stability of predictors and the forecasting of foreign exchange rates

BUSN RES 1986:14:37-46 37

Stability of Predictors and the Forecasting of Foreign Exchange Rates

Sarkis J. Khoury University of California-Riverside

The forecasting of foreign exchange rates is like reading tea leaves to some and a sophisticated form of economic analysis to others. Several firms currently earn substantial profits selling exchange-rate forecasts based on various models and with different track records. This study critically reviews the pitfalls and the merits of existing approaches to forecasting foreign exchange rates and introduces a new element in the forecasting model: the stability of predictors. The findings are that stability variables do improve the forecasting ability of an econometrically based model. The results of the suggested model are superior to those derived using the forward rate and the current spot rate as forecasting tools for future spot rates. The forecasting model developed here is shown to be transferable from one currency to another.

The utilization of complex statistical techniques in the forecasting of foreign exchange rates depends on whether or not the foreign exchange markets are efficient. The foreign exchange market that is efficient in any sense (weak, semistrong, and strong) is signaling foreign exchange managers that regardless of the forecasting technique employed-sophisticated econometric models, simple forecasting tools, or chart reading-the market cannot be beaten. A simple, costless forecasting tool continuously observable in the marketplace, such as the forward rate, should prove to be a sufficient predictor of the future spot rate if markets are functioning efficiently.

Empirical tests on the efficiency of the foreign exchange markets suffer the following drawbacks:

1.

2.

3.

The model specification is usually incorrect. Efficiency per se is usually not being tested contrary to the claims of certain authors [19, 211; The statistical technique used to test the hypothesis is either inadequate or incomplete. The evidence offered is almost never conclusive [7, 161; The test results are not decisive. Most tests allow the researcher not to reject the null hypothesis (H,: the market is efficient). This is not equivalent to accepting the null hypothesis [16, 20, for example]; and

Address correspondence to Sarkis J. Khoury. University of California-Riverside, Graduate School of Management, Riverside, CA 92521.

Journal of Business Research 14, 37-46 (1986) 0 Elsevier Science Publishing Co., Inc. 1986 52 Vanderbilt Ave., New York, NY 10017

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S. J. Khoury

4. The transferability (the duplication) of the test results from one time period to another or from one currency to another has never been achieved with uniform success.

A review of empirical studies on the efficiency of the foreign exchange market

is beyond the scope of this study. The reader should consult the excellent reviews of the empirical literature by Levich [19] and Kohlhagen [17].

The doubt about the efficiency of the market has been supported by several

studies not covered by Levich. Booth, Kaen; and Koveos [4] found evidence that the foreign exchange market is not efficient even in a weak sense. Their conclusion held for the British pound, the Canadian dollar, the French franc, the deutsche mark, and the Japanese yen, all relative to the U.S. dollar.

David Longworth [22] examined the efficiency of the Canadian-U.S. exchange market and found the market inefficient.

Against this backdrop, we offer the following comments: 1) The very definition of efficiency has been suspect for a long time. A new

definition offered by Beaver (21 merits close examination. Beaver distinguishes between two types of efficiency: Y-efficiency and q-efficiency. Beaver writes that:

A securities market is efficient with respect to a signal Y’, if and only if the configuration of security prices {P,t} is the same as it would be in an otherwise identical economy (ie., with an identical configuration of preferences and endowments) except that every individual receives Y’, as well as Y,,. A securities market is efficient with respect to q’, if and only if Y efficiency holds for every signal (y’,) from q’t [2, p. 281.’

Beaver cites the advantages of the definition, but acknowledges the difficulty of

directly testing his concept of efficiency. The mode1 we introduce below represents, therefore, an indirect test of efficiency in Beaver’s sense. A forecasting mode1 yielding results superior to those generated by a random walk model or by the foreign exchange market itself (forward and futures rates, for example) indicates improper “signals” or inadequate interpretations of them and, consequently, unex- ploited excess profit opportunities.

