You are given the following information: U.S. France Japan Nominal one year inte

Question

You are given the following information: U.S. France Japan Nominal one year interest rate 5% 6% 7% Spot rate ----- $1.16 $0.008 Interest rate parity exists between the U.S. and France as well as the U.S. and Japan. The international Fisher effect exists between the U.S. and France as well as the U.S. and Japan. Bill (based in the U.S.) invests in a one-year CD (certificate of deposit) in France and sells euros one year forward to cover his position. Erica (based in France) invests in a one-year CD in Japan and does not cover her position. What are the returns on funds invested for Bill and Erica respectively? Please justify your explanation both in terms of theory and calculations. (2.5 points) (Hint: You can get the exchange rate between euro and Japanese Yen from their respective rate to USD)

Explanation / Answer

Exchange rates

For 1 Euro you can get $1.16

Or, 1 Euro = $1.16

For 1 Japanese Yen you can get $0.008

Or, 1 Japanese Yen = $0.008

Japanese Yen and Euro exchange rate would be -

1 Japanese Yen = $0.008 / $1.16 per Euro = Euro 0.00689655172

So, we can say that for 1 Japaneses Yen you can get Euro 0.00689655172.

Forward exchange rates

The forward exchange rates calculations as per the interest rate parity and international fisher effect are the same as they both suggest that the future exchange rates are a reflection of the interest rates of the respective countries. The only difference being in the terms, i.e., as per IRPT, the forward rate would be reflective of the interest rates in the respective countries whereas as per International Fisher effect, Estimated Spot rate would be reflective of the interest rate in the respective countries.

The forward exchange rate is calculated as follows

FR or ESR = SR x (1 + rh) / (1 + rf)

Where, FR = Forward Rate, ESR = Estimated spot rate, SR = Spot Rate expressed as the price in currency h (home country) of one unit of currency F (foreign currency), rh and rf = The real interest rates for the respective currencies

If the Forward rates are equal to the rates calculated using the two theorems, their would be no arbitrage opportunity, i.e., whether you invest in US or France or Japan, the return would be equal to the respective interest rate in the resspective countries. Now, we have two situation, one for Bill who has US as the home country and one for Erica who has France has home country, so we would require two forward rates. Interest rates being 5% in US, 6% in France and 7% in Japan.

Forward rate for Bill, considering US as home country and France as foreign country, Euro to dollar forward rate would be -

Euro 1 = $1.16 x (1 + 0.05) / (1 + 0.06) = $1.14905660377

Similarly, Forward rate for Erica considering France as the home country and Japan as the foreign country, Yen to Euro forward rate would be -

Yen 1 = Euro 0.00689655172 x (1 + 0.06) / (1 + 0.07) = Euro 0.00683209796

Return for Bill

Bill purchased CD in france and sells euro one year forward to cover his position, i.e., he will receive euros from the CD after one year and will sell these euros @ forward rate of Euro 1 for $1.14905660377 at that time.

Lets say he invests Euro 1 -

Amount Invested = Euro 1 or $1.16

After 1 year he would receive from the CD = 1 Euro + 6% of Euro 1 = Euro 1.06

Now, he converts the same @ 1 year forward rate and receives -

Amount received = Euro 1.06 x $1.14905660377 / Euro = $1.21799999999 or $1.218

Return = ($1.218 - $1.16) / $1.16 = 5.00%

Which is the rate of interest in US.

Return for Erica

Amount invested = Yen 1 or Euro 0.00689655172

Amount received after 1 year = Yen 1 + 7% of Yen 1 = Yen 1.07

Now, she will convert the same at the future estimate sport rate and will receive -

Amount received = Yen 1.07 x Euro 0.00683209796 / Yen 1 = Euro 0.00731034481

Return = (Euro 0.00731034481 - Euro 0.00689655172) / Euro 0.00689655172 = 6%

which is equal to the interest rate in France.

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