Suppose you were to sell £1000.00 of U.K. bonds and then
convert the funds into U.S. dollars and purchase $2000.00 of
U.S. bonds. Since the interest rate is the same on both bonds
there will be no gain in interest. In one year the principal
and interest on your U.S. investment will be $2100.00. So enter
into a forward contract to sell $2100.00 for £1105.26 one
year from now at the forward exchange rate of £1.00 = $1.90.
You will have made a sure gain of £55.26 on top of the £50
interest that you would have obtained had you left the funds in
the U.K. This represents a profit of 55.26/1050 or about 5 percent .
Note that the size of the above profit is completely independent of
what happens to the pound/dollar exchange rate over the next year---all
of your profit on the transaction is represented by the forward discount
on the pound. It may be that the market believes that the pound will
devalue by 5 percent over the year, and if the market is right you can
make a 5 percent profit over and above your interest earnings without
covering yourself. In that case, however, your extra profit will be a
speculative profit, based on a correct assessment of the magnitude and
direction of future movements in the dollar/pound exchange rate,
not an arbitrage profit that depends only on your ability to
simultaneously make the several transactions.
An arbitrage opportunity like the above will not go unnoticed by the rest
of the market. Traders everywhere will try to sell U.K. one-year
government bonds and use the funds to buy U.S. one-year government bonds.
The price of the U.K. bond will fall and the price of the U.S. bond will
rise. Since the coupon yields on these bonds will be unaffected, the
changes in bond prices will imply changes in the interest rates on the
bonds in the opposite directions. The interest rate on the U.K. bond will
rise and the interest rate on the U.S. bond will fall.
The interest rate will rise in the U.K. and fall in the U.S. until arbitrage
is no longer profitable. This will be the case when the U.K. interest rate
exceeds the U.S. interest rate by the amount of the forward discount on the
pound. Suppose, for example, that the U.K. interest rate rises to 9 percent
and the U.S. interest rate falls to 4 percent. Then an investor will forego
9 percent on the U.K. bonds in order to obtain 4 percent on the U.S. bonds
plus 5 percent gain on the forward cover, earning a zero net profit.
The relationship between the forward discount on a currency in terms of
another currency and the interest rates on equally-risky bonds denominated
in the two currencies can therefore be expressed
Let us suppose that the spot exchange rate between the U.S. dollar and the
British pound is currently £1.00 = $2.00 and that the
one-year forward rate is £1.00 = $1.90. Suppose further that
nominal interest rates on one-year government bonds are 5% in both
Britain and the United States and that there is zero probability that
either government will default. Can you think of a sure-fire arbitrage
opportunity here?
where id and if are the domestic and foreign interest rates and Ψ is the forward discount on the domestic currency.
In general, there is no reason to assume that government bonds in different countries are equally risky. And risk differences are even more likely when we compare private debt obligations in different countries. Accordingly, it is more appropriate to write the equation above as
where ρd is the difference in the risk from holding the two bonds. We can use this equation as a general description of the relationship between the overall levels of interest rates in two countries---after allowing for risk, the realized returns to investment should be the same in both. This gives ρd a broader interpretation than we gave it in setting up the above equation since it now applies to any pair of similar domestic and foreign securities.
The risk represented by ρd is often termed political risk or country-specific risk to distinguish it from the risk of an unforeseen change in the exchange rate, represented in the previous topic by ρx and termed foreign exchange risk. Political or country-specific risk arises independently of movements in the exchange rate.
Political risk arises because governments often do things that affect the realizable returns from investments in assets issued in both the private and public sectors. Taxes may be imposed in one country and not in others. The government of a country may legislate that earnings from domestic capital owned by foreigners cannot be repatriated abroad. A country might also be specialized in the production of natural resource and other products that involve more risk than the industries in which other countries specialize. This will cause additional country-specific risk differentials on private assets.
The basic equation above is called the interest parity condition---domestic interest rates will exceed foreign interest rates by the forward discount on the domestic currency plus the country-specific risk premium for holding domestic rather than foreign bonds. Covered interest parity is deemed to hold if the excess of the domestic over the foreign interest rate is equal to the forward discount on the domestic currency---that is, if the risk premium is zero.
Before going further we need a test to make sure that you are fully on top of the ideas expressed above. Think up your own answers before looking at the ones provided.
Question 1
Question 2
Question 3
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