2) The presence of 23 foreign exchange forecasting services (see Goodman [ 131) selling forecasts to banks, industrial corporations, and to investors at considerable rates has interesting implications for the efficiency of the foreign exchange market. The payment of a positive price for a forecast, while a free market forecast em- bodied in the forward rate or the futures rate is available, could indicate that the market is inefficient, that there is a positive value to having an agent onto whom the burden resulting from an error in the foreign exchange market is shifted, or that the purchasers of the forecast are being systematically and consistently duped by sales agents. The latter suggests an inefficient labor market in which workers are earning a wage exceeding their marginal product.

An efficient market should eliminate the need for forward contracts, because the cost of the forward cover would equal the expected depreciation in the spot

The author acknowledges with gratitude the assistance provided by Rodney Ganey, Assistant Director of the Social Science Data Center, and by two gifted students: Frank Oelerich and David Yeh. The comments of Animesh

Ghoshal and James Rakowski were very valuable. Financial support for this research was provided by the University

of Notre Dame. College of Business Administration.

Stability of Predictors J BUSN RES 1986:14:37-46

rate. But the sale of forward contracts goes on. This implies that all forward contract buyers are risk averse, opting for a certain gain (loss) instead of an expected value.

3) The findings of Stephen Goodman [13] suggest that the foreign exchange market is inefficient. Goodman compared the performance of six economically oriented services with four technically oriented services on the basis of their predictive accuracy of six currencies against the dollar. The results indicate that technical analysis was clearly superior and that above-average profits could be realized using technical analysis as a predictive tool.

The increased offering of books on technical analysis and their steadily improving market share is another evidence in support of Goodman’s findings, unless buyers are irrational or stupid.

4) Several studies use the unbiasedness of the forward rate test as a basis for testing market efficiency [12, 51. This methodology is suspect on the following grounds:

1. The efficiency of the foreign exchange market is ordinarily measured by testing whether or not the 30-day forward rate is an unbiased predictor of the future spot rate. The inference from the nonrejection of the null hypothesis is that the forward exchange market is efficient. The problem here is that an efficient 30-day forward market does not necessarily mean that the 60-day or the 90-day or any other maturity forward rate is equally an unbiased predictor. The conclusion regarding the efficiency of the forward market, however, may be acceptable only if the dominant forward transactions are in the 30-day category and if the speculators’ schedules are infinitely elastic (an unrealistic assumption).

2. A forward rate that is an unbiased predictor of the spot rate implies only that speculation in the foreign exchange market is a fair game and does not prove that the market is efficient. Speculative interests should dry up if speculation is unprofitable in the long run. The expected return from speculation is zero when the forward rate is an unbiased predictor of the spot.

3. The fact that a particular forecasting method generates “positive and negative errors which over long periods of time cancel out, does not make that method the optimum one for investors who should be interested in the mean square error of a forecast. . . it is possible for a biased forecast to have a lower mean square error than an unbiased one” [15].

4. All empirical tests rely on historical data. Exante efficiency is radically different from expost efficiency. If excess profit opportunities were available in the marketplace then why were they not exploited (in an exante sense)? Speculators either did not observe these opportunities or knew of them but did not act. The reasons for the latter could be high transactions costs, laziness (given their preferences, it was not worth the speculators’ bother), or irrationality. Not much progress can be made in the development of a model based on the laziness or the irrationality of economic agents.

5. Long-run efficiency is a meaningless concept from a speculator’s point of view, for his concern is with the slightest deviation from equilibrium over any period of time, no matter how short (even a minute).

To ignore all the evidence the market itself offers about the inefficiency with which it operates and to play fiddle with statistical methodologies makes no sense.

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Having just raised sufficient doubts about the efficiency of the foreign exchange market, we proceed with the development of our forecasting model, which is based on the assumption of trends in the data. The model we present builds on several existing studies and introduces a new dimension to forecasting techniques.

The Model

The model developed here uses multiple discriminant analysis (MDA) in forecasting foreign exchange rates. The model only identifies whether or not a currency will appreciate or will depreciate. The extent of the appreciation or depreciation in the value of currency can be incorporated into the model by simply adding a require- ment that a currency rises or falls by x% before classifying it as appreciating or depreciating.

