Bhundia and Ricci (2005) note that between end-April and end-August in 1998, the rand depreciated by 28% in nominal terms against the U.S. dollar. This was accompanied by increases of around 700 basis points in short-term interest rates and long-term bond yields, while sovereign U.S. dollar-denominated bond spreads increased by about 400 basis points. At the same time share prices fell by 40% and output contracted during the third quarter of 1998 (quarter-on-quarter). Once again, in 2001, the rand depreciated by 26% in nominal terms against the U.S. dollar between end-September and end-December, but short-term interest rates remained stable, long-term bond yields increased by less than 100 basis points and sovereign U.S. dollar-denominated bond spreads narrowed by about 40 basis points. Share prices rose by 28%, and real GDP increased.

What drives such extraordinary changes in relative currency valuations, and can we predict their direction and magnitude? On the one hand, the answer must be yes, since financial institutions devote substantial resources to producing forecasts for their clients, and forecasting firms successfully market currency forecasts. However, the answer may be no, since economic models often fail to explain exchange rate movements after the fact.

Corporations use currency forecasts in a variety of contexts: quantifying foreign exchange risk, setting prices for their products in foreign markets, valuing foreign projects, developing international operational strategies, and managing working capital. International portfolio managers use exchange rate forecasts to evaluate the desirability of investing in particular foreign equity and bond markets and whether to hedge the associated currency risks.

Should managers purchase currency forecasts? If markets are relatively efficient, it should be difficult to produce better short-term forecasts than forward exchange rates suggest or better long-term forecasts than uncovered interest rate parity predicts. Yet, we have seen evidence that would suggest that these parity conditions do not always hold, especially in the short run. Therefore, currency forecasts are potentially valuable. This motivates our discussion of the two essential techniques that are used to forecast exchange rates: fundamental analysis and technical analysis.

The covered interest rate parity (CIRP) relationship, links forward rates, spot rates, and interest rate differentials. Uncovered interest rate parity (UIRP), which is sometimes referred to as the international Fisher relationship (named for the eminent economist Irving Fisher), links expected exchange rate changes and interest rate differentials, whereas the unbiasedness hypothesis links forward rates and expected future exchange rates. Purchasing power parity (PPP), provides a link between inflation rates and rates of change of exchange rates. To close the loop between expected future exchange rate changes, forward rates, interest rates, and rates of inflation, we need another well-known relationship: the *Fisher hypothesis*. After discussing the Fisher hypothesis, we demonstrate how all the parity conditions together lead to a world in which currency forecasting is not necessary. This hypothetical world constitutes an interesting benchmark for judging the potential value of currency forecasts.

The interest rates we have discussed thus far are nominal interest rates. That is, they promise a nominal or money rate of return. For example, if the 1-year rand interest rate is 3%, you receive R1.03 in 1 year for every rand you deposit today. Fisher (1930) noted that nominal interest rates should reflect expectations of the rate of inflation. This is easy to understand.

Your happiness with the 3% return will depend on how prices evolve over the year. If prices increase by less than 3%, the purchasing power of your R1.03 is greater than the purchasing power of your R1.00 today. You experience a positive real return. Conversely, if prices increase by more than 3%, your purchasing power is lower. You realize a negative real return. Thus, if you expect prices to increase by more than 3% over the course of the year, you are reluctant to accept a 3% deposit rate since the 3% return is insufficient to maintain the purchasing power of the money you are lending.

Recall from our discussion on purchasing power parity that if \(P_t\) denotes the South African price level at time \(t\), \(\frac{\mathsf{R}1}{P_t}\) is the purchasing power of 1 rand. Inflation, the rate of increase of the price level, drives down the purchasing power of the money. Lending money to receive future nominal interest exposes the lender to the risk of loss of purchasing power during the time of the loan because of 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 R1, you sacrifice \(\frac{\mathsf{R}1}{P_t}\) real goods now. But in 1 year, you get back \(\frac{1+i}{P_{t+1}}\) in real goods, where \(i\) is the nominal rate of interest. We calculate the *ex post* real return, denoted by \(r^{ep}\), by dividing the real amount you get back by the real amount that you invest:

where \(P_{t+1}/P_t\) is 1 plus the rate of inflation between time \(t\) and \(t+1, \pi_{t+1}\). If we subtract 1 from each side of Equation (1.1), we have

\[\begin{eqnarray*} r^{ep}=\frac{(1+i)}{(1+\pi)}-\frac{(1+\pi)}{(1+\pi)}=\frac{i-\pi}{1+\pi} \end{eqnarray*}\]which is often approximated as

\[\begin{eqnarray} r^{ep} \approx i-{\pi} \tag{1.2} \end{eqnarray}\]Equation (1.2) states that the *ex post* real interest rate equals the nominal interest rate minus the actual rate of inflation.^{1} Hence, if the nominal interest rate is 3% and the actual rate of inflation is 2%, the *ex post* real interest rate is 1%.

As the inflation rate is uncertain at the time an investment is made, the real rate of return on a loan is uncertain. By taking the expected value of both sides of Equation (1.2), 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 \(r^{e}\):

If we rearrange the terms in Equation (1.3), we have

\[\begin{eqnarray} i_t=r^{e}+\mathbb{E}_{t}[\pi_{t+1}]=r^{e}+{\pi}^{e} \tag{1.4} \end{eqnarray}\]where we define \({\pi}^{e}\) as expected inflation, \(\mathbb{E}_{t}[\pi_{t+1}]\)

Equation (1.4) states that the nominal interest rate is the sum of the expected real interest rate and the expected rate of inflation. This decomposition of the nominal interest rate is often referred to as the Fisher hypothesis, or the *Fisher equation*.

If expected real interest rates are similar across countries, countries with high expected inflation rates will have high nominal interest rates, and countries with low expected inflation rates will have low nominal interest rates. The real interest rate is important, since it influences investment decisions. Firms borrow money and invest in projects only if the expected real rate of return on the investment is greater than the real interest rate.

The Fisher hypothesis is a reasonable approximation for thinking about a long-run link between inflation and interest rates. Figure 1 graphs average long-term government bond yields on the vertical axis versus average inflation rates on the horizontal axis for 16 countries between 1990 and 2010. As the Fisher hypothesis suggests, the relationship is clearly positive, and the slope of the regression line is insignificantly different from 1. That is, for each additional 1% of inflation, the nominal government bond yield is about 1% higher. Hence, for long-term averages, real interest rates appear to be equal across countries. The intercept on the vertical axis of 2.40% is also a reasonable estimate of the real interest rate. We discuss this graph in more detail later.^{2}

The covered interest rate parity (CIRP), uncovered interest rate parity (UIRP), and purchasing power parity (PPP) relationships, together with the Fisher hypothesis, are sometimes referred to as the international parity conditions. To review these conditions, consider the numeric example in Figure 2, which examines exchange rates, interest rates, and expected inflation rates for the United Kingdom and Switzerland. Exchange rates are measured as Swiss francs per British pound, CHF/GBP, and the horizon is 1 year.

At the bottom of Figure 2, the nominal interest differential is 2%. From the covered interest parity, we can relate the interest differential to the forward premium:

\[\begin{eqnarray*} \mathsf{Forward} \; \mathsf{premium} = \frac{\mathsf{Forward} \; \mathsf{rate} - \mathsf{Spot} \; \mathsf{rate}}{\mathsf{Spot} \; \mathsf{rate}} \end{eqnarray*}\]The 1-year forward premium is -1.90%. Since the U.K. interest rate is higher, its currency is at a discount in the forward market to prevent arbitrage.^{3}

If the forward rate is an unbiased predictor of the future spot rate, the forward discount on the pound means that the market expects the pound to depreciate by the amount of the forward discount, which brings us to the top of the diagram. We could have also moved to the top directly by observing that the higher pound interest rate means British investors in Swiss francs must expect a capital gain on holding Swiss francs to increase their expected return up to the higher pound return.

Relative PPP requires that the expected change in the exchange rate reflects the differential in inflation rates, so if the British pound is expected to weaken versus the Swiss franc, British inflation is expected to be higher than Swiss inflation by about 2%. This brings us to the right-hand side of Figure 2, where the inflation differential is 1.96% (also about 2%). (The small difference in percentage calculations arises because we are using inflation rates calculated in simple percentage terms. The percentage changes are identical if the computations use continuously compounded rates.)

