bekaert_2e_sm_ch10

Chapter 10Exchange Rate Determination and Forecasting

QUESTIONS

1. What is the difference between the ex ante and the ex post real interest rate?

Answer: The ex post interest rate corrects the nominal interest rate with the realized or ex post rate of inflation; whereas the ex-ante (or expected) real interest rate corrects the nominal interest rate for expected inflation.

As a lender, you care about the real return on your investment, which is the return that measures your increase in purchasing power between two periods of time. If you invest $1,

you sacrifice $1

P(t)real goods now, where P(t) is the price level. In 1 year, you get back

1 + i

P(t+1), where i is the nominal rate of interest. We calculate the real return by dividing the

real amount you get back by the real amount that you invest. Thus, if rep is the ex post real rate of return and ex post real interest rate, we have

( )ep

1 + i1 + iP(t+1)

1 + r = = 1 P(t+1)

P(t) P(t)

⎛ ⎞⎜ ⎟⎝ ⎠⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Notice that the real rate of interest depends on the realization of the rate of inflation because P(t + 1)/P(t) = 1 + π(t + 1), where π(t + 1) is the rate of inflation between time t and t + 1. For simplicity, we drop the time notation and simply write

ep (1 + i)1 + r =

(1 + ∂)If we subtract 1 from each side, we have

ep (1 + i) (1 + ∂) i - ∂r = - =

(1 + ∂) (1 + ∂) (1 + ∂)which is often approximated as

rep = i – π

©2012 Pearson Education, Inc.

Chapter 10: Exchange Rate Determination and Forecasting

The approximation involves ignoring the term (1 + π) in the denominator, which is close to 1 if inflation is not too high. Thus, the ex post real interest rate equals the nominal interest rate minus the actual rate of inflation.

Because the inflation rate is uncertain at the time an investment is made, the lender cannot know with certainty the real rate of return on the loan. By taking the expected value of both sides of the equation, conditional on the information set at the time of the loan, we derive the lender’s expected real rate of return, which is also called the expected real interest rate, or the ex ante real interest rate, which we denote re:

e ept tr = E [r ] = i(t) - E [∂(t+1)]

2. Suppose that the international parity conditions all hold and a country has a higher nominal interest rate than the United States. Characterize the country’s inflation rate compared to the United States, the country’s expected exchange rate change versus the dollar, the country’s currency forward premium (or discount) versus the dollar, and the country’s real interest rate compared to the U.S. real interest rate.

Answer: When all the parity conditions hold, real interest rates are equalized across countries, so the country’s real interest rate should equal that of the United States. The country’s higher nominal interest rate therefore must reflect a higher expected rate of inflation relative to the United States. Since the parity conditions hold, a higher expected rate of inflation implies that country’s currency should be expected to depreciate relative to the dollar, and the currency will trade at a forward discount relative to the dollar.

3. How do fundamental analysis and technical analysis differ?

Answer: Fundamental analysis typically uses formal economic models of exchange rate determination and macroeconomic fundamental data such as money supplies, inflation rates, productivity growth rates, and the current account of the balance of payments to predict exchange rates. Technical analysis uses only past exchange rate data, and perhaps some other financial data, such as the volume of currency trade, to predict future exchange rates.

4. Would technical analysis be useful if the international parity conditions held? Why or why not?

Answer: If the parity conditions held, technical analysis would not be useful in the sense of providing profitable trading information or information about expected exchange rates that could not be obtained elsewhere. If the parity conditions held, the best predictor of the future exchange rate would be the forward rate, and exchange rate forecasts based on other indicators would not lead to systematic profits on currency speculation.


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5. Describe three statistics you should obtain from a currency-forecasting service in order to judge the quality of its currency forecasts.

Answer: Three important statistics are the Root Mean Squared Error (RMSE) or Mean Absolute Deviation of its forecasting record, which would provide information on accuracy; the percentage of times they were on the correct side of the forward rate, which would provide useful information on the profitability, and a risk–return statistic (such as the Sharpe ratio), which would provide a characterization of the profitability of using their forecasts in a real time trading strategy.