Previous attempts at forecasting foreign exchange rates using MDA [9, 111, although taking major steps forward, failed to account for the stability of predictors over time as an additional explanatory variable in the discriminant function. In addition, their results were not particularly robust.

The stability of predictors was successfully introduced by Dambolena and Khoury [6] in a discriminant function for predicting corporate failure. The stability of ratios allowed the authors to predict corporate failure with an 82.6% accuracy five years before failure. This constituted a 12.3% improvement in the predictive power of the model over those that ignored the stability argument.

An examination of the variables that have been traditionally used in regression- type analyses to predict exchange rate changes reveals considerable instability (variation) in the levels of these variables and a strong association between high levels of instability and the size of the changes in foreign exchange rates. The argument with regard to stability is best understood if one focuses, for example, on money supply growth rates-a relevant variable in the model below. A vacillating growth rate in the money supply, monetarists argue, produces changes in inflationary expectations and consequently in currency values. The impact was sum- marized well by Norbert Walter in an article published in the May 5, 1982 issue of The Wall Street Journal:

If one closely watched foreign exchange markets in recent years, it seemed apparent that almost every U.S. money supply figure was evaluated against the Fed’s announced policy of a tough anti-inflationary stance. So each overshooting of the target rate was considered likely to trigger a future tightening of monetary policy. Because interest rates were expected to rise as a result, financial agents moved into liquid funds, a factor that caused money market interest rates to increase instantly. Owing to the resulting international interest rate differential widening in favor of U.S. financial markets, the dollar strengthened and other currencies weakened.

Similar arguments can be made with regard to the stability of the other variables in the model.

Three stability measures of predictors were used by Dambolena and Khoury [6] (DK): the standard deviation, the coefficients of variation, and the standard error. The evidence presented by DK offers support for the superiority of the standard deviation in improving the predictive power of the discriminant function. The same conclusion was reached by the authors with regard to using standard deviation as a measure of the stability of predictors in a foreign exchange forecasting model.

Stability of Predictors J BUSN RES 1986:14:37-46

41

The Predictors

The selection of the independent variables for the discriminant analysis relied on the established theories (relationships) that usefulness and accuracy have proven time and again, on the signals used by the Federal Reserve System for intervention in the foreign exchange market, and on conventional wisdom. Those signals used by the Fed are reported on a quarterly basis in the Federal Reserve Bulletin [8]. An exhaustive review of these reports, beginning with the first quarter of 1972, was conducted and a list of leading indicators for Fed intervention was tabulated.

The independent variables considered, therefore, are: 1) Ratio of exports-imports to total official reserves (measured in SDRs). The

impact of the trade sector on exchange rates, ceteris paribus, was established by Adam Smith and David Ricardo. The division by official reserves is necessary, because trade imbalances, whether positive (exports [Xl > imports [MI) or negative (X < M), are more meaningful if related to the country’s reserves. Official reserves represent the accumulated external economic performance of previous years. The larger they are the greater the ability of countries to defend the value of their currencies through dirty floats. This truth holds whether the weakness of the currency is due to trade, to capital movements, or to speculative runs against the currency. The division by official reserves is, therefore, a way to normalize trade deficits or surpluses. The lower the trade imbalance is in relation to official reserves, the less its impact on the level and the stability of foreign exchange rates.

2) Growth rate in the money supply (Ml) in country i relative to the money supply growth rate in the United States.

The excess growth in the money supply in country i in relation to that of the United States will produce higher prices in country i relative to those in the United States, which will result, ceteris paribus, in a depreciation of the currency of country i. That is, changes in exchange rates are primarily a monetary phenomenon [ 1, lo].

3) Unit labor costs in country i relative to those of the United States. This ratio represents the trend in relative productivity and the pressure on the

cost structure both in the short and in the long run. The higher the ratio, the larger the depreciation in the value of country i’s currency.

