International Finance FINA 5331 Lecture 8: The market for foreign exchange, continued. Read: Chapters 5 Aaron Smallwood Ph.D.
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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.
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