Assignment #2: The Foreign Exchange Market and the Balance of Payments.

1. At noon, Jan. 4, 1991, the U.S. dollar was quoted at $1.1515 Canadian. Canadian treasury bills maturing in 1 year were yielding 10.97%. U.S. treasury bills maturing in 1 year were yielding 6.42%.

• Using this information alone, make a rough prediction of the one-year forward price of the U.S. dollar in terms of the Canadian dollar.

• It turns out that, in fact, the 1 year forward price of the U.S. dollar was $1.1903. How would you explain the discrepancy between your rough calculation and the actual observed forward rate?

• If you expect that in 1 year the U.S. dollar will be worth $1.10 Canadian and are willing to commit $100,000 Canadian to speculation on the Canadian dollar, what should you do?

• How much profit (in Canadian dollars) will you make if the U.S. dollar turns out in fact to be equal to $1.10? If it remains at its current value of $1.1515? If it turns out to be worth its current 1 year forward value of $1.1903?

2. Are the following statements true? Explain.

• Domestic interest rates always exceed foreign interest rates by the forward discount on foreign currency.

• For interest parity to hold, the forward exchange rate must equal the expected future spot rate.

• Adjustments of forward relative to spot exchange rates can protect investors from exchange risk but not political and other forms of risk.

• The interest parity theorem implies that risk adjusted real interest rates must differ between countries by the expected rate of change in the exchange rate.

• Since traders use interest differentials to set the forward exchange rates they will charge customers, forward rates do not reflect expected future changes in exchange rates and therefore cannot be the driving force behind interest rate differentials.

3. Show that the following relationship must exist between the forward and spot exchange rates between any two currencies and nominal interest rates on securities denominated in those two currencies.

F = S (1 + id) / (1 + if)

where F and S are the forward and spot prices of foreign currency in units of domestic currency and id and if are the domestic and foreign nominal interest rates.

[Hint: Calculate the amount of domestic currency one could obtain in one year by a covered investment of x units of domestic currency abroad. Then calculate the amount of domestic currency one could obtain in one year by investing x units of domestic currency at home.]

Under what circumstances will the forward discount be approximately equal to the interest rate differential (id - if)?

4. During the past 20 years substantial professional effort has been devoted to testing whether the foreign exchange market is efficient. The question has been posed at two levels: First, do agents use all available information in making decisions? Second, does the forward exchange rate equal the market's expectation of the future spot rate?

• Is the second of these propositions a logical consequence of the first?

• Are these propositions testable and, if so, how can one go about testing them? Outline the problems involved in doing this.

• Has existing empirical work established that the foreign exchange market is efficient?

• Can the interest rate parity proposition be tested in a similar way?

5. A major insight in foreign exchange research during the past couple of decades is that foreign exchange is a financial asset.

• Quite apart from any inadequacies in our econometric techniques and in the data, is this perspective sufficient to enable a full explanation of exchange rate behavior?

• Is the volatility of exchange rates evident since 1973 the result of financial factors relating to the asset properties of foreign exchange holdings?

• Does the fact that nominal exchange rates are serially correlated make it profitable to use trading rules that exploit this autocorrelation.

6. Substantial controversy has been evident during the past few years about whether or not real exchange rates are really random walks.

• Why might one expect that the exchange rate would follow a random walk?

• Why might one expect mean reversion?

• Is Purchasing Power Parity a good way of estimating the equilibrium long-run real exchange rate? Why or why not?

• Is the real exchange rate a useful device for measuring the competitiveness of domestic goods in international markets?

7. Suppose that the real exchange rate is a random walk. What does this imply about the forward discount? About the coefficient of the difference between the logarithms of the forward and spot exchange rates in a regression of the increase in the logarithm of the spot rate from period t to period t+1 on this variable? Show how and under what circumstances this coefficient can be given an errors in variables interpretation.

8. The first three of the four files

• ass2data.xls
• ass2data.gdt
• ass2data.tab
• ass2data.cat

Perform the statistical operations below. The free statistical program Gretl is the easiest one to use for these purposes.

• Plot the forward and spot exchange rates and describe in words the relationship between the two series.

• Plot current period spot rates together with forward rate predictions from the previous period both as time series and cross-sectionally. Comment on what you see.

• Plot the change in the logarithm of the spot rate from period t-1 to period t and the difference between the logarithms of the spot and forward rates in period t-1 both as time series and scatter charts, and comment on what this evidence indicates.

• Calculate the percentage prediction errors that arise when one uses the forward rate to forecast next period's spot rate and, alternatively, when one simply assumes that today's spot rate is the best predictor of next period's spot rate. Calculate the evident bias in the two forecasts and compare their mean squared errors. Plot the percentage forecast errors obtained from the two methods on a single histogram and compare the two forecasting methods. Do the month-to-month percentage changes in spot rates appear to be normally distributed?

• Regress the logarithm of the spot rate on the logarithm of the previous period's forward rate.

• Regress the change in the logarithm of the spot rate from period t-1 to period t on period t-1's difference between the logarithms of the forward and spot rates.

• Calculate the month-to-month percentage inflation rates and test whether the past month's inflation rate has any predictive power in explaining the current month's percentage forward discount. Do the same using the year-to-year percentage inflation rates. Do the average inflation rates over the entire period help to explain the average percentage forward discounts across countries?

• Calculate the real exchange rates of the Canadian dollar, mark, pound, and yen with respect to the U.S. dollar and plot them on the same time series graphs as the respective nominal exchange rates. Calculate the ratios of the nominal price levels of the respective countries to the U.S. price level and plot them on the same charts as the corresponding real and nominal exchange rates. Describe what you observe on these charts.

• Perform Dickey-Fuller unit root tests to investigate whether the real exchange rate series of the three countries are stationary (use the simple rather than the augmented Dickey-Fuller test). If you are using a statistical program that does not provide P-Values, confidence intervals are available in the file statabs.pdf. What do you find? What does it mean to say that these tests have low power? If you were to use an augmented Dickey-Fuller test, how would you decide on the number of lags to use?

  
  

  9. One frequently hears the argument in Canada that the country's nearly continuous current account deficit is bad for the health of the economy. Some argue that the country is "spending beyond its means". In other countries whose current accounts are in deficit one frequently hears the argument that the deficit is "unsustainable" and will eventually require painful adjustments to eliminate. Frequently the proposed remedy is a tariff or other policy designed to improve the current account by reducing imports or increasing exports. Comment on these arguments. Will the imposition of a tariff "improve" the current account? Is it appropriate that the current account balance be zero? Is the long-run equilibrium current account balance zero?

  
  

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