EXPECTED EXCHANGE RATES AND THE TERM STRUCTURE OF INTEREST RATES

There is no such thing as the interest rate for a country. Interest rates within a country vary for different investment opportunities and for different maturity dates on similar investment opportunities. The structure of interest rates existing on investment opportunities over time is known as the term structure of interest rates. For instance, in the bond market we will observe three-month, six-month, one-year, three-year, and even longer-term bonds. If the interest rates rise with the term to maturity, then we observe a rising term structure. If the interest rates are the same regardless of term, then the term structure will be flat. We describe the term structure of interest rates by describing the slope of a line connect- ing the various points in time at which we observe interest rates.

There are several competing theories that explain the term structure of interest rates. We will discuss three:

1. Expectations. This theory suggests that the long-term interest rate tends to be equal to an average of short-term rates expected over the long- term holding period. In other words, an investor could buy a long- term bond or a series of short-term bonds, so the expected return from the long-term bond will tend to be equal to the return generated from holding the series of short-term bonds.

2. Liquidity premium. Underlying this theory is the idea that long-term

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supply and demand in each market. If the markets are segmented then the returns in the long-term bond market can be very different from the short-term bond market. Although we could use these theories to explain the term structure of

interest rates in any one currency, in international finance we use the term structures for different currencies to infer expected exchange rate changes. For instance, if we compared Euro-dollar and Euro-euro deposit rates for different maturities, like one-month and three-month deposits, the difference between the two term structures should reflect expected exchange rate changes, as long as the expected future spot rate is equal to the forward rate. Of course, if there are capital controls, then the various national markets become isolated and there would not be any particular relationship between international interest rates.

Figure 6.1 plots the Eurocurrency deposit rates at a particular time for 1- to 12-month terms. We know from the interest rate parity condition that when one country has higher interest rates than another, the high-interest-rate currency is expected to depreciate relative to the low-interest-rate currency. The only way an interest rate can be above another one is if the high-interest-rate currency is expected to depreciate; thus, the effective rate, i 1 (F 2 E)/E [as shown in Equation (6.4) , with the forward rate used as a predictor of the future spot rate], is lower than the observed rate, i, because of the expected depreciation of the currency (F , E).

1.50 ate

1.00 Interest r

Exchange Rates, Interest Rates, and Interest Parity 123

If the distance between two of the term structure lines is the same at each point, then the expected change in the exchange rate will be constant. To see this more clearly, let us once again consider the interest parity relation given by Equation (6.3) :

i $ 2i d 5 ðF 2 EÞ=E

This expression indicates that the difference between the interest rate in two countries will be equal to the forward premium or discount when the interest rates and the forward rate reflect the same term to maturity. If the forward rate is equal to the future spot rate, then we can say that the interest differential is also approximately equal to the expected change in the spot rate. This means that at each point in the term structure, the difference between the national interest rates should reflect the expected change in the exchange rate for the two currencies being compared. By examining the different points in the term structure, we can determine how the exchange rate expectations are changing through time. One implication of this is that even if we did not have a forward exchange market in a currency, the interest differential between that currency and other currencies would allow us to infer expected future exchange rates.

Now we can understand why a constant differential between two interest rates implies that future changes in the exchange rate are expected to occur at some constant rate. Thus, if two of the term structure lines are parallel, then the exchange rate changes are expected to be constant (the currencies will appreciate or depreciate against each other at a constant rate). On the other hand, if two term structure lines are diverging, or moving farther apart from one another, then the high-interest-rate currency is expected to depreciate at an increasing rate over time. For term structure lines that are converging, or moving closer together, the high-interest-rate currency is expected to depreciate at a declining rate relative to the low-interest-rate currency.

To illustrate the exchange rate term structure relationship, let us look at Figure 6.1 . In Figure 6.1 the term structure line for Japan lies below

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Looking at the other currencies in Figure 6.1 we can see differences in the expected changes in the exchange rates. The term structure line for the U.K. lies above that of the United States so we should expect the pound to depreciate in value against the dollar and sell at a forward discount against the dollar. The fact that the term structure of the euro lies above all others indicates that the euro is expected to depreciate against all the other currencies in the table. A particularly interesting case is the term structure for the Canadian dollar and the U.K. pound, because these intersect. The Canadian dollar is expected to depreciate or sell at a forward discount at shorter maturities, but at the 12-month maturity the Canadian dollar sells at forward premium against the U.K. pound.

EXPECTED EXCHANGE RATES AND THE TERM STRUCTURE OF INTEREST RATES