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Given 3 Bonds $A$, $B$ and $C$ with \begin{matrix} & \text{Bond } A& \text{Bond } B& \text{Bond } C& \\ \text{Price:}& 101,12\%& 99,03\%& 102,95\%\\ \text{Mat. in years:}& 0,5& 1,5& 2,5\\ \text{Coupon:}& 2\%& 1\%& 3\% \\ \text{Coupon frequency:}& \text{per year}& \text{per year} & \text{per year}\\ \text{Nominal value:}& 1.000& 10.000& 1.000\\ \end{matrix}

How can I determine the spot rates implied by these bonds? I.e. what would be the spot rate for the next 0,5 years, the next 1,5 and 2,5 years?

I assume that it is not correct to just claim that the spot rate for 0,5 years is 1% (the accrued interest from Bond $A$)?

Furthermore, how can I calculate the forward rate from these rates? Is it correct to calculate the 6x18 forward rate $F$ via the equation $(1 + \frac12r_{0,5})(1+F) = (1+\frac32r_{1,5})$ where $r_{0,5}$ and $r_{1,5}$ are the spot rates for the given duration?

Thanks in advance!

Edit: The return I can realise on Bond $A$ would be the following: I can buy at 102,12% (accounting for accrued interest), after 0,5 years, I get 102%. Does solving $$ 102,12 \cdot (1 + \frac12 r_{0,5}) = 102 $$ yield the desired spot interest rate? In this case $r_{0,5} = -0,24\%$?

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  • $\begingroup$ The coupon is not the spot rate -- you need to calculate yields first from the price, coupon and TTM. $\endgroup$
    – oronimbus
    Commented Jun 19, 2023 at 11:55
  • $\begingroup$ I edited the post, is this now the correct way to calculate the spot rate? $\endgroup$
    – julian2000P
    Commented Jun 19, 2023 at 16:53

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