In other words, investors should earn precisely the
same returns – and borrowers should incur precisely
the same costs – whether they invest (or borrow) at the
domestic interest rate or at the foreign interest rate
whenever they use forwards to hedge (or ‘cover’) their
foreign exchange rate risk. For this reason, this type of
IRP is often referred to as covered interest parity (CIP).
The logic behind the CIP is simple. Assume, for example,
that investors can earn higher interest rates in the domestic
currency, so that R* is less than i, t Ri,t. If the foreign
currency did not trade at a premium in the
forward market, so that Fi,t was higher than St, arbitrageurs
could make a riskless profit by borrowing money
in the foreign currency, exchanging it in the spot market,
investing the proceeds in domestic currency, and
ultimately paying off their loan at maturity with the foreign
currency they purchase in the forward market at
the undervalued rate.
While this fairly straightforward arbitrage logic underpins
CIP, the IRP argument is often taken one step
further by asserting that alternatives 1 and 3 should be
equal as well. In other words, investors (or borrowers)
should earn the same expected returns (or incur the same
expected costs) in foreign and domestic currency even if
they do not purchase forward contracts and instead simply
sell their foreign currency principal at maturity at the
prevailing spot exchange rate. Equation (15.2) summarizes
this equality: