This is “Short-Run Determinants of Exchange Rates”, section 18.4 from the book Finance, Banking, and Money (v. 1.0).
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As Figure 18.6 "South Africa-United States exchange rate, June 2006" shows, exchange rates can be very volatile. In a single month (June 2006), the South African rand depreciated from about 6.6 to 7.4 rand to 1 USD, with various ups and downs along the way. The rand then reversed course and appreciated toward 7.1 rand/USD. Such fluctuations are by no means unusual. Why do exchange rates undergo such gyrations? Figure 18.7 "Determinants of exchange rates in the short run" summarizes the major factors affecting exchange rates in the short run. Note that it looks very much like Figure 18.5 "Determinants of exchange rates in the long run" but with three key differences. First, instead of actual relative price levels, trade barriers, exports, imports, and productivity driving changes, expectations of their future direction drive changes. Given the discussion in Chapter 7 "Rational Expectations, Efficient Markets, and the Valuation of Corporate Equities", this should not be surprising. Second, two additional variables have entered the equation: foreign and domestic interest rates. The intuition behind the first variables is the same as those discussed above, but in the short run, the mere expectation of a change in a variable moves the market. The intuition behind the interest rates is also straightforward. If something increases demand for the domestic currency, like domestic interest rates increasing or foreign interest rates decreasing, it will appreciate. If something reduces demand for the domestic currency, like domestic interest rates decreasing or foreign interest rates increasing, it will depreciate. (If this doesn’t make sense to you, review the discussion in Chapter 5 "The Economics of Interest-Rate Fluctuations" regarding the theory of asset demand.) Because expectations and interest rates change frequently, so, too, do exchange rates under the current floating rate regime.
Figure 18.6 South Africa-United States exchange rate, June 2006
Figure 18.7 Determinants of exchange rates in the short run
We learned in Chapter 4 "Interest Rates" that there is an important distinction between real and nominal interest rates. Through the Fisher Equation, we know that the nominal interest rate equals the real interest rate plus inflation expectations. Is that distinction important when considering foreign exchange markets?
Absolutely, and here is why. An increase in nominal interest rates caused by a rise in the real interest rate would leave expectations about future exchange rates unchanged and hence would cause the domestic currency to appreciate. An increase in nominal interest rates caused solely by an increase in inflation expectations, by contrast, would cause the expected future exchange rate to decrease through the expected and actual price level effects. So the domestic currency would depreciate instead.
The third difference between the long and short terms is that, in the short term, the expectation of the future direction of the exchange rate plays an important role. The easiest way to see this is to compare two investments with a one-year time horizon: a domestic (say, USD-denominated) bank account that pays 5 percent per year and a foreign (say, pound-sterling-denominated) account paying 6 percent per year. Before you jump for the sterling (6 > 5), you need to consider that, in a year, you’re going to want dollars again because you reside in the United States and need USD to buy lunch, pay the rent, and so forth. If the dollar appreciates more than 1 percent over the course of the year, you’d be better off with the dollar deposit. Say that you invest $10,000 in sterling when the exchange rate is $1.50/£1 or, in other words, £.6667/$1. Your investment today would buy 10,000 × .6667 = £6,667. Multiply that by the interest on the sterling deposit (1.06) and you get £7,067.02 in a year. If the exchange rate is unchanged, you’re cool because you’ll have 7,067.02 × 1.50 = $10,600.53, which is greater than $10,000 invested at 5 percent, which equals 10,000 × 1.05 = $10,500.00. But what if, over the course of that year, the dollar appreciated strongly, to $1.25 per pound? Then your £7,067.02 would buy you only 7,067.02 × 1.25 = $8,833.78. You just took a bath, and not the good kind, because you should have invested in the dollar deposit! Of course, if the dollar depreciated to, say, $1.75, you’ll be pheeling phat at 7,067.02 × 1.75 = $12,367.29.
