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151
CHAPTER 10
THE TERM STRUCTURE AND
INTEREST RATE DYNAMICS
SOLUTIONS
1 . ree forward rates can be calculated from the one-, two-, and three-year spot rates. e
Additionally, the rate on a two-year loan that begins at the end of Year 1 can be computed
from the one- and three-year spot rates; in the following equation one would solve for
2 . For the two-year forward rate one year from now of 2%, the two interpretations are as
follows:
in a zero-coupon bond that matures in two years.
3 . A at yield curve implies that all spot interest rates are the same. When the spot rate is the
152 Part II: Solutions
4 . A . e yield to maturity of a coupon bond is the expected rate of return on a bond if
than the initial yield to maturity, a bond holder may experience lower realized returns.
5 . If forward rates are higher than expected future spot rates, the market price of the bond
6 . e strategy of riding the yield curve is one in which a bond trader attempts to generate a
total return over a given investment horizon that exceeds the return to bond with maturity
7 . Some countries do not have active government bond markets with trading at all matur-
ities. For those countries without a liquid government bond market but with an active
8 . e Z-spread is the constant basis point spread added to the default-free spot curve to
correctly price a risky bond. A Z-spread of 100 bps for a particular bond would imply
9 . e TED spread is the di erence between a Libor rate and the US T-Bill rate of matching
maturity. It is an indicator of perceived credit risk in the general economy. In particular,
because sovereign debt instruments are typically the benchmark for the lowest default
1 0 . e local expectations theory asserts that the total return over a one-month horizon for a
11 . Both theories attempt to explain the shape of any yield curve in terms of supply and
demand for bonds. In segmented market theory, bond market participants are limited to
(1) changes in the level of the yield curve, (2) changes in the slope of the yield curve,
and (3) changes in the curvature of the yield curve. Changes in the level refer to up-
Chapter 10 e Term Structure and Interest Rate Dynamics 153
for intermediate maturities. In this situation returns on short and long maturities are
likely to rise while declining for intermediate maturity bonds.
B . Empirically, the most important factor is the change in the level of interest rates.
C . Key rate durations and a measure based on sensitivities to level, slope, and curvature
in ve years. at is, f (2,3) is calculated as follows:
5
[]
e equation above indicates that in order to calculate the rate for a three-year loan be-
ginning at the end of two years you need the ve-year spot rate r (5) and the two-year spot
rate r (2). However r (5) is not provided.
curve is downward sloping. is turn implies a downward sloping yield curve where lon-
ger term spot rates r ( T + T *) are less than shorter term spot rates r ( T ).
[1 + r (2)] 2 = [1 + r (1)] 1 [1 + f (1,1)] 1
Using the one- and two-year spot rates, we have
2 = (1 + .04)
1 [1 + f (1,1)] 1 , so 1 .05
2
()
+
[1 + r (3)] 3 = [1 + r (1)] 1 [1 + f (1,2)] 2
Using the one-and three-year spot rates, we nd
(1 + 0.06)
1 0.04 1
1
()
+− = f (1,2) = 7.014%
[1 + r (3)] 3 = [1 + r (2)] 2 [1 + f (2,1)] 1
Using the two-and three-year spot rates, we nd
3 = (1 + 0.05)
2 [1 + f (2,1)] 1 , so 1 0.06
3
()
+
154 Part II: Solutions
[1 + r (3)] 3 = [1 + r (1)] 1 [1 + f (1,1)] 1 [1 + f (2,1)] 1
So [1 + r (3)] 3 = (1 + 0.04)
1 (1 + 0.06)
1 (1 + 0.08)
1 , 1.1906 1
3− = r (3) = 5.987%.
P (1) = 1
1.05 1
()
= 0.9524. e forward pricing model is P ( T * + T ) = P ( T *) F ( T *, T )
year Treasury rate plus the swap spread: 2% + 0.5% = 2.5%.
three-month Treasury bill rate. If the T-bill rate falls and Libor does not change, the TED
spread will increase.
yield curve, will provide the correct discount rates to price a particular risky bond.
price the bond. e resulting 7% discount rate will be the same for all of the bond’s cash-
ows, since the yield curve is at. A 7% coupon bond yielding 7% will be priced at par.
discount rate will make the price of Bond B lower than Bond A.
observed term structure.