To see this, remember that relative PPP predicts

\[\begin{eqnarray*} \frac{S_{t+1}}{S_{t}}-1=\frac{1+\pi_{\text{SW}}}{1+\pi_{\text{UK}}}-1=\frac{\pi_{\text{SW}}-\pi_{\text{SW}}}{1+\pi_{\text{SW}}} \end{eqnarray*}\]Since of the presence of U.K. inflation in the denominator, the inflation differential is slightly larger than the percentage rate of change of the exchange rate. Now we know that inflation is the fundamental reason for the higher British nominal interest rates observed in the first place. U.K. expected inflation is higher than Swiss expected inflation, which brings us back to the bottom of the exhibit if expected real interest rates are equal through the Fisher relationship.

What are the real interest rates in the United Kingdom and Switzerland? According to Equation (1.3), the real interest rate is

\[\begin{eqnarray*} r^{e}=i-{\pi}^{e} \end{eqnarray*}\]Plugging in the numbers for both the United Kingdom and Switzerland gives real interest rates of about 2% in both cases.^{4} This is no coincidence. If the parity conditions all hold simultaneously, real interest rates are equal across countries. If uncovered interest rate parity and PPP hold, the nominal interest rate differential between the United Kingdom and Switzerland reflects only an expected inflation differential. Then, by rearranging terms, we find that the real return is the same in each country.

In a world where all the parity conditions hold, multinational business would be rather simple. International pricing would be easy, since prices in foreign countries would move in line with domestic prices after converting currencies. The expected real cost of borrowing would be the same everywhere in the world. Finally, if a company wanted to know what the future exchange rate was likely to be - for example, to help quantify its transaction exposure - the best predictor for the future exchange would be the forward rate, since the unbiasedness hypothesis holds. International investors would not need to worry about predicting currency values either. A higher nominal interest rate in one country would simply reflect the fact that the country’s currency was expected to depreciate.

Unfortunately, the world is not as simple as just described. From the empirical evidence discussed previously, we know that the international parity conditions, except CIRP, are best viewed as long-run relationships. In the short run, there are significant deviations from these conditions. Since PPP deviations are sizeable and prolonged, identical nominal returns represent very different real returns for investors in different countries. Our previous discussion of the forward bias implies that returns in different currencies can have different currency risk premiums. In the long-run, we know that PPP holds better and that high interest rate currencies depreciate relative to low interest rate currencies. Hence, it would seem more likely that real interest rate parity holds in the long run. Real returns across countries can also differ because of political risks or the threat of capital controls, which prevent investors from taking advantage of higher returns in other countries. This is particularly true in developing countries.

Studies have found that real interest rate parity holds neither in the short nor the long run. Consider Figure 1, which at first seems largely consistent with real interest rate parity. The world interest rate is 2.40%, and if the slope of the regression line is actually 1, each percent of additional expected inflation implies an extra percent of nominal bond yield, keeping real interest rates the same across countries. However, the estimated slope coefficient is 1.45 instead of 1.00. This suggests that higher inflation countries have higher real interest rates. For example, if a country has an expected inflation rate of 3%, the regression line predicts a nominal bond yield of 2.40% + 1.45 \(\times\) 3% = 6.75%, and a real rate of 6.75% - 3% = 3.75%. Now, consider a country with an expected inflation rate of 5%. Following the same computations, we find that the country’s real rate is 4.65%, almost 1% higher than the real rate of the low-inflation country.

Of course, real interest rate differentials between countries reflect differential risks, but they also offer multinational businesses opportunities - for example, opportunities to reduce costs of funds or to invest excess cash more profitably. Knowing the source of an observed real interest rate differential is important to making the right decisions. When the parity conditions break down, forecasting becomes important. The next section reviews the types of forecasting techniques that are used in practice.

While there may be as many exchange rate forecasting techniques as there are exchange rate forecasters, Figure 3 organizes them into meaningful categories. The parity conditions suggest the forward rate as a predictor. If no forward market exists for a particular currency, nominal interest rates and UIRP can be used to extract a market-based forecast. Other forecasting techniques do not rely directly on the predictions embodied in forward rates and interest rates and can be split into two main categories: *fundamental analysis* and *technical analysis*. We briefly describe these in turn and end this section with a discussion of how to evaluate the quality of a forecast.

Some forecasters predict exchange rates using fundamental analysis typically based on formal economic models of exchange rate determination, which link exchange rates to macroeconomic fundamentals such as money supply, inflation rates, productivity growth rates, and the current account balance. The models involve parameters that govern the relationship between the exchange rate and the fundamentals. For example, if the current account deficit as a percentage of gross domestic product (GDP) increases by \(x\)%, the model predicts that the domestic currency will depreciate relative to the foreign currency by \(\phi\) multiplied by \(x\)%. The parameter \(\phi\) has to be determined, and this is typically accomplished by estimating the relationship from the data using econometric techniques such as regression analysis. Alternatively, some forecasters simply examine economic information and use educated analysis to derive an exchange rate forecast based on their judgement of future macroeconomic relationships. Fundamental analysis is typically concerned with multi-year forecasts, since the fundamental economic forces operate at longer horizons.

Technical analysis is usually used for short-term forecasts. Technical analysts usually rely on past exchange rate data, although other financial data, such as the volume of currency trade, may be incorporated to predict future exchange rates. Consequently, all the information about the future exchange rate is assumed to be present in past trading behaviour and past exchange rate trends. The original technical analysts were called *chartists*, since they studied graphs of past exchange rates. Now, technical analysis refers to the use of any type of financial data to predict future exchange rates outside the confines of a fundamental model. Some technical analysts employ sophisticated econometric techniques to discover what they hope are predictable patterns in exchange rates. Therefore, we distinguish between chartists and *statistical technical analysts*.

Technical analysis is often derided in academic circles, since it is not based on any economic theory and is thought to be inconsistent with efficient markets. Nevertheless, it is important to discuss technical analysis for four reasons.

First, forex dealers and currency fund managers make extensive use of technical analysis (see, for example, Gehrig and Menkhoff (2006)). Second, fundamental analysis has some inherent problems. Fundamental forecasters must pick the right exchange rate model. Then, the model’s fundamental variables must be forecast. Moreover, the macroeconomic inputs to fundamental analysis are not all available at frequent intervals. Some variables are measured weekly, some monthly, and some only quarterly or even annually, and the measurements are often poor and are frequently subject to revision. The data used by technical analysts are of much higher quality and are available much more frequently, often on a daily or even intra-daily basis.

The third reason technical analysis may have forecasting ability is that the forward rate may not be an unbiased predictor of the future spot rate, even in an efficient market. Previously we suggested that rational risk premiums can separate forward rates from expected future spot rates. Moreover, we see differences of opinion on the future direction of exchange rates, even among relatively specialized foreign exchange experts. Consequently, it is conceivable that technical analysis might uncover a predictable component in exchange rate changes not present in forward rates.

A fourth reason technical analysis may have value is that if a sufficiently large segment of the trading world is using technical analysis, demands and supplies to trade currencies will be influenced by these traders even if they are irrational. A truly rational trader would therefore need to know technical analysis to understand why irrational traders are doing what they are doing.

What constitutes a good forecast? In general, it depends on how the forecast will be used. Ultimately, exchange rate forecasts are “*good*” when they lead to “*good*” decisions. Next, we distinguish three dimensions of the forecast quality.

One dimension is the accuracy of the forecast. Suppose that today is time \(t\), and we are forecasting over a \(h\)-period horizon (say \(h\) months). Let \(S_{t+h}\) be the actual exchange rate at time \(t+h\), and let \(\hat{S}_{t+h}\) be the forecast at time \(t\). The closer \(\hat{S}_{t+h}\) is to \(S_{t+h}\), the more accurate the forecast, and the smaller the forecast error:

\[\begin{eqnarray*} e_{t+h}=S_{t+h}-\hat{S}_{t+h} \end{eqnarray*}\]Of course, we cannot judge a forecaster by just one forecast, since he or she may have just been lucky. Instead, we need a substantial record of forecasts and realizations to allow for an informed statistical analysis. This would usually involve an extensive out-of-sample exercise, where we would generate successive forecasts over a period of time before evaluating all the forecasting errors.

