With a minimal amount of research, you determine the following information regar

Question

With a minimal amount of research, you determine the following information regarding the U.S. dollar and the British Pound: United States Great Britain

Investor’s Required Rate of Interest (real) 2.25% 2.25%

Nominal interest rate 9.0 12.75

Spot Rate $1.56/ £

6-month forward rate $1.54/ £

Call premium at strike price of $1.56 2.25%

With the above information, determine the following: Future $ spot rate in 6 months of the dollar to the pound. Using the Fisher Effect relationship, determine the expected inflation. Determine the International Fisher Effect.

Explanation / Answer

Future $ spot rate in 6 months of the dollar to the pound is $1.53

The fisher effect can be represented mathematically as follows:

1 + Nominal rate = (1 + Real rate)(1 + Expected inflation rate)

1 + r = (1 + a) (1 + i)

Thus (1 + 0.09) = (1 + 0.0225)(1 + Expected inflation rate)

(1 + Expected inflation rate) = (1 + 0.09)/(1 + 0.0225)

(1 + Expected inflation rate) = 1.066015

Expected inflation rate = 1.066015 – 1 = 0.066015

Expected U.S inflation rate = 6.60%

Thus (1 + 0.1275) = (1 + 0.0225)(1 + Expected inflation rate)

(1 + Expected inflation rate) = (1 + 0.1275)/(1 + 0.0225)

(1 + Expected inflation rate) = 1.1026895

Expected inflation rate = 1.1026895 – 1 = 0.1026895

Expected Great Britain inflation rate = 10.27%

Multiplying the current spot exchange rate by the nominal annual U.S. interest rate and dividing by the nominal annual U.K. interest rate yields the estimate of the spot exchange rate 6 months from now:

$1.56 * (1 + 0.045)/(1 + 0.06375) = $1.5325

E (e) = (4.5% - 6.375%)/(1 + 6.375%) = -0.0176263 = -1.76%

The expected percentage change in the exchange rate is a depreciation of 1.76% for the GBP (it now only costs $1.53 to purchase 1 GBP rather than $1.56), which is consistent with the expectation that the value of the currency in the country with a higher interest rate will depreciate.

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