4) Net covered interest rate differential. This variable was calculated as follows:

(T bill rate),,,, - [(T bill rate); - (forward rate) - spot rate

spot rate

This variable represents the incentive for arbitrage between country i and the United States. The more positive the differential is, the higher the appreciation in the value of the dollar, other things remaining the same. This variable illustrates, once again, the importance of monetary factors.

5) Net capital movements. This variable guages capital flows between one country and another. If the trade balance is in equilibrium, negative net capital movement would indicate a depreciating currency and a positive number an appreciating currency.

6) Employment index. An index of economic activity (the employment index) was chosen based on the strong arguments advanced by Murenbeeld [23] and on the fact that the lower the employment index, the more likely a government will tinker with the foreign exchange market and will take strong monetary and fiscal

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S. J. Khoury

measures intended to correct domestic economic conditions. It is assumed, therefore, that a stable/appreciating foreign exchange rate is related to a healthy economy.

7) Stability measures. For each of the variables discussed above, three measures of stability over time were calculated: the standard deviation, the coefficient of variation, and the standard error. Repeated tests proved the predictive superiority of the standard deviation. The calculation of the standard deviation was made as follows: using monthly data beginning in June 1971, the standard deviation was calculated using eight months’ data (June 1971-January 1972, inclusive) the resulting standard deviation is matched with the variable level in the eighth month. The standard deviation for the ninth month is calculated using eight observations achieved by dropping the first month (June 1971) and adding the ninth month (February 1972), and so on.

The standard deviation of the net covered interest rate differential was later dropped. The reason is that an arbitrageur looking at the interest rate differential is concerned not with its stability over time but rather with whether or not the differential exists. If it does, and this is readily available information, a decision to invest funds across national borders is then made.

The number of predictors is therefore equal to eleven: six variable levels and five standard deviations.

The dependent variable is the change in the spot exchange rate (average monthly bid price). A positive change is an appreciation in price of the currency, and a negative change is a depreciation in the price of the currency.

Few Qualifications

A model for predicting the direction of foreign exchange rates must represent an improvement over naive forecasting tools such as the forward rate and the current spot rate, which are available at no cost. Even if the model predicts as well as the forward rate, its validity would still be in doubt, because the forward rate predicts not only the direction but also the level of exchange rates. Additionally, any currency forecasting model must be able to forecast more than one currency; that is, it must be transferrable.

We begin our analysis with a test of the model’s ability to forecast the direction of the Japanese yen. We then compare the results with those obtained using naive forecasting tools, and then we show the applicability of the model to the deutsche mark (DM) market. The choice of these two currencies (yen and DM) was made on the basis of data availability and the importance of the two currencies in world trade.

Data

The data used were monthly data on the Japanese yen. It begins on June 1971 and ends in December 1980. The total number of observations is equal to 112. The actual data used begin on January 1972, the month during which the floating exchange rate system effectively began. The earlier data (June 1971 to January 1972) were used to calculate the standard deviation as indicated above.

The data sources are The International Financial Statistics, International Finance (published by the Economics Group of the Chase Manhattan Bank), the Federal

Stability of Predictors J BUN RES 1986:14:37-46

Reserve Bulletin, and the Main Economic Indicators published by the Organization for Economic Cooperation and Development (OECD).

The lag structure used in the discriminant analysis is a function of the availability of data in relation to the month for which exchange rate appreciation or depreciation is to be predicted and of the size of the correlation coefficient between the spot rate and the various lag structures of a given independent variable.

Test Results

Using the stepwise discriminant analysis routine in BMDP [3] on the 11 predictors, the following discriminant function was obtained:

Y = 1.83859 + 7.72437X, - 0.35288X, + 0.00106X, - 0.01959X,

- 20.64090X, - 1.59731X,; (1)

where

Y = A in the $ spot rate (> 0, appreciating; < 0, depreciating) Japanese yen / U.S. $;

X, = {(exports - imports) / total official reserves}, _ 5;

X, = (net covered interest rate differential), _ ,;

X, = (net capital movements), _

X, = (the standard deviation of



4;

(Money supply growth rate),,,,

(Money supply growth rate),.,.

