FM for Actuaries

Bond Yields and the Term Structure 237
4. The term structure may be estimated using bond price data in the market. The
bootstrap method and the least squares method can be used to estimate the
periodic compounding spot-rate curve. There are, however, data limitations
which restrict the use of these methods.
5. Assuming continuous compounding, the instantaneous forward rate can be
estimated using bond price data. The step function of instantaneous forward
rates can be calculated from a sequence of bonds with possibly irregularly
spaced maturities. This method is quite versatile and has fewer data limitations.
Upon estimating the instantaneous forward rates, the spot-rate curve
can be calculated by averaging the instantaneous forward rates.
6. There are several theories that explain the determination of the term structure.
The most widely used theory is probably the pure expectations hypothesis,
which implies that the forward rate is an unbiased estimate of the future spot
rate. The expectations hypothesis, liquidity premium hypothesis, market segmentation
hypothesis and preferred habitat hypothesis are other competing
theories.
Exercises
7.1 A $1,000 par value 10-year bond with redemption value of $1,080 and coupon
rate of 8% payable semiannually is purchased by an investor at price P .
(a) Find the yield to maturity of the bond if P =$1,000.
(b) Find the yield to maturity of the bond if P =$1,080.
(c) Determine P if the yield to maturity of the bond is 8% per annum convertible
semiannually.
7.2 The following shows the information of an investment-grade bond.
Type of Bond Corporate bond
Issue Date March 2, 2015
Maturity Date March 2, 2021
Face Value $1,000
Redemption Value $1,035
Coupon Rate 9% payable semiannually
If the 1-year forward rates are 7% for the first 3 years and 10% for the last 3
years, find the price of the bond at issue. What is the yield to maturity of the
bond?