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Discusses relationship between two countries Interest rates and Exchange Rates.




Discusses relationship between two countries Interest rates and Exchange;Rates. The Difference between Interest rates in two countries has a known;and predictable relationship with Exchange Rates.;Formally Stated;The Interest Rate differential between two countries, that do not have restrictions;on Capital flows, should equal the difference between the Spot and Forward;Exchange rates.;Example;Consider two countries, Say England and U.S.A.;Let the current Exchange rate be;Spot Rate 1 Pound = 1. 5 dollars;Let Annual Interest Rate of Risk free security in England be: 8%;Let Annual Interest Rate of Risk free security in USA be;4%;What should the three month Forward Exchange Rate be?;As per this theory [IRP], the forward exchange Rate should be;1 pound = 1.4853 dollars.;Why this should be so is explained by this theory.;Problem;We examine this from the perspective of an Investor in England.;Let us assume that one person in England has a 1 million pounds to invest on April;1, 2013. He wants to invest for 3 months till July 1, 2013. He has two choices.;Choice 1;He can invest in England on April 1, 2013 and get a return of 2%.;[Annual Return = 8%, Hence, three month Return = 2%];On July 1, 2013 he would have 1.02 million pounds.;Choice 2;Alternatively, he can convert his money to U.S. dollars on April 1, 2013. Given that;the Spot Exchange rate is 1 pound = 1.5 dollars, he would get, 1.5 million dollars.;He can then invest it in USA risk free securities for 3 months. He would get a return;of 1%. On July 1, 2013 he would have 1.515 million dollars.;This amount he can convert it back to British pounds. Since he can lock in the;forward exchange rates on April 1, 2013 itself, he can convert it to England at the;predetermined, locked-up exchange rate. The lock in exchange rate hence should be;at: 1 pound = 1.4853 dollars, Thus, and hence he will receive, 1.02 million pounds.;Spot Rate (dollar for pound);Forward Rate (dollar for pound);Forward Exchange Rate changes by;=;=;=;1.5;1.4853;2% - 1%;= 1%;FIRST VERSION Multiplying Spot Exchange Rate by this we arrive at the;SPOT EXCHANGE RATE 1 Pound = $ 1.5;Domestic Interest Rate = (UK 3 Month Rate) = 2%;Foreign Interest Rate = (USA 3 Month Rate) = 1%;Interest Rate Differenentials = Domestic Interest Rate Foreign Interest Rate;= [ 2 % -- 1 % ] = 1%;The New Forward Exchange rate, three months from today should be;Spot Exc. Rate x (100 difference in Interest) = Forward Exchange Rate;THEORETICAL EQUATION ONE;Switching Sides;Forward Exchange Rate = Spot Exc. Rate x (100 difference in Interest);PRACTICAL solution in the above problem from perspective of a British Investor;=;=;=;=;1.50 x (100% 1%);1.50 x (99%);1.50 x (99/100);1.485;LIMITATIONS: Other thing being Equal.;Important Note;This example is constructed from a British investor point of view. We can use the;same example from an American investor point of view. Then what we see as a;Forward Discount will become a Forward Premium;WHAT HAPPENS WHEN THE FORWARD RATE IS NOT 1.4850?;You have potential for Arbitrage, Make Riskless money;Say the three month forward rate is also 1.50 like the spot rate.;Say either you or your friend wants to invest $3,000,000 in US T.Bill market.;Instead of investing in USA T. Bill market ($3,000,000) in the USA, you;Convert the money to British Pounds, at the spot Exchange rate of 1.50, Get;2,000,000 British pounds, Invest it in UK for three months at the risk free;rate at 2%, Get 2,040,000 at the end of three months. At the same time you;Lock in the Forward Rate of 1.50 today. At