(unit labor costs),,,,,

(unit labor costs),,,, I _ 2; and

the U.S. employment index), _ 4.

The resulting classification matrix is:

Percent Number of Cases Classified into Group

Group Correct

Depreciation 68 Appreciation 80

Total 74

Depreciation Appreciation

34 16 10 40 44 56

The results were validated using the Jacknife technique, a form of Lachenbruch validation [18]. The resulting classification matrix is:

Group Percent Correct

Number of Cases Classified into Group


Depreciation 68 34 16 Appreciation 72 14 36

Total 70 48 52

44 J BUSN RES 1986:14:37-46

S. J. Khoury

The drop in the overall classification of the model upon validation is not very significant. We can, therefore, accept the results of the discriminant analysis.

Interpretation of Results

The first three predictors X,, X,, and X,, are perfectly consistent with established theories. The standard deviation of the growth rate of the money supply in Japan relative to that in the United States represents the powerful effect of monetary policy and of the stability of this policy. The higher the instability of this ratio, the larger the change in the expected foreign exchange rate-a very potent signal to speculators.

The stability of the unit labor costs represents the long-run pressures on the foreign exchange market. The cost differentials will reflect themselves eventually in higher prices in one of the two countries, a result that leads to the depreciation of its currency.

The stability of the domestic economy is a welcome addition to foreign exchange forecasting models. The greater the instability, the greater the probability of an interventionist policy by the central government either directly or indirectly in the foreign exchange market. The net result is a movement in the foreign exchange rate.

Further Validations

To further show the efficacy of the model, we compared its results with those of the forward rate and the current spot rate.

Using end-of-month data for forward and spot rates for the same period as covered in the model, we tested the relationship between the forward premium (discount) (F, - S,) and (S, + r - S,). The results showed that the forward premium (discount) on the Japanese yen predicted only 50% of the time the direction of spot rates. This result is substantially below the predictive power of the model.

To test another naive forecasting model we used the change in the spot as a predictor of future changes in the spot. Specifically, we tested the relationship between (S, - S, _ 1) and (S, +, - S,) and found the predictive capacity to be 57%, which is significantly below the model’s.

Transferability

The transferability of the model was tested by using the exact variables from Equation (1) on West German data for exactly the same period. The lag structure, however, was changed, as one should expect, to accommodate the facts that information does not flow at the same rate in both Japan and West Germany and that the reaction times in both countries are different.

The resulting discriminant function was:

Y = 0.699 + 3.66034X, - 0.15149X, - 0.00010X, - 0.01425X, - 23.4238X, - 0.00424X,.

The lages were: 4 in XI; 1 in X,; 2 in X,; 2 in X,; 4 in X,; and 3 in X,. The resulting classification matrix was:

(2)

Stability of Predictors .I BUSN RES 1986:14:37-46

Group

Percent Correct

Number of Cases Classified into Group


Depreciation 62.5 25 1.5

Appreciation 16.2 15 48

Total 70.9 40 63

Using the forward premium (discount) to further validate the results, we found its predictive power to equal only 54%. The current DM spot rate was equally less effective in forecasting future spot rates.

This inadequacy of the forward DM rate to predict even the direction of spot rates is consistent with the findings of Levich [20].

Conclusions

The efficiency of the foreign exchange market is suspect. Forecasting models of various types have been devised and successfully (profitably) implemented by various firms. The model offered here has a long-standing theoretical foundation and introduces the stability of predictors as a potent element for predicting whether or not a currency will appreciate or depreciate on a month-to-month basis. Thus, it is a useful model for both speculators and arbitragers, and it represents a considerable improvement over the fair-game proposition. The 70% predictive power the model achieves could not go unnoticed by international money managers and should be taken into account by academicians, those with a great interest in market efficiency, in particular.

Now that the stability argument is established, further refinements should be expected.

References

4.

Batten, Dallas S., Foreign Exchange Markets: The Dollar in 1980, Review 63 (April 1981): 22-30.

Beaver, William H., Market Efficiency, The Accounting Review 56 (January 1981): 23- 27.

