# Finance 581: Arbitrage and Purchasing Power Parity Conditions Module 5: Lecture 1 [Speaker: Sheen Liu] [On Screen]

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2 balance of payments and interest rate parity is a widely used method of forecasting exchange rates [Emphasized]. REVIEW: ARBITRAGE Arbitrage is a money machine. 1. Has no risk 2. Does require investment. [Sheen Liu]: What is an arbitrage? An arbitrage is a transaction that makes a risk free profit at zero cost. In other words, arbitrage is a money machine. Whenever there is an arbitrage opportunity, you can make money without taking any risk and without investment [Emphasized]. Arbitrage must satisfy two conditions. The first is making money without taking risk and the second is making money without investment [Emphasized]. You may hit the jackpot in Las Vegas and make a lot of money, but it s not arbitrage. You have to take the risk of losing your money to hit jackpot. The first condition is not satisfied. You may invest your money into Treasury bill and have a risk free return on your investment. It s risk free, but it s not arbitrage because of the risk free profit coming from your investment. The second condition is not satisfied. So what s really an arbitrage? Imagine you are on the street and penniless. Once you spot and arbitrage opportunity, you can become a millionaire or billionaire after carrying out arbitrage. REVIEW: ARBITRAGE Arbitrage is a money machine. 3. Has no risk 4. Does require investment. Buying and selling identical financial instruments - At different prices - On different markets [Sheen Liu]: So how do we arbitrage? To put it in a simple way, you buy and sell the same good at different prices on different markets [Emphasized]. Next slides show an example. REVIEW: ARBITRAGE Example: One ounce of gold costs \$1000 in England and \$990 in France - Is there any arbitrage opportunity - If yes, how to arbitrage? Arbitrage procedure - Borrow \$990 to buy 1-oz gold in France; 2

4 Arbitrage opportunities are like money lying on the street, they will quickly disappear [Emphasized]. Money should not be lying on the street all the time. The arbitrage opportunity should be rare. In normal markets, identical goods should have one single price this is the law of one price [Emphasized]. So far, arbitrage sounds simple, however it can get complicated. The financial transactions that generate the same cash flows are identical instruments [Emphasized]. The same cash flows can be generated through many different transactions in the financial market. The triangular arbitrage in foreign exchange market is an example we ll discuss next. INTERMARKET ARBITRAGE Some currency pairs are not actively traded, so their exchange rate is determined through their relationship to a third currency (cross rate). - Example: Exchange rate between Japanese yen ( ) and Mexican peso (Ps) o /\$ o Ps /\$ [Flow Chart of exchange rate between Japanese yen and Mexican peso] [Sheen Liu]: Some currency pairs are not actively traded, so their exchange rate is determined through their relationship to a widely traded third currency. The exchange rate established this way is the cross rate [Emphasized]. For example, Japanese yen and Mexican peso are not actively exchange; to have the exchange rate between them we use their exchange rate with U.S. dollars [Emphasized]. You may make the following exchanges: Exchange yen for a dollar then exchange a dollar for Mexican pesos. This operation is equivalent to exchanging Japanese yen for Mexican pesos. So the cross rate is Japanese yen per Mexican peso. It is also the arbitrage free exchange rate between Japanese yen and Mexican peso. We can check it quickly. One dollar exchanged for pesos then exchange pesos for Japanese yen, finally exchange back for 1 dollar, there is no gain or losses. INTERMARKET ARBITRAGE Cross rates can be used to check on opportunities for intermarket arbitrage. - Assume that a bank quotes a spot rate of /Ps, differing from the cross rate /Ps. - Arbitrage profit is \$ for each dollar. - Banks and financial institutions are able to borrow large sums of money. [Flow Chart of intermarket arbitrage] 4

5 [Sheen Liu]: Cross rates can be used to check opportunities for arbitrage. Let s say a bank quotes a spot rate of 9.8 Japanese yen per peso which is different from the cross rate Japanese yen per peso [Emphasized]. There is an arbitrage opportunity here. To see it, let s borrow 1 dollar. Exchange one dollar for pesos, next exchange Mexican pesos at 9.8 yen per peso for Japanese yen. Finally, exchange Japanese yen at the per dollar for dollars. Arbitrage profit is cents for each dollar. You may say it s only one cent profit per dollar. If you start with 100 million dollars, you d be able to make one million dollars profit. Banks and financial institutions are able to borrow large sums of money [Emphasized]. Arbitrage is not just a fairy tale; there is a group of investors and fund managers who are actively engaging in arbitrage activities. They are the arbitragers. If an exchange rate differs from the arbitrage free cross rate, the arbitrage activities push the exchange rate back to the arbitrage free cross rate. ABSOLUTE PURCHASING POWER PARITY (PPP) Example: A Big Mac in China costs 12.5 Yuan, while in US it costs \$3.57. the exchange between dollar and Yuan is Yuan 6.83/\$ Arbitrage o Borrow \$ (= Yuan 12.5 Yuan 6.83/\$ ); o Exchange \$ for Yuan 12.5; o Buy a Big Mac in China; o Sell it in US for \$3.57; o The arbitrage profit is \$ PPP (arbitrage-free exchange rate) is S = Yuan 12.5 \$3.57 = Yuan 3.50 \$ = pyuan p \$ [Sheen Liu]: Let s look at another example of arbitrage. A Big Mac in China costs 12.5 Yuan, while in the US it costs \$3.57 [Emphasized]. The exchange rate between dollar and Yuan is 6.83 Yuan per dollar [Emphasized]. You probably see the arbitrage opportunity in this situation. Let s borrow dollars, exchange dollars for 12.5 Chinese Yuan, buy a Big Mac in china, sell it in US for \$3.57 [Emphasized]. In this case, the arbitrage profit is not trivial, it is dollars [Emphasized]. It is easy to see that to eliminate the above arbitrage opportunity, 12.5 Yuan must be exchanged for 3.57 dollars. No matter if you hold \$3.57 or exchange \$3.57 for Chinese Yuan, your money buys one Big Mac. Therefore, the arbitrage-free exchange rate must be 12.5 Yuan for 3.57 dollars or 3.5 Yuan per dollar. This argument can be extended to any pair of currencies. Once you convert money, a Big Mac should cost the same no matter where you go, this is another form of the Law of One Price. It refers to the international arbitrage condition for goods and services. The Law of One Price requires that goods and services should be selling for the same price in a given currency across countries. Otherwise, one can arbitrage by buying goods at a cheaper price in one country, ship them to another country where goods are more expensive, and sell them. 5

