Interest Rate Parity

Interest rate parity states that the forward rate premium (or discount) of a currency should reflect the differential in interest rates between the two countries.

The discounted interest rates differential equals the percentage forward discount. The spot rate is the present value of the forward rate. The interest rate is a bridge. Interest rate parity is equivalent to the statement that one unit of foreign currency, deliverable on a particular future date, must cost the same amount independently of whether it is obtained through the forward market or by means of the spot market.                      The difference in the spot and forward rates for currencies are due solely to differentials in interest rates.

Covered Interest Arbitrage

 A simple currency swap in which the counterparties exchange currencies at both the spot and forward rates simultaneously. The forward swap restores currency exposures to the original position without a currency gain or loss-making this a way to adjust exposure to a narrowing or widening of interest rate differentials rather than adjusting currency exposures. Covered interest arbitrage also insures interest rate parity because this relationship prevents speculators from profiting by borrowing in a low interest rate country and simultaneously lending in a high interest rate country and hedging the currency risk.

Covered interest rate parity

Covered interest parity: interest rates denominated in different currencies are the same once you "cover'' yourself against possible currency changes. The argument follows the standard logic of arbitrage in finance.

Consider two relatively riskless strategies for investing a Dollar for one year:

  1. Invest dollar in US deposit.  After one year, you have (1+i) dollars where i is the dollar rate of interest.
  2.  Alternate strategy has several steps:
  • Convert the $ to DM, giving e DMs where e is the spot exchange rate.
  • Invest the money in a DM deposit, earning if which leaves you with  (1+if)e  DMs at the end of the year.
  • We could convert back to $ at whatever the exchange rate happens to be at the end of the year, but that exposes you to the risk that the DM will fall.
  • To protect against a DM depreciation, you could sell DMs forward.  You will have (1+if)e  DM at the end of the year that you will want to convert back to $ which can be arranged with a one year forward contract at the exchange rate f.  Thus, at the end of the year, you would have (1+if)e/f  $. 
Join now!

Which strategy is better?


    Yield of (1 + i) or yield of  (1+i
f)e/f ?


Well, if either strategy had a higher payoff, you could short one and go long the other, earning huge profits with no risk. We should make sure that the
forward exchange rate is set so that the returns are equal:
 

(1 + i) = ( 1 + if) e/f 

OR:         f  = e ( 1 + if)  / (1 + i)  

Covered interest parity condition.

Example:  If the US interest rate is i = 8% and the German rate if = 6% and the ...

This is a preview of the whole essay