Quiz 14: Exchange Rates and the Foreign Exchange Market: an Asset Approach


Price of one bratwurst is 5euros and the price of hot dog is $4 Exchange rate = $1.05/per euro So, price of one bratwurst = 5 euros × $1.05 = $5.25 Since the price of both bratwurst and hotdog is expressed in dollar terms, the price of bratwurst in terms of a hot dog = img = 1.3125 So one bratwurst is equal to 1.3 hotdogs, Therefore, img Now, when the exchange rate is $1.25/per euro Price of one bratwurst = 5 euros ×$1.25 = $6.25 The price of bratwurst in terms of a hot dog = img = 1.5625 Therefore, one bratwurst is equal to 1.6 hotdogs, Therefore, img With the change in exchange rate, that is dollar depreciates, each bratwurst is fetching more hotdogs implying that hot dog become cheaper than before. img

Suppose it is cheaper to purchase Swiss francs with dollars and later on exchange these francs with Israeli shekels than to directly purchase shekels with dollars. This will open a window for people to earn money through arbitraging. The above scenario is characterized by an increase in the demand for Swiss francs from people who hold dollars. This would lead to a rise in the value of Swiss franc against the value of dollar. This means that the Swiss franc will appreciate against the dollar until the price of a shekel would be exactly the same whether it was purchased directly with dollars or indirectly through Swiss francs. For example, consider the exchange rate between the Swiss franc, the US dollar, and the Israeli shekels. A dollar is worth 0.9351 Swiss francs, while a Swiss franc is worth 3.8595 shekels. To rule out the triangular arbitrage, compare the value of exchange rates (direct and indirect))and find out which one gives a higher value of shekels. Consider first, that Swiss francs are purchased with dollars (at an exchange rate of 0.9351 Swiss francs per dollar). Later on, these francs are used to buy Shekels. In other words, compute the following case: img Here, ' E ' stands for the exchange rate. Hence, one dollar is worth 3.6090 shekels. Therefore, in order to rule out triangular arbitrage, this indirect rate should exactly be equal to the direct exchange rate of shekels with dollars. As the calculated value of shekels per dollar is greater than to the direct rate of shekels per dollar , there is a possibility of arbitrage. The triangular arbitrage is " approximately " ruled out in above case for several reasons given as follows: • First, rounding error means that there may be some small discrepancies between the direct and indirect exchange rates calculated above. • Second, the transactions cost on trading currencies is a factor that will prevent the occurrence of arbitrage.

Triangular arbitrage is the process of converting one currency to another, converting it again to a third currency and, finally, converting it back to the original currency within a short time span. This opportunity for riskless profit arises when the currency's exchange rates do not exactly match up. For example, take up Indian Rupees as one currency where we can rule out the possibility of triangular arbitrage. The data used is as follows: img The arbitrage opportunity can be discussed as follows: img There is a loss of Rupees 37 in the arbitrage which may be due to the transaction costs or taxes. Thus, the arbitrage here earns no profit or loss and the initial amount which was started with, returned back to approximately the same amount. The word approximation is used here because, the calculation was done on real time data and a difference can be obtained because of daily fluctuations in the exchange rate or the inclusion of transaction costs or taxes put on arbitrage which are not known.