If investors are rational they will bid forward exchange rates into line
with where they expect the spot rates to be on the date the forward
contracts mature plus or minus an adjustment to allow for the risks of
holding the relevant currency forward. This enables us to express the
forward discount on the domestic currency as
1. Ψ = Eπ + ρx
where Ψ is the forward discount on the domestic currency,
ρx is a premium to cover foreign exchange risk and
Eπ is the expected rate of depreciation of the domestic
currency over the contract period. If you don't understand where this
relationship comes from, go back and review Topic 3.
The equation above says that the forward discount on the domestic currency
must equal the expected rate of depreciation of that currency over the life
of the forward contract plus an allowance for the risk of holding the
domestic currency forward. This condition, which follows from the
proposition that market participants use, as best as they can, all information
available to them in making their portfolio decisions, is called the efficient
markets condition.
If investors exploit all available arbitrage opportunities a second
condition must also hold. The excess of the domestic over the foreign
interest rate must be equal to the forward discount on the domestic
currency, plus or minus an adjustment for the differential political and
other non-foreign exchange risks of holding domestic relative to foreign
assets.
2. id - if = Ψ
+ ρd
where id and if are the
domestic and foreign interest rates, and ρd is
the difference in the country-specific risk of holding the two countries'
assets. This equation is called the interest rate parity condition.
The efficient markets and interest parity conditions can be combined by
substituting equation 1 into equation 2 to yield.
3. id - if =
Eπ + ρx + ρd
By consolidating the political and foreign exchange risk into a single risk
premium,
ρ = ρx
+ ρd
we can express rewrite equation 3 as
4. id - if =
Eπ + ρ
This expression can be rearranged to yield an equation expressing the
domestic interest rate as
5. id = if +
Eπ + ρ
It says that after adjusting for the difference in risk, the domestic
interest rate must equal the foreign interest rate plus the expected rate of
depreciation of the domestic currency in terms of foreign currency.
This equation turns out to be very important because it imposes a
constraint on domestic government policy. It says that, regardless of what
the mechanism is by which government policy operates on the economy, the
government can only change the domestic interest rate by either inducing a
change in the risk from holding domestic as opposed to foreign assets or
inducing a change in the market's expectations about the future course of
the exchange rate. This assumes, of course, that the domestic government
cannot affect interest rates in the rest of the world. Any sensible theory
of the determination of domestic output, employment, prices, and the
government's role in determining them must deal with this constraint, the
validity of which depends only on the propositions that asset holders behave
rationally and are able to buy and sell assets across international
borders.
Note that the observed market interest rates that appear in this constraint
are nominal interest rates. To pursue the analysis further we must take
account of the differences between nominal and real interest rates analyzed
in the Lesson entitled Interest Rates and Asset Values.
The next step is to extend the analysis to incorporate the relationships
between real and nominal interest rates.
But first, we need a test to make sure you have a good command of the basic
idea developed here. As always, think up your own answers before looking at
the ones provided.
You should now understand what spot and forward exchange rates are and what
is meant by the forward discount (or premium) on domestic currency. You
should also understand the relationship between the forward discount,
foreign exchange risk, and the expected future change in the spot exchange
rate. Finally, you should understand the relationship between the forward
discount, the domestic/foreign interest rate differential, and political and
other country-specific risk. These relationships, known as the efficient
markets and interest parity conditions have important implications for how
the level of domestic nominal interest rates is determined in an economy
whose asset markets are integrated with the markets for assets in the rest
of the world. We now combine the efficient markets and interest rate
parity conditions in order to examine these implications.