In addition, we also cannot judge the accuracy of the forecasting record by simply taking the average forecast error because large errors with opposite signs would sum to a negligable amount and would provide a small average error. The two summary measures most frequently used to judge accuracy of forecasts are the mean absolute error (MAE) and the root mean squared error (RMSE):

\[\begin{eqnarray*} MAE &=& \frac{1}{T}\sum_{r=1}^{T}\Big|e_{t+h} \Big|\\ RMSE &=&\sqrt{\frac{1}{T}\sum_{r=1}^{T} e_{t+h}^{2}} \end{eqnarray*}\]where \(T\) is the total number of available observations. The MAE is the average of the absolute values of the forecast errors. The RMSE is the square root of the average squared forecast errors. It has the same units as the standard deviation of exchange rate changes and may be used for comparative purposes.

When comparing forecasts, a number of obvious benchmarks come to mind. For example, we could simply replace the forecast with the current exchange rate or with the current forward rate for maturity \(h\). We hope that a forecaster’s MAE or RMSE is smaller than such simple forecasts. If it weren’t, why would we need to pay money for it?

Forecast accuracy is economically meaningful in a number of settings. For example, suppose we need to evaluate a foreign investment project that will generate foreign currency profits. This would require a forecast for the future rand values of the cash flows generated by the project (by converting future foreign currency profits into future rand values) that would then be discounted at an appropriate discount rate to determine whether the investment project will be profitable. If these calculations lead to the acceptance of the project and a currency crisis erupts in the country in which we invested (resulting in a significant currency depreciation), then the currency crisis will depress the company’s rand earnings, if local competition prevents us from passing through the currency loss in the form of higher local prices. In this case accuracy matters, as the investment decision would have been a disaster. A more accurate assessment of the future would have led us to forgo the investment.

Even if the foreign currency appreciates after the investment is made and the investment decision looks good, forecasting accuracy still matters. A better exchange rate forecast might have caused the firm to invest more in the foreign country. Pricing decisions and long-term strategic planning are other examples in which the accuracy of exchange rate forecasts matters a great deal. Note that in many of these cases, firms may be more concerned with predicting the real exchange rate rather than the nominal exchange rate.

There are situations in which accuracy may not be the most relevant quality measure. Simply being on the right side of the forward rate is enough. If the forecast relative to the forward rate suggests a long position in the forward market, and the future exchange rate is indeed above the forward rate, the forecast was on the right side of the forward rate. Conversely, if the forecast relative to the forward rate suggests a short position in the forward market, and the future exchange rate is below the forward rate, the forecast was not on the right side of the forward rate. We illustrate this with an example.

**Currency forecasts of a South African mining company**

Consider the situation of a South African mining company, which owes an American investor $1,000,000 in 90 days. The current exchange rate is R15.00 / $, and the forward rate is R15.30 / $. To decide whether to hedge its currency exposure, suppose the mining compnay is considering using one of two forecasts that have been provided. The first predicts that the exchange rate will be R16.50 / $, whereas the second predicts that the exchange rate will be R15.10 / $. After 90 days, the exchange rate turns out to be R15.50 / $. Which forecast is more accurate? Which forecast is more economically useful to the mining company?

To find out, let’s examine how the forecasts are used in a hedging decision. Suppose the mining company hedges when the forecast of the future spot rate is above the forward rate, and it does not hedge when the forecast is less than the forward rate (because it thinks the rand cost of the dollars will be lower than if it uses the forward rate). The following table summarizes the situation:

Forecast One | Forecast Two | |
---|---|---|

Forecast | R16.50/$ | R15.10/$ |

Forecast Relative to Forward Rate | ||

(forward rate: R15.30 / $) | Higher | Lower |

Decision | Hedge | Do not hedge |

Forecast Error | R1.00 / $ | R0.40 / $ |

Ex Post Cost Relative to Forward Rate | Zero | Positive |

So, although the second forecast turns out to be more accurate, it leads to a decision not to hedge, because it predicts an exchange rate lower than the forward rate. Since the dollar actually appreciates to a level above the forward rate, not hedging proves costly. Not hedging would cost $1,000,000 \(\times\) (R15.50 - R15.30)/ $ = R200,000. The prediction of the first forecast, which is quite inaccurate, would lead the mining company to hedge, which *ex post* leads to a lower dollar cost than if the dollars had to be purchased at the future spot rate.

This example shows that it is often more important to be on the correct side of the forward rate than to be accurate. It is also important to realize that the relevant benchmark is the forward rate, not the current spot rate, Since the forward rate is the currently available rate for future transactions.

To evaluate a forecasting record, the percentage of times the forecaster was on the correct side of the forward rate seems to be a natural indicator. Since just flipping a coin could lead to a 50% correct record, this “percentage correct signals” statistic should be strictly larger than 50% for the forecaster’s services to add value to your decision-making process. We can view this as a test of market timing ability.^{5}

Technical analysts assert that the percentage-correct-signals metric does not accurately measure how well they perform. They claim that they can give valuable advice and should not be required to be right more than 50% of the time. This is true, since the overall size of the profits and losses a company earns as a result of the advice matters, too. A technical forecaster’s performance may be characterized by a relatively small number of successful forecasts in which large profits are made and a relatively large number of incorrect predictions in which small losses are incurred. As long as you do not lose too much money when you are wrong and you make a lot of money when you are right, you can be wrong more than 50% of the time and still be valuable.

To evaluate forecasters on this basis, we can simply compute the profits or losses made based on a forecaster’s advice and compare those returns to the returns on alternative investments that do not require forecasts. Again, it is important to determine that the profits are not simply due to chance.

This section examines forecasting techniques that rely on models of exchange rate determination and fundamental economic factors. From the parity conditions, we know that exchange rates are likely to be influenced by interest differentials, relative price levels, and inflation rates. Interest rates and the current account are the most talked-about fundamental factors, judging from countless articles in the financial press.

We first review the poor performance of fundamental models of exchange rates in predicting future exchange rates. This poor performance is not surprising from the perspective of two main approaches to exchange rate determination: the asset market approach and an equilibrium model linking current accounts, real exchange rates, and interest rates. We also discuss an increasingly popular method to forecast exchange rates over longer horizons, building on PPP.

In a famous article, Meese and Rogoff (1983) analyse the forecasting power of fundamental models of exchange rate determination. The models link the current spot rate to relative money supplies, interest differentials, relative industrial production, inflation differentials, and the difference in cumulated trade balances, which represents the level of net foreign assets. They estimate the parameters of these models and use them to predict future exchange rate values. Since the fundamental information is not known when the forecast is made, these predictions would normally necessitate forecasting the fundamentals first, so that the forecast is truly “out-of-sample”. However, Meese and Rogoff use actual values for the future fundamentals combined with the parameters to predict the exchange rate. This approach gives the fundamental models an advantage relative to the other models considered, which use only current information to predict future exchange rates. As benchmarks, they considered several alternative models, including the random walk \([\hat{S}_{t+h}=S_t]\), where, again, the caret symbol denotes a forecast today for horizon \(h\), the unbiasedness hypothesis \([\hat{S}_{t+h}=F_{t, h}]\) and several statistical models that link the current exchange rate to past exchange rates and past values of other variables.

Computing the root mean squared error (RMSE) for the predictions at various horizons, Meese and Rogoff found that the random walk model beat all the other models in the majority of the cases considered. Particularly surprising was that the fundamental models did not even perform better at longer horizons. This result has been confirmed by a large number of researchers over the years and continues to puzzle international economists (see Rogoff (2009)).

Recent research by Meese and Prins (2011) points to the importance of order flow in the short-run determination of exchange rates and market fundamentals in the longer run. They find that market fundamentals do a poor job of explaining the time series movements of exchange rates, especially at short horizons, whereas fundamentals perform better cross-sectionally and at longer horizons.

Given the poor performance of fundamental models in forecasting exchange rates, we provide only a cursory overview of the major models. However, fundamental models still provide useful insights, and, as we will see, it may not be so surprising that they are beaten by a random walk model in forecasting exchange rates.

