please solve using proper mathematical notations and () in the correct order 9.
ID: 2808447 • Letter: P
Question
please solve using proper mathematical notations and () in the correct order
9. Consider a 10-year bond with annual coupon rate 8%. Suppose that the term structure is at at 8%, ie.' spot rates for all maturities are 8 (a) What is the bond price and YTM? b) Suppose that you buy the bond today and hold it for 10 years. What is your return (expressed as an annual rate) if the term structure stays at 8% for the whole 10 years during which you hold the bond? (c) what is your return if the term structure moves down to 6% (still staying at) 6 months after you buy the bond, and then stays at 6% for the remainder of the 10 years? (d) what is your return if the term structure moves up to 10% (still staying at) 6 months after you buy the bond, and then stays at 10% for the remainder of the 10 years? (e) Comment on the relation between the bond's YTM and the 10-year return on the bond.Explanation / Answer
Hi,
Let us assume the face value of his bond is 100
a) Since the bond has a coupon of 8%and a spots for all maturities are at 8%, this means that the bond is trading at par, please remember that when the coupon rate is equal to the discount rate, the market price is equal to the face value. Therefore the bond price is 100
The YTM is clearly mentioned in this question as 8 for all maturities
b) as we discused when the coupon rate is equal to the yield, the bond trades at par and hence there is no difference between the price and the face value and hence we earn 0 returns in this case
c) We will now have to discount every years cash flow as a process to calculate the price of this bond:
the discont rate is 0.06 and the cash flows are 8 for 9 years and 108 for the last year, applying the discounting:
the return therefore would be 14.72%
d) doing the same process with discount as 10%
The returns would currebtly be negative
e) With 200 bps movement in the YTM, the returns are moving by 14%, there is a 1:7 reltionship betwen the bond price and the YTM
Discount factor= 0.06 Year 1 2 3 4 5 6 7 8 9 10 Cash 8 8 8 8 8 8 8 8 8 108 PV 7.547169811 7.119972 6.716954 6.336749 5.978065 5.639684 5.320457 5.019299 4.735188 60.30664 Net cash flow = 114.7202the return therefore would be 14.72%
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