The Big Mac Index

Some people read tea leaves to predict the future, The Economist magazine prefers hamburgers. The magazine started the Big Mac Index in 1986 as a light-hearted guide to test whether currencies are at their ?correct? exchange rate based on the Law of One Price. Under the Law of One Price, the price of the Big Mac should be the same if its local price is converted into dollars at the current exchange rates.

In July 2014, the average price of a Big Mac was 2.80 in Britain and $4.20 in the U.S. The actual exchange rate was $1.60/. Please answer the following questions:

Where can you buy cheaper hamburgers: Britain or U.S.?

Calculate the ?correct? exchange rate based on the law of one price.

Based on PPP, was the British pound overvalued or undervalued and by how much?

Triangular Arbitrage

Suppose you are given the following three quotes:

BankQuote

Citibank$2.0/

UBSSF 1.20/$

Deutsche BankSF 2.5/

1) Is there any opportunity to make risk-free profit? Explain.

2) If the answer is yes, please demonstrate how, assuming you have SF2,400,000.

Pease show all transactions and calculate the net profit.

3. Interest Rate Parity and Arbitrage

Suppose you have the following information:

Current spot rate: S = $1.30/?

Interest rate on dollars: i$ = 5%

Interest rate on euros: i? = 2%

Based on the Interest Rate Parity, what should the 1-year forward exchange rate be?

If the actual forward rate is quoted at $1.34/?, is there any covered interest arbitrage opportunity? Please explain.

If yes, how can you make an arbitrage profit? Assume you can borrow up to $1,300,000 or ?1,000,000. Please show all transactions necessary to make the profit.

