bond value using forward-rates-calculated spot rate
I’m having hard time understanding this concept.
Schweser Book 5 - FIXED INCOME, DERIVATIVES, AND ALTERNATIVE INVESTMENTS, page 52, says that you can calculate 2 year spot rate the following way: (1+S2)2=(1+S1)*(1+1y1y), which means that S2=[(1+S1)*(1+1y1y)]1/2-1
On page 55 there is this example:
“The current 1-year rate, S1, is 4%, the 1-year forward rate for lending from time = 1 to time = 2 is 1y1y = 5%, and the 1-year forward rate for lending from time = 2 to time = 3 is 2y1y = 6%. Value a 3-year annual-pay bond with a 5% coupon and a par value of $1,000.”
According to Schweser, the answer is:
bond value = 50/(1+S1)+50/[(1+S1)*(1+1y1y)]+1,050/[(1+S1)*(1+1y1y)*(1+2y1y)]=
however, when I calculate the 3-year spot rate using the forward rates: S3=(1.04*1.05*1.06)1/3-1=4,99968% and I use this 3-year spot rate to calculate the bond’s present value using the calculator, I get a very different number than when doing it using the individudal forward rates, why is that?
On financial calculator: N=3, I/Y=4,99968%, PMT=50, FV=1000, CPT, PV. PV= $1,000,08646
Thank you very much in advance for the explanation!