Let’s revisit the theory of uncovered interest rate parity to see what it has to say about the *level* of the exchange rate:

where the exchange rate is expressed in domestic currency per foreign currency, \(i^{*}\) is the foreign interest rate, and \(i\) is the domestic interest rate. Everything else equal, an increase in the domestic (foreign) interest rate lowers (increases) \(S_t\); that is, the domestic currency appreciates (depreciates). However, “*everything else equal*” involves keeping expected values of the future exchange rate constant. Of course, changes in interest rates would also affect exchange rate expectations. More intuition can be gained rewriting Equation (3.1) as

where \(\log[S_t]\) is the natural logarithm of the level of the exchange rate. This equation uses the continuously compounded form of uncovered interest rate parity. Equation (3.2) suggests that not only current but also expected future values of the exchange rate (which in turn is influenced by future interest rates) may affect the current exchange rate.

Just as the equity value of a firm is the expected discounted value of all future cash flows accruing to the firm’s shareholders, the exchange rate is easily linked to current and future fundamentals. The asset market approach to exchange rate determination recognizes that the exchange rate is the relative price of two currencies, and it notes that currencies are assets, which makes the exchange rate an asset price. Hence, exchange rates should fluctuate quite randomly, and the value of an exchange rate of, say, dollars per euro should be determined by people’s willingness to hold the outstanding supplies of dollar-denominated and euro-denominated assets. These demands, in turn, depend on the expectations of the future values of these assets.

To capture this idea, we view the exchange rate as a weighted average of the current fundamental and its expected future value. The equity price of a stock can also be thought of as the value of the current cash flow (the dividend) and the discounted expected value of the future equity price, the price at which you can sell the stock in the future.

\[\begin{eqnarray} \log[S_t]=(1-\phi)\mathsf{fund}_t + \phi \mathbb{E}_{t}\Big[ \log[S_{t+1} ] \Big] \tag{3.3} \end{eqnarray}\]In Equation (3.3), \(\mathsf{fund}_t\) is the generic name we use to indicate the value of market fundamentals at time \(t\), and the coefficient \(\phi\) is a discount factor that is less than 1 but may be very near 1.

Equation (3.3) states that the exchange rate depends on current fundamentals and on what people think the exchange rate will be in the next period. If we iterate Equation (3.3) one step forward to solve for \(\log[S_{t+1}]\) and plug the result back into that equation, we obtain the following:

\[\begin{eqnarray} \log[S_t]=(1-\phi) \mathsf{fund}_t + \phi \mathbb{E}_{t}\Big[(1-\phi)\mathsf{fund}_{t+1} + \phi \mathbb{E}_{t+1}\big[\log[S_{t+2}] \big] \Big] \tag{3.4} \end{eqnarray}\]Since expectations at time \(t\) of expectations at some future time reduce to expectations at time \(t\), as in \(\mathbb{E}_{t}\Big[\mathbb{E}_{t+1}\big[\log[S_{t+2}]\big]\Big]=\mathbb{E}_{t}\big[\log[S_{t+2}]\big]\), iterating Equation (3.4) forward leads to:^{6}

Hence, the current exchange rate embeds all information about current and expected future fundamentals, and the exchange rate changes as the fundamentals change or as we get news about future fundamentals. Note that even a small change in current fundamentals may induce a large change in the exchange rate if it also changes the expected value of all future fundamentals. Thus the value of the exchange rate may move a lot in response to what seems to be a small piece of news.

While many exchange rate models fit this framework, the best-known asset market model is the monetary exchange rate model. In this model, the menu of assets is fairly simple. There are distinct demands for non-interest-bearing domestic and foreign currencies. The demand for nominal money arises from the demand for real money balances. That is, people are only concerned with the real value of the nominal money they are holding.

The fundamentals in this model are a simple function of relative money supplies and relative real income levels in the two countries. The model implies that the domestic currency weakens if the domestic money supply increases today or if news arrives that leads people to believe that the future domestic money supply will increase. In contrast, the domestic currency strengthens if the foreign money supply increases today or if news arrives that causes people to think that foreign money supplies will be higher in the future. These effects arise directly from the influence an increased supply of money has on prices with the demand for money held constant. Higher prices in turn weaken the currency, since PPP is assumed to hold. 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. Real income positively affects the demand for real money balances, since the higher the real income, the greater the number of monetary transactions required to support the real transactions of an economy. Hence, a decrease in real income lowers the demand for real balances and given a fixed money supply, causes an increase in prices to lower the *real* money supply. The increase in prices therefore weakens the currency through the PPP channel.

The predictions of the monetary model are quite reasonable at long horizons, but as a short-run theory, the monetary model’s reliance on PPP is questionable. An important extension of the monetary model relaxes the assumption of PPP, assuming that nominal prices of goods are “sticky” and do not adjust immediately to an increase in the money supply or to other shocks that hit the economy (see, Dornbusch (1976)). Models with sticky prices predict more volatility in nominal and real exchange rates than occurs in the monetary model because asset prices, including the exchange rate, do all of the immediate adjusting to the shocks that hit the economy, whereas nominal goods prices only adjust slowly over time.

Consider how the economy responds to a permanent increase in the money supply in such a model. According to the monetary model, in the long run, an increase in the money supply causes a depreciation of the domestic currency by the same percentage that the money supply increases. What happens in the short run? Since asset prices are flexible, the asset markets will remain in equilibrium. Now, we know that an increase in the nominal money supply with goods prices fixed must increase the supply of real balances. For the money market to remain in equilibrium, the demand for real balances must increase. This can be accomplished by an increase in real income, but real income is unlikely to adjust quickly. Another channel is a decrease in the nominal interest. A lower interest rate positively affects the demand for money, since it decreases the opportunity cost of holding real money balances. Thus, the increase in the money supply causes the domestic interest rate to fall (and fall below the foreign interest rate). Since the monetary exchange rate model also assumes uncovered interest rate parity, the domestic currency must be expected to appreciate when the domestic interest rate is less than the foreign interest rate. But if people are rational, they know that, in the long run, the domestic currency will be weaker than it was before the increase in the money supply. The only path for the exchange rate that allows for a long-run depreciation of the domestic currency and an expected appreciation in the short run is for the domestic currency to immediately weaken by more than it will weaken in the long run. Thus, the exchange rate overshoots its new equilibrium: The exchange rate (in domestic currency per unit of foreign currency) jumps up when the money supply is increased and subsequently falls over time toward its new higher equilibrium value.

Engel and West (2005) note that the finding that a random walk model would usually outperform fundamental models when forecasting the exchange rate may not necessarily imply that the fundamental models are false. While their arguments are sophisticated, Equation (3.3) hints at the main argument. If the discount factor is close to 1, the equation implies that \(\log[S_t]=\mathbb{E}_{t}\big[\log (S_{t+1}) \big]\). But that is the random walk model! The authors argue that, in many practical cases, the discount factor is indeed close to 1 and that, moreover, the fundamentals themselves behave like random walks. Together, this implies that the current exchange rate adequately reflects the expected value of future fundamental values. However, for this to be true, the exchange rate should also predict future fundamental values. Engel, Mark, and West (2007) show that this is indeed the case. They also document that novel forecasting techniques that efficiently exploit the information across fundamentals in multiple countries predict exchange rates out of sample better than the random walk model. Finally, at longer horizons, such as 3 to 4 years into the future, fundamental models do have predictive power for exchange rates (see, Mark (1995)).

