Question

Beth Miller does not believe that the International Fisher Effect holds. Current 1-year interest rates in Europe are 5%, while 1-year interest rates in the U.S. are 3%. Beth converts $100,000 to euros and invests them in Germany. One year later, she converts the euros back to dollars. The current spot rate of the euro is $1.10.

According to the IFE, what should the spot rate of the euro be in 1 year?

If the spot rate of the euro in 1 year is $1.00, what is Beth's percentage return from her strategy?

If the spot rate of the euro in 1 year is $1.08, what is Beth's percentage return from her strategy?

What must the spot rate of the euro be in 1 year for Beth's strategy to be successful?

Answer 1

Part A:

Fwd rate :

Acc to IFE,

Fwd rate = Spot rate * [ (1+Hi) / ( 1 + Fi) ]

Hi = Int rate in US
Fi = Int rate UK

Particulars	Amount
Spot Rate	$ 1.1000
Hi	3.000%
Fi	5.000%
Home Country	US
Foreign Country	Germany
Forward rate for	1

According to Int Rate parity Theorm,
Fwd rate After 1 Years = Spot rate * [ ( 1 + Hi ) ^ n ] / [ ( 1 + Fi ) ^ n ]
= $ 1.1 * [ ( 1 + 0.03) ^ 1 ] / [ ( 1 + 0.05 ) ^ 1 ]
= $ 1.1 * [ ( 1.03) ^ 1 ] / [ ( 1.05 ) ^ 1 ]
= $ 1.1 * [ 1.03 ] / [ 1.05 ]
= $ 1.1 * [ 0.981 ]
= $ 1.079
Part B:

Amount Invested = $ 100000
Convert them into Euro using spot Rate
= 100000 / 1.1
= 90909.09
Invest them in Gemany for 1 Year and realize the matuiry
Maturity Value = 90909.09 * 1.05
= Euro 95454.55
Convert Them into USD using Spot Rate on Maturity
= 95454.55 * 1.00
= 95454.55

Ret = [ AMount Returned - AMount Invested ] / AMount Invested
= [ 95454.55 - 100000 ] / 100000
= -4545.45 / 100000
= -0.0455 I.e -4.55%

Part C:

Amount Invested = $ 100000
Convert them into Euro using spot Rate
= 100000 / 1.1
= 90909.09
Invest them in Gemany for 1 Year and realize the matuiry
Maturity Value = 90909.09 * 1.05
= Euro 95454.55
Convert Them into USD using Spot Rate on Maturity
= 95454.55 * 1.08
= 103090.91

Ret = [ AMount Returned - AMount Invested ] / AMount Invested
= [ 103090.91 - 100000 ] / 100000
= 3090.91 / 100000
= 0.0309 I.e 3.09%

Part D:

Strategy to be successful, The exchange rate shall be more than IFE forward Rate ( $ 1.079 ) as calculated in Part A.