 # Covered Interest Rate Parity

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## Essay title: Covered Interest Rate Parity

INTRODUCTION

Efficiency of money markets has often been subject of debates. The theory of CIRP (Covered Interest Rate Parity)

Keynes citation

DISCUSSION

I. The theory of CIRP

A forward contract represents an agreement between two parties to exchange currencies at a future date and at a forward exchange rate, both being defined in the contract. In this context, the forward premium must be equal to the difference between the forward exchange rate Ft and the spot exchange rate S0 of one currency, divided by this spot exchange rate S0.

The theory of CIRP (assumed without transaction cost) states that the forward premium and the interest rates differential between similar assets of two countries are related as follows in an efficient market over a specified period, i.e. a market where there are no arbitrage opportunities:

F0,t - S0 = i - i* (1)

S0 1+ i*

leading to F0,t = 1+ i

S0 1+ i*

where F0,t , S0, i and i* are respectively the forward exchange rate, the spot exchange rate, the domestic interest rate and the foreign interest rate.

To obtain this equation, we assume that CIRP holds. Therefore, it is possible to assume that an investor buys today units of foreign currency at a spot exchange rate of the domestic market, 1/S0, and invests this amount in foreign treasury bonds at a yield of i*. He will obtain (1/ S0)(1+ i*) units of foreign currency at the end of the defined period.

Furthermore, he may sell this amount today at a forward exchange rate F0,t; it will result in (1+S0)(1+i*)F0,t units of domestic currency at the end of the forward contract. If the market is efficient, this yield should be equal to the yield obtained from investing one unit of national currency at a rate of 1+i.

II. Empirical test for Euro and US dollar currencies

In order to validate this theory, let us consider a transaction involving the US dollar (\$) and the Euro (в‚¬) as of November, 15th 2007. Spot exchange rates and one year forward exchange rates have been collected from the Financial Times website; the domestic interest rate is related to French treasury notes and the foreign interest rate to US treasury notes, both rates are based on a one year investment.

Indeed, as Aliber (1973) has recognized, CIRP can only provide relevant results if the interest rates are based on comparable assets with the same maturity as the one of the forward exchange used.

The information collected is as follows:

The \$/в‚¬ spot rate S0 = 1.4628

The one year \$/в‚¬ forward rate F0,360= 1. 4632

US interest rate i 3.50% per annum (data adjusted from US Federal Reserve)

French interest rate i* 4.00% per annum (data adjusted from Banque de France)

In a first part, it is necessary to verify if the interest rate parity between both currencies is covered using equation (1):

Let us calculate the forward premium: F0,t - S0 = (1.4632 вЂ“ 1.4628) = 0.00027

S0 1.4628

and the interest rate differential: i - i* = 0.0349 вЂ“ 0.0401 = -0.35198

1+ i* 1+ 0.0401

Obviously, we can conclude that the forward premium is not equal to the interest rate differential, therefore CIRP doesnвЂ™t hold and an arbitrage activity might be possible.

Since, the forward premium is greater than the interest rate differential, we can deduct:

i < (S0 / F0,t) (1+ i*) вЂ“ 1 (2)

This means that it would be more profitable to invest money on the French market than on the US one.

As French treasury notes often require an important minimum investment, it would be useful to have an order of magnitude of an investorвЂ™s arbitrage profit.

To illustrate that, let us assume an American investor who wants to invest 1,000,000\$:

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