One implication of Engel and West’s interpretation of the performance of the monetary exchange rate model is that *exchange rate changes* are unpredictable, but they should still reflect news about fundamentals. If there is news about the money supply or real income, and it does not change the exchange rate in the required direction, this would be strong evidence against the fundamental models. Several authors have used high-frequency data on exchange rates and macroeconomic announcements to investigate how exchange rates react to macroeconomic news (see Andersen et al. (2003), Andersen et al. (2007); and Faust et al. (2007)). The studies are careful to measure the *announcement news* by subtracting from the reported number an estimate of its expected value according to a survey by Money Market Services (MMS). Every week, MMS records forecasts by some 40 money managers at financial institutions regarding all macroeconomic indicators. One prediction of the monetary exchange rate model is borne out in the data. The dollar indeed appreciates relative to positive news about U.S. real income, as revealed by news about U.S. GDP, retail sales, and construction spending. Currency markets also prove efficient in that the news is incorporated into prices quickly (typically in less than 15 minutes). However, the studies reveal a somewhat strange reaction to news about inflation and increases in the money supply: The dollar appreciates, whereas it should depreciate according to the monetary exchange rate model. One interpretation is that the appreciation reflects the anticipation of an aggressive monetary policy response to the higher inflation; that is, if monetary policy sharply raises interest rates in response to positive inflation news, the exchange rate should indeed be expected to appreciate (see Clarida and Waldman (2008)).

The popular press often mentions that high real interest rates go hand in hand with “*strong*” real exchange rates. We first show that such a relationship is implied by a real version of uncovered interest rate parity and “*mean-reverting*” real exchange rates. We also assess whether the relationship holds up empirically. The popular press also often mentions a strong link between the current account and exchange rates, suggesting that a current account deficit should put downward pressure on the exchange rate. However, even casual observation suggests that this link does not always hold. After all, the United States has run a current account deficit for a very long time and has had spells during which the dollar appreciated strongly even while the current account worsened. We briefly describe an equilibrium model that simultaneously determines the level of the (real) exchange rate and the current account balance.

To see why the level of the real exchange rate should be related to the differential between the real interest rates on different currencies, we need to convert uncovered interest rate parity from a relationship between nominal interest rates and nominal rates of depreciation into a relationship between real interest rates and expected real rates of depreciation. To do so, let’s rearrange Equation (3.2) and subtract the expected inflation differential between the home and foreign countries, \(\mathbb{E}_{t}[\pi_{t+1}-\pi^{*}_{t+1} ]\) from both sides of the uncovered interest rate parity expression:

\[\begin{eqnarray*} &&i_t - \mathbb{E}_{t}[\pi_{t+1}]-\Big(i^{*}_t-\mathbb{E}_{t}[\pi^{*}_{t+1} ] \Big) \dots \\ &&= \mathbb{E}_{t}\Big[\log[S_{t+1}]\Big] - \log[S_t]- \mathbb{E}_{t}\Big[\pi_{t+1} - \pi^{*}_{t+1}\Big] \end{eqnarray*}\]Note that the inflation rates should be continuously compounded, as we are working with logarithmic exchange rates. Of course, \(\log[S_{t+1}]-\log[S_t]\) will be close in practice to the simple percentage change in the exchange rate, which we usually define as \(s_{t+1}\).

From the definitions of the real interest rate and of the rate of change of the real exchange rate, this equation reduces to the following:

\[\begin{eqnarray} r^{e}_t - r^{e*}_t = \mathbb{E}_{t}\Big[\log [RS_{t+1}] - \log[RS_t] \Big] \tag{3.6} \end{eqnarray}\]where \(r^{e}_t\) denotes the domestic real interest rate, \(r^{e*}_t\) denotes the foreign real interest rate, and \(\log[RS_t]\) denotes the logarithm of the real exchange rate. Equation (3.6) indicates that when the foreign real interest rate is greater than the domestic real interest rate, the right-hand side of Equation (3.6) is negative and the domestic currency is expected to appreciate in real terms.

To link the expected real interest rate differential to the *level* of the real exchange rate instead of the expected rate of change of the real exchange rate, we must explain the idea of mean reversion.

A mean-reverting process is always expected to move back or be pulled toward its unconditional mean. A random walk is a good example of a process that is *not* mean reverting. Whether the exchange rate is unusually high or low does not matter in forecasting future exchange rates; your best predictor remains the current exchange rate. In a mean-reverting process, whether the current exchange rate is above or below the long-run mean is what drives the direction of the forecast. When you are above the mean, you should be expected to be pulled back toward the mean, so the forecast of the expected exchange rate change should be *negative*. When you are experiencing unusually low real exchange rates, you should expect to be pulled toward the mean, so your forecast of the change in the real exchange rate should be positive. Let’s use \(\overline{RS}\) as our estimate of the long-run mean for the logarithm of the real exchange rate. This could be the long-run historical average, but may also be implied by a theoretical model. The idea of mean reversion implies

where \(\kappa\) is a negative number. Substituting Equation (3.6) into Equation (3.7) gives

\[\begin{eqnarray} r^{e}_t - r^{e*}_t = \kappa \big[ \log[RS_t] - \overline{RS} \big] \tag{3.8} \end{eqnarray}\]Equation (3.8) indicates that when the real exchange rate is above its long-run equilibrium - that is, when \(\Big[\log \big[ RS_t \big] - \overline{RS} \Big] > 0\) and it is expected to decline to its mean - the real interest rate in the home country is smaller than the real interest rate in the foreign country (because \(\kappa\) is negative). By way of example, when the local currency is at R15.00 / $ and above the long-term mean of R14.00 / $, then it is currently relatively weak and would be expected to strengthen over time. In such a case, the South African real interest rate would be expected to be below the foreign real interest rate. Hence, we have demonstrated that when the rand is weak in real terms relative to foreign currencies, the real interest rate on rand assets should be below the real interest rate on the foreign currency assets. Conversely, when real interest rates in South Africa are relatively high, the rand should be strong in real terms and expected to depreciate.

Academic researchers who have examined the relationship between the real value of the dollar and the real interest rate differential have found the relationship to be weak.^{7} In Figure 4, we look at recent evidence for the dollar from 1992 to 2010. The solid line in Figure 4 represents an equally weighted real exchange rate of the dollar relative to 15 major currencies expressed as foreign currency per dollar. Hence, increases (decreases) in the real exchange rate in Figure 4 represent real appreciations (depreciations) of the dollar relative to foreign currencies. The dotted line in Figure 4 represents the U.S. real interest rate defined from long-term bond yields minus an equally weighted average of the real interest rates on the other 15 countries’ long-term bonds. Our estimate for expected inflation is simply current annual inflation.

It is apparent from Figure 4 that when the U.S. real interest rate seems relatively high compared to foreign real interest rates, the dollar is relatively strong in real terms. Also, when the U.S. real interest rate differential is relatively low, the dollar is relatively weak. The correlation between the two time series is 0.70.^{8}

Now that we have successfully linked real interest rate differentials and the level of the real exchange rate, albeit more in the long run than the short run, we are in a position to discuss how other important market fundamentals help to simultaneously determine the real exchange rate and the current account of the balance of payments. Recall that the balance of payments is an identity in which the sum of the current account and the financial (capital) account must be zero. Hence, the value of the financial (current) account surplus or deficit equals the value of the capital account deficit or surplus, respectively. The real exchange rate and other variables adjust to ensure that the balance of payments balances. Hence, economic shocks to the accounts of the balance of payments affect the real exchange rate.

These shocks may come from the “real” side of the balance of payments, the trade balance, which records exports and imports, and from the “financial” side of the balance of payments, the capital account, which records purchases and sales of assets. Models of the real exchange rate recognize that real exchange rates affect these two parts of the balance of payments differently, as we now discuss in detail.^{9}

When currencies strengthen in real terms, foreign goods become less expensive than domestic goods. Hence, a real appreciation is typically associated with a deterioration of the trade balance - that is, a rise of imports relative to exports. Conversely, a real depreciation of a country’s currency enhances a country’s competitiveness in world markets and improves the trade balance. In this case, exports typically increase relative to imports.

Remember that the current account of the balance of payments is the trade balance plus the flows of income that are generated by a country’s net international investment position - that is, by its net foreign assets. Hence, the current account is related negatively to the country’s real exchange rate through its effect on the trade balance.

The real exchange rate also influences the capital account, which measures changes in a country’s net foreign assets. A country with a capital account deficit (surplus) is acquiring (losing) net foreign assets. Remember, also, that the excess of a country’s gross national income over its gross national expenditure is related by an identity to the rate of change of net foreign assets. Thus, the economic forces that determine a country’s desired excess of income over expenditures determine the country’s acquisition or loss of net foreign assets. When a country’s income exceeds its expenditures, or when savings exceed investment, the country builds up net foreign assets. This requires that the country run a financial (capital) account deficit and a current account surplus.