6. Does a large increase in the domestic money supply always lead to a depreciation of the currency?

Answer: Most theories of the determination of exchange rates would predict that a large increase in the money supply would imply a depreciation of the currency, definitely in the long run, and especially as economists say when “everything else is equal.” However, it is possible that the change in the money supply is accompanied by an increase in real income that increases the demand for money and thus offsets the money supply’s effect on the exchange rate.

7. Is a current account deficit always associated with a strong real exchange rate (that is, one that is overvalued compared to the PPP prediction)?

Answer: Not necessarily. It is best to view the current account and the real exchange rate as being determined in an equilibrium that depends on many forces, such as movements in net foreign assets, government spending, productivity growth, and the expectations and risk tolerances of domestic and foreign investors.

8. Describe how three macroeconomic fundamentals affect exchange rates.

Answer: According to the monetary exchange rate model, the domestic currency weakens (strengthens) if the domestic (foreign) money supply increases today or if news arrives that leads people to believe that the future domestic (foreign) money supply will increase. The domestic currency also weakens if domestic real income falls, if foreign real income rises, or if news arrives that causes people to expect lower domestic real growth or faster foreign real growth. Finally, according to the equilibrium theory regarding the real exchange rate and the current account, an increase in government spending or a decrease in taxes that causes a budget deficit should increase the real exchange rate (and hence likely also the nominal exchange rate). This is because an increase in government spending increases aggregate demand in the economy, which causes the real interest rate to rise. The rise in the interest rate reduces investment and encourages private saving.


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9. Which simple statistical model yields some of the best exchange rate predictions available? What does this imply for the value of models of exchange rate determination to multinational businesses?

Answer: It is surprisingly difficult to beat the forecasts of the random walk model. This model uses the current exchange rate as the predictor of the future exchange rate. If this model provided the best forecast, the unbiasedness hypothesis (which says the forward rate is the best predictor) would be violated. If there were a forward premium on the foreign currency, the forward rate would be above the expected future spot rate, and you would want to sell the foreign currency in the forward market.

10. What is chartism?

Answer: Chartists graphically record the actual trading history of an exchange rate and then try to infer possible future trends based on that information alone.

11. What is an x% filter rule?

Answer: An x% rule states that you should go long in the foreign currency (buy) after the foreign currency has appreciated relative to the domestic currency by x% above its most recent trough (or support level) and that you should go short in the foreign currency (sell) whenever the currency falls x% below its most recent peak (or resistance level). Common x% filter rules are 1% or 2%.

12. What is a moving-average crossover rule?

Answer: Moving-average crossover rules use moving averages of the exchange rate to indicate trade directions. An n-day moving average is just the sample average of the last n trading days, including the current rate. A (y, z) moving-average crossover rule uses averages over a short period (y days) and over a long period (z days). The strategy states that you should go long (short) in the foreign currency when the short-term moving average crosses the long-term moving average from below (above). Common rules use 1 and 5 days (1, 5), 1 and 20 days (1, 20), and 5 and 20 days (5, 20).

13. Have currency traders been successful in exploiting their exchange rate forecasts?

Answer: While there exists scant empirical evidence on the forecasting ability of exchange rate forecasting services, the number of active currency traders, mostly organized as hedge funds, has grown considerably over the past decade. Because many of these currency traders report returns to various indices, we can analyze their performance. If such funds fail to forecast exchange rates, they should


