Lecture Notes: Chapter 7
Arbitrage is known as “riskless” profit. This chapter focuses on how exchange rates across the globe will be equal if there is no central trading location. Stocks that trade on the NYSE are physically traded at one location, so the price is determined at that one location. Currencies are traded at banks located all over the world. So how do we know what the “equilibrium” exchange rate is, if it is being traded at so many locations?
Back the gas example:
Assume that gas stations not only sold gallons of gas also bought gallons of gas from the general public. In other words, at any point in time a gas station would have two prices, the price at which they buy gas from you at (BID) and the price at which they would sell gas to you at (ASK). If this were the case, then barring any transportation costs, we would be more likely to see gas approach an equilibrium price within a community. If gas were priced at a bid of $2.82 and an ask of $2.85 per gallon in Jackson, but priced at a bid of $2.87 and an ask of $2.89 per gallon in Cape, then you simply go to Jackson and buy as many gallons as you could hold in Jackson for $2.85 per gallon and sell them to the Cape gas station for $2.87 per gallon. Your riskless profit would be $0.02 per gallon. How long do you think this opportunity will last? Of course, you would expect the “ask” price at Jackson to eventually increase and the “bid” price at Cape to eventually decrease until it was no longer possible to earn an arbitrage profit.
Foreign Currency Locational Arbitrage:
Because of the nature of foreign currency trading, (electronic transfers) there is virtually no cost to carry currencies. However, the prices at which currencies are quoted are for a limited quantity of currency. When you call a bank and get a quote on a currency, you will be given a limit on how much you can buy or sell at the given prices. Let’s say you call a bank and request a quote on 5 million Euros. The quotes you are given are good for about 10 seconds and are only good for up to 5 million Euros. In practice, foreign exchange dealers compare quotes from banks on computer screens and the first program to spot an arbitrage opportunity will take advantage of it. Once someone has spotted the opportunity and taken advantage of it, future quotes will adjust until there are no more opportunities left. As you might imagine, this happens very quickly.
Consider the following direct quotes on the Euro EUR:USD (quotes are for 100,000 Euros):
Bid AskBid Ask
Bank A:1.1265 1.1267 Bank B:1.12611.1263
1)How would you be able to use Locational Arbitrage to make a profit and what would your profit be?
Execute a buy of 100,000 Euros from Bank B at $1.1263/1EUR and immediately execute a sell of 100,000 Euros to Bank A at $1.1265/1EUR. Your profit will be $20.
2)What would happen to the next price quotes from Bank A and Bank B?
The ask price from Bank B would rise and the Bid price at Bank A would fall, until there is no opportunity for an arbitrage profit.
Foreign Currency Triangular Arbitrage:
Triangular Arbitrage: Cross rates for all currencies will be in equilibrium due to triangular arbitrage.
BidAsk
Bank:#Cad/ 1 USD = 1.032551.03285
#JPY/ 1 USD =107.455107.474
Cross Rate# Cad/ 1 JPY =.009607.009612
Here we are looking at the indirect rates on the Canadian dollar and the Japanese Yen. Notice, in theory, the cross rate for the value of the Japanese Yen in terms of Canadian dollars are found by using the indirect bid rate on the Canadian dollar divided by the indirect ask rate on the Japanese Yen. Triangular arbitrage is a little more complicated in that theoretically, any bid or ask on currencies relative to the dollar and any bid or ask on the cross rates from any bank will be in equilibrium. IF you were to find a cross rate quote that was not in equilibrium, there would exist an opportunity for triangular arbitrage and that opportunity would disappear as quotes adjusted.
Covered Interest Arbitrage and Interest Rate Parity:
Covered Interest Rate Arbitrage is the process of capitalizing on the interest rate differential between two currencies while covering your exchange rate risk with a forward contract. The forward premium (Forward Rate – Spot Rate)/ Spot Rate is approximately equal to the difference in interest rates over the same period (interest rates US – interest rates ForCurrency), where the Forward and Spot rate are given as a direct quotes (#US$/1ForCurrency).
Interest rate parity:
Covered interest arbitrage is not possible for points along the IRP line. US investors benefit in situations below the IRP line. Foreign investors benefit in situations above the IRP line.
Example Problems:
1)Assume the bid rate of a New Zealand dollar is $.646 while the ask rate is $.648 at Bank X. Assume the bid rate of the New Zealand dollar is $.642 while the ask rate is $.644 at Bank Y. Given this information, what would be your gain if you use $100,000 and execute locational arbitrage? That is, how much will you end up with over and above the $100,000 you started with?
$______
2)National Bank quotes the following for the British pound and the New Zealand dollar:
Quoted Bid PriceQuoted Ask Price
Value of a British pound (£) in $$1.255/1£$1.259/1£
Value of a New Zealand dollar (NZD) in $$.752/1NZD$.757/1NZD
Value of a British pound in
New Zealand dollars NZD 1.681/1GBPNZD 1.695/1GBP
What should the Cross be between the British pound and NZD in terms of # of NZD per 1 GBP.
BidAsk
______
Assume you have $100,000 to conduct triangular arbitrage. What is your profit from implementing this strategy?
$______
3)Assume the following information:
Current spot rate of New Zealand dollar =$.615
One-year forward rate of the New Zealand dollar =$.625
Annual interest rate on New Zealand dollars =2.3%
Annual interest rate on U.S. dollars =2.8%
a)Given the information in this question, the additional profit from covered interest arbitrage by U.S. investors with $100,000 to invest is equal to $______
b)Would Covered interest Arbitrage work for a New Zealand investor with 100,000 NZD to invest?
4)Assume the following information:
Current spot rate of MXP =$0.10
One-year forward rate of the MXP=$0.098
Annual interest rate on MXP=6%
Annual interest rate on U.S. dollars =4.8%
a)Given the information in this question, the additional profit from covered interest arbitrage by a Mexican Investor with 100,000 MXP to invest.
______Pesos
b)Would covered interest arbitrage work for a US investor with $100,000 to invest?
5)National Bank quotes the following for the Euro and the Peso:
Quoted Bid PriceQuoted Ask Price
Value of a Euro in $$1.125/1EUR$1.127/1EUR
Value of a Peso in $$.055/1Peso$.058/1NZD
Value of a Euro in
Pesos MXN 21/1EURMXN 22/1EUR
What should the Cross be between the Euro and Peso in terms of # of Peso per 1 Euro
BidAsk
______
Assume you have $100,000 to conduct triangular arbitrage. What is your profit from implementing this strategy?
$______