One of the most important variables that affects a country’s aggregate saving and investment is the real interest rate. Since higher real interest rates increase saving and decrease real investment, higher real interest rates are associated with financial (capital) account deficits and current account surpluses. From the previous section, we know that higher real interest rates are also associated with temporarily strong real exchange rates so that the currency can be expected to depreciate in real terms over time. This is also important for the demand for assets, since it ensures that the perceived rate of return on assets denominated in different currencies is the same. Thus, we have another relationship between the real exchange rate and the balance of payments, but this time, real appreciations are associated with current account surpluses.

Clearly, the current account and the real exchange rate are determined in a complex equilibrium. On the one hand, a real appreciation of the home currency causes imports to rise relative to exports, which lowers the current account surplus. On the other hand, a real appreciation of the home currency is associated with an expected real depreciation and thus with a higher real interest rate at home than abroad. The increase in the real interest rate decreases investment and increases saving, which creates a larger current account surplus. Just as supply and demand for any good force an equilibrium price and quantity, the opposing forces of the real exchange rate on the current account through a “goods” channel and a “savings and investment” channel lead to an equilibrium real exchange rate and an equilibrium current account balance. Hence, a particular current account balance may be consistent with various levels of the real exchange rate. Also, variables that shift demand between domestic and foreign goods and variables that affect savings and investment will cause the equilibrium to change.

Let’s give a few examples of how certain economic variables can affect the equilibrium. An increase in government spending or a decrease in taxes that causes a budget deficit increases aggregate demand in the economy. The real interest rate increases to reduce private investment and encourage private saving. The domestic currency strengthens in real terms to allow increased purchases from abroad, and the current account turns to deficit. Thus, although an observer who only sees the high real interest rate might think the country is attracting capital, the capital account is actually in surplus.

These effects of government spending are consistent with the experience of the United States in the early 1980s. When President Reagan increased government spending and decreased taxes, real interest rates increased, the dollar experienced a massive real appreciation, and U.S. current account deficits grew to unprecedented levels.

How would new information that signals increases in future GDP affect the equilibrium? The news encourages firms to invest more today; likewise, consumers feel wealthier, so they want to consume more. To ration investment and consumption, it will again be the case that for every possible current account balance, a stronger domestic currency is required. In equilibrium, there will be a real appreciation and a current account deficit. The counterpart of the current account deficit is an inflow of foreign capital, which finances some of the investment and allows consumption to be higher than it otherwise could be. An example of this effect is the sustained strength of the dollar from 1995 through 2000 and the corresponding large U.S. current account deficits. These effects were thought to be the result of the attractive growth potential associated with the U.S. economy during the information technology boom.

Previously, we showed that purchasing power parity (PPP) is a reasonably good long-term model for the exchange rate. It is fair to say that PPP-based models, with some whistles and bells, are currently the most popular fundamental exchange rate models. Most brokers and banks have developed “fair value” exchange rate models. Typically, rather than relying completely on PPP, which predicts a real exchange rate of exactly 1, they attempt to adjust this value for various effects, such as the productivity trends described previously. This is particularly important for developing countries, which otherwise may have persistently undervalued exchange rates. The models then use the deviation between the current value and the fair value of the exchange rate to predict the direction of change.

A number of academic studies have examined the forecasting prowess of related models. Jordà and Taylor (2009), for example, define the fundamental real exchange rate simply to be its long-run mean. Their evidence suggests that a 10% real overvaluation leads to a 2% monthly nominal depreciation prediction, everything else equal, and they find some evidence that the effect becomes stronger if the deviation becomes very large. Yet, when they use this information in a trading strategy, it performs poorly. However, they claim that using fundamental information in this way is helpful in reducing the tail risks of a carry strategy, even during the disastrous 2008 period. Clements and Lan (2010) also find that PPP deviations have forecasting power for nominal exchange rates at medium to long horizons using the Big Mac index to define the theoretical real exchange rate. They also stress that many countries show very persistent over-or-undervaluations, so that the theory must be adjusted for an expected long-run real exchange rate (also taken to be the historical average). They also demonstrate that when the real exchange rate reverts back to its long-run mean, it is primarily the nominal exchange rate that adjusts, not relative price levels. Wu and Hu (2009) find evidence that a PPP model adjusted for the Harrod-Balassa-Samuelson effect (productivity differences across countries, see the section on Purchasing Power Parity) beats the random walk model in out-of-sample forecasts, especially at medium and long forecasting horizons.

Whereas fundamental forecasters use macroeconomic data to forecast future exchange rates, technical analysts focus entirely on financial data. Next, we examine different technical forecasting methods in order of increasing sophistication: chartism, filter rules, regression analysis, and non-linear analysis. Active currency managers tend to primarily use technical analysis, and we end the section discussing their performance.

Chartists graphically record the actual trading history of an exchange rate and then try to infer possible future trends based on that information alone. Figure 5 graphs a daily exchange rate series, which we use to introduce some chartist terminology.^{10}

A support level is any chart formation in which the price has trouble falling below a particular level. A resistance level is any chart formation in which the price of an instrument has trouble rising above a particular level. Support levels and resistance levels define a trading range, which might be short term, medium term, or long term. When a trading range is broken, a sudden rise or fall in prices is expected and is called a breakout.

Chartists argue that a number of different patterns in data clearly signal future trends. One well-known pattern is the “head and shoulders”, which indicates a pending fall in the exchange rate once “the neckline is pierced”. Clearly, chartists do not believe in efficient financial markets but in markets that are driven by irrational whims that induce prolonged trends of rising or falling prices that are predictable.

Since chartists rely on graphs to detect trends rather than on statistics, the patterns they identify may be spurious. For example, Figure 5 does not represent data corresponding to an actual exchange rate. The data are an artificial series based on the random walk model that we generated using a random number generator. The random walk model implies that \(\mathbb{E}_{t}[S_{t+1}]=S_t\). Thus, the model states that the best predictor for the future exchange rate is today’s exchange rate, and the best prediction for the change in the exchange rate is zero.

If exchange rates truly follow random walks, potentially profitable trading strategies nonetheless do present themselves. For example, whenever the forward rate does not equal the current spot rate, the forward rate would not be equal to the expected future spot rate, and you would have an incentive to speculate in the forward market. For example, if the euro is at a discount relative to the dollar \((F_t < S_t)\), and if the $/€ exchange rate follows a random walk, there is an expected profit to be made from buying euros forward. This is true, because the future exchange rate at which you expect to sell euros for dollars in the future, which would be the current spot rate, is higher than the forward rate at which you can buy future euros with dollars today. Random walk behaviour of exchange rates is consistent with the regression evidence regarding the unbiasedness hypothesis. That evidence suggests that investing in a currency trading at a forward discount is profitable.

The recommendations of chartists are very subjective. As you see from the graph in Figure 5, it is possible for the eye to pick up what seem to be predictable patterns that are simply not there. Moreover, it is difficult to statistically analyse the predictions chartists make. For example, we must formalize what it means to see a head-and-shoulders pattern or another rule in a formula that can be applied to the data. One interesting study by Chang and Osler (1999) compared the profitability of the head-and-shoulders pattern with other trend-predicting rules. Although Chang and Osler found that trading on the head-and-shoulders patterns is profitable, the profitability is dominated by other, simpler trading rules, which we discuss next.

Filter rules are popular methods for detecting trends in exchange rates. In general, filter rules are trading strategies based on the past history of an asset price that provide signals to an investor, which would act as an instruction for when to buy and when to sell currencies. We investigate two often-used techniques, which we describe from the perspective of a dollar-based investor who is examining exchange rates in dollars per foreign currency.

An \(x\)% rule states that you should go long (buy) in foreign currency after the foreign currency has appreciated relative to the dollar by \(x\)% above its most recent trough (or support level) and that you should go short (sell) in foreign currency whenever the currency falls \(x\)% below its most recent peak (or resistance level). Common \(x\)% rules are 1%, 2%, and so forth. Panel \({B}\) of Figure 6, illustrates this rule for an upward trend of the currency.