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not consistently produce high returns! Pojarliev and Levich (2008) conducted a study on the returns earned by currency managers reporting to the Barclay Currency Traders Index (BCTI) between January 1990 and December 2006. All of these returns are reported net of fees. Hedge funds typically charge a fixed fee of 2% and a variable fee of 20% on the performance over a benchmark (which can be zero or the Treasury bill return). The study first tries to establish what techniques the currency managers use: Do they use the carry strategy, do they follow trends, or do they trade based on fundamentals? To do so, the investigators use historical data to create returns to carry-trade, trend-following, and fundamental strategies for the major currencies, and they use regression analysis to investigate whether the returns of the various managers correlate with these benchmark returns. The majority of the funds (and the average index) appear to follow trend-following strategies; many also show positive carry exposure, but there is not much of a link with the return on fundamental strategies. Recent academic research has shown that the returns to simplistic trend following strategies are no longer statistically significant, but currency traders may follow more sophisticated strategies. The average excess return earned over 34 different managers with relatively long track records between 2001 and 2006 is 5.45%, and the average (annual) Sharpe ratio is 0.47, which is higher than the Sharpe ratio generated by the equity market. Pojarliev and Levich also check whether the managers outperform the benchmark returns. Deutsche Bank, among others, has introduced easily tradable funds that mimic the simple strategies represented by the benchmarks. For an investor, it would make little sense to pay the heavy fees hedge funds charge for exposure to an index that can be bought for a small fixed fee. Pojarliev and Levich find that only eight of the 34 managers significantly outperform a combination of benchmark indices that best describes their investment style.

14. Are devaluations of pegged exchange rates totally unexpected?

Answer: While there is a debate about their predictability, some theories suggest that devaluations may be partially predictable. These models argue that growing budget deficits, fast money growth, and rising wages and prices usually precede devaluations. Increases in nominal interest rates typically reflect a combination of the probability and magnitude of a possible devaluation.

15. Construct a list of a country’s economic statistics you would assemble to help determine the probability of a devaluation of its currency within the coming year.

Answer: Based on theoretical and empirical work, the following economic variables should prove useful predictors: PPP-based measures of currency overvaluation, current account


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balances and monetary growth rates. In addition, if liquid financial markets exist, information about forward rates or interest rates, currency option prices, and so on may prove useful in terms of forecasting devaluations.

PROBLEMS

1. Suppose the 1-year nominal interest rate in Zooropa is 9%, and Zooropa’s expected inflation rate is 4%. What is the real interest rate in Zooropa?

Answer: The expected real interest rate is approximately 9% - 4% = 5%. The correct computation is: (1 + 0.09) / (1 + 0.04) – 1 = 0.0481 or 4.81%.

2. You were recently hired by the Doolittle Corporation corporate treasury to help oversee its expansion into Europe. Blake Francis, the CFO, wants to hire a foreign exchange forecasting company. Blake has asked you to evaluate three different companies, and he has obtained information on their past performances. Out of a total of 50 forecasts for the $/€ rate, the companies reported the number of times they correctly forecast appreciations and depreciations:

Correct Down Forecasts

Correct Up Forecasts

Morrissey Forex Advisors

20 5

Pixie Exchange Land 20 4FOREX Cures 12 12

There are a total of 35 dollar appreciations (down periods) and 15 dollar depreciations (up periods) in the sample. Blake wants to know two things:

a. Can anything be said about the companies’ forecasting ability with the available data?

Answer: Yes, one can compute the number of correct “directional” forecasts. Morrissey has the highest correct proportion with 25 out of 50 correct, whereas the other firms have less than 50% correct. However, note that the dollar over this period was relatively strong and appreciations (down forecasts for the $/€ rate) dominate. Hence, forecasts in the down period may be more useful (see footnote 3 in the chapter). If we look at correct conditional forecasts, we see that Morrissey is correct 20/35 or 57.14% of the time when the dollar appreciates, but only 5/15 or 33.33% of the time when the dollar depreciates. According to the Henriksson–Merton test, the sum of these two proportions should be over 1 for a firm to have market timing ability. However, the sum in this case is only 90.47%. While Morrissey obviously dominates Pixie Land Exchange, it is not clear that it is better than FOREX Cures. The proportions of correct conditional forecasts of FOREX Cures are 12/35 (34.29%) and


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12/15 (80%) for a sum of 114.29%. Consequently, only FOREX Cures shows directional forecasting ability.

b. What additional information should Blake try to obtain in order to form a better judgment?

