
be attracted to take positions on bonds from other points on the maturity
spectrum, provided they are sufficiently incentivized. According to the theory, if
returns expected to be earned by investors deviate from their preferred
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UNDERSTANDING THE YIELD CURVE
maturities, or habitats become attractive enough, institutions will deviate from
their preferred maturities or habitats. For instance, if the expected returns on longterm bonds exceed those on short-term bonds or securities by an attractive
margin, banks and other non-bank investors will lengthen the maturities of their
assets.
The hypothesis relies on the realistic assumption that economic agents or investors
will assume additional risk in return for additional expected returns. Beyond
regulatory requirements, both market expectations and the institutional factors
stressed in the segmented markets theory affect the yield curve. Thus, banks may
at some times invest in longer-dated bonds when the price of the bonds falls to a
certain threshold, ensuring that the return on the bonds justifies the risk associated
with holding them. In the same vein, long-term investors may be induced to hold
short-dated debts, based on the same consideration of high expected returns on
such bonds. In essence, the theory posits that all investors have specific zones on
the maturity spectrum in which they want to operate, which is their preferred
habitat. However, they can operate outside their preferred habitat if they are
sufficiently compensated through higher returns. The theory recognizes investors’
flexibility to operate outside regulatory or legal requirements to invest in wherever
in the yield curve they perceive that value lie. This may attract sanctions in a
regulatory environment where such investments switching are not allowed.
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UNDERSTANDING THE YIELD CURVE
SECTION FOUR
Yield Curve Strategies
Investors adopt yield curve strategies to cash in on perceived opportunities for
returns maximization based on the slope of the curve.
4.1
Bullet Strategy
In this strategy, a bond portfolio is formed in a manner that allows the maturities of
the assets to be highly concentrated at a particular point of the yield curve. An
example of a bullet strategy is having a portfolio of bonds in which most of the
bonds would mature exactly in 20 years. Bullet strategies tend to outperform
when the yield curve steepens.
4.2
Barbell Strategy
In this strategy, the maturities of the securities in a portfolio are structured at two
extreme points on the yield curve. For example, an investor with a portfolio of
mainly of bonds that are to mature in 7 and 25 years is adopting this strategy.
Barbell strategies are known to perform well when the yield curve flattens.
4.3
Ladder Strategy
Under this strategy, the portfolio includes equal amounts of different securities
maturing from time to time, usually yearly. Investors essentially employ this strategy
to match a steady liability stream and manage the re-investment risks they are
exposed to in a low interest-rate environment.
4.4
Riding the Yield Curve
Holders and managers of fixed-income portfolios can maximize returns by riding
the yield curve. An investor is said to be riding the yield curve when he buys a
longer-tenored security and disposes it prior to maturity in order to gain from
specific interest rate environments. For instance, when the yield curve is relatively
steep and interest rates are stable in relative terms, the investor will profit by riding
the curve rather than holding a short-maturity instrument to maturity. The risk
involved in riding the yield curve, however, is the greater interest rate risk an
investor faces as interest rates becomes volatile. If an investor is riding and interest
rates or yields rise significantly, he will incur a capital loss on the riding position. If
the investor had held positions on instrument that matched his investment horizon,
he would have earned a positive return.
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UNDERSTANDING THE YIELD CURVE
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UNDERSTANDING THE YIELD CURVE
SECTION FIVE
Uses of Yield Curve
5.1
A leading Indicator of Economic Conditions
The yield curve has often been an impressive leading indicator of economic
conditions, signaling to investors, policy makers and other economic agents
about an impending economic downturn and reflecting the market expectation
about future economic conditions.
5.2
Benchmark for Pricing Securities with Similar Characteristics
The yield curve may be used as a basis for fixing the price of many other securities
with similar characteristics. For instance, given that the Federal Government of
Nigeria (FGN) bonds are expected to be risk-free, corporate bonds and
municipal bonds, which do entail credit risk, are priced with higher yields. For
instance, a 5-year, high-quality corporate bond could be priced to yield 2.0%, or
200 basis points, higher than the 5-year FGN bond.
5.3
Indicator of Yield-Maturity Trade-Offs
The yield curve is used to indicate the prevailing trade-off between maturities
and yields that fixed income investors face. It reflects the gain or loss associated
with a particular investor’s decision to alter the maturity of his portfolio. Given a
positively sloped yield curve, for instance, an investor may be able to achieve
higher expected annual yield on a bond portfolio by extending the average
maturity of his portfolio. Although, prices of bonds on the longer end of the yield
curve tend to exhibit higher volatility, thus, creating greater risk of capital loss.
5.4
Detecting Overpriced and Underpriced Securities
Yield curves are also used by investors to determine securities that are temporarily
overpriced or underpriced. This particular use derives from the fact that, at
equilibrium, the yields on all securities with similar risk characteristics should lie
along the yield curve at their appropriate maturity spectrum. In an efficient
market, it is expected that individual securities’ deviations from the yield curve will
be transitory; such that investors act swiftly upon identifying a security whose yield
lies momentarily below or above the curve. If a security’s yield is above the yield
curve, it signals to investors that the security is at the moment underpriced relative
to other securities of the same maturity features. Other things being equal, this
represents a buy signal, which some investors will exploit to drive the price
upward toward the yield curve.
