# Exchange Rate Effects of Changes in the Expected Exchange Rate using a RoR Diagram

Suppose that
the 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 the adjoining diagram. Next suppose investors beliefs shift
so that E^{e}_{$/£}, rises, ceteris paribus. Ceteris
paribus means we assume all other exogenous variables remain fixed at their
original values. In this model, the US interest rate, i_{$}, 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 £ to appreciate, they now expect it to appreciate even more.
Likewise, if investors had expected the $ to depreciate they now expect
it to depreciate more. Alternatively, if they had expected the £
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 £ 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 indicted by step 1.

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

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, as 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. (see 20-7). The result would be a
curve, like the original, but shifted entirely to the right.

Immediately after the increase, before the exchange rate changes, RoR_{£}
> RoR_{$}. The adjustment to the new equilibrium will follow
the "exchange rate too low"
equilibrium story presented in 20-8. Accordingly,
higher expected British rates of return will make British £ investments
more attractive to investors leading to an increase in demand for £s
on the FOREX, resulting in an appreciation of the pound, a depreciation
of the dollar and an increase in E_{$/£}. The exchange rate
will rise to the new equilibrium rate E"_{$/£} as indicted
by step 2.

In brief: *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 US dollar). *

In reverse: *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 US assets, and result
in a decrease in the $/£ exchange rate (i.e., a depreciation of
the British pound and an appreciation of the US dollar).*

*International Finance Theory and Policy - Chapter 20-11: Last
Updated on 2/19/05*