International Finance Lecture 8: The market for foreign exchange, continued. Read: Chapters 5 Aaron Smallwood Ph.D.

The Bid-Ask Spread USD Bank Quotations American Terms European Terms Pounds 1.5902 1.5908 .6286 .6289 A dealer pricing pounds in terms of dollars would likely quote these prices as 02–08. Anyone trading $10m knows the “big figure.”… 1.59

The Bid-Ask Spread Notice that the reciprocal of the direct bid quote gives the ask price: USD Bank Quotations American Terms European Terms Bid Ask Pounds 1.5902 1.5908 .6286 .6289

What are her proceeds from conversion? Sample Problem A businesswoman has just completed transactions in Italy and England. She is now holding €250,000 and £500,000 and wants to convert to RMB. Her bank provides this quotation: GBP/RMB 0.10109 – 0.10112 RMB/EUR 8.2540 – 8.2588 Pounds: ? Euros: ? Total: ? What are her proceeds from conversion? $1,353,502.58

Proceeds Pounds: We buy RMB in the market for RMB: £500,000/0.10112=RMB 4,944,620.25 Euros: We sell euros in the market for euros: €250,000*8.2540 = RMB 2,063,500 Total: RMB 7,008,120.25

Spot FX Trading In the interbank market, the standard size trade is about U.S. $10 million. A bank trading room is a noisy, active place. The stakes are high. The “long term” is about 10 minutes.

Cross rates with bid-ask spreads USD Bank Quotations American Terms European Terms Bid Ask Pounds 1.5902 1.5908 0.6286 0.6289 RMB 0.1622 0.1630 6.1350 6.1652

So? What are the RMB/pound bid and ask prices? Suppose a trader sells £10,000. How much do they receive? The trader effectively sells pounds for RMB9.7559.

What about selling yuan? Suppose we sell RMB10,000 (buy pound). We could figure the cross-currency rate, by asking: - How much do we receive when we first buy dollars with RMB? RMB10,000*0.1622 = $1,622 - How much do we receive from selling dollar for pounds? $1,622/1.5908 = £1,019.61. Effectively RMB ask price for the pound: 10,000/1,019.16= RMB 9.8076 BID/ASK price: 9.7559 – 9.8076

Concept of arbitrage Suppose you are lucky enough to see two currency windows next to each other. At the first window you see the following quote for the euro: RMB 8.2455 – 8.2498 At the second window you observe the following: RMB 8.2508 – 8.2555

What? Can easily profit: Buy euros at the first bank for RMB8.2498. Sell them at the second bank for RMB 8.2508. Maybe not too realistic. Let’s consider triangular arbitrage: Involves three markets. Let’s start with a simple example.

Triangular Arbitrage $ ¥ £ Suppose we observe these banks posting these exchange rates. $ £ ¥ Credit Lyonnais S($/£)=1.50 Credit Agricole S(¥/£)=125 Barclays S(¥/$)=100 First calculate the implied cross rates to see if an arbitrage exists. 12

Triangular Arbitrage $ ¥ £ The implied S(¥/£) cross rate is S(¥/£) = 150 $ Credit Lyonnais S($/£)=1.50 Credit Agricole S(¥/£)=125 ¥ £ Barclays S(¥/$)=100 Credit Agricole has posted a quote of S(¥/£)=125 so there is an arbitrage opportunity. So, how can we make money? Buy the £ @ ¥125; sell @ ¥150. 13

Triangular Arbitrage Sell $100,000 for ¥ at S(¥/$) = 100 receive ¥10,000,000 Sell ¥10,000,000 for £ at S(¥/£) = 125 receive £80,000 Sell £ 80,000 for $ at S($/£) = 1.50 receive $120,000 profit per round trip = $ 120,000- $100,000 = $20,000 14

Review: Triangular Arbitrage Suppose we observe these banks posting these exchange rates. ¥ € $ Budapest: S(¥/€) =126.8145-127.2045 Madrid S($/€)=1.29670-1.29675 Tokyo S($/¥) =0.01002-0.01008 First calculate the implied cross rates to see if an arbitrage exists.

Review: Triangular Arbitrage Sell $10,000,000 for ¥ at S($/ ¥) ask = $ 0.01008 receive ¥992,063,492.06 Sell our ¥992,063,492.06 for € at S(¥/ €) = ¥127.2045 receive €7,798,965.38 Sell € 7,798,965.38 for $ at S($/€) =1.29670 receive $10,112,918.41 profit per round trip = $ 10,112.918.41- $10,000,000 = $112,918.41

Triangular Arbitrage: One more We want to consider another example with bid-ask spreads. See example in the textbook, with the following quotes: Market for pounds: $1.9712-17 Market for euros: $1.4739-44 Market for pounds: €1.3305-10 Implied price in the third market is 1.3370-77. POUND UNDERVALED!

Exploit the arbitrage opportunity Suppose we start with $1,000,000 First, we need to get euros so we can buy pounds in the 3rd market. Start by selling dollars for euros: We receive: $1,000,000/1.4744 = €678,242.00 Sell euros for pounds: We receive: €678,242.00/1.3310 = £509,573.25 Finally, sell pounds for dollars We receive: £509,573.25*1.9712 = $1,004,470.79 PROFIT: $4,470.79.