20-Term Structure Page 601 Wednesday, February 4, 2004 1:33 PM
Term Structure Modeling and Valuation of Bonds and Bond Options 601The estimated on-the-run yield for all intermediate whole-year maturi-
ties is found by adding to the yield at the lower maturity the amount
computed from the above formula.
For example, using the September 5, 2003 yields, the 5-year yield is
3.25% and the 10-year yield is the 4.35%% are used to obtain the
interpolated 6-year, 7-year, 8-year, and 9-year yields by first calculating:(4.35% – 3.25%)/5 = 0.22%Then,interpolated 6-year yield = 3.25% + 0.22% = 3.47%
interpolated 7-year yield = 3.47% + 0.22% = 3.69%
interpolated 8-year yield = 3.69% + 0.22% = 3.91%
interpolated 9-year yield = 3.91% + 0.22% = 4.13%Thus, when market participants talk about a yield on the Treasury
yield curve that is not one of the on-the-run maturities—for example,
the 8-year yield—it is only an approximation. Notice that there is a
large gap between the maturity points. This may result in misleading
yields for the interim maturity points when estimated using the linear
interpolation method.
Another factor complicates the relationship between maturity and
Treasury yield in constructing the Treasury yield curve. The yield for
on-the-run Treasury issues may be distorted by the fact that these secu-
rities can be financed at cheaper rates and as a result can offer a lower
yield than in the absence of this financing advantage. There are inves-
tors who purchase securities with borrowed funds and use the securities
purchased as collateral for the loan. This type of collateralized borrow-
ing is called a repurchase agreement. Since dealers, for whatever reason,
want to obtain use of these securities for their own trading activities,
they are willing to loan funds to investors at a lower interest rate than is
otherwise available for borrowing in the market. Consequently,
impounded into the price of an on-the-run Treasury security is the
cheaper financing available, resulting in a lower yield for an on-the-run
than would prevail in the absence of attractive financeability.
From a practical viewpoint, the key function of the Treasury yield
curve is to serve as a benchmark for pricing bonds and setting yields in all
other sectors of the debt market—bank loans, mortgages, corporate debt,
and international bonds. However, the Treasury yield curve is an unsatis-
factory measure of the relation between required yield and maturity. The
key reason is that securities with the same maturity may actually carry
different yields. This phenomenon reflects the role and impact of differ-