International FinanceFINA 5331

Lecture 8: The market for foreign exchange, continued.

Read: Chapters 5

Aaron Smallwood Ph.D.

The Bid-Ask Spread

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

USD Bank Quotations

American Terms European Terms

Bid Ask Bid Ask

Pounds 1.5902 1.5908 .6286 .6289

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 Bid Ask

Pounds 1.5902 1.5908 .6286 .6289

Sample ProblemA 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?

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 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

$

£¥

Credit Lyonnais

S($/£)=1.50

Credit Agricole

S(¥/£)=125

Barclays

S(¥/$)=100

Suppose we observe these banks posting these exchange rates.

First calculate the implied cross rates to see if an arbitrage exists.

Triangular Arbitrage

Barclays

S(¥/$)=100

The implied S(¥/£) cross rate is S(¥/£) = 150

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.

$Credit Lyonnais

S($/£)=1.50

Credit Agricole

S(¥/£)=125¥ £

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

Review: Triangular Arbitrage

¥

€$

Budapest: S(¥/€) =126.8145-127.2045

Madrid

S($/€)=1.29670-1.29675

Tokyo S($/¥)

=0.01002-0.01008

Suppose we observe these banks posting these exchange rates.

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 $1,000,000First, 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.