finance assignment

The following are quotes for several US currency dealers.

Inter-dealer arbitrage

1a. Is there an arbitrage opportunity in Singapore dollars?  If so, what exchanges should you make to take advantage of it? (Be specific about which dealer you would select, which currency you would buy from or sell to that dealer, and how much of the other currency you would pay or receive.

Buy US$ from C (at 1.4277), sell them to A (at 1.4278)

b. How profitable is a round trip trade? (State the profitability either in percent or basis points.)

.7% or .007 basis points (1.4278/1.4277-1)

2a. Is there an arbitrage opportunity in British pounds?  If so, what exchanges should you make to take advantage of it? (Be specific as indicated in question 1.)

Buy £ from E (at 1.4248), sell them to D (at 1.4250)

b. How profitable is a round trip trade? (State the profitability either in percent or basis points.)

.014% or 1.4 basis points (1.4250/1.4248-1)

Triangular arbitrage (Inter-market) - assume that the highest bid and lowest ask for each currency are equal (so that the bid-ask spread is zero)

3. In the NY currency market, the exchange rate for Japanese yen (USC/JPY) is 118.9055 and the rate for Thai baht (USD/THB) is 32.623. What must the quote for the baht in Tokyo (THB/JPY) be if no arbitrage opportunity exists?

3.6448 [118.9055/32.623]

4a. Using the spot exchange rates indicated in the previous questions, if the exchange rate in Tokyo for the baht is 3.3182, what trades should you make to take advantage of the arbitrage opportunity? (For each transaction, be specific about where the trade takes place, which currency you would purchase (or sell) and which currency you would use to pay (or receive).)

In Tokyo, sell ¥1 to buy ฿0.301368 [1/3.3182]. In NY, sell ฿0.301368 to receive $0.0092379 0.301368/32.623]; the sell $0.0091379 to receive ¥1.09844 [0.0092379*118.9055].

b. How profitable is a round trip trade? State the profitability either in percent or basis points.

9.844% or 984.4 basis points (3.6448/3.3182-1)

5a. In the NY currency market, the exchange rate for the Kuwaiti Dinar (USD/KWD) is 0.3035 and the exchange rate for the euro (EUR/USD) is 1.0868. If the dinar trades in Paris (EUR/KWD) for 0.3302, what trades should you make to take advantage of the arbitrage opportunity? (For each transaction, be specific as indicated in question 4.)

Implied cross rate is EUR/KWD 0.32984 [0.3035/1.0868]. In Paris, sell €1 to obtain 0.3302 ك.د. [1*0.3302] In NY, sell 0.3302  ك.د to obtain $1.08797 [0.3302/0.3035]; sell $1.08797 to obtain €1.00108 [1.08797/1.0868]

b. How profitable is a round trip trade? (State the profitability either in percent or basis points.)

0.108% or 10.8 basis points [0.3035/0.3302-1]

6. In the NY currency market, the exchange rate for the Australian dollar (AUD/USD) is 0.7070 and the exchange rate for the British pound (GBP/USD) is 14252. If Australian dollars trade in London (GBP/AUD) for 2.0142, what trades should you make to take advantage of the arbitrage opportunity? (For each transaction, be specific as indicated in question 4.)

Implied cross rate is 2.0158 [1.4252/0.7070]. In London, use A$2.0142 to buy £1. In NY, sell £1 to buy $1.4252, sell $1.4252 to buy A$2.0158.

b. How profitable is a round trip trade? (State the profitability either in percent or basis points.)

.0815% or 8.15 basis points [2.0158/2.0142-1]

Covered interest arbitrage (Inter-temporal) - assume that the highest bid and lowest ask are equal (i.e., that the bid-ask spread is zero)

7. Assume the interest rate of 1-year risk free debt denominated in US dollars is 1.24% and the interest rate on 1-year risk free debt denominated in euros is 0.10%, if today’s spot market exchange rate for euros is 1.0863, what is the 1-year forward exchange rate if interest rate parity holds?

