Solutions: The Foreign Exchange Market

1. Using the table:
   (a) what is the Canadian dollar–euro spot cross-exchange rate?
   = =
   (Note: €0.722 = CAD1 OR So (CAD/€) = 1.3846 are also correct)
   (b) what is the 6-month forward pound–yen cross-exchange rate?
   = =
   (Note: ¥200/£ is also correct)
   (c) what is 3-month forward premium or discount (expressed as an annual percentage
   rate) for the British pound in terms of U.S. dollars?
   0.28% = ×
2. You are given the following foreign exchange quotations by a bank:
   Yen = 1AUD GBP = 1 AUD USD = 1 AUD
   Spot 113.33/14.22 0.4876/85 0.6870/79
   3 month 106.22/09.02 0.4454/89 0.6770/84
   6 month 102.45/04.11 0.4211/95 0.6612/76
   (a) For a client, how many Yen could 1 million GBP buy, spot?
   Sell 1 million GBP for AUD and receive
   GBP 1,000,000/(GBP 0.4885/AUD) = AUD 2,047,082.9
   Sell AUD for Yen to receive
   AUD 2,047,082.9 * Yen 113.33/AUD = ¥ 231,995,906.19
   (b) At what rate would the customer buy Yen 3 months forward?
   Buy Yen at ¥ 106.22 (the quote is ¥/AUD, the bank is buying/selling AUD. Here, the customer is
   buying ¥ in exchange for AUD. Since the quote is from the bank’s perspective, it will buy AUD
   at the bid/buy price.)
   (c) At what rate would a client buy GBP for USD, 3 months forward?
   Sell USD at 0.6784/AUD and
   Buy GBP at 0.4454/AUD
   The rate is GBP 0.6565/USD (0.4454/0.6784)
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   (d) At what rate would the customer buy Yen and sell pounds, spot?
   Sell £ at 0.4885/AUD and
   Buy ¥ at 113.33/AUD
   1 £ = 113.33/0.4885 = ¥ 231.99/£
   (e) How many USD could 10 million Yen buy, six months forward?
   Sell ¥ 10m to receive = ¥ 10,000,000/(¥ 104.11/AUD) = A$ 96,052.25
   Sell AUD for USD = A$ 96,052.25*(U$ 0.6612/$A) = U$ 63,509.75
   (f) At what rate could a client buy Yen for GBP, six months forward?
   Buy ¥ (6mth forward rate) at ¥ 102.45/$A
   Sell £ (6mth forward rate) at £ 0.4295/$A
   1 £ = ¥ 102.45/( £ 0.4295/$A) = ¥ 238.53
3. As a foreign exchange trader for Mitsubishi Bank, one of your customers would like a
   spot yen quote on Australian dollars. Current market rates are:
   ¥101.37 – 85/USD
   AUD1.2924 – 44/USD
   What bid and ask rates would you quote for the ¥/AUD exchange rate?
   We must calculate the rate at which the bank will buy or sell $A in exchange for Yen.
   Bid Price for AUD is given by:
   $A 1.2944 = Yen 101.37
   $A = Yen 78.31
   Ask price for AUD is given by:
   $A 1.2924 = Yen 101.85
   $A = Yen 78.81
   Bid – Ask Price = Yen 78.31 – 78.81/$A
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4. Restate the following one-, three-, and six-month outright forward European term bidask
   quotes in forward points.
   Spot 1.3431-1.3436
   One-month 1.3432-1.3442
   Three-month 1.3448-1.3463
   Six-month 1.3488-1.3508
   Swap points are the difference between the outright forward rate and the spot rate. Swap
   points are 01-06, 17-27 and 57-72 for one-, three- and six-months respectively.
5. Given the following information, what are the NZD/S$ currency against bid-ask
   quotations.
   American terms European terms
   Bid Ask Bid Ask
   US$/NZ$ 0.4660 0.4667 NZ$/US$ 2.1427 2.1459
   US$/Sing$ 0.5705 0.5710 Sing$/US$ 1.7513 1.7528
   Note: American terms is direct quote from the perspective of the US$ ie US$/FC.
   The cross-rate that we are after is the rate at which the bank will buy/sell S$ in exchange for
   NZ$. The quote is calculated using the two currencies exchange rate relative to the US$.
   Cross rate (NZ$/S$)  (US$/S$)/(US$/NZ$)
   Buy/Bid for S$: Bank sells US$ in exchange for S$ (0.5705) and then sells NZ$ in exchange for
   US$ (0.4667)
   Sell/Ask for S$: Bank buys NZ$ in exchange for US$ (0.4660) and then sells S$ in exchange for
   US$ (0.5710)
   NZ$/S$: 1.2224 – 1.2253 (rounded to 4 decimal places)
6. The Euro quote is Euro 1.0242/$1 (from Dresdner Bank) and the CHF 1.5030/$ (from
   Credit Suisse). UBS is quoting Euro/CHF at 0.6750/CHF. Show how you can make a
   triangular arbitrage by trading at these prices. Assume that you have $5,000,000 with
   which to conduct the arbitrage. What happens if you initially sell $ for CHF? What
   Euro/CHF price will eliminate triangular arbitrage?
   The synthetic cross-rate is 0.68141 Euro/CHF (1.0242/1.5030) while the actual cross rate is
   0.6750 euro/CHF, i.e. the Euro is overvalued (fewer euros are required to by 1 CHF)
   1 This is just an approximation. If you want to get to dollar precision, you would need 0.6814371Euro/CHF (7
   digits) since we have $5mil (7 digits) in this case.
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7. Sell $5,000,000 for Euro @ Euro 1.0242/S to Dresdner. This will yield Euro 5,121,000
   ($5,000,000*1.0242).
8. Sell Euros for CHF at Euro 0.6750/CHF. This action will yield CHF 7,586,667
   (5121000/0.6750).
9. Resell CHF for US$ at CHF 1.5030/$. This results in $5,047,682. The arbitrage profit is
   $47,682.
   The Euro/CHF cross rate should be 0.6814. At this rate triangular arbitrage opportunities will not
   exist. Profit is a function of the purchase of CHF at too low a rate in comparison to the
   equilibrium rate.
   Strategy: Buy CHF and Sell Euro
   $
   *€1.0242/$
   €
   Strategy: Buy CHF & Sell Euro
   ÷ (€0.6750/CHF)
   CHF
   ÷$1.5030/$

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