Jun 04

Interest rate parity – Practice question (Par 3+ difficulty)

by David Harper, CFA, FRM, CIPM

FRM |

Five quid ten bucks

Assume:

  • U.S. rate = 2%
  • U.K. rate = 5%
  • Spot exchange rate, $/GBP = $1.96 (currently accurate)

Question:

  • How is interest rate parity (IRP) merely a version of the cost of carry model?
  • What is the implied forward currency exchange rate under continuous compounding (John Hull)?
  • What is the implied forward rate under annual compounding (Saunders)?

 

(don't peek until you try)

 

 

 

 

 

 

 

 

 

Answer:

Cost of carry says forward = spot*EXP[(rate – dividend/convenience yield)(Time)]. In other words, a dividend or convenience yield accrues to the benefit of the asset holder/owner; it therefore reduces the price of the forward. As Hull says, "a foreign currency can be regarded as an investment asset paying a known yield." As such, the forward = spot*EXP[(domestic rate – foreign rate)(Time)].

See the EditGrid below. Note I am using EditGrid's cool ability to dynamically retrieve exchange rates! Below the implied forward, I illustrated the no-arbitrage idea. Under the first "scenario," you invest domestically at 5%. Under the second scenario, you convert to GBP at the spot, invest at the foreign 5%, then convert back to dollars at the implied forward. Here the U.K. rate is higher, so the implied forward is lower than today's spot: it ensures we don't have a "free lunch" by investing at the U.K. rate.

Also, two compounding scenarios. Same concept, only mechanical difference.

EditGrid:

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