Answer: Directional forecasting ability in the foreign exchange market is not particularly useful if the forecasts are to be used in speculative strategies. To this end, it would have been more useful to know whether the forecasting firms were on the correct side of the forward rate. Ideally, a full record of forecasts would be obtained. Then, accuracy statistics (like the RMSE) and profitability statistics (like the Sharpe ratio) could be computed.

3. Mini-Case: Currency Turmoil in ZooropaFad Gadget has never worked so hard in his entire life. It is near midnight, and he is still poring over statistics and tables. Fad recently joined Smashing Pumpkins, a relatively young but fast-growing British firm. Smashing Pumpkins produces and distributes an intricate device that turns fresh pumpkins into pumpkin pie in about 30 minutes. Recently, the firm has started exporting to Zooropa. Some of the largest and tastiest pumpkins are grown in Zooropa, and Zooropa’s population boasts the highest per capita pumpkin consumption in the world. A recent analysis of the pumpkin market in Zooropa has left the company’s senior managers very impressed with the profit potential.

Although Zooropa consists of 10 politically independent countries, their currencies are linked through a system called the Currency Rate Linkage System (CRLS) that works exactly like the former Exchange Rate Mechanism (ERM) of the EMS worked before the currency turmoil started in September 1992. The anchor currency is the banshee of Enigma, the leading country in Zooropa.

Initial contacts with importers in Zooropean countries indicated that they typically insist on payment in their own local currency. About a week ago, Cab Voltaire, the CEO of Smashing Pumpkins, expressed concerns about this development and asked Fad to lead a research team to further examine the present state of the currency system of Zooropa. Cab viewed the outlook for the banshee relative to the pound quite favorably and did not predict any substantial depreciation of the banshee against any other major currency. However, the precarious economic situation of some of the countries in Zooropa and the growing importance of speculative pressures in Zooropa’s currency markets last week suddenly made him suspicious about the possibility of realignments within the system. He even doubted the long-term viability of the system. Cab instructed Fad to examine the following issues:

Which currencies in the system exhibit the highest realignment risk? If a currency realigns and gets devalued, what are the effects on our sales

and profit margins in this particular country? Can we take the realignment possibility into account in our pricing?


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Suppose a currency is forced to leave the CRLS. What are the effects on exchange rates, interest rates, and the outlook for sales in that country? What is the likelihood of this occurring for the different countries?

Fad Gadget felt nervous. A meeting was scheduled with Cab the day after tomorrow. He wanted to write a thorough and insightful report. At the last management meeting, he had the uneasy feeling that some senior managers doubted his abilities. Some managers were naturally suspicious of a young Australian newcomer with his MBA. His earring and punk hairdo did not exactly help either. His team of analysts had already assembled a table with relevant macroeconomic and financial data (see Exhibit 10.11). “If only I could use this to rank the different countries according to realignment risk,” he thought.

a) Realignment rankings

The data provided are a scrambled version of an Exhibit that appeared in the Economist of September 19, 1992, when a currency crisis in Europe had just erupted. The Exhibit presented macro-economic statistics for all the countries participating in the European system. To prevent students guessing where the data are from, we scrambled the country names two ways. First, we gave each European country another name that did provide a vague hint on the actual European country of origin. However, we then randomly assigned the actual data to the fictitious countries. Here is the “key”:

Zooropa Country Reference to European Country

Data from European country

Sinead Ireland (Irish singer) Ireland Carmen Carmen (Spanish opera) France Marquee UK (club in London) Spain Fries Belgium (French fries are Belgian!) Portugal Ney Denmark (No in Danish) Denmark HelpIsink the Netherlands (below sea level) Belgium Benfica Portugal (soccer team) the NetherlandsChe Ora Italy (only Italian Geert knows) UK Vachement France (French stop word) Italy Enigma Germany (pop band) Germany

We now reproduce the original Economist table from the article “A Ghastly Game of Dominoes.”

