The document discusses the term structure of interest rates, which refers to the relationship between interest rates and the time to maturity of debt securities. It specifically focuses on how the yield curve is constructed based on Treasury securities of different maturities. To construct the term structure, spot rates are determined for theoretical zero-coupon Treasury securities of different maturities by considering the theoretical value of coupon Treasury securities as a package of zero-coupon securities. The graphical depiction of the relationship between spot rates and maturities is called the spot rate or theoretical spot rate curve.

1. Term Structure of Interest Rates
Phiwokwakhe Aaron Mabaso
201582603

2. Outline
• Meaning of Term Structure of Interest Rates
• Significance of Term Structure of Interest Rates
• What is Yield Curve?
• A spot rate and a forward Rate
• Theories of Term Structure of Interest Rates

3. Why practically homogeneous bonds of different maturities
have different interest rates?
• This question issue is of great significance to both borrowers and lenders.
• Should a lender invest in short-term bonds and have to worry about the rates at
which to reinvest when short-term bond matures? Or should the lender buy
long-term bonds and run the risk of an uncertain liquidating value if selling is
necessary before maturity?
• Borrowers are faced with the choice of whether to borrow short-term or long-
term. Short-term borrowing runs the risk that refinancing may be at higher
rates. Long-term financing runs the risk that a high rate may be locked in.
• A study of the yield-curve and term-structure of interest rates can help
borrowers and lenders in making the right decision.

4. What is a Yield Curve?
• A graphical depiction of the relationship between the yield on bonds of the
same credit quality, but different maturities is known as the yield curve.
• Term structure of interest rates may be defined as the relation between yield to
maturity of zero coupon securities of the same credit quality and maturities of
those zero-coupon securities.
• Yield-to-maturity on zero-coupon securities for different maturities is also the
spot rate for that maturity. Therefore, term structure of interest rate may also
be defined as the pattern of spot rates for different maturities.

5. How to Construct the Term Structure of Interest Rates?
• The yield on Treasury securities is a benchmark
for determining the yield curve on non-Treasury
securities. Consequently, all market participants
are interested in the relationship between yield
and maturity for Treasury securities.

6. continue
• The graphical depiction of the relationship between the
yield on Treasury securities for different maturities is
known as the yield curve. While a yield curve is
typically constructed on the basis of observed yields
and maturities, the term structure of interest rates is
the relationship between the yield on zero-coupon
Treasury securities and their maturities.
• Therefore, to construct term structure of interest rates,
we need the yield on zero-coupon Treasury securities
for different maturities.

7. Continue
• Zero-coupon Treasuries are issued with maturities
of six-months and one-year, but there are no zero-
coupon Treasury securities with maturity more than
one-year.

8. continue
• Thus, we cannot construct such term structure
solely from market observed yields.
• Rather, it is essential to construct term structure
from theoretical consideration applied to yields of
actually traded Treasury debt securities.
• Such a curve is called “Theoretical Spot Rate Curve”
• Any noncallable security can be considered as a
package of zero-coupon securities

9. continue
• Each zero coupon security in the package has a
maturity equal to its coupon payment date and, in
the case of principal, equal to maturity date
• The value of the Treasury coupon security should be
equal to the value of the package of zero-coupon
securities

10. Continue
• If this equality does not hold, it will be possible to
create arbitrage profits.
• To determine the value of each zero coupon security,
it is necessary to know the yield on the zero-coupon
Treasury corresponding to that maturity. This yield is
called the Spot Rate

11. Continue
• The graphical depiction of the relationship between the
spot rate and maturity is called the spot rate curve.
• Such a curve is also known as “Theoretical Spot Rate
Curve”
• Remember spot rate is a zero-coupon rate. The
theoretical spot rates for Treasury securities represent
the appropriate set of interest rates that should be used
to value default-free cash flows