Moving-average crossover rules use moving averages of the exchange rate. 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) . Panel A of Figure 6 shows how the short-run moving-average line, which in this case is the exchange rate itself, since we are using a 1-day rule, more rapidly picks up the upward trend in the left-hand portion of the graph and cuts through the long-run moving average line from below, signalling a buy.^{11}

How well do filter rules work? Early studies found that technical trading rules generated statistically significant profits, which were unlikely to be generated by chance (see, for example, LeBaron (1999)). However, the sample period in these studies was dominated by long swings in the value of the dollar, which appreciated substantially in the first half of the 1980s before depreciating substantially in the second half of the 1980s.^{12} Newer work by Pukthuanthong-Le, Levich, and Thomas (2007) finds that the era of easy profits from simple trend-following strategies is over, at least for the major currencies. These authors show that the average profits generated by three moving-average rules for the Japanese yen, Deutsche mark, British pound, and Swiss franc over the 1975 to 1994 period are highly statistically significantly different from zero. The profits range from 6.20% per year for the Swiss franc to 13.94% for the yen, and the standard error for these averages is about 2.7%. For most currencies, we can be very confident that these profits are different from zero.^{13} The Canadian dollar generated positive but insignificant profits. Over the 1995 to 1999 period, the yen is the only currency with positive (and significant) profits, and for the 2000 to 2006 period, no currencies generate significantly positive profits. The authors interpret these results as indicating that foreign exchange markets have become more efficient over time, although it is puzzling that this process would have taken so long. They also demonstrate that over the 2000 to 2006 period, less liquid currencies, such as the New Zealand dollar, and emerging market currencies, such as the Brazilian real, the South African rand, and the Russian ruble, do generate significant profits when simple moving-average rules are followed. The Mexican peso generates positive but insignificant profits.

The evidence against the unbiasedness hypothesis suggests that interest rate differentials may contain information about future exchange rates that can be profitably exploited. Both academic analysts and foreign exchange professionals have explored regression models that link future exchange rate changes to interest rate differentials and other easily available information (such as past exchange rates) to predict future exchange. Essentially, the regression uses future returns on forward market positions [\(fmr_t\)] as the dependent variable and current information, such as the forward premium [\(fp_t\)], and other variables as the independent variables. The fitted value of the regression can then be interpreted as the expected return on a long forward position.

In a trading strategy, the regression framework is used each trading period to find a value for the expected forward market return. If the expected return is positive (negative), the strategy goes long (short) in the foreign currency.

Increased computing and mathematical and statistical sophistication have led researchers and practitioners to use more complex models to forecast exchange rates. Going beyond simple linear regression models as discussed earlier, researchers have, for example, tried to model the idea that as currencies move further from fundamentals (such as their PPP values) or as the volatility of the exchange rate increases, interest rate differentials may work less well as predictors of future exchange rate changes (see, Jordà and Taylor (2009); and Clarida, Davis, and Pedersen (2009)). Going beyond simply pre-specifying the trading rules, more recent studies have applied sophisticated computer techniques, such as genetic algorithms, to search for optimal trading rules. Without going into details, these techniques apply a Darwinian-like, natural selection process to filter rules applied to past data that eventually breeds the “best” trading rules. Neely, Weller, and Dittmar (1997) found that adhering to such trading rules was, indeed, profitable. In a subsequent study, Neely and Weller (2001) found that additional information about central bank interventions further improved profitability.

One way to ascertain whether profits are being made in the foreign exchange market using technical analysis is to look at the forecasting records of actual forecasting services. Forex advisory services are a diverse lot. All of them generate exchange rate forecasts, but their clienteles, techniques, and forecast horizons differ. Unfortunately, there exists scant empirical evidence on the forecasting ability of such services. However, that is changing because currencies are more and more viewed as an asset class and the number of active currency traders, mostly organized as hedge funds, has grown considerably over the past decade. Since many of these currency traders report returns to various indices, we can analyse their performance. If such funds fail to forecast exchange rates, they should 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. 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.

Currency forecasts are usually incorporated in the evaluation of international projects, strategic plans, pricing, working capital management, and the analysis of portfolio investments. When all the international parity conditions hold, currency forecasting models have little value. In this case, the forward rate is the best predictor of the future spot rate; and the current real exchange rate is the best predictor of the future real exchange rate. Hence, the costs of funding and returns to investment or equalised in real terms, across countries, as the real interest rates or equalised across countries. However, empirical evidence rejects the notion of equality in the real interest rates across countries.

The two main forecasting techniques that may be employed rely on fundamental analysis and technical analysis. Fundamental analysis links exchange rates to fundamental macroeconomic variables, such as GDP growth and the current account, either through a formal model or through judgemental analysis. Technical analysis uses financial data, such as past exchange rate data, to predict future exchange rates.

To evaluate the predictive accuracy of a forecast one could use the mean absolute error (MAE) or root mean squared error (RMSE) statistic. The percentage of correct signals relative to the forward rate could also be employed to judge the usefulness of the forecasting model. A third method for evaluating forecasts could incorporate the measurement of trading profits on the foreign exchange market.

The asset market approach to exchange rate determination assumes that the exchange rate is an asset price. Hence, the current value depends on current fundamentals, such as relative money supply and the respective output levels of countries. In addition, this analysis also depends on the expected values of future economic fundamentals. Any change in current fundamentals or news about future fundamentals changes the exchange rate.

Two of the most frequently mentioned determinants of exchange rates are real interest rate differentials and current-account balances. These variables are simultaneously determined. The complexity of the relationships that determine the current account and the exchange rate may explain why fundamental exchange rate models perform rather poorly when forecasting future exchange rates.

Chartists record the actual trading history of an exchange rate and try to infer possible trends based on this information alone, although it is unlikely that the naked eye can pick up trends in a randomly fluctuating series. Filter rules, which include the \(x\)% and moving average rules, are trading rules that are designed to detect training behaviour in exchange rates. Although early empirical studies that focused on data from the 1980s found strong trends in exchange rates, more recent work suggests that this behaviour is no longer contained in the data. More sophisticated technical analysis use regression models or other econometric techniques to link exchange rates to financial data, such as forward premiums. The evidence on the success of these strategies is limited.

Andersen, Torben G., Tim Bollerslev, Francis X. Diebold, and Clara Vega. 2003. “Micro Effects of Macro Announcements: Real Time Price Discovery in Foreign Exchange.” *American Economic Review* 93: 38–62.

———. 2007. “Real-Time Price Discovery in Global Stock Bond and Foreign Exchange Markets.” *Journal of International Economics* 73: 251–77.

Baxter, Marianne. 1994. “Real Exchange Rates and Real Interest Differentials: Have We Missed the Business Cycle Relationship?” *Journal of Monetary Economics* 33: 5–37.

Bhundia, A.J., and L.A. Ricci. 2005. “Post-Apartheid South Africa: The First Ten Years.” In, edited by M. Nowak and L.A. Ricci, 156–73. Washington: International Monetary Fund.

Chakrabarti, Avik. 2006. “Real Exchange Rates and Real Interest Rates Once Again: A Multivariate Panel Cointegration Analysis.” *Applied Economics* 38: 1217–21.

Chang, P.H. Kevin, and Carol L. Osler. 1999. “Methodical Madness: Technical Analysis and the Irrationality of Exchange-Rate.” *Forecasts Economic Journal* 109: 636–61.

Clarida, Richard H., and Daniel Waldman. 2008. “Asset Prices and Monetary Policy.” In, edited by John Campbell. Chicago: University of Chicago Press.

Clarida, Richard H., Josh Davis, and Niels Pedersen. 2009. “Currency Carry Trade Regimes: Beyond the Fama Regression.” *Journal of International Money and Finance* 28: 1375–89.

Clements, Kenneth W., and Yihui Lan. 2010. “A New Approach to Forecasting Exchange Rates.” *Journal of International Money and Finance* 29: 1424–37.

Dornbusch, Rudiger. 1976. “Expectations and Exchange-Rate Dynamics.” *Journal of Political Economy* 84: 1161–76.

Edison, Hali J., and B. Dianne Pauls. 1993. “A Re-Assessment of the Relationship Between Real Exchange Rates and Real Interest Rates: 1970-1990.” *Journal of Monetary Economics* 31: 165–87.