the end of 3 months, you convert;your accumulated British Pounds to US Dollars. You will get $3,060,000.;Alternatively, If you had invested at USA T. Bill market you would have;gotten only, 1% return and you would have only $3,030,000.;You have made $30,000 extra money.;Covered Interest Rate Parity;No Risk Involved, all positions are locked up before entering into transactions.;Uncovered Interest Rate Parity;Risk involved, do not lock up the forward exchange rates.;Limitations to IRP;1.;2.;Transactions Costs imposed by Traders;Capital Controls imposed by Nations;STEPS IN SOLVING INTEREST RATE PARITY PROBLEM;1. Identify a country as Home Country and another as Foreign Country;2. Solve the problem from the perspective of Home Country Investor;3. Identify the Domestic Interest Rate for the time period in question;4. Identify the Foreign Interest Rate for the time period in question;5. Identify the Current Spot Rate;6. Solve for the Forward Rate;OTHER VERSIONS OF INTEREST RATE PARITY;IRP has been widely developed by many researchers and various formulations exist.;Here below we examine three different ways of calculating IRP and the Forward;Exchange rates. However, in problems use any one of the versions. You do not need;to use all of them. They all should give you the same results, Remember that some;are approximations and there may be small (very minute) differences.;[Why are we looking at Four different ways of doing the same thing?! Because some;books, or researchers use a different method, and I just wanted to make sure that;you recognize that it is the same concept, but analyzed and detailed a differnet way].;SECOND VERSION: Theoretical Interest Rate Parity is;[Spot Exc. Rate / Forward Exc. Rate] (1 + Forgn Int. Rate);= (1 + Dom Int. Rate);Rewriting the Equation;[Spot Ex. Rate / Forward Ex. Rate];=;(1 + Dom Int Rate) / (1 + Foreign Int Rate);Rewriting the Equation to Solve for Foreign Exc. Rate;Spot Ex. Rate [1 + Forgn Int. Rate] / [ 1 + Dom Int Rate] = Forward Ex. Rate;THEORETICAL EQUATION TWO;Switching Sides;Forward Exc. Rate = Spot Exc. Rate [1 + Forgn Int. Rate] / [ 1 + Dom Int Rate];PRACTICAL solution in the above problem from perspective of a British Investor;Solving for Forward Rate =;[Spot Exc. Rate x 1.01] / [1.02];= (1.50 x 1.01) / 1.02 = 1.485294;THIRD VERSION: Approximately: Interest Rate Parity is;THEORETICAL EQUATION THREE;(Forward Ex. Rate Spot Ex. Rate) / Spot Ex. Rate = Foreign Int Rate Dom Int Rate;Forward Ex. Rate Spot Ex. Rate = [Foreign Int Rate Dom Int Rate] X (Spot Ex. Rate);Forward Ex. Rate = [(Foreign Int Rate Dom Int Rate) X (Spot Ex. Rate)] + Spot Ex Rate;PRACTICAL solution in the above problem from perspective of a British Investor;Forward Ex. Rate = [(1% -- 2%) X (1.50)];+ [1.50];= [(-- 1 %) X 1.50] + 1.50;= - 0.015 + 1.50;= 1.4850;FOURTH VERSION;THEORETICAL EQUATION FOUR;Forward Exchange Rate Discount, or Premium = Difference in Interest Rates;If the difference is Positive, Your currency has appreciated;If the difference is Negative, Your currency has depreciated.;PRACTICAL solution in the above problem from perspective of a British Investor;Difference in Interest Rates = Foreign Interest Rates Domestic Interest Rates;= 1%;- 2 % = - 1%;Forward Exchange Rate therefore depreciates by 1% and goes to 1.485;Optional Homework Problem;1.;2.;3.;4.;5.;6.;Identify the Interest Rate for Brazil;Identify the Interest Rate for South Korea;Examine whether Interest Rate Parity Theorem holds for the last year?;What are the implications of this How do you make money?;What data do you need?;Where would you get the data?


Paper#34088 | Written in 18-Jul-2015

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