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M06_MCDO8122_01_ISM_C06

# M06_MCDO8122_01_ISM_C06 - Chapter 6 The Wide World of...

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Chapter 6 The Wide World of Futures Contracts Question 6.1 The current exchange rate is 0.02 /¥, which implies 50¥/ . The euro continuously compounded interest rate is 0.04, the yen continuously compounded interest rate is 0.01. Time to expiration is 0.5 years. Using the foreign exchange forward formula, (6.2), we find: (0.04 0.01) 0.5 (0.01 0.04) 0.5 euro/yen forward 0.02 0.02 1.015113 0.020302 yen/euro forward 50 50 0.98511 49.2556 e e × × = = × = = = × = Note that when we use euro/yen, our “home” currency is the euro; hence, when applying the formula, we are European. It is the price we (as Europeans) have to pay for the “foreign” currency (the yen). Hence we use our home interest rate (i.e., 4%) r = in the forward exchange formula and we use the yen interest rate as the foreign interest rate (i.e., 1%). y r = Similarly, when we use yen/euro, our “home” currency is the yen; hence when applying the formula, we are Japanese. It is the price we (as Japanese) have to pay for the “foreign” currency (the euro). Hence we use our home interest rate (i.e., 1%) r = in the forward exchange formula and we use the euro interest rate as the foreign interest rate (i.e., 4%). y r = Question 6.2 The current spot exchange rate is \$0.008/ ¥, the one-year continuously compounded dollar interest rate is 5%, and the one-year continuously compounded yen interest rate is 1%. This means that we can calculate the no-arbitrage price of a one-year \$/yen forward to be: (0.05 0.01) dollar/yen forward 0.008 0.008 1.0408108 0.0083265 e = = × = We can see that the observed forward exchange rate of 0.0084 \$/ ¥ is too expensive, relative to the fair forward price. We therefore go short the forward contract and synthetically create a long forward position (buy yen): Today At expiration of the contract Description in \$ in yen in \$ in yen Sell \$/ ¥ forward 0 \$0.0084 1 Buy yen for 0.0079204 dollar 0.0079204 0.99005 Lend 0.99005 yen 0.99005 1 Borrow 0.0079204 dollar + 0.0079204 0.0083265 Total 0 0 0.0000735 0

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72 McDonald • Fundamentals of Derivatives Markets Note that, when we enter into the short forward position, we short 1 yen. This is why we buy 0.99005 yen as .01 0.99005. e = We could have done an arbitrage by buying 1 yen and shorting 1.01005 .01 (i.e. ) e yen forward. With the above arbitrage strategy, we’ve earned 0.0000735 dollars, without any exchange risk or initial investment involved. We have exploited the arbitrage opportunity and would like to increase the scale of this strategy as much as possible (i.e., buy as many yen on the spot market and sell them forward). With a forward exchange rate of 0.0083, the observed price is too cheap. We will buy the forward and synthetically create a short forward position. Today At expiration of the contract Description in \$ in yen in \$ in yen Buy \$/ ¥ forward 0 0.0083\$ + 1 Sell yen for 0.0079204 dollar + 0.0079204 0.99005 Borrow 0.99005 yen + 0.99005 1 Lend 0.0079204 dollar 0.0079204 + 0.0083265 Total 0 0 0.0000265 0 Therefore, we made an arbitrage profit of 0.0000265 dollars.
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M06_MCDO8122_01_ISM_C06 - Chapter 6 The Wide World of...

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