hi Sir
i am having difficulties in attempting the following question which is in the student article : estimating yield curve
The following data has been collected on government treasury notes ( annual coupon, $100 face and redemption value)
Years to redemption coupon market price
One 7% $103
Two 6% $102
Three 5% $98
Calculate the one- year, two year and three- year treasury spot rates (yield rates)
i cannot understand the solution.
should you start the calculation by calculating the IRR. can you choose two DF like 5% and 10%?
yrs cash flows DF (5%) PV DF (10%)
0 (103) 1 (103) 1 (103)
1 7 0.952 6.664 0.909 6.363
1 100 0.952 95.2 0.909 90.9
(1.136) (5.737)
IRR = 3.80%
but in the marking scheme it was done that way
Bond A: $103 = $107 x (1+r1)-1 r1 = 107/103 – 1 = 0.0388 or 3.88%
could you kindly help me out sir?
thank you
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bootstrapping
11y ago#1I cannot really follow your working because tables do not work very well on here.
However, for each of them you certainly do need to calculate the IRR.
But they each need calculating separately.
So....for the one year spot rate you need the IRR of the flows that are as follows:
0 103 (the current market value)
1 7 (the interest)
1 100 (the redemption amount).
Since it is only one year, then more accurate that making two guesses and approximating, then if 'r' is the IRR, then 107/(1+r) = 103.
So r = 107/103 - 1 = 0.0388 or 3.88%
For the others, you do need to make two guesses and any guesses are OK. Depending on which rates you use the answer may be very slightly different, but that is not a problem and does not lose marks.
thank you so much sir for helping me out.
11y ago#3You are welcome :-)
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