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Explain why the fixed annual-rate of interest of 3.76¼% is less than the 4-year yield curve rate of 3.8%
The equivalent fixed rate of 3.7625% is less than the 3.8% 4-year yield curve rate because the 3.8% represents a zero-coupon bond with one payment in the fourth year. The relevant bond here pays coupons at different time periods when the yield curve rates are lower, hence the fixed rate is lower.
sir i am not able to understand the given answer, can u pls make it simpler to understand..
sir i have another question with regards to this question,
Gross amounts of interest receivable from Ratus Bank based on Year 1 spot rate and Years 2–4 forward rates
why year 1 spot and 2-4 forwards?
First question:
Sembilan will be receiving interest from Ratus each year at the spot yield curve rates (so 2.5% in the first year rising to 3.8% in the fourth year) and wants this because they have have to pay bond interest at floating rate. So the ‘average’ interest they are getting from Ratus is somewhere between 2.5% and 3.8%. In return they have to pay fixed interest to Ratus of 3.7625% which is between 2.5% and 3.8% (higher than the average partly because obviously Ratus wants to profit out of the deal but also because the yield curve rates are likely to increase as indicated by the forward rates).
Second question:
The actual receipts from Ratus will depend on what the actual interest rates turn out to be. The forward rates are used as the best estimate of what the future rates will be. There is no forward rate given for year 1 and so we have no choice but to assume that the current rate of 2.5% is fixed for year 1.
They will be receiving 2.5% in the first year, rising to 3.8% in the fourth year, so the average interest per year is somewhere between the two. Does that (together with the rest of what I typed before) help?
They will be receiving low interest at the start and high interest at the end, and in return they will be paying fixed interest of somewhere in between.
yeah that i understood, but why the fixed annual-rate of interest of 3.76¼% is less than the 4-year yield curve rate of 3.8%
Because it is only the year 4 receipt that is at 3.8%, the other receipts are at lower rates of interest. So the fixed interest that Ratus wants in return will be somewhere in-between the four different rates.
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