Arbitrage in the foreign exchange market Session 4 Chapter 7 & 8 WARNING This material has been reproduced and communicated to you by or on behalf of the Victoria University, Melbourne in accordance with section 113P of the Copyright Act 1968 (Act). The material in this communication may be subject to copyright under the Act. Any further reproduction or communication of this material by you may be the subject of copyright protection under the Act. Do not remove this notice will know the application of law of one price and different arbitrage opportunities Learning Objectives will understand how arbitrageur capitalising the profit-making opportunities in the foreign exchange market and how arbitrage activities in the foreign exchange market affect to correct any mispricing in the market The law of one price • Assume, all markets in the world are perfect. • Identical products and services are selling in different markets; • no entry/exist restrictions; • no market frictions and • Transportation costs of moving the product between markets are equal, then • the products price should be the same in every markets. • This is called the law of one price (also called purchasing power parity, or PPP) The law of one price • However, the price of the same product in different places may not be the same due to • Transportation costs and barriers to trade • Non-existence of competitive markets for the goods and services • Tradability of goods (immobile goods such as houses, and many services that are local, are of course not traded between markets). Arbitrage • Both arbitrageurs and speculators aim to involve in buying & selling to make profit. • Arbitrageurs target current market price anomalies and gain riskless profit. • Foreign exchange arbitrage – simultaneous purchase (buy low) and sale (Sell high) of currencies in different markets in order to profit from quoted exchange rate differences (market anomalies) in two or more locations • The effect of arbitrage on demand and supply is to cause prices to realign, such that no further risk-free profits can be made. International Arbitrage • Arbitrage can take place in four different forms in foreign exchange and international money markets: • • • • Locational arbitrage Triangular arbitrage Covered interest arbitrage Uncovered interest arbitrage Locational Arbitrage - (With Direct Quote) • To make locational arbitrage, the arbitrageur should be able to buy currency from one location and sell those purchased on a higher rate into another location. • Arbitrageurs can buy foreign currencies from dealer’s selling price (ask) and sell on the dealers buying price (bid). • Therefore, locational arbitrage is possible when buying price (bid price) in one location (bank) is higher than selling price (ask price) in another location for the same currency unit. Locational Arbitrage β’ Example: Bank Bid Ask C AUD0.9350/ NZD AUD0.9400 / NZD D AUD0.9450 / NZD AUD0.9500 / NZD β’ Are there any opportunity for locational arbitrage? Locational Arbitrage You can ask Crate buy NZD Bank from CBank foris lower lower than than the bid 0.9400AUD and sellthe for rateand in Bank 0.9450AUD profitD. 0.0500AUD for every NZD Bank C ask rate is lower than the bid rate in Bank D. β’ Example Bank Bid Ask C AUD0.9350/ NZD AUD0.9400 / NZD D AUD0.9450 / NZD AUD0.9500 / NZD Buy NZD from Bank C @ AUD0.9400, and Sell it to Bank D @ AUD 0.9450. Profit = AUD0.005/NZD for every NZD dealing with. If arbitrageur put AUD100,000, πππ· Buy NZD: π΄ππ·100,000 × π΄ππ·0.9400 = πππ·106,382.98 Sell NZD:πππ·106,382.98 × Her profit AUD531.90 π΄ππ·0.9450 πππ· = π΄ππ·100,531.92 Locational Arbitrage - (With Indirect Quote) (Buy more sell less) • To make locational arbitrage (when quotes indirect), the arbitrageur should be able to buy more foreign currency units for one local currency unit from one location and sell those purchased using a rate which they can exchange lower amount of foreign currency units for one local currency unit. • Arbitrageurs can buy foreign currencies from dealer’s selling price (ask) and sell on the dealers buying price (bid). • Therefore, locational arbitrage is possible with indirect quotes, when buying price (bid price) in one location (bank) is lower than the selling price (ask price) in another location for the same currency unit. Locational Arbitrage - (With Indirect Quote) β’ Bank Example: Bid Ask C NZD 1.0695/AUD NZD 1.0638/AUD D NZD 1.0582/AUD NZD 1.0526/AUD • Are there any possibility to make profit on locational arbitrage? • How? Locational Arbitrage (With Indirect Quote) To get one AUD, you need to sell only