7 not frictions in the markets [Emphasized]. However, any of the frictions that create a deviation from the law of one price can also cause a deviation from the absolute purchasing power parity. Clearly transactions costs, such as the cost of shipping, generate deviations from the absolute purchasing power parity. Tariffs and quotas on imports and exports also create deviations. Empirical testing of purchasing power parity shows that the absolute purchasing power parity holds up well over the long run, but poorly for shorter time periods [Emphasized]. RELATIVE PURCHASING POWER PARITY (RPPP) Example: A Big Mac in China costs Yuan, while in US it costs \$3.57. The exchange between dollar and Yuan is Yuan 6.83/\$. o The rate of China inflation is 5% o The rate of US inflations is 3% Next year, a Big Mac o In China costs Yuan (= 24.38(1+0.05)) o In US costs \$3.68 (= \$3.57(1+0.03)) Next year s arbitrage-free exchange rate should be Yuan24.38( ) S(next year) = = Yuan25.60 = Yuan6.96 \$3.57( ) \$3.68 \$ = PYuan (1 + π Y ) P \$ (1 + π \$ = S 1 + πy ) 1 + π \$ S(next year) = 1 + πy S 1 + π \$ = = [Sheen Liu]: Managers and investors are interested in not only determining spot exchange rates but also forecasting future exchange rates. Let s extend the absolute purchasing power parity to next year. A Big Mac in China costs Yuan, while in US it costs 3.57 dollars [Emphasized]. The exchange rate between dollar and Yuan is the price ratio which is 6.83 Yuan per dollar. The rate of China inflation is 5 percent [Emphasized]. The rate of US inflation is 3 percent [Emphasized]. Next year a Big Mac in China costs Yuan times 1 plus 5 percent inflation rate which gives Yuan. A Big Mac in US costs 3.57 times 1 plus 3 percent inflation which give 3.68 dollars. The law of one price requires that the next year s exchange rate much be the next year s price ratio on Yuan and 3.68 dollars which is 6.98 Yuan per dollar [Emphasized]. In principle, next year, once you convert money, a Big Mac should cost the same no matter where you go. The current exchange rate, the spot rate, may not satisfy the absolute purchasing power parity. In such case, we may relax our interpretation of the relation and then rewrite the equation looking at the ratio between next year s exchange rate and spot rate [Emphasized]. The ratio is between the inflations of the two countries. It is between China inflation and US inflation. The ratio says that Chinese Yuan will be weakened by 1.94% because of higher inflation in China. The second equation tells the trend of the future exchange rate. It does require that the law of one price must hold. The ratio tells which currency will be weakened and which one will be strengthened. Even the absolute purchasing 7

10 levels. The price elasticity of demand for any good is the percentage change of quantity of the good demanded as a result of the percentage change in the good s price. The smaller the elasticity, the higher the pass-through. In other words, if the price increase does not change much of the demand, the exchange rate change will pass-through the price. EXHANGE RATE PASS-THROUGH Example - Euro appreciates for 20% against US dollar. - The PPP implies that the dollar prices of the cars made in Germany increase by 20%. - Assume that price elasticity of demand is large in US. - German car makers may decide to increase their car prices by 14.29% (<20%) - German car makers absorb 5.71% ( = 20% %). - The pass-through is Pass through = 14.29% 20% = 71% [Sheen Liu]: The example illustrates the exchange rate pass-through. Euro appreciates for 20 percent. The purchasing power parity implies that the prices of the cars made in Germany increase by 20 percent accordingly [Emphasized]. Let s assume that the price elasticity of demand is large in US [Emphasized]. That is to say, a 20 percent increase in the car price would reduce German car sales a lot. German car makers may decide to increase their car prices by less than 20 percent [Emphasized]. They may increase the car prices by percent and the German car makers absorb 5.71 percent. This results in a 71 percent pass-through, that is percent increase in dollar divided by 20 percent appreciation in euro [Emphasized]. This concludes module 5. 10

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