HW#5 FIN 525 International Financial Management Fall/2015 Name_______________________ 1. The Big Mac Index Some people read tea leaves to predict the future, The Economist magazine prefers hamburgers. The magazine started the Big Mac Index in 1986 as a light-hearted guide to test whether currencies are at their \"correct\" exchange rate based on the Law of One Price. Under the Law of One Price, the price of the Big Mac should be the same if its local price is converted into dollars at the current exchange rates. In July 2014, the average price of a Big Mac was 2.80 in Britain and $4.20 in the U.S. The actual exchange rate was $1.60/. Please answer the following questions: 1) Where can you buy cheaper hamburgers: Britain or U.S.? 2) Calculate the \"correct\" exchange rate based on the law of one price. 3) Based on PPP, was the British pound overvalued or undervalued and by how much? 2. Triangular Arbitrage Suppose you are given the following three quotes: Bank Quote Citibank $2.0/ UBS SF 1.20/$ Deutsche Bank SF 2.5/ 1) Is there any opportunity to make risk-free profit? Explain. 2) If the answer is yes, please demonstrate how, assuming you have SF2,400,000. Pease show all transactions and calculate the net profit. 3. Interest Rate Parity and Arbitrage Suppose you have the following information: Current spot rate: S = $1.30/ Interest rate on dollars: i$ = 5% Interest rate on euros: i = 2% 1) Based on the Interest Rate Parity, what should the 1-year forward exchange rate be? 2) If the actual forward rate is quoted at $1.34/, is there any covered interest arbitrage opportunity? Please explain. 3) If yes, how can you make an arbitrage profit? Assume you can borrow up to $1,300,000 or 1,000,000. Please show all transactions necessary to make the profit. The Big Mac Index Some people read tea leaves to predict the future, The Economist magazine prefers hamburgers. The magazine started the Big Mac Index in 1986 as a light-hearted guide to test whether currencies are at their \"correct\" exchange rate based on the Law of One Price. Under the Law of One Price, the price of the Big Mac should be the same if its local price is converted into dollars at the current exchange rates. In July 2014, the average price of a Big Mac was 2.80 in Britain and $4.20 in the U.S. The actual exchange rate was $1.60/. Please answer the following questions: 1) Where can you buy cheaper hamburgers: Britain or U.S.? Solution2.80 * $1.60/ = $4.48 hamburgers in U.S. were cheaper 2) Calculate the \"correct\" exchange rate based on the law of one price. Solution$4.20 / 2.80 = $1.50/ 3) Based on PPP, was the British pound overvalued or undervalued and by how much? Solution$1.60/ - $1.50/ / $1.50/ * 100 = 6.7% the British pound was overvalued by 6.7%. 1. Triangular Arbitrage Suppose you are given the following three quotes: Bank Quote Citibank $2.0/ UBS SF 1.20/$ Deutsche Bank SF 2.5/ 1) Is there any opportunity to make risk-free profit? Explain. SolutionCross Rate between UBS and Deutsche Bank is $2.0/ * SF1.20/$ = SF2.40/ This cross rate is not the same as Deutsche Bank's quotation of SF 2.5/, so an opportunity exists to make a risk-free profit from arbitrage between the three markets. 2) If the answer is yes, please demonstrate how, assuming you have SF2,400,000. Solution Buy $ from UBS SF2,400,000 / SF1.20/$ = $2,000,000 Buy from Citibank $2,000,000 / $2.0/ = 1,000,000 Sell for SF 1,000,000 * SF2.5/ = SF2,500,000 Net profit = SF2,500,000 - SF2,400,000 = SF100,000 Please show all transactions and calculate the net profit. 3. Interest Rate Parityand Arbitrage Suppose you have the following information: Current spot rate: S = $1.30/ Interest rate on dollars:i$ = 5% Interest rate on euros: i = 2% 1) Based on the Interest Rate Parity, what should the 1-year forward exchange rate be? SolutionF= S* [1+i$ / 1+i ] = $1.30/ * [1.05 / 1.02] = $1.3382/ 2) If the actual forward rate is quoted at $1.34/, is there any covered interest arbitrage opportunity? Please explain. SolutionYes, there is an arbitrage opportunity, since the actual forward rate is bigger than the 1-yr forward rate ($1.34/ > $1.3382/) 3) If yes, how can you make an arbitrage profit? Assume you can borrow up to $1,300,000 or 1,000,000. Please show all transactions necessary to make the profit. SolutionToday Borrow $1,300,000 at i$ = 5% Convert $ to 1,000,000 Invest 1,000,000 at 2% , receive 1,020,000 Enter into a 1 yr Forward to sell 1,020,000 at F.= $1.34/ One year later Receive 1,020,000 Honor the forward contract, sell 1,020,000*$1.34/ = $1,366,800 Pay loan $*1,365,000 Net profit = $1,366,800 - $1,365,000 = $1,800 The Big Mac Index Some people read tea leaves to predict the future, The Economist magazine prefers hamburgers. The magazine started the Big Mac Index in 1986 as a light-hearted guide to test whether currencies are at their \"correct\" exchange rate based on the Law of One Price. Under the Law of One Price, the price of the Big Mac should be the same if its local price is converted into dollars at the current exchange rates. In July 2014, the average price of a Big Mac was 2.80 in Britain and $4.20 in the U.S. The actual exchange rate was $1.60/. Please answer the following questions: 1) Where can you buy cheaper hamburgers: Britain or U.S.? Solution2.80 * $1.60/ = $4.48 hamburgers in U.S. were cheaper 2) Calculate the \"correct\" exchange rate based on the law of one price. Solution$4.20 / 2.80 = $1.50/ 3) Based on PPP, was the British pound overvalued or undervalued and by how much? Solution$1.60/ - $1.50/ / $1.50/ * 100 = 6.7% the British pound was overvalued by 6.7%. 1. Triangular Arbitrage Suppose you are given the following three quotes: Bank Quote Citibank $2.0/ UBS SF 1.20/$ Deutsche Bank SF 2.5/ 1) Is there any opportunity to make risk-free profit? Explain. SolutionCross Rate between UBS and Deutsche Bank is $2.0/ * SF1.20/$ = SF2.40/ This cross rate is not the same as Deutsche Bank's quotation of SF 2.5/, so an opportunity exists to make a risk-free profit from arbitrage between the three markets. 2) If the answer is yes, please demonstrate how, assuming you have SF2,400,000. Solution Buy $ from UBS SF2,400,000 / SF1.20/$ = $2,000,000 Buy from Citibank $2,000,000 / $2.0/ = 1,000,000 Sell for SF 1,000,000 * SF2.5/ = SF2,500,000 Net profit = SF2,500,000 - SF2,400,000 = SF100,000 Please show all transactions and calculate the net profit. 3. Interest Rate Parityand Arbitrage Suppose you have the following information: Current spot rate: S = $1.30/ Interest rate on dollars:i$ = 5% Interest rate on euros: i = 2% 1) Based on the Interest Rate Parity, what should the 1-year forward exchange rate be? SolutionF= S* [1+i$ / 1+i ] = $1.30/ * [1.05 / 1.02] = $1.3382/ 2) If the actual forward rate is quoted at $1.34/, is there any covered interest arbitrage opportunity? Please explain. SolutionYes, there is an arbitrage opportunity, since the actual forward rate is bigger than the 1-yr forward rate ($1.34/ > $1.3382/) 3) If yes, how can you make an arbitrage profit? Assume you can borrow up to $1,300,000 or 1,000,000. Please show all transactions necessary to make the profit. SolutionToday Borrow $1,300,000 at i$ = 5% Convert $ to 1,000,000 Invest 1,000,000 at 2% , receive 1,020,000 Enter into a 1 yr Forward to sell 1,020,000 at F.= $1.34/ One year later Receive 1,020,000 Honor the forward contract, sell 1,020,000*$1.34/ = $1,366,800 Pay loan $*1,365,000 Net profit = $1,366,800 - $1,365,000 = $1,800