1. MBA (Finance specialisation) & MBA – Banking and Finance (Trimester) Term VI Module : – International Financial Management Unit II: Foreign Exchange Markets Lesson 2.3 (Theories of Exchange rate – Interest rate parity theory and International fisher effect )

2. Interest Rate Parity relationship This relationship links interest rates of two countries with spot and future exchange rates. It was made popular in 1920s by economists such as John M. Keynes. The theory underlying this relationship says that premium or discount of one currency against another should reflect interest rate differential between the two countries. In perfect market conditions, where there are no restrictions on the flow of money and there are no transaction costs, it should be possible to gain the same real value of one's monetary assets irrespective of the country (or currency) in which they are invested.

3. Interest Rate Parity relationship For example, an investor has one unit of pound sterling. He can invest it in the UK money market and earn an interest of it on it. The resulting value after one year will be: £1 (1 +i £ ) Alternatively, he can buy So dollars (the current exchange rate being So dollars = 1 pound sterling) and invest this dollar amount in US money market. The end value after one year will be: $S o (1 + i $ ) The equilibrium condition demands that these two sums be equal. If the two sums were not equal, then the investor would invest in that currency where the end value of their monetary assets is going to be more.

4. Interest Rate Parity relationship But once this action is generalized by the similar expectations of all investors, equilibrium is going to be reestablished. Thus, in equilibrium situation, $S 0 (1 + i $ ) = £1(1 + i £ ) $S 0 [ (1 + i $ )/(1 + i £ ) ] = £1 This expression on the left side of the above equation is future exchange rate. We can write S 1 = S 0 [ (1 + i $ )/(1 + i £ ) ] This expression can be written for any two currencies, A (home currency) and B (foreign currency), by replacing dollar and pound sterling. Thus, S 1 = S 0 [ (1 + i A )/(1 + i B )]. The above equation is known as Interest rate parity relationship.

5. Interest Rate Parity relationship S 1 = S 0 [ (1 + i A )/(1 + i B )]. For simplicity, we can re write the above equation as F = S [ (1 + i home )/(1 + i foreign )] Or F/S = [ (1 + i home )/(1 + i foreign )] Subtracting ‘1’ from both the sides, we have (F – S)/S = [(i home – i foreign )/ (1 + i foreign )] As a limiting case, if we assume that foreign interest rates are small as compared to unity then the denominator (1 + i foreign ) in the limit tends to ‘1’ and the above relation would be given as (i home – i foreign ) = Premium/Discount for a unit period i.e. the forward premium and discount rate are to be equal to interest rate differential between the domestic and foreign interest rates for no interest arbitrage situations.

6. Interest Rate Parity relationship S 1 = S 0 [ (1 + i A )/(1 + i B )]. For simplicity, we can re write the above equation as F = S [ (1 + i home )/(1 + i foreign )] Or F/S = [ (1 + i home )/(1 + i foreign )] Subtracting ‘1’ from both the sides, we have (F – S)/S = [(i home – i foreign )/ (1 + i foreign )] As a limiting case, if we assume that foreign interest rates are small as compared to unity then the denominator (1 + i foreign ) in the limit tends to ‘1’ and the above relation would be given as (i home – i foreign ) = Premium/Discount for a unit period i.e. the forward premium and discount rate are to be equal to interest rate differential between the domestic and foreign interest rates for no interest arbitrage situations.

7. Interest Rate Parity relationship The arbitrage process due to difference in forward premium/discount and interest rate differential would become clear from the following examples: Rule 1: If (F-S)/S X 12/N x 100 is less than ( R(Home) – R(foreign)  Borrow money from foreign country  Convert into home currency using spot rate  Invest in home country at R(home)  Reconvert the money into foreign currency using forward rate.  The money available after reconversion will be more than (money borrowed in foreign currency + interest on money borrowed in foreign currency).

8. Interest Rate Parity relationship Consider example given below Given ( Home Country : India, Foreign Country : U.S.) Spot Rate (Rs/$) = 62 6 mths Forward rate = 62.5 Interest rate in India = 12% Interest rate in U.S. = 8% Step 1: Calculate forward premium/discount using the formula (F-S)/S X 12/N x 100 Forward premium/discount = [(62.5 – 62)/62 ] x (12/6) x 100 = 1.612 Dollar is at premium Step 2: Given interest rate differential ( Rindia – Rus ) = 4% Step3: Since interest rate differential is greater than forward premium, borrow from the country where interest is lower and invest in the country where interest rate is higher.

9. Interest Rate Parity relationship Step 4: Borrow $ 10000 at the rate of 8% p.a. Dollars to be refunded after six months = 10000 + Interest for six months @ 8% (400) = $ 10,400 Step 5 Convert dollars into rupees using spot rate 10000 x 62 = Rs 62000 Step 6 Invest rupees at the rate of 12% p.a. for six months: 62000 ( 1.06) = 657200 Step7: Covert Rs 657200 into dollars using forward rate : 657200/62.5 = $ 10515.2 Step 8: Gain = $ (10515.2 – 10400) = $ 115.2

10. Interest Rate Parity relationship Rule 2: If (F-S)/S X 12/N x 100 is more than ( R(Home) – R(foreign)  Borrow money from home country.  Convert into foreign currency using spot rate.  Invest in foreign country at R(foreign).  Reconvert the money into home currency using forward rate.  The money available after reconversion will be more than (money borrowed in home currency + interest on money borrowed in home currency).

11. Interest Rate Parity relationship Consider example given below Given Home Country : India, Foreign Country : U.S. Spot Rate (Rs/$) = 62 6 mths Forward rate = 63 Interest rate in India = 12% Interest rate in U.S. = 10% Step 1: Calculate forward premium/discount using the formula (F-S)/S X 12/N x 100 Forward premium/discount = [(63 – 62)/62 ] x (12/6) x 100 = 3.225806 Dollar is at premium Step 2: Given interest rate differential ( RIndia – R u.s.) = 2% Step3: Since interest rate differential is smaller than forward premium, borrow from the country where interest is higher and invest in the country where interest rate is lower.

12. Interest Rate Parity relationship Step 4: Borrow Rs 10000 at the rate of 12% p.a. Rupees to be refunded after six months = 10000 + Interest for six months @ 12% (600) = $ 10,600 Step 5 Convert rupees into dollars using spot rate 10000 / 62 = 161.29 Step 6 Invest dollars at the rate of 10% p.a. for six months 161.29 ( 1.05) = 169.35 Step7: Convert $ 169.35 into rupees using forward rate 169.35 x 63 = 10669.35484 Step 8: Gain = Rs (10669.35 – 10600) = Rs 69.35

13. International Fisher effect According to relative form of purchasing parity theory Forward /premium discount = difference in inflation rate of two countries According to interest rate parity theory Forward /premium discount = difference in interest rate of two countries. Combining the two, we have, Difference in inflation rate = Difference in interest rate, or (r home – r foreign ) = (i home – i foreign ) (r home – i home ) = (r home – i foreign ) The above equation implies that, in the absence of restrictions on trade flows and capital flows the expected real rate of return on capital tends to equalise. The above equation is referred as Fisher Open Condition or International fisher effect.