Suppose we have the following exchange rate quotes: Assume interest rate parity

ID: 2784083 • Letter: S

Question

Suppose we have the following exchange rate quotes:

Assume interest rate parity holds, and the current six-month risk-free rate in the United States is 1.37 percent. The six-month risk-free rate in Great Britain, Japan, and Switzerland must be percent ,percent , and percent , respectively.

     Spot rate      6-month
     forward rate   Great Britain (£) .6232         .6227            Japan (¥) 86.47         86.39            Switzerland (Fr) .9249         .9232

Explanation / Answer

According to Interest Rate Parity (IRP) forward exchange rate can be calculated as a function of Spot exchange rate and interest rate differential between domestic and foreign currency. The formula for IRP is:

F=S× (1+rf)/(1+rd)……(1)

Where F = forward exchange rate

S=Spot exchange rate

rd= Domestic interest rate

rf=Foreign interest rate

In the given problem the following quotes for spot and 6 month forward rates are already given:

Currency Problem

USD/GBP

0.6232

0.6227

USD/JPY

86.47

86.39

USD/CHF

0.9249

0.9232

(Note: In exchange rate quoting convention the currency to the left is the base/domestic currency, and the currency to the right is called the quote currency. So an USD/GBP quote of 0.6232 would be read as that 1 unit of USD (base/domestic currency) can buy 0.6232 units of GBP (quote currency)).

We are also provided the U.S. (domestic) risk free interest rate of 1.37%. The question asks for risk free interest rates in Great Britain, Japan, and Switzerland or the rfcomponent of equation 1. In terms of rf equation 1 can be written as:

rf= ((F/S)× (1+rd))-1……….(2)

Now we simply have to plug in the values in the above equation:

Great Britain (rf) = (0.6227/0.6232) × (1.0137)-1

= 1.012887-1

=0.012887=1.2887%=1.29%

Japan(rf)= (86.39/86.47) × (1.0137)-1

= 1.012762-1

=0.012762=1.2762%=1.28%

Switzerland (rf) = (0.9232/0.9249) × (1.0137)-1

= 1.011837-1

=0.011837=1.1837%=1.18%