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Bootstrapping. Complete problem 31 of Chapter 10 (shown below), and
submit to your instructor. Show your calculations and the algebraic
manipulation of the price equation for the bond. In addition to solving the
problem, write a 100 to 200 word essay on the term structure of fixed income
securities.
One method used to
obtain an estimate of the term structure of interest rates is called
bootstrapping. Suppose you have a one-year zero coupon bond with a rate of r1
and a two-year bond with an annual coupon payment of C. To bootstrap
the two-year rate, you can set up the following equation for the price (P)
of the coupon bond:
Because you can
observe all of the variables except r2, the spot rate for two years,
you can solve for this interest rate. Suppose there is a zero coupon bond with
one year to maturity that sells for $949 and a two-year bond with a 7.5 percent
coupon paid annually that sells for $1,020. What is the interest rate for two
years? Suppose a bond with three years until maturity and an 8.5 percent annual
coupon sells for $1,029. What is the interest rate for three years?
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