Quick way to answer this question

CFA Level II Fixed Income
#1

Is there a quick way to calculate how many forward rates can be calculated when given multiple spot rates for zero coupon bonds ?

#2

If you’re given n spot rates, the number of forward rates you can calculate (which are distinct from those spot rates) is:

\dfrac{n\left(n - 1\right)}{2}

So, given:

  • 1 spot rate, you can calculate \dfrac{1\left(0\right)}{2} = 0 forward rates
  • 2 spot rates, you can calculate \dfrac{2\left(1\right)}{2} = 1 forward rate
  • 3 spot rates, you can calculate \dfrac{3\left(2\right)}{2} = 3 forward rates
  • 4 spot rates, you can calculate \dfrac{4\left(3\right)}{2} = 6 forward rates
  • and so on
#3

That is such a helpful formula, thank you :pray: