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VRM Ch.11 Bond Yields

dtammerz

Member
Subscriber
Hello, for the LO: "Define and interpret the spread of a bond and explain how a spread is derived from a bond price and a term structure of rates.", I am having trouble understanding this formula on P1.T4.Ch.11 Notes p.7. How come there would be two different forward rates in one coupon period?

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David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
@dtammerz forward rates chain to the spot rate; e.g., if f(1) = 1.0% and f(1,2) = 3.0%, then z(2) = sqrt(1.01*1.03) - 1 ~= 2.0%, such that to discount the 2-year annual coupon we can multiply the coupon by 1/1.02^2 = 1/(1.01*1.03). You are correct: just as the Law of One Price says each maturity has only one discount factor (spot rate), it follows that it must also be true that any forward interval can be occupied by only one forward rate. But the above chaining is just parsing a spot rate into its implied chain of forwards.
 

dtammerz

Member
Subscriber
@dtammerz forward rates chain to the spot rate; e.g., if f(1) = 1.0% and f(1,2) = 3.0%, then z(2) = sqrt(1.01*1.03) - 1 ~= 2.0%, such that to discount the 2-year annual coupon we can multiply the coupon by 1/1.02^2 = 1/(1.01*1.03). You are correct: just as the Law of One Price says each maturity has only one discount factor (spot rate), it follows that it must also be true that any forward interval can be occupied by only one forward rate. But the above chaining is just parsing a spot rate into its implied chain of forwards.

Thank you, this is helpful.
 
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