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# VRM Ch.11 Bond Yields

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#### David Harper CFA FRM

##### David Harper CFA FRM
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@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
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@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.