Question

Suppose the spot exchange rate is €1 =$1.10, the expected exchange rate one year in the future is €1 =$1.122, the dollar interest rate is 4%, and the euro interest rate is 2%.

b) To check for interest parity:

i)Calculate the expected dollar rate of return on dollar deposits.

ii)Calculate the expected dollar rate of return on euro deposits.

iii)Does interest parity condition hold?

c)Which currency deposits will the investors want to hold and how will the spot exchange rate change (find the new value) if:

I)The dollar interest rate increases to5%.

ii)The dollar interest rate remains4%, but the expected exchange rate changes to€1 =$1.144

.d)If spot exchange rate is €1 =$1.10, the dollar interest rate is 5%, and the euro interest rate is 2%,and covered interest rate parity holds, what should be the forward exchange rate one year in the future?

Answer 1

Spot Exchange rate €1 =$1.10
1 year future expected exchange rate €1 =$1.122
$ Interest Rate = 4%
€ Interest Rate = 2%
Interest Parity - The theory of interest rate parity states that the difference between the interest rate in two countries is equal to the differential between the forward rate.
b) To check for interest parity:
i) Calculate the expected dollar rate of return on dollar deposits.
>	Assume dollar is the domestic currency
>	Rate of return is simply the interest rate on dollar
>	After 1 year the $1 is expected to yield $1.04.
>	Return = ($1.04-$1)/$1 = 4%
ii)Calculate the expected dollar rate of return on euro deposits (calculation are rounded off to nearest $)
>	Assume dollar is the domestic currency
>	Now suppose we have $100 then it can be exchanged today for €91 (100/1.10)
>	The €91 will yield €93 (€91*1.02) after one year
>	These €93 are expected to be worth $1.122/€1 x €93 = $104
>	The rate of return in terms of dollars from investing in euro deposits is ($104-$100)/$100 = 4.0%.
iii)Does interest parity condition hold?
1 year future expected exchange rate €1 if interest parity condition hold
* Future direct quote	=	1+ $ Interest Rate (D)	* Spot direct quote	=	1.04	* 1.1	=	1.122
		1+€ Interest Rate (F)			1.02
D = Domestic Currency
F = Foreign Currency
Spot direct quote = the domestic currency is variable and the foreign currency is fixed at one unit
Yes interest parity hold because one year expected exchange rate based on interest differential is same of expected exchange rate one year in the future
c)Which currency deposits will the investors want to hold and how will the spot exchange rate change (find the new value) if:
i)The dollar interest rate increases to5%.
New spot exchange rate based on 5% dollar interest rate
* Spot direct quote	=	1+ $ Interest Rate (F)	* Future direct quote	=	1.02	* 1.122	=	1.09
		1+€ Interest Rate (D)			1.05
ii)The dollar interest rate remains4%, but the expected exchange rate changes to€1 =$1.144
New spot exchange rate based on 5% dollar interest rate
* Spot direct quote	=	1+ $ Interest Rate (F)	* Future direct quote	=	1.02	* 1.144	=	1.12
		1+€ Interest Rate (D)			1.04
As long as the interest parity hold between these currencies the investor will be neutral for deposits.
d)If spot exchange rate is €1 =$1.10, the dollar interest rate is 5%, and the euro interest rate is 2%,and covered interest rate parity holds, what should be the forward exchange rate one year in the future?
1 year future expected exchange rate €1 if interest parity condition hold
* Future direct quote	=	1+ $ Interest Rate (D)	* Spot direct quote	=	1.05	* 1.1	=	1.132
		1+€ Interest Rate (F)			1.02