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July 5, 2018 at 1:17 am #460990duybachhpvn
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In this question, the issuer of the 4-year bond has to pay the interest rate at its spot yield curve rate plus certain basis point. The questions then continue to give the 4-year spot yield curve rate at 3.8% and we have to swap it for a fixed rate at ~3.76%. The question was why the fixed rate is lower than 3.8%.
In the answer, it was stated that: “The equivalent fixed rate of 3.7625% is less than the 3.8% four-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”
1. I am really confused here, because when I read the article on this section, I understood that for a 4-year bond with a 4-year spot yield curve rate of 3.8% like this, it should mean that the issuer has the option to pay interest rate at 3.8% for each of the 4 years. Another option to pay is to pay interest rate of year 1 at spot yield curve rate and the rest at forward rates. However in the answer it is stated that 3.8% represents a zero-coupon bond with 1 payment in 4th year instead of annual payment of 3.8% and it is really confusing me.
Hope you can help me clarify if I understand the answer incorrectly or not.
2. 1 more thing I want to ask for your clarification is the method of calculating forward rate using spot yield curve. For example, if we are given the spot yield curve for year 1 and 2, then the formula for calculating forward rate at year 2 will be (1 + spot yield year 2) ^2 = (1 + spot yield year 1) * (1 + forward rate year 2). This means that we are compounding the spot yield rate when doing this and I dont know why we have to compound it, as the bond pay interests separately from its principal and does not have compounding effect.
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