Who’s Next?Legend for Chart:

A - Currency's ERM position Sept 15th B - Currency's over/under valuation, % C - Reserves, import coverD - Budget deficit as % of GDP, 1992


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E - Inflation rate %, latestF - GDP growth, %, 1992G - Devaluation risk

A B C D E F GItaly 27 2 0.5 -11.3 5.2 1.3 1Britain -90 3 2.6 -4.6 3.6 -0.8 2Spain 16 11 8.2 -4.9 5.7 2.0 3Portugal -3 11 11.7 -5.4 9.5 2.8 4Denmark -22 -2 2.5 -2.1 2.2 2.1 5=Belgium 31 -18 1.3 -5.5 2.1 1.6 5=Holland 30 -16 1.5 -3.4 3.5 1.6 5=France -36 -12 3.1 -2.3 2.7 2.0 8Ireland -6 -10 2.9 -1.9 3.6 2.4 9Germany 36 -- 1.7 -3.4 3.5 1.3 --

Sources: OECD; IMF; government statistics; NatWest; The Economist poll of forecasters. A indicates the currency value as a % of permitted divergence from the central rate, B indicates the central rate against the DM relative to PPP, C indicates foreign-exchange reserves (mid September estimates) in number of months' imports, D, E, and F are forecasts, G indicates devaluation risk with 1=greatest risk, 9=least risk.

Based on this article, we can actually use the data given to come up with a realignment ranking. For example, the position in the CRLS system (the divergence indicator in the EMS, a summary measure of the currency’s position in its bands relative to all other currencies), and the reserves import cover are direct indicators of devaluation pressure. An overvalued currency, a large budget deficit, high inflation, and low GDP growth are “bad” economic fundamentals that may contribute to speculative pressure on the currency. The Economist did a very simple exercise. It ranked all the countries on these criteria from “worst” (most speculative pressure) to “best” (least speculative pressure). It then added up the ranks and came up with an overall devaluation risk ranking. Using the information provided on fundamentals leads to a surprisingly accurate realignment risk ranking. These ranks are reproduced in the last column of the Economist table. Italy and Britain were actually forced out of the EMS during the September currency crisis. Spain was forced to devalue and Portugal later followed suit. The other countries with better fundamentals duly survived.

Whether the currency crisis in 1992 was actually predictable is still a topic of academic debate. Some important scholars in the area have argued that the crisis was almost completely unpredictable. Our case seems to indicate otherwise, although more formal analysis is necessary (and is still being conducted by many scholars). Finally, while some countries, such as France, still looked relatively “safe,” another currency crisis erupted in July August 1993, which led to rather drastic changes in the operation of the EMS, including a widening of the bands to 15%.

b) Effects of Realignments/Exits for the Firm


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Since the British firm agrees to local currency pricing, the risk is that the Zooropa currencies get devalued. Two cases must be considered:

(1) The price remains fixed. In this case, the revenue per unit sold in pounds decreases and the profit margin is squeezed because the firm’s costs are local (in pounds). Except for “dynamic effects” (see below), there need not be any effect on the number of units sold. Sales may remain unchanged in local currency, but sales go down in pounds.

(2) The firm tries to “pass through” the exchange rate change and raises the price of the pumpkin device as in Chapter 9. The optimal response will be to raise the domestic price because the firm does not want to sell as much quantity in that market. The amount of the price increase depends on the elasticity of the demand curve. The price will rise less, the more elastic is the demand – that is, the larger the percentage change in quantity with a given percentage change in price.