1.0987 [1.0863*1.0125/1.001]

8. If the 1-year forward exchange rate for euros is 1.1011 and the spot market exchange rate and interest rates are as indicated in question 7, what trades should you make to take advantage of the arbitrage opportunity? (Immediate transactions will include: borrowing one currency at the risk free rate, exchanging one currency for another, investing one currency in risk free debt, and entering a long or short forward contract for a currency. Transactions in one year will include: repaying the loan, closing out the investment, and buying or selling a currency pursuant to the forward contract. Be specific about both current and future transactions.

Actual forward, 1.1011 > implied forward, 1.0987. So sell in forward market, buy in spot (buying and selling euros) (Profit is 1.1011/1.0987-1 = .00221.)

In spot market, borrow $, sell $ to obtain €, invest €, enter forward contract to sell €. (E.g. in spot market borrow $1m; sell $1m to obtain €920,566 [1m/1.0863]; invest 920,566; enter forward to sell €921,477.)

In forward market, close out € investment, sell € to obtain dollars, repay loan. (E.g., in forward market close out investment to receive €921,477 [920,566*1.001]; sell €921477 pursuant to forward contract to obtain $1,014638 [921477*1.1011]; use $1,012,400 [1000000*1.0124] to repay loan; keep $2,237.85 profit.

b. How profitable is a round trip trade? (State the profitability, either in dollars or euros and in percent.)

Profit is $2237.85 (or €2032.38 if forward contract was to buy only enough $ euros to repay the loan) or 22.4%.  (Present value of profit is 2,210.44 [=2237.85/1.0124], 22.1 basis points or .221% [= 1.1011/1.0987-1])

9.  Assume the interest rate on 6-month risk free debt denominated in US dollars is 0.45%, the interest rate on 6-month risk free debt denominated in Indonesian rupiah is 7.25%, if today’s spot market exchange rate for the rupiah (USD/IDR) is 13,882.0, what must the 6-month forward rate on the rupiah be if interest rate parity holds?

14344.18 [13882*(1.0725/1.0045)1/2] or 14352.93 [13882*(1+.0725/2)/(1+.0045/2)]

10a. If the 6-month forward exchange rate for Indonesian rupiah is 14492.5 and the spot market exchange rate and interest rates are as indicated in question 9, what trades should you make to take advantage of the arbitrage opportunity? (Immediate transactions will include: borrowing one currency at the risk free rate, exchanging one currency for another, investing one currency in risk free debt, and entering a long or short forward contract for a currency. Transactions in 6 months will include: repaying the loan, closing out the investment, and buying or selling a currency pursuant to the forward contract. Be specific about both current and future transactions.

Actual forward, 14492.5 > implied forward, 14344.18. So sell in forward market, buy in spot (buying and selling dollars) (Profit is 14492.5/14344.18-1 = 0.01034.)

In spot market, borrow Rp, sell Rp to obtain $, invest $, enter forward contract to sell $. (E.g. in spot market borrow Rp$1m; sell Rp1m to obtain $72.04 [1m/12882]; invest 72.04; enter forward to sell $72.20.)

In forward market, close out $ investment, sell $ to obtain Rp, repay loan. (E.g., in forward market close out investment to receive $72.20 [72.04*1.00451/2]; sell $72.20 pursuant to forward contract to obtain $1,046324 [72.20*1.44492.5]; use Rp1,035,616 [1m*1.07251/2] to repay loan; keep Rp10,708.

b. How profitable is a round trip trade? (State the profitability, either in dollars or rupiah and in percent.)

Profit is Rp10,708 (or $0.74 if forward contract was to buy only enough Rp to repay the loan) or 1.071%. (Present value of profit is Rp10,340 [10708/1.0725.5], 103.4 basis points or 1.034% [=14482.5/14344.18-1])