Understanding Term Structure of Interest Rates: Theories and Factors

This report provides a comprehensive overview of the term structure of interest rates, which refers to the relationship between interest rates on short-term and long-term securities. It explains the concept of the yield curve, which graphically represents this relationship. The report delves into the factors determining the term structure, including risk preference, supply and demand conditions, and expectations and uncertainty. Furthermore, it explores various theories, with a detailed analysis of the expectations theory, including its assumptions, explanation, policy implications, and criticisms. The expectations theory posits that long-term interest rates are essentially an average of expected short-term interest rates. The report also touches upon the impact of government policies and central bank actions on the term structure of interest rates, and its limitations. This analysis aims to provide a clear understanding of the dynamics of interest rates and their implications for financial markets and investment strategies.

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Term Structure of Interest Rates: Meaning, Factors and Theories
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In this article we will discuss about: Meaning of the Term Structure of Interest Rates 2. Factors
Determining the Term Structure of Interest Rates 3. Theories.
Meaning of the Term Structure of Interest Rates:
The term structure of interest rates refers to the relationship between market rates of interest on short-
term and long-term securities. It is the interest rate difference on fixed income securities due to
differences in time of maturity. It is, therefore, also known as time-structure or maturity-structure of
interest rates which explains the relationship between yields and maturities of the same type of
security.
If two securities are identical in every respect except maturity, it is likely that they will sell in the market
at different prices (or yields or interest rates). Generally, their prices will change in the same direction. If
the short-term securities rise in price, the long-term securities will also rise in price.
People generally hold both short-term securities and they adjust their holdings of securities depending
on the relative yields. Usually the long term securities tend to fluctuate more in price than the short-
term securities, even though their yields do not fluctuate as much.
The relationship between yields and terms to maturity is depicted graphically by a yield curve. Figure 1
shows three yield curves. When short-term interest rates are above long-term interest rates, the yield
curve slopes downward, as the curve FF. When short-term interest rates are below long-term interest
rates, the yield curve slopes upward, as the curve RR. When the short-term yields equal long-term
yields, the yield curve is flat, as the curve HL.
Factors Determining the Term Structure of Interest Rates:

What determines the shape of the yield curve? There are three factors which determine the term
structure of interest rates. They are risk preference, supply and demand of securities, and expectations
and uncertainty. These factors determine whether short-term interest rates are above or below long-
term interest rates.
We discuss these factors as under:
1. Risk Preference:
Long-term security prices are sensitive to changes in interest rates because the chances to default are
higher on long-term securities as compared to short-term securities. Therefore, lenders prefer to lend
for short-term, if short-term and long-term securities have identical yields.
This would push up short-term prices of securities and bring down their yields. Hence the yield curve
slopes upward. On the other hand, borrowers prefer to borrow for long period because they will not
have to worry about rising interest rates or to renew their loans frequently.
They are, therefore, willing to pay more for long-term securities as compared to short-term securities.
This will also cause the yield curve to slope upward. Thus the preferences of both lenders and borrowers
lead to low rates on short-term securities and high rates on long-term securities, thereby bringing about
an upward sloping yield curve.
2. Supply-Demand Conditions:
When the supply of short-term securities falls and that of long-term securities rises, the short-term
interest rate comes down and the long-term interest rate is pushed up. The yield curve is upward
sloping and vice versa.
If the demand for securities is more in the short-run market and the supply is more in the long-run
market, this will lead to high short-term and low long-term interest rates, and the yield curve will be
downward sloping. The opposite supply-demand conditions will lead to an upward sloping yield curve.
3. Expectations and Uncertainty:

