Forex rates movement-Classical Interest rate differentiel theory
Let me start with a warning note, reason for Forex movements, that is movements between currencies and the premia or discount that one currency commands over a period depend on various factors.Just to list a few, the reasons range from Interest rates,short term availaibility and requirement of the currency, Balance of payments of trade movement in the short term between two countries ,and of course the most important , Government regulations and restrictions .
Discussion is on forex movements and not on the base rate itself. The base currency rate between two or more currencies depend on factors starting from Purchase power parity , Balance of payments of trde as of a certain date and various other factors which is possibly a subject for discussion for another day.
This piece is only on movement of Forex rates .
While the actual reason is quite complex and is driven by various factors which affect the market including imperfect market, restriction on currency movements, restrictions on trade and short term imbalances between supply and demand for currencies, the one compelling theory and what could be termed as a classical one on forex movement is the one with reference to Interest rate differentiel between currencies. This is the simplest , most logical and something which should work if the market is perfect and there are no restrictions on currency movement, investment or borrowing in the currencies under study.
Let us do a simple one between USD and INR. Let us assume a base rate of INR 40 to a 1 USD. Let us assume prevailing interest rates of 10 % PA in the case of INR and 5% PA in the case of USD. For the sake of simplicity we will have to assume no interest rate differentiel between borrowing and Investing .This is to make the example easier . INR 40 at the end of one year will be equivalent to INR 44 and the in the case of USD, $ 1 at the end of one year at an interest rate of 5% be $1.05. Equilibrium forward rate of USD to INR for one year period should be 44/1.05 , that is INR 41.9048 to1 USD. If the rate is anything other than this , there arises an opportunity to make riskless profit.
Normally the currency on which interest rate is lower will be at a premium and the one whose interest rate is higher will be at a discount.
Let us assume that at the interest levels specified, the actual forward rate quoted at the end of one year is at INR 40 to a USD.
Easy way to make profit is
- borrow in USD,
- convert to INR immediately,
- deposit in INR ,
- simultaneously take a forward cover to buy USD at INR 40.
Let us calcuate the flows .
Since you have borrowed in USD , you will have to pay $ 1.05 with interest at the end of one year.
USD converted to INR 40 and deposited would become INR 44 at the end of one year since INR deposit attracts 10 % interest.
Since a forward cover has been taken , you would be in a position to buy USD of 1.05 for a total outflow of INR 1.05*40= 42. This leaves you Rs 2 as riskless profit.
In the same case, if at the same interest rates, INR forward rate had been 46 to USD, we will be doing the borrowing in INR, depositing in USD, forward cover to sell USD .
Let us work out the simple math in this sequence.
You had borrowed INR 40 at the end of one year , to be returned is Rs 44 .
INR borrowed was converted to USD at the beginning has been deposited as USD deposit .At the end of one year we get USD 1.05.
Since we had a cover to sell USD at the rate of INR 46 to a USD, we will sell the $ 1.05 at INR 46 to a USD and get on hand INR 48.03. We pay off the INR 44 and left with INR 4.03 rsikless
We have assumed no difference in interest rates between borrowing and investing and also no difference between buying and selling of currency. Margins between these two will make a slight difference in the calculations but the theory holds good.
As a thumb rule,arbitrage opportunity will arise when the currency forward rate is different from the interest rate differentiel. Normally in such situations the demand/supply for the currencies adjusts in such a way that the interest rates move and nullify the advantage. If this kind of anamoly were to persist , every one will be doing this set of transaction and the interest rates and the demand for the currency will drastically undergo a change till such time equilibrium is attained.
This is theory and will continue to be theory till such time, we have free currency movements and unrestricted deposit and borrowings in any currency in any country or atleast in the countries of the currencies in question/discussion.
Let me start with a warning note, reason for Forex movements, that is movements between currencies and the premia or discount that one currency commands over a period depend on various factors.Just to list a few, the reasons range from Interest rates,short term availaibility and requirement of the currency, Balance of payments of trade movement in the short term between two countries ,and of course the most important , Government regulations and restrictions .
Discussion is on forex movements and not on the base rate itself. The base currency rate between two or more currencies depend on factors starting from Purchase power parity , Balance of payments of trde as of a certain date and various other factors which is possibly a subject for discussion for another day.
This piece is only on movement of Forex rates .
While the actual reason is quite complex and is driven by various factors which affect the market including imperfect market, restriction on currency movements, restrictions on trade and short term imbalances between supply and demand for currencies, the one compelling theory and what could be termed as a classical one on forex movement is the one with reference to Interest rate differentiel between currencies. This is the simplest , most logical and something which should work if the market is perfect and there are no restrictions on currency movement, investment or borrowing in the currencies under study.
Let us do a simple one between USD and INR. Let us assume a base rate of INR 40 to a 1 USD. Let us assume prevailing interest rates of 10 % PA in the case of INR and 5% PA in the case of USD. For the sake of simplicity we will have to assume no interest rate differentiel between borrowing and Investing .This is to make the example easier . INR 40 at the end of one year will be equivalent to INR 44 and the in the case of USD, $ 1 at the end of one year at an interest rate of 5% be $1.05. Equilibrium forward rate of USD to INR for one year period should be 44/1.05 , that is INR 41.9048 to1 USD. If the rate is anything other than this , there arises an opportunity to make riskless profit.
Normally the currency on which interest rate is lower will be at a premium and the one whose interest rate is higher will be at a discount.
Let us assume that at the interest levels specified, the actual forward rate quoted at the end of one year is at INR 40 to a USD.
Easy way to make profit is
- borrow in USD,
- convert to INR immediately,
- deposit in INR ,
- simultaneously take a forward cover to buy USD at INR 40.
Let us calcuate the flows .
Since you have borrowed in USD , you will have to pay $ 1.05 with interest at the end of one year.
USD converted to INR 40 and deposited would become INR 44 at the end of one year since INR deposit attracts 10 % interest.
Since a forward cover has been taken , you would be in a position to buy USD of 1.05 for a total outflow of INR 1.05*40= 42. This leaves you Rs 2 as riskless profit.
In the same case, if at the same interest rates, INR forward rate had been 46 to USD, we will be doing the borrowing in INR, depositing in USD, forward cover to sell USD .
Let us work out the simple math in this sequence.
You had borrowed INR 40 at the end of one year , to be returned is Rs 44 .
INR borrowed was converted to USD at the beginning has been deposited as USD deposit .At the end of one year we get USD 1.05.
Since we had a cover to sell USD at the rate of INR 46 to a USD, we will sell the $ 1.05 at INR 46 to a USD and get on hand INR 48.03. We pay off the INR 44 and left with INR 4.03 rsikless
We have assumed no difference in interest rates between borrowing and investing and also no difference between buying and selling of currency. Margins between these two will make a slight difference in the calculations but the theory holds good.
As a thumb rule,arbitrage opportunity will arise when the currency forward rate is different from the interest rate differentiel. Normally in such situations the demand/supply for the currencies adjusts in such a way that the interest rates move and nullify the advantage. If this kind of anamoly were to persist , every one will be doing this set of transaction and the interest rates and the demand for the currency will drastically undergo a change till such time equilibrium is attained.
This is theory and will continue to be theory till such time, we have free currency movements and unrestricted deposit and borrowings in any currency in any country or atleast in the countries of the currencies in question/discussion.