BMDP, Biomedical Computer Program P Series, 1979, Health Services Computing Facilities, Department of Biomathematics, School of Medicine, University of California, L.A., University of California Press, 1979.

Booth, G. Geoffrey, Kaen, F., and Koveos, P., Efficiency Tests and Foreign Exchange Markets, paper presented at the 15th Annual Meeting of the Eastern Finance Association, Washington, D.C., 1979.

Bradford, Cornell, Spot Rates, Forward Rates and Exchange Market Efficiency, Journal of Financial Economics 5 (1977): 55-65.

Dambolena, Ismael and Khoury, Sarkis J., Ratio Stability and Corporate Failure, The Journal of Finance 35 (September 1980): 1017-1026.

Eastman, Harry C., The Hedging of Commercial Transactions Between U.S. and Canadian Residents: A Canadian View, in Canadian-United States Financial Relationships, Federal Reserve Bank of Boston Conference Series No. 6, Federal Reserve Bank of Boston, Boston, 1971.

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S. J. Khoury

8. Federal Reserve Bulletin, issues from January 1970 to December 1980, Board of Governors of the Federal Reserve System, Washington, D.C.

9. Folks, William R., Jr., and Stansell, Stanley R., The Use of Discriminant Analysis in Forecasting Exchange Movements, Journal of International Business Studies 6 (Spring 1975): 33-50.

10. Frenkel, Jacob A., A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence, in The Economics of Exchange Rates. Jacob A. Frenkel and Harry G. Johnson, eds., Addison-Wesley, Reading, Massachusetts, pp. l-25.

11. Ghoshal, Animesh, A Forecasting Model for Foreign Exchange Rate Changes. Working Paper, DePaul University, 1981.

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13. Goodman, Stephen, Foreign Exchange Forecasting Techniques: Implication for Business and Policy, Journal of Finance 34 (May 1979): 415-427.

14. Kaserman, D.L., The Forward Exchange Rate: Its Determination and Behavior as a Predictor of the Future Spot Rate, Proceedings of the American Statistical Association (1973): 417-422.

15. Khoury, Sarkis J., and Ghoshal, Animesh, The Management of Foreign Exchange. Rink Riverside Printing, South Bend, Indiana, 1981, p. 88.

16. Kohlhagen, Steven W., The Forward Rate as an Unbiased Predictor of the Future Spot Rate. mimeo. The University of California-Berkeley, 1974.

17. Kohlhagen, Steven W., ‘The Behavior of Foreign Exchange Markets-A Critical Survey of the Empirical Literature, New York University Monograph Series in Finance and Economics, No. 1978-3. Solomon Brothers Center, New York, 1978.

18. Lachenbruch, P.A., An Almost Unbiased Method of Obtaining Confidence Intervals for the Probability of Misclassification in Discriminant Analysis, Biometrics 23 (December 1967): 639.

19. Levich, Richard M., The Efficiency of Markets for Foreign Exchange: A Review and Extension, in International Financial Management: Theory and Application. Donald Lessard ed., Warren Gorham and Lamont, Boston, 1979.

20. Levich, Richard M., Are Forward Exchange Rates Unbiased Predictors of Future Spot Rates?, Columbia Journal of World Business 14 (Winter 1979): 49-58.

21. Levich, Richard, On the Efficiency of Markets for Foreign Exchange, in International Economic Policy: An Assessment of Theory and Evidence. Rudiger Dornbusch and Jacob A. Frenkel, eds., Johns Hopkins University Press, Baltimore, 1979.

22. Longworth, David, Testing the Efficiency of the Canadian-U.S. Exchange Market Under the Assumption of No Risk Premium, The Journal of Finance 36 (March 1981): 43-48.

23. Murenbeeld, Martin, Economic Factors for Forecasting Foreign Exchange Rates, Columbia Journal of World Business 10 (Summer 1975): 81-95.

24. Rodriguez, Rita, Corporate Exchange Risk Management: Theme and Aberrations, The Journal of Finance 36 (May 1981): 427-439.

stability of predictors and the forecasting of foreign exchange rates

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