Lesson 6 of 7 · All lessons in this module
  1. Forward price versus forward value: inception and expiration
  2. Valuing a forward during its lifeVideo lesson
  3. Forwards on assets with costs and benefits
  4. Pricing and valuing FX forwardsVideo lesson
  5. Term structure: zero rates and discount factors
  6. Implied forward ratesVideo lesson
  7. Forward rate agreements (FRAs)Video lesson

Lesson 6 of 7 · 13 min

Implied forward rates

An implied forward rate is the breakeven reinvestment rate that makes investing short and rolling over earn exactly the same as investing long, so it follows directly from two zero rates.

In short

  • An interest rate forward names both the start date and the tenor: '2y3y' (F2,3F_{2,3}) is a three-year rate starting in two years; '3m6m' is a six-month rate starting in three months.
  • No arbitrage: (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.
  • Equivalently, 1+IFRA,B−A=(DFA/DFB)1/(B−A)1+IFR_{A,B-A} = (DF_A/DF_B)^{1/(B-A)}.
  • Rates must have the same periodicity before applying the formula; convert with (1+APRm/m)m=(1+APRn/n)n(1+APR_m/m)^m = (1+APR_n/n)^n.
  • Uses: breakeven test for 'invest short and roll vs invest long', building a forward curve, and setting the no-arbitrage fixed rate of an FRA and, later, swaps.

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