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
S
F
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%
Currency Problem
S
F
USD/GBP
0.6232
0.6227
USD/JPY
86.47
86.39
USD/CHF
0.9249
0.9232