Hi,
Why is the equation equated to 100 in the CFAI book?
The yield to maturity (“par rate”) for a benchmark one-year annual-pay bond is 2%, for a benchmark two-year annual-pay bond is 3%, and for a benchmark three-year annual-pay bond is 4%. A three year, 5% coupon, annual-pay bond with the same risk and liquidity as the benchmarks is selling for 102.7751 today (time zero) to yield 4%. Is this value correct for the bond given the current term structure?
Solution:
The first step in the solution is to find the correct spot rate (zero-coupon rates) for each year’s cash flow.3 The spot rates may be determined using bootstrapping, which is an iterative process. Using the bond valuation equation below, one can solve iteratively for the spot rates, zt (rate on a zero-coupon bond of maturity t), given the periodic payment, PMT, on the relevant benchmark bond.
100 =PMT/(1+z1)1+PMT/(1+z2)2+⋯+(PMT+100)/(1+zN)N