Lesson 4 of 6 · 14 min

Implied forward rates from spot rates

An implied forward rate is the rate for a future period that makes investing short and rolling over earn exactly the same as investing long today, so it is the breakeven reinvestment rate.

In short

  • A spot rate applies to money invested from today; a forward rate applies to a period that starts in the future, agreed today.
  • Implied forward rates (forward yields) are calculated from spot rates: (1+ZA)A(1+IFRA,B−A)B−A=(1+ZB)B(1+Z_A)^A(1+IFR_{A,B-A})^{B-A} = (1+Z_B)^B.
  • Notation 'AyBy': first number = when the period starts (years from today); second = its tenor. 3y1y is a 1-year rate starting in 3 years.
  • The forward is the breakeven reinvestment rate: the incremental (marginal) return for extending maturity by the extra period.
  • If you expect the future rate to exceed the forward, invest short and roll over; if below, invest long now.
  • Take the (B−A)(B-A)th root to annualize a multi-year forward. The maths is unchanged with negative rates.

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Implied forward rates from spot rates · The Term Structure of Interest Rates: Spot, Par, and Forward Curves