Other factors affecting the yield curve are expectations and uncertainty. The expectation of the rise in
the long-term interest rate explains that the short-term interest rate remains much below the long-term
interest rate for any length of time. This produces an upward sloping yield curve.
Further, certain risks and uncertainties may lead to the same results. For instance, if people expect war,
social disturbances, political upheavals, uncertainties, inflationary pressures, etc., they will not purchase
long-term securities except at a low price or low current yield.
Theories of Term Structure of Interest Rates:
Many theories have been put forth by economists to explain differences in the structure of interest rates
on short-term and long-term securities.
They are discussed as under:
1. The Expectations Theory:
The expectations theory regards future interest rates as the principal determinant of the present
structure of interest rates. The theory originated with Irving Fisher, was perfected by Hicks in his Value
and Capital, and is closely identified with Lutz.
Its Assumptions:
The expectations theory is based on the following assumptions:
1. All investors have definite expectations with respect to future short-term interest rates, and these
expectations are held with complete confidence.
2. The objective of investors is to maximise 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 disinvestment in securities. It means that there are
no transaction costs.
4. The short-term and long-term interest 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 maximisers who hold such financial assets in their portfolios which maximize
return over a period they are held.
7. All investors hold with certainty the same expectations of how future rates are going to behave.
Explanation:
Given these assumptions, the theory states that the long-term interest rate at any point in time
represents an average of expected short-time interest rates. Suppose a long-term security maturing
after three years sells at the short-term interest rate of 2 per cent in the first year, and that the expected
short-term interest rates in the second and third years are 3 per cent and 4 per cent respectively.
The long-term interest rate on this security will be the average of the short-term interest rates over the
three years, that is 3 per cent (=2 per cent + 3 per cent+4 per cent=9 per cent/3). If the interest rate on
the short-term security for the first year is expected to decline by 1 per cent the long-term yield on the
three-year security will be 2.67 per cent (=1 per cent+3 per cent+4 per cent=8 per cent/3). On the other
hand, if the interest rate is expected to increase by 1 per cent on the three-year security, then the long-
term yield will be 3.33 per cent (=2 per cent+3 per cent+5 per cent=10 per cent/3).
The expectations theory holds that differences in yields on securities of different maturities are due to
the fact that the market expects the interest rates on different securities to be the same over an equal
period of time.

If this is not the case, the investor will buy security of one maturity by selling security of another
maturity that he expects to provide him the highest yield. It is this “arbitrage procedure” (buying
security of one maturity and selling of another maturity) which brings the equality of expected yields of
different maturities.
According to Warren L. Smith, “Investors generally have repressive interest rate expectations. That is to
say, at any particular time they have an opinion regarding the level of interest rates they regard as
normal, and as short-term rates rise above or fall below this level, they expect them to regress back
towards this normal level. Thus, as rates rise above normal, investors expect them to fall; and as rates
fall below normal, investors expect them to rise.”
This relationship implies that:
(a) When short- term rates are expected to fall, current short-term rates will be above long-term rates
and the yield curve will be negatively sloped, and
(b) When rates are expected to rise, current short-term rates will be below long-term rates and the yield
curve will be positively sloped. By the same reasoning, when the short-term rate is at approximately the
level judged to be normal and is expected neither to rise nor to fall, rates for all maturities will
approximate a horizontal line.
These relationships between short-term and long-term interest rates are illustrated in Figure 1 where
time to maturity, short or long-term, is taken on the horizontal axis, and yield or interest rate is taken on
the vertical axis.
In the first case, when the current short-term rates are above the long-term rates and are expected to
fall, the yield curve FF is negatively sloped. In the second case, when the current short- term rates are
below the long-term rates, and are expected to rise, the yield curve RR is positively sloped. In the third
case, when the current short-term rates equal the long-term rates and the short-term rates are
expected neither to rise nor to fall, the yield curve HL is a horizontal line.
Time to Maturity and Yield

Prof. Lutz calls these yield curves as expectations curves which represent “the line up of the’ subjective’
long rates which correspond to people’s expectations after the latter have changed.” The key to the
expectations theory is that both short and long-term securities are perfect substitutes for each other in
the portfolios of investors.
If the supply of long-term securities goes up and that of short-term securities goes down, it makes no
difference as far as yields are concerned. Long- term securities will be exchanged for short-term
securities with no change in yields as long as expected future short-term rates are unchanged.
Its Policy Implications:
The policy implications of this theory are that if the government wishes to replace a given amount of
long-term debt with an equivalent amount of short-term debt, such a policy will have no impact on the
Structure of interest rates. This is because both long-term and short-term debts are regarded as perfect
substitutes in the portfolio of investors.
This is shown in Figure 2 (A) and (B). Panel (A) depicts the demand and supply of short-term debt and
Panel (B) that of long-term debt. Each type of debt is measured on the horizontal axis and yield on the
vertical axis.
The demand curves Ds and DL are drawn with infinite elasticity because both debts are perfect
substitutes. The supply curves Ss and SL are drawn perfectly inelastic because the quantities of short-run
and long-term debts are fixed. Assume that the long-term interest rate (yield) lies above the short-term
interest rate, i.e.., ORL > ORs.
Long-Term Debt, Short-Term Debt and Yield
This is because the future short-run interest rate is expected to be higher than the current short-run
rate. If the government wishes to redeem (retire) SL– SL1 of long-term debt and replaces it with Ss-Ss1
of short-term debt, this is possible without any change in the relative yields of the two kinds of debt.
These remain the same at ORL and ORs respectively.

Again, as all types of short-term and long-term bonds (securities) are perfect substitutes, therefore the
central bank cannot influence the term structure of interest rates as long as it does not affect the
expectations of borrowers and lenders.
Its Criticisms:
However, the expectations theory has been criticised on several points:
1. Lenders may have expectations about long-term interest rates that may be independent of their
expectations about short-term interest rates.
2. The theory presupposes that investors can make long-term expectations about short-term interest
rates. But it is doubtful if such predictions can be made accurately.
3. Critics doubt the efficacy of changes in the central bank discount rates to influence the long-term
interest rates. For instance, a reduction in the discount rate can bring a fall in the long-term rates only if
the expectation is generated that short-term interest rate will remain low. This will prevent the discount
rate being changed very often by the central bank.
4. If open market operations which influence the slope of the yield curve are not successful, the
expectations theory fails. Suppose the central bank tries to keep long-term rates higher than short-term
rates by supplying short-term market with large funds.
In this situation, investors expecting that they will gain over the long period would shift from short-term
to long-term securities. This would tend to equalize the short-term and long-term rates and the yield
curve would be horizontal like HL, rather than like RR in Figure 1.
5. The assumption of the theory that investors hold with certainty expectations of future short-run
interest rates is not correct. This is because expectations of people for short-run interest rates are
occasionally certain.

6. This assumption is also away from reality that the expectations of borrowers and lenders are similar.
In fact, the expectations of borrowers and lenders regarding short-term and long-term rates are quite
different from each other.
7. The theory fails to explain how expectations relating to future short-term interest rates are formed.
8. It is also wrong to assume that transaction costs are zero. In reality, borrowers and lenders are
required to incur transaction costs every time when they buy and sell securities.
2. The Segmented Markets Theory:
The segmented markets theory is known by various names such as institutional, hedging or
segmentation. According to this theory, investors are much averse to risk. So they hedge against risks by
matching the maturity of their assets with that of their liabilities.
If the maturity of an investor’s assets is longer than that of his liabilities, he incurs a capital loss when he
is forced to sell his assets before they are due for redemption. On the other hand, if the maturity of an
investor’s assets is shorter than that of his liabilities, he runs the risk of income loss. In order to avoid
the two kinds of risks, investors match the maturities of their assets and liabilities.
Its Assumptions:
This theory is based on the following assumptions:
1. Assets of different maturities are imperfect substitutes with each other.
2. Markets for assets of different maturities are divided into separate markets.

3. Interest rates for one type of asset in every market are determined by their demand and supply
which, in turn, affect the yield to maturity.
4. There is uncertainty about the behaviour of interest rates in future.
The Theory:
The segmented markets theory holds that short-term and long-term interest rates are determined in
several separated or segmented markets. Some investors prefer short-term securities, while other
investors, such as insurance companies, prefer long-term securities. Thus securities of different
maturities are imperfect substitutes for buyers and sellers of securities in the market.
Consequently, the yield curve is the result of several demand and supply curves for securities of
different maturities. Given the demand for securities, if the supply of short-term securities is less than
the demand for long-term securities, the short-term interest rate will be higher than the long-term
interest rate. In this situation, the yield curve will slope downward to the right, as shown by the curve Y
in Fig. 3 (C).
Short-Term Debt, Long-Term Debt, Term to Maturity and Interest Rate
In Panel (A) of the figure, Ds and Ss are the demand and supply curves of short-term debts respectively
which are in equilibrium at point Es. Thus they determine 6% equilibrium interest rate on short-term
securities. In Panel (B), DL and Ds are the demand and supply curves respectively of long-term debts
which determine 5% equilibrium interest rate at point E1 on long-term securities. These interest rates
provide the downward sloping yield curve Y in Panel (C).
On the contrary, given the demand for securities, when the supply of short-term securities is greater
than the demand for them, the short-term interest rates will be lower than the long-term interest rates.
In such a situation, the yield curve will slope upward to the right, as shown in Fig. 4 (C).

In Panel (A) of the figure, Ds and Ss curves determine 4% short-term equilibrium interest rate at point Es
on short-term assets. Similarly in Panel (B), D, and SL curves determine 5% long-term equilibrium
interest rate at point Er .These interest rates provide the upward sloping yield curve Y in Panel (C). Thus,
according to the segmented market theory, the market rates on securities of different maturities are
determined by separate conditions of demand and supply in each maturity. Across the maturity
spectrum, there are a number of separate markets.
Short-Term Debt, Long-Term Debt, Term to Maturity and Interest Rate
Its Policy Implications:
The policy implications of this theory are that if the government wishes to replace a given amount of
long- term debt by a short-term debt, it will be successful in twisting the structure of interest rates. In
this theory, Ds and Dl are the demand curves for long-term and short- term debts respectively which are
less than perfectly elastic with respect to yield rates, as shown in Figure 5 (A) and (B).
This is because the two types of debt are not perfectly substitutable. Suppose that the government
wants to retire B-BL1 of long-term debt and replace it with Bs1-Bs short- term debt. Notice that the
spread between the rates has been reduced. When the government substitutes long-term debt by
short-term debt, the supply of long-term debt is reduced from SL to SL1 and the long-term interest rate
rises from RL to RL1, as shown in Panel (B) of the figure.
On the other hand, the supply of short-term debt increases from Ss to Ss1 which brings a fall in the
short-term interest rate from Rs to Rs1 as shown in Panel (A) of the figure. Notice that the fall in the
short-term interest rate is less than the rise in the long-term interest rate: RS-RS1 < RL-RL1.
Short-Term Debt, Long-Term Debt and Yield
Another implication of this theory is that the central bank can affect the yields to maturity of securities
or the term structure of interest rates by permitting the relative supplies of long-term and short-term
securities. Again, the central bank cannot affect the long-term interest rate by changing only the supply
of short- term securities.

Its Criticisms:
The segmented market theory has been criticised on the following grounds:
1. This theory explains that changes in preferences for securities of different maturities will alter in the
form of the yield curve. But it does not explain changes in the structure of yields.
2. This theory is based on the assumption that short-term and long-term interest rates are not related to
each other. But empirical evidence does not support it. It shows that short-term and long-term interest
rates move together. When short-term interest rates fall or rise, the long-term interest rates move in
the same direction.
Conclusion:
Despite these criticisms, the segmented markets theory is supported by institutional practices.
Accordingly, commercial banks which place emphasis on liquidity, deal in short-term securities, and
insurance companies with long-term securities. Similarly, inventories are financed with short-term loans,
and purchases of houses with long-term mortgages.
Its Superiority Over Expectations Theory:
The segmented market theory is superior to the expectations theory on the following counts:
1. The segmented market theory is superior to the expectations theory because it does not assume the
unrealistic assumption of the expectations theory that short-term and long-term securities are perfect
substitutes. The risks in short-term securities are less than those in long-term securities.

If a person sells his security before its maturity and the interest rate is more than expected, the price of
the long-term security will be less as compared with the short-term security. Thus, short-term and long-
term securities are not perfect substitutes.
2. The segmented market theory is also superior to the expectations theory because it rejects the
assumption of the latter that the future interest rates are known with certainty. In reality, they are
uncertain. Due to large price-changes of long-term securities, there is much uncertainty in holding them.
On the other hand, there is great uncertainty of future yields in holding short-term securities.
3. Another reason of the superiority of segmented market theory over the expectations theory is that it
does not explain the term structure of interest rates on the basis of the average of expected short-term
interest rates. Rather, the segmented market theory determines both the short-term and long-term
interest rates in the form of demand and supply of a particular security, as happens in reality in a
financial market.
4. As against the expectations theory, the segmented market theory does not explain a unique relation
between short-term and long-term interest rates. In reality, the behaviour of short-term and long-term
interest rates depends on the relation between money market and bond market. Short-term and long-
term interest rates in both markets are determined by the demand and supply of each type of security.
5. The segmented market theory is also superior to the expectations theory because it is supported by
institutional practices. Accordingly, commercial banks which place emphasis on liquidity deal in short-
term securities, and insurance companies with long-term securities. Similarly, inventories are financed
with short- term debts and purchases of houses with long-term mortgages.
3. The Substitutability Theory:
The substitutability theory holds that short-term and long-term securities are substitutes for borrowers
and lenders. When buyers and sellers of securities are engaged in arbitrage and switching operations,
they tend to eliminate discrepancies between long-term and short-term interest rates in the short run.
For such operations, the theory assumes optimising behaviour on the part of buyers and sellers, and
relatively free and unrestricted markets.