Engel, Charles, and James D Hamilton. 1990. “Long Swings in the Dollar: Are They in the Data and Do Markets Know It?” *American Economic Review* 80 (4): 689–713.

Engel, Charles, and Kenneth D. West. 2005. “Exchange Rates and Fundamentals.” *Journal of Political Economy* 113: 485–517.

Engel, Charles, Nelson C. Mark, and Kenneth D. West. 2007. “NBER Macroeconomics Annual.” In, edited by Daron Acemoglu, Kenneth Rogoff, and Michael Woodford, 22:381–441. Chicago: University of Chicago Press.

Faust, Jon, John H. Rogers, Shing-Yi B. Wang, and Jonathan H. Wright. 2007. “The High-Frequency Response of Exchange Rates and Interest Rates to Macroeconomic Announcements.” *Journal of Monetary Economics* 54: 1051–68.

Fisher, Irving. 1930. *The Theory of Interest*. New York: Macmillan.

Gehrig, Thomas, and Lukas Menkhoff. 2006. “Extending Evidence on the Use of Technical Analysis in Foreign Exchange.” *International Journal of Finance and Economics* 11: 327–38.

Henriksson, Roy D., and Robert Merton. 1981. “On Market Timing and Evaluation Performance 2: Statistical Procedures for Evaluating Forecasting Skills.” *Journal of Business* 54: 513–33.

Jordà, and Alan M. Taylor. 2009. “The Carry Trade and Fundamentals: Nothing to Fear but Feer Itself.” National Bureau of Economic Research Working Paper 15518. National Bureau of Economic Research.

LeBaron, Blake. 1999. “Technical Trading Rule Profitability and Foreign Exchange Intervention.” *Journal of International Economics* 49: 125–43.

Mark, Nelson C. 1995. “Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability.” *American Economic Review* 85: 201–18.

Meese, Richard, and John Prins. 2011. “On the Natural Limits of Exchange Rate Predictability by Fundamentals.” Manuscript. Princeton University.

Meese, Richard, and Kenneth Rogoff. 1983. “Empirical Exchange-Rate Models of the Seventies â€” Do They Fit Out of Sample?” *Journal of International Economics* 14: 3–24.

———. 1988. “Was It Real? The Exchange Rate Interest Rate Differential Relation over the Modern Floating Rate Period.” *Journal of Finance* 43: 933–48.

Mussa, Michael. 1984. “Exchange Rate Theory and Practice.” In, edited by J.F.O. Bilson and R.C. Marston. Chicago: University of Chicago Press.

Neely, Christopher, and Paul Weller. 2001. “Technical Analysis and Central Bank Intervention.” *Journal of International Money and Finance* 20: 949–70.

Neely, Christopher, Paul Weller, and Robert Dittmar. 1997. “Is Technical Analysis in the Foreign Exchange Market Profitable? A Genetic Programming Approach.” *Journal of Financial and Quantitative Analysis* 32: 405–26.

Pojarliev, Momtchil, and Richard M. Levich. 2008. “Do Professional Currency Managers Beat the Benchmark?” *Financial Analysts Journal* September/October: 18–32.

Pukthuanthong-Le, Kuntara, Richard M. Levich, and Lee R. Thomas. 2007. “Do Foreign Exchange Markets Still Trend?” *Journal of Portfolio Management* Fall: 114–18.

Rogoff, Kenneth. 2009. “Exchange Rates in the Modern Floating Era: What Do We Really Know?” *Review of World Economics* 145: 1–12.

Sollis, Robert, and Mark E. Wohar. 2006. “The Real Exchange Rate-Real Interest Rate Relation: Evidence from Tests for Symmetric and Asymmetric Threshold Cointegration.” *International Journal of Finance and Economics* 2: 139–53.

Wu, Jyh-Lin, and Yu-Hau Hu. 2009. “New Evidence on Nominal Exchange Rate Predictability.” *Journal of International Money and Finance* 28: 1045–63.

There is no approximation in going from Equation (1.1) to Equation (1.2) if one uses continuously compounded interest rates and rates of inflation.↩

Note: The vertical axis measures average government bond yields for 1990-2010. The horizontal axis measures the average annual inflation rate over the same period. The diamonds represent 16 countries: Australia, Austria, Belgium, Canada, Denmark, France, Germany, Ireland, Italy, Japan, the Netherlands, New Zealand, Sweden, Switzerland, the United States, and the United Kingdom. The line represents a regression of yield \((y)\) on inflation \((\pi)\). The standard error of the estimate is between parentheses. Data are from the International Monetary Fund’s International Financial Statistics.↩

Note: UH = unbiasedness hypothesis; PPP = purchasing power parity; CIRP = covered interest rate parity; UIRP = uncovered interest rate parity (international Fisher relation).↩

The small differences arise since Figure 2 does not make approximations so that \(r^{e}=\frac{i-{\pi}^{e}}{i+{\pi}^{e}}\).↩

Henriksson and Merton (1981) developed market timing tests for stock market returns, where forecasters predict the stock market to go up or down. However, stock returns are expected to be positive, so always predicting the market to go up is likely to lead to a better-than-50%-correct forecasting record. Similarly, if it rains on 80% of the days, a weather forecaster has an 80% success rate by always forecasting rain. Analogously, if during the period that you record the forecasting performance, the forward rate is consistently below the spot rate, a forecaster who ends up with a 100% correct forecasting record may have superior forecasting knowledge or may have simply failed to change his forecast, and this laziness led to the perfect record. Since the market direction did not change, there is little information on timing the market in this sample. Henriksson and Merton show how to correct for such a bias. Basically, you should add the proportion of correct forecasts conditional on the eventual spot rate being above the forward rate to the proportion of correct forecasts conditional on the eventual spot rate being below the forward rate. If the sum of these proportions is higher than 1, there is evidence of market timing ability. Indeed, our lazy forecaster, who just got lucky, would end up with a score of 1.0 and would not be dubbed a forecasting genius with such a test.↩

This property of expectations is known as the

*law of iterated expectations*, and it follows from the fact that we necessarily have less information now (at time*t*) than we will have in the future (at time \(t+1\)).↩For example, Meese and Rogoff (1988) and Edison and Pauls (1993) perform various statistical tests that are designed to find the relation between real exchange rates and the real interest rate differential. Each pair of authors concludes that the relation is very weak. Baxter (1994) finds statistical support for a long-run relation but not a short-run relation between the level of the real exchange rates and real interest rate differentials. The more recent evidence remains mixed; see, for instance, Chakrabarti (2006), who finds no link, and Sollis and Wohar (2006), who do find a link.↩

Note: The solid line is the real exchange rate calculated as an equally weighted average of the real exchange rates of 15 currencies versus the U.S. dollar using consumer price indexes (CPIs) as the price levels. The dotted line is the U.S. real interest rate minus the equally weighted average real interests of the 15 countries. The countries are Australia, Austria, Belgium, Canada, Denmark, France, Germany, Ireland, Italy, Japan, the Netherlands, New Zealand, Sweden, Switzerland, and the United Kingdom. Data are from the International Monetary Fund’s International Financial Statistics.↩

An interesting formal model that simultaneously determines both the real exchange rate and the current account is the seminal analysis of Mussa (1984).↩

Note: The top graph shows a daily exchange rate series (about 250 days per year) over a time span of 20 years. The graph appears to display some clear trends. The bottom panel investigates these short-term trends more closely by lifting the part in the box at the top and blowing it up. The apparent trends are then interpreted using chartist jargon.↩

Note: In Panel A, the solid line represents the actual exchange rate, \(S_ t\), which serves as the short-run moving average (SRMA). The dashed line is the long-run moving average (LRMA), averaging the current and past exchange rates. In Panel B, we graph only the exchange rate and illustrate the use of an \(x\)% filter rule.↩

Engel and Hamilton (1990) developed a statistical model that clearly identifies these long swings.↩

To establish the confidence level formally, we divide the average by its standard error, square the resulting statistic, and check where this value lies in a chi-square distribution with 1 degree of freedom. For example, the statistic for the Swiss franc profits is (6.20/2.7)

^{2}= 5.27. Given a chi-square distribution with 1 degree of freedom, we have 97.8% confidence that the profits are different from zero.↩