Question

Discuss IRP, the IFE, and international arbitrage opportunities with interest and currency exchange rates.

Answer 1

Interest Rate Parity (IRP) theory states that the difference in relative exchange rates of two countries can be explained by their relative interest rate differential with the currency of the country with higher rates depreciating vis-a-vis the lower interest rate country. In simple terms if there are 2 countries A & B and their relative exchange rates are 1A = 2B and their interest rates are r_A and r_B with r_B>r_A. Now if the exchange rates remain static, then a trader can borrow in country A and invest in country B at higher rate and then again convert back into currency A and earn higher returns in currency A even though the interest rates for currency A are lower. Under the no arbitrage condition, either the interest rates in country B will have to come down or the exchange rate vis-a-vis A will have to depreciate such that the returns across both the currencies are similar.

International Fisher Effect (IFE) states that the relative difference between two countries exchange rates can be explained by their relative nominal interest rate differences. The idea behind this theory is that nominal interest rates will also capture inflation expectation in them and a country with lower nominal rates and hence lower inflation will see its currency purchasing value increase in relative terms and hence its currency should also reflect the same by relative appreciation.

Both these theories provide theoretical foundation which can be used to scout for aribtrage opportunities whenever the market prices (exchange rates & interest rates) deviate from the theoretical levels, it can be used to arbitrage and eventually the demand supply created due to arbitrage trades will lead to theoretical equilibrium. For example if country A and B have relative exchange rate of 1A = 100B and their interest rates are 2% and 10%. As per IRP, the 1 year hence rate should be :

1 year hence rate = 100 * (1+10%)/(1+2%) = 107.8431; any other forward rate will lead to arbitrage . So if the forward rate was 104, then a trader can borrow 100A at 2% for 1 year and convert it into B at 100. Use these 10000B to invest at 10% for 1year and receive 11000. Use the forward at 104 to lock into conversion rate after 1 year at 104, which means receive 105.7692 (11000/104) A currency out of which pay the borrowed amount and interest of 102A back . The residual of 3.7692 is pure arbitrage profit As more and more people move into this trade, the supply of 1 year hence currency B will increase such that the forward rate converges to 107.8431 where there will be no arbitrage.