the differences in the td b) You are given the following pattens of forward rate
ID: 2790438 • Letter: T
Question
the differences in the td b) You are given the following pattens of forward rates: Year Forward rate 4% 5% 5.5% If one year from now, the term structure of interest rates changes so that it looks exactly the same way it does today, what would be your holding period return if you purchased a 3-year zero coupon bond today and held it for one year? c) You have the following information about a bond: $1000 18 years Par value Time to maturity Coupon Current price Yield to maturity paid yearly $917.99 10% Given the bond described above, if interest was paid semi-annually (rather than annually) and the bond continued to be priced at $917.99, what would be the resulting effective annual yield to maturity? (5 marks)Explanation / Answer
a.) Price of 3-Year Zero Coupon Bond today = 1000/(1.04x1.05x1.055) =$868.01
Price of same Zero Coupon Bond after 1 year = 1000/(1.04x1.05) =$915.75
Holding Period Return = (915.75 - 868.01)/868.01x100 =47.74/868.01x100 =5.50%
b.) Price of Bond =$917.99
Time to Maturity =18 years or 36 semi-annual periods
Coupon Rate =9% or 4.5% semi-annual
YTM =??
917.99 = 45x{(1-(1+y)-36)/y} + 1000/(1+y)36
Using Trial and Error method to evaluate y,
For y=0.10 RHS=467.79
For y=0.05 RHS=917.26
For y=0.04 RHS=1094.54
For y=0.049953 RHS=917.99
Hence, annual yield to maturity in this case =2x0.049953 =0.09990 or 9.99%
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