NZD1.0582 to Bank D β’ Example: For NZD1.0638 Bank C ask only one AUD from you Bank Bid Ask C NZD 1.0695/AUD NZD 1.0638/AUD D NZD 1.0582/AUD NZD 1.0526/AUD • Are there any possibility to make profit on locational arbitrage? • How? Buy more for one dollar and sell less. Isn't it good? Locational Arbitrage (With Indirect Quote) β’ Bank Example: Bid Ask C NZD 1.0695/AUD NZD 1.0638/AUD D NZD 1.0582/AUD NZD 1.0526/AUD • Are there any possibility to make profit on locational arbitrage? • How? Assume you got AUD100,000 for the deal… 1.Buy NZD from bank C at NZD1.0638/AUD using AUD100,000 πππ·1.0638 π΄ππ·1000,000 × = π΅ππ«πππ, πππ π΄ππ· 2.Sell the purchased NZD to Bank D at NZD1.0582/AUD π΄ππ· πππ·106,380 × = π¨πΌπ«πππ, πππ. ππ πππ·1.0582 Your profit from the deal = AUD529.20 Triangular (inter-market) arbitrage • Triangular arbitrage (sometimes called three-point or inter-market arbitrage) is the act of exploiting an arbitrage opportunity resulting from a pricing discrepancy among three different currencies in the foreign exchange market. • A typical triangular arbitrage strategy involves three trades and it offers a risk-free profit (in theory). http://en.wikipedia.org/wiki/Triangle_arbitrage Triangular arbitrage Example 1: You deal EUR, AUD and CHF Suppose EUR0.6152/AUD AUD1.4065/CHF EUR0.8882/CHF • Is their any arbitrage opportunity? Triangular Arbitrage • You can find triangular arbitrage opportunities by examining the cross exchange rate equilibrium in the FX market. • To examine cross exchange rate equilibrium, you need equal number of exchange rates to the number of currencies you plan to deal (eg. 03 FX rate for 03 currencies). • Each currency should be in the numerator in one exchange rate and in the denominator of another exchange rate. • For currencies EUR, AUD and CHF , possible exchange rate combinations for testing the cross exchange equilibrium are given below. πΈππ 0.6152 π΄ππ·1.4065 πΆπ»πΉ × × π΄ππ· πΆπ»πΉ1.6485 πΈππ 0.8882 = π βππ’ππ ππ 1 OR π΄ππ· πΆπ»πΉ πΈππ 0.8882 × × πΈππ 0.6152 π΄ππ·1.4065 πΆπ»πΉ • = π βππ’ππ ππ 1. If the equilibrium condition is not fulfilled it is indicate, there is an opportunity for triangular arbitrage. Triangular arbitrage: Cross exchange rate equilibrium • Alternate equilibrium condition π¨πΌπ« πͺπ―π π¬πΌπΉπ. ππππ π. πππππ × × = π. πππππ¬πΌπΉ π. πππππ¨πΌπ« πͺπ―π π • The estimated value is less than one. Market is not in-equilibrium. An arbitrage opportunity exists. • One unit of denominator currency worth 1.02469 times in numerator currency. • That’s mean, numerator currency undervalue against the denominator currency (or denominator currency overvalue against the numerator currency. • To make profit, you need to buy the undervalue currency and sell the overvalue currency. • Sell EUR and buy AUD – • Sell AUD and buy CHF – • Sell CHF and buy EUR – Step 3 Step 1 Step 2 • If the equilibrium estimate is greater than ONE, It indicates that if you start with one currency unit, at the end of the arbitrage, you will get 1.02649 currency units. • If you start with AUD100,000, at the end, you will get AUD102,649. Triangular arbitrage: Cross exchange rate equilibrium • Estimate equilibrium condition π. πππππ¬πΌπΉ π. πππππ¨πΌπ« πͺπ―π π. ππππ × × = π¨πΌπ« πͺπ―π π. πππππ¬πΌπΉ π • The estimated value is less than one. Market is not in-equilibrium. An arbitrage opportunity exists. • One unit of denominator currency worth 0.9742 times in numerator currency. • That’s mean, numerator currency overvalue against the denominator currency (or denominator currency undervalue against the numerator currency. • To make profit, you need to buy the undervalue currency and sell the overvalue currency. • Sell EUR and buy AUD – • Sell AUD and buy CHF – • Sell CHF and buy EUR – Step 3 Step 1 Step 2 • If the estimated equilibrium estimate is less than one it indicates that if you start with one currency unit, at the end of arbitrage, you will get 1/0.9742 (1.02649) currency units. • If you start with AUD100,000, at the end, you will get [AUD100,000/0.9742] AUD102,649. Triangular arbitrage • Assume, you hold 100,000AUD πΆπ»πΉ =CHF71,098.47 1.4065π¨πΌπ· 0.8882πΈππ πΆπ»πΉ71,098.47 × =EUR63,146.66 πΆπ»πΉ π΄ππ· πΈππ 63,146.66 × =AUD102,649.00 0.6152πΈππ • ππππ π΄ππ·100,000 πππ ππ’π¦ πΆπ»πΉ ; 100,000π¨πΌπ« × • ππππ πΆπ»πΉ 71,098.47 πππ ππ’π¦ πΈππ ; • ππππ πΈππ 63,149.66 πππ ππ’π¦ π΄ππ·; π΄ππ·100,000 × πͺπ―π π.πππππ¨πΌπ« × ππππππ¬πΌπΉ πͺπ―π × π¨πΌπ« π.πππππ¬πΌπΉ = π¨πΌπ«πππ, πππ × π = π.ππππ =AUD102,649.00 • At the end of transaction (triangular arbitrage) you will receive 102,649AUD with Profit =102,649AUD100,000AUD=2,649AUD
