International Finance Theory and Policy
by Steven M. Suranovic

Finance 20-8

# Exchange Rate Equilibrium Stories using the RoR Diagram

Any equilibrium in economics has an associated behavioral story to explain the forces that will move the endogenous variable to the equilibrium value. In the foreign exchange (FOREX) model, the endogenous variable is the exchange rate. This is the variable that is determined as a solution in the model and will change to achieve the equilibrium. Variables that do not change in the adjustment to the equilibrium are the exogenous variables. In this model, the exogenous variables are Ee\$/£, i\$, and i£ . Changes in the exogenous variables are necessary to cause an adjustment to a new equilibrium. However, in telling an equilibrium story it is typical to simply assume that the endogenous variable is not at the equilibrium (for some unstated reason), and then to explain how and why the variable will adjust to the equilibrium value.

Suppose, for some unspecified reason, the exchange rate is currently at E"\$/£ as shown in the adjoining diagram. The equilibrium exchange rate is at E'\$/£ since at this rate, rates of return are equal and interest rate parity (IRP) is satisfied. Thus, at E"\$/£ the exchange rate is too high. Since the exchange rate, as written, is the value of the pound, we can also say that the pound value is too high relative to the dollar to satisfy IRP.

With the exchange rate at E"\$/£, the rate of return on the dollar, RoR\$, is given by the value A along the horizontal axis. This will be the value of the US interest rate. The rate of return on the pound, RoR£ is given by the value B, however. This means that RoR£ < RoR\$ and IRP does not hold. Under this circumstance, higher returns on deposits in the US will motivate investors to invest fund in the US rather than Britain. This will raise the supply of £s on the FOREX as British investors seek the higher average return on US assets. It will also lower the demand for British £s by US investors who decide to invest at home rather than abroad. Both changes in the FOREX market will lower the value of the pound and raise the US \$ value, reflected as a reduction in E\$/£.

In more straightforward language, when the rate of return on \$ deposits is higher than on British deposits, investors will increase demand for the higher RoR currency and reduce demand for the other. The change in demand on the FOREX raises the value of the currency whose RoR was initially higher (the US dollar in this case) and lowers the other currency value (the British pound).

As the exchange rate falls from E"\$/£ to E'\$/£, RoR£ begins to rise up, from B to A. This occurs because RoR£ is negatively related to changes in the exchange rate as described in 20-7. Once the exchange rate falls to E'\$/£, RoR£ will become equal to RoR\$ at A and IRP will hold. At this point there are no further pressures in the FOREX for the exchange rate to change, hence the FOREX is in equilibrium at E'\$/£.

Exchange Rate too Low

If the exchange rate is lower than the equilibrium rate, for some unspecified reason, the then adjustment will proceed in the opposite direction. At any exchange rate below E'\$/£ in the diagram, RoR£ > RoR\$. This condition will inspire investors to move their funds to Britain with the higher rate of return. The subsequent increase in the demand for pounds will raise the value of the pound on the FOREX and E\$/£ will rise (consequently the dollar value falls). The exchange rate will continue to rise, and the rate of return on pounds will fall, until RoR£ = RoR\$ (IRP holds again) at E'\$/£.

International Finance Theory and Policy - Chapter 20-8: Last Updated on 2/19/05