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UNDERSTANDING THE YIELD CURVE
Conversely, should a security’s yield stay momentarily below the yield curve, it
shows that the security is temporarily overpriced, because it has a yield that is
below those of other securities with the same maturity. Some holders of such
security would sell it, leading to a fall in its price and drive its yield back up toward
the yield curve.
5.5
Uses by Financial Intermediaries
The shape of the yield curve is important to financial intermediaries like the
deposit money banks. Generally, a rising yield curve appeals to these institutions,
given that they mobilize funds through short term deposits and lend a large
proportion of the funds on medium-to-long term basis. The steeper the slope of
the yield curve, the larger the margin between lending and borrowing rates and
the higher the prospect of profitability for the depository institutions. On the other
hand, if the yield curve starts to flatten out, this would alert portfolio managers to
take actions towards managing the ensuing risk of loss.
5.6
Forecasting Interest Rates
Yield curve can be used to forecast the future course of interest rates in line with
the expectations theory. It provides bondholders with information about the
future trajectory of interest rates. With an upward sloping yield curve, the investor
could be advised to consider investment vehicles that would help him divest from
bonds and long dated securities to assets whose prices are less sensitive to
interest rate volatility. On the other hand, a downward sloping yield curve would
suggest the probability of near term decline in interest rates and a rise in the
prices of bond provided the forecast of lower rates materializes.
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UNDERSTANDING THE YIELD CURVE
SECTION SIX
Yields and Bond Prices
The association between yield and bond price is a negative one. A rise in the
required yield on a bond would lead to a fall in the bond’s price; and a fall in the
bond yield will lead to a rise in bond’s price. When this relationship is illustrated
graphically, it takes the following shape in figure 6.1 below.
Figure 6.1: Bond Yield and Price Relationship
Bond
Price
Price – Yield
Relationship
Bond Yield
Figure 6.1 indicates that when bond price goes up, yield goes down and vice
versa. It shows that the bond’s price and its yield are inversely related. The buyer
of a bond wants to earn high yields. The moment he purchases the bond at a
high yield, he has already locked in the interest rate, and so he would be hoping
the price of the bond rises to enable him cash out by selling the bond in the
future.
6.1
Monetary Policy and the Yield Curve
Monetary Policy is the use of some policy measures by the monetary authority like
the Central Bank of Nigeria (CBN) to influence credit conditions and control the
supply of money in an economy. The main goal of monetary policy is the
attainment of non-inflationary growth. Monetary policy tools include interest rate
(i.e. monetary policy rate), Open Market Operations (OMO), Cash Reserve
Requirement (CRR) and exchange rate, amongst others. Monetary policy can be
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UNDERSTANDING THE YIELD CURVE
contractionary or expansionary. Contractionary monetary policy is aimed at
restricting the growth of credit and money supply in the economy. A
contractionary monetary policy measure is intended to control inflation and
prevent deterioration of asset values and attendant socio-economic
consequences. On the other hand, expansionary monetary policy increases
money supply and encourages credit expansion in the economy. Expansionary
monetary policy measures are usually employed to stimulate growth and combat
unemployment via reduction in interest rates in the expectation that easy credit
would encourage businesses expansion.
Monetary policy affects the yield curve slope in a number of ways. A tight policy
stance, characterized by contractionary monetary policy measures, tends to
cause short-term interest rates to rise. The yield curve in response to a tight policy
stance shifts upward. On the other hand, a loose monetary policy induces a low
interest rates environment, which tends to shift the yield curve downward.
Inflation expectations play a major role in yields determination for long-term
bonds. When market expectation about future is high in the future, bond investors
will require a higher yield to compensate them for the expected loss in the value
of the long term bonds at maturity. Thus, in the wake of high inflation
expectations, yields on longer maturity bonds spikes up, whereas a short maturity
bonds do not rise as much, resulting in a steeper yield curves.
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UNDERSTANDING THE YIELD CURVE
SECTION SEVEN
Conclusion
Bond market participants often pay keen attention to yields on debt securities or
bonds for several reasons. The understanding of yields dynamics of specific
bonds, market or its segments is useful in price determination, portfolio selection,
profit expectations, cost considerations and value maximizations, amongst others.
A yield curve depicts the relationship between yield on short term bond and long
term bond. It reflects the range of yields that debt investors may expect to get on
their investments over a set of maturity terms. It is normal for the curve to be
generally upward sloping. This indicate the relatively higher yields that investors in
long term bonds would generally expect to receive in exchange for investing
capital for longer period of time.
The different shapes assumed by yield curves, represents the interaction between
market forces influenced by prevailing perception about market fundamentals,
expectation about key macroeconomic variables and reaction to the monetary
policy environment. Investors adopt yield curve strategies to cash in on perceived
opportunities for returns maximization based on the slope of the curve. The yield
curve may be used as a leading indicator of economic conditions and also as a
benchmark for pricing many other fixed-income securities. The monetary policy
stance at any point in time has significant influence on the yield curve. A tight
monetary policy generally tends to shift the yield curve upwards while a loose
monetary condition depresses the yield curve.
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