Lesson 4 of 6 · All lessons in this module
  1. Spot rates and the spot curve
  2. Pricing a bond with spot ratesVideo lesson
  3. Par rates and the par curveVideo lesson
  4. Implied forward rates from spot ratesVideo lesson
  5. Spot rates from forward rates, and pricing with forwardsVideo lesson
  6. Comparing the spot, par and forward curves

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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