Transcript Term Structure of Interest Rates

Term Structure of Interest Rates
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
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.
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.
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.
 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.
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 oneyear.
 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
 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
 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
 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