These are the immediate effects. The realignment restores the general competitiveness of the Zooropean country. If the devaluation is successful, it accomplishes a decrease in real wages locally and shifts resources to the export sector. It should also make potential local competitors to Smashing Pumpkins more competitive. However, the case seems to indicate that these are non-existent. Initially, this may lower the demand for all imports (the whole idea of the devaluation in the first place). If the economy was not producing at full capacity, the increased competitiveness may spur considerable additional economic growth. This, in fact, happened in Britain and Sweden after the 1992 devaluations. Higher growth may then lead to higher imports and increase the demand for the pumpkin device. These are potential dynamic effects. Eventually, this may cause inflationary pressures to creep back into the economy. Unsuccessful devaluations will let higher import prices (if there is some pass through or most import products are priced in foreign currency) affect wages and the general price level. In this case, there may be only small effects for the British firm. Hence, the dynamic effects depend on the success of the devaluation.

All of this analysis goes through for exits from the target zone. In fact, the effects for realignments are probably considerably smaller, since an exit may lead to much lower exchange rates and in some cases to lower interest rates, which further help the Zooropa economy become more competitive.

It has to be said that these are all “elaborate guesses,” since in reality new shocks to the economy may cause completely different outcomes.

c) Incorporating Realignment Risk into Pricing/Hedging

The market will anticipate the realignment. In fact, if UIRP holds, the interest differential with Britain and the forward rate relative to the pound will reflect the expected currency depreciation (the probability of a devaluation multiplied by the magnitude of the devaluation). Hence, hedging the risk will automatically lead to lower pound revenue in the future. Ideally, one establishes a pricing scheme that takes potential realignments into account, for example using forward rates. Your personal view on realignment risk may differ from the forward rates though.


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Alternatively, a dynamic real exchange rate risk sharing formula as in the SAFE AIR case could be proposed.

d) Effects of devaluation/exits on exchange and interest rates

Exchange rates fall, by definition. The effect on the interest rate however may be different in both cases. With devaluation it is very likely that the interest rate will drop. That is because the interest rate was most probably very high during the speculative attack preceding the realignment and it now drops back to normal levels, which are still likely to be above the interest rate of the anchor currency. With an exit, the pressure of a speculative attack gets relieved as well, and now the interest rate need not exceed the rate on the anchor currency. However, the exiting currency loses its “inflation credibility mechanism” by leaving the target zone, and hence, interest rates may go up reflecting higher expected inflation in the future. When Britain exited the ERM, its interest rates dropped substantially at the short end, but they remained quite high at the long end. In Mexico, after the December 1994 crisis, peso interest rates rose reflecting fears of future depreciation and inflation. Both market responses seem justified both by the data at the time of the event and the subsequent experiences of the economies.

4. Web Problem: Go to www.oanda.com/currency/big-mac-index. Oanda reports the last available Big Mac index but then updates the exchange rates on a regular basis to compare them with the PPP-based exchange rates. What are currently the most under-valued and over-valued exchange rates? How would you use this information in forecasting exchange rates?

On June 6, 2011, the most overvalued currency versus the dollar was the Norwegian kroner (NOK). The actual exchange rate was NOK5.3407/USD and the implied PPP rate was 12.1. The dollar would have to strengthen by 126.56% if the current exchange rate were to go to the implied PPP rate. The most undervalued currency versus the dollar was the Ukrainian hryvnia (UAH). The actual exchange rate was UAH8.0544/USD and the implied PPP rate was 3.88. The dollar would have to weaken by 51.83% if the current exchange rate were to go to the implied PPP rate. If there is a tendency for large PPP deviations to correct themselves, one would forecast that the NOK was going to weaken versus the dollar and the UAH was going to strengthen versus the dollar. One might even want to speculate that the NOK would weaken relative to the UAH. You could borrow NOK, convert to dollars, convert to UAH, and invest the UAH money market.


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bekaert_2e_sm_ch10

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parity conditions hold

exchange rate determination

actual exchange rate

average crossover rule

real exchange rate

current exchange rate

implied ppp rate