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Magnitude of arbitrage profit and covered arbitrage process

Assume that the current spot exchange rate is FF6.25/$ & three-month forward exchange rate is FF6.28/$. In the U.S. the interest rate of three-month is 5.6% per annum and 8.8% per annum in France. Suppose that you can borrow up to $1,000,000 or FF6,250,000.

a. Estimate how to realize a definite profit by means of covered interest arbitrage, considering that you desire to realize profit in terms of U.S. dollars. Estimate the magnitude of arbitrage profit.

b. Suppose that you desire to realize profit in terms of French francs. Illustrates the covered arbitrage procedure and find out the arbitrage profit in French francs.

The market data is concise as:

   S = FF6.25/$ = $0.16/FF; 

   F = FF6.28/$ = $0.1592/FF; 

   I$ = 1.40%;   iFF = 2.20%

   (1+I­) = 1.014 <  (1+iFF)(F/S) = (1.022)(.1592/.16) = 1.0169 

a. (1) Borrow $1,000,000; repayment $1,014,000.

    (2) Buy FF6, 250,000 spot for $1,000,000.

    (3) Invest in France; maturity value is FF6, 387,500.

    (4) Sell FF6, 387,500 forward for $1,017,118.

    Arbitrage profit $3,118 = $1,017,118 - $1,014,000.

b. (1) Borrow $1,000,000; repayment $1,014,000

    (2) Buy FF6, 250,000 spot for $1,000,000.

    (3) Invest in France; maturity value FF6, 387,500.

    (4) Buy $1,014,000 forward for FF6, 367,920.

    Arbitrage profit will be FF19, 580 = FF6, 387,500-FF6, 367,920.

 

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