We learned in Chapter 5 "The Economics of Interest-Rate Fluctuations" that increases in the growth rate of the money supply will eventually cause the price level to increase, but its effect on nominal interest rates in the short term can vary: rates can dip strongly, then rebound but remain permanently lower than the previous level, decrease temporarily before increasing permanently, or increase immediately. What does this mean for the market for foreign exchange?
The fact that a major short-run determinant of the exchange rate, foreign and domestic interest rates, moves around a lot helps to explain why the foreign exchange market is volatile. That market is also volatile because expectations of many things, including future differential price levels, productivity, and trading levels, will affect it via the E^{ef} variable.
As noted above, the markets for foreign exchange and bonds/deposits are highly competitive and efficient, so we wouldn’t expect discrepancies in returns to last long. The law of one price, of course, applies most stringently to financial markets in which international capital mobility is allowed because huge sums of money (deposits) can be sent hither and thither almost immediately and cost-free, ideal conditions for the law of one price to prevail. So what economists call the interest parity condition often holds (is true). More formally,
$${i}^{D}={i}^{F}-({E}^{ef}-{E}^{t})/{E}^{t}$$where:
i^{D} = domestic interest rate
i^{F} = foreign interest rate
E^{ef} = expected future exchange rate
E^{t} = exchange rate today
In plain English, if the so-called interest parity condition holds, the domestic interest rate should equal the foreign interest rate minus the expected appreciation of the domestic currency. If i^{F} is > i^{D}, the domestic currency must be expected to appreciate; otherwise, everyone would sell their domestic deposits to buy the foreign ones. If i^{F} is < i^{D}, the domestic currency must be expected to depreciate (have a negative sign, two of which make a positive, augmenting i^{F}); otherwise, everyone would sell the foreign deposits and buy the domestic ones. If you find this confusing, there is another, more intuitive way of stating it: the domestic interest rate must equal the foreign interest rate plus the expected appreciation of the foreign currency. If i^{F} is < i^{D}, the expected appreciation of the foreign currency compensates for the lower interest rate, allowing equilibrium. You can practice calculating interest parity in Exercise 1.
Use the interest parity formula (i^{D} = i^{F} – (E^{ef} – E^{t})/E^{t}) to calculate the following:
Foreign Interest Rate | Expected Future Exchange Rate | Exchange Rate Today | Answer: Domestic Interest Rate |
---|---|---|---|
5 | 1 | 1 | 5 |
5 | 1.1 | 1 | 4.9 |
5 | 1.2 | 1 | 4.8 |
5 | 1.3 | 1 | 4.7 |
5 | 0.9 | 1 | 5.1 |
5 | 0.8 | 1 | 5.2 |
5 | 0.7 | 1 | 5.3 |
6 | 1 | 1 | 6 |
6 | 1 | 1.1 | 6.090909 |
6 | 1 | 1.2 | 6.166667 |
6 | 1 | 1.3 | 6.230769 |
6 | 1 | 0.9 | 5.888889 |
6 | 1 | 0.8 | 5.75 |
6 | 1 | 0.7 | 5.571429 |
15 | 1 | 1 | 15 |
15 | 10 | 1 | 6 |
15 | 1 | 10 | 15.9 |
Expected Future Exchange Rate | Exchange Rate Today | Domestic Interest Rate | Answer: Foreign Interest Rate |
---|---|---|---|
1 | 1 | 2 | 2 |
1.1 | 1 | 2 | 2.1 |
1.2 | 1 | 2 | 2.2 |
1.3 | 1 | 2 | 2.3 |
0.9 | 1 | 2 | 1.9 |
0.8 | 1 | 2 | 1.8 |
0.7 | 1 | 2 | 1.7 |
1 | 1 | 10 | 10 |
1 | 1.1 | 10 | 9.909091 |
1 | 1.2 | 10 | 9.833333 |
1 | 1.3 | 10 | 9.769231 |
1 | 0.9 | 10 | 10.11111 |
1 | 0.8 | 10 | 10.25 |
1 | 0.7 | 10 | 10.42857 |
1 | 1 | 0 | 0 |
10 | 1 | 0 | 9 |
1 | 10 | 1 | 0.1 |