5.7 Exchange Rate Effects of Changes in the Expected Exchange Rate Using the RoR Diagram

Suppose that the foreign exchange market (Forex) is initially in equilibrium such that RoR_£ = RoR_$ (i.e., interest rate parity holds) at an initial equilibrium exchange rate given by E′_$/£. The initial equilibrium is depicted in Figure 5.9 "Effects of an Expected Exchange Rate Change in a RoR Diagram". Next, suppose investors’ beliefs shift so that E_$/£^e rises, ceteris paribus. Ceteris paribus means we assume all other exogenous variables remain fixed at their original values. In this model, the U.S. interest rate (i_$) and the British interest rate (i_£) both remain fixed as the expected exchange rate rises.

An expected exchange rate increase means that if investors had expected the pound to appreciate, they now expect it to appreciate even more. Likewise, if investors had expected the dollar to depreciate, they now expect it to depreciate more. Alternatively, if they had expected the pound to depreciate, they now expect it to depreciate less. Likewise, if they had expected the dollar to appreciate, they now expect it to appreciate less.

This change might occur because new information is released. For example, the British Central Bank might release information that suggests an increased chance that the pound will rise in value in the future.

The increase in the expected exchange rate (E_$/£^e) will shift the British RoR line to the right from RoR′_£ to RoR″_£ as indicated by step 1 in the figure.

The reason for the shift can be seen by looking at the simple rate of return formula:

$$Ro{R}_{\text{£}}=\frac{E_{\text{\$/£}}^{\text{e}}}{E_{\text{\$/£}}}(1+i_{\text{£}})-1.$$

Suppose one is at the original equilibrium with exchange rate E′_$/£. Looking at the formula, an increase in E_$/£^e clearly raises the value of RoR_£ for any fixed values of i_£. This could be represented as a shift to the right on the diagram from A to B. Once at B with a new expected exchange rate, one could perform the exercise used to plot out the downward sloping RoR curve. The result would be a curve, like the original, but shifted entirely to the right.

Immediately after the increase and before the exchange rate changes, RoR_£ > RoR_$. The adjustment to the new equilibrium will follow the “exchange rate too low” equilibrium story presented in Chapter 5 "Interest Rate Parity", Section 5.4 "Exchange Rate Equilibrium Stories with the RoR Diagram". Accordingly, higher expected British rates of return will make British pound investments more attractive to investors, leading to an increase in demand for pounds on the Forex and resulting in an appreciation of the pound, a depreciation of the dollar, and an increase in E_$/£. The exchange rate will rise to the new equilibrium rate E″_$/£ as indicated by step 2.

In summary, an increase in the expected future $/£ exchange rate will raise the rate of return on pounds above the rate of return on dollars, lead investors to shift investments to British assets, and result in an increase in the $/£ exchange rate (i.e., an appreciation of the British pound and a depreciation of the U.S. dollar).

In contrast, a decrease in the expected future $/£ exchange rate will lower the rate of return on British pounds below the rate of return on dollars, lead investors to shift investments to U.S. assets, and result in a decrease in the $/£ exchange rate (i.e., a depreciation of the British pound and an appreciation of the U.S. dollar).