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International Journal of Academic Research in Business and Social SciencesJuly 2011, Vol. 1, No. 2

17 www.hrmars.com/journals

FORWARD RATE UNBIASEDNESS HYPOTHESISIN THE TUNISIAN EXCHANGE RATE MARKET

Dhekra AZOUZIPhD student in Finance and Member of IFGTunisia, Faculty of Management and Economic Sciences of

Tunis El Manar University.Email: [email protected]

Rohit Vishal KUMARAssociate Professor, Department of Marketing Management, Xavier Institute of Social Service

Jharkhand, IndiaEmail: [email protected]

Chaker ALOUIInternational Finance-Group Tunisia, Faculty of Management and Economic Sciences of Tunis El Manar

University, Tunis Cedex, Tunisia

ABSTRACT

Based on a linear framework, this paper aims to examine the relationship between future spot rates andforward exchange rates using USD-TND data, thanks to traditional regressions and to the Vector ErrorCorrection Model (VECM) in order to check if the Unbiasedness Forward Exchange Rate (UFER)hypothesis is satisfied and if the forward premiums contain valuable information useful to forecast thesubsequent path that will be taken by spot exchange rates. The empirical analysis reveals that the UFERhypothesis is rejected and that the forward premium is a crucial tool, at short term, to detect the futuremovements of spot exchange rates. A potential enrichment of such a paper will rely on a non linearframework.Keywords: UFER hypothesis, cointegration, VECM, Tunisia.

1. INTRODUCTION

Economists have been fascinated by anomalies for a long time – and one of the most undecipherableenigmas, in the economic literature, has been the forward premium puzzle. In fact, relentless waves ofresearches have been focused on studying the forward rate unbiasedness hypothesis (FRUH) whichbelieves that the forward exchange rate fully reflects the available information about the exchange rates(1988). The FRUH is based on the assumption that in the exchange rate market, individuals or businessarrange in advance to buy or sell the foreign exchange at a pre-determined rate for making futureinternational payments (Polito, 2001). This pre-determined rate of the future is assumed to reflect thecollective wisdom of the market regarding the spot rate that would be prevailing in the future. Thus, a



future exchange rate prevalent today can be looked upon as the spot rate of the future date. Under theassumption that the forward exchange market is efficient or rational, the spot rate prevailing at thefuture date should match with the future rate for that date prevailing in the market today. Moreformally “The forward exchange rate Ft observed for an exchange at time t+1 is the market determinedcertainty equivalent of the future spot exchange rate St+1” (Fama, 1984).

However, in reality, a major divergence is seen between the forward exchange rate and the spot rateprevailing at the future date and empirical findings have not been able to yield an irrefutablepresumption that the forward exchange rate should be an unbiased predictor of the future spotexchange rate giving rise, hence, to the forward premium puzzle.

The objective of this paper is to test the FRUH in the Tunisian Foreign Exchange Market and to check ifthe forward exchange premiums are useful to provide valuable information regarding the subsequentmovements of the spot exchange rate. The rest of this paper is organized as follows: section 2 reviewsthe major works done on the FRUH, section 3 provides a bird’s eye view on the Tunisian foreignexchange system, section 4 describes the dataset, defines the scope of this study which will rely only onthe linear framework and displays the characteristics of the exchange rates’ behavior on the light of themain results and section 5 is concluding and opening the door to future studies.

2. REVIEW OF LITERATURE

There exists an enormous literature available on whether the forward exchange rate is an unbiasedpredictor of the future spot exchange rate. Due to the vast nature of the literature present in the field,we only refer to some important work in this paper. We also divide the section into two parts – the firstis dealing with theoretical studies and their methodologies and the second is dealing with theexplanations for the forward premium puzzle.

2.1 Overview of Theoretical Studies

The earliest studies in the subject dealt with the regressions (on the logs) of the future spot exchangerate (st+k) on the current forward exchange rate (ft). An error term with a conditional mean of zero

( is also compulsory.

(1)

This is the traditional “level specification” in the literature. In this equation, to establish the FRUH it isrequired that the joint hypothesis (i) α=0 and (ii) β =1 holds simultaneously. Proponents of this specification have generally supported the FRUH hypothesis such as (Cornell, 1977; Frenkel, 1980;Levich, 1979). However, the model was found to be weak as both the forward and the spot rates wereshown to be non-stationary series. Subsequently, to resolve this problem, the model was modified andthe FRUH was tested by running the regression of the change in the future spot exchange rate (st+k-st) onthe Forward Premium (ft- st).

(2)

This specification has been referred to as the “Forward Specification” in the literature. Such a test isexpected to yield a coefficient of unity provided the forward markets are efficient. However, empirical



tests have overwhelmingly output a coefficient that is significantly less than unity and frequentlynegative (Bilson, 1981; Frenkel & Froot, 1989). This has been termed as the “forward premium puzzle”in the economic literature.

Proponents of the forward specification were of the view that since the forward premium specificationinvolves stationary I(0) variables, the resulting regression coefficient would be consistent (Isard, 1995; R.Meese, 1989; R. Meese & Singleton, 1982). They argue that since the variables in the level form are non-stationary I(1) variables, they have unit roots and therefore the levels regression is not a valid regressionequation because of the spurious regression problem as described in Granger and Newbold (1974).

Subsequent theoretical developments showed that even if the variables have unit roots, regressionwould not lead to inconsistent parameter estimation provided the variables are cointegrated. In fact,the regression estimates would be super consistent ((R. F. Engle & Granger, 1987; Hamilton, 1994). Haiet al. (1997) used dynamic OLS estimator on the “levels regression” to provide evidence that Ft and St+1

are cointegrated with cointegrating vector [1,-1]. These developments lead to a renewed interest in“level specification” as it was no longer needed to focus only on “forward premium” specification toevaluate market efficiency (Chakraborty & Haynes, 2005).

Subsequent work in the field has taken many different forms. Zellner (1962) has argued that since mostof the exchange rates are measured in terms of a common currency viz. the US Dollar, the disturbancesto the foreign exchanges would be correlated and hence Seemingly Unrelated Regressions (SUR) shouldprovide a better estimate than the regression approach. In testing level formulation, many authors havefound significant changes in the results when correlations across currencies are accounted for in themodel ((Bailey, Baillie, & McMohan, 1984; Barnhart & Szakmary, 1991; Bilson, 1981; Cornell, 1989;Evans & Lewis, 1995). The presence of non-normality in the foreign exchange data led Hodgson, Linton& Vorkink (2004) to apply SUR under elliptical symmetry and conclude that unbiasedness holds in theforeign currency markets.

Another area in which economists were puzzled was the topic of forecasting exchange rates. Meese andRogoff (1983) showed that a simple random walk model for forecasting foreign exchange was betterthan the standard empirical exchange rate models. Boothe & Glassman (1987) showed that theconditional distribution of nominal exchange rate changes is well described by a mixture of normaldistribution, and therefore a Markov Switching Model may be a logical characterization of exchange ratebehaviour. Various authors applied “Vector Equilibrium Correction Model” (VECM) and “MarkovSwitching VECM” (MS-VECM) to resolve the problem of forecasting exchange rates and found thatalthough Markov models fit the data very well, but they do not produce superior forecast (Engel, 1994;Engel & Kim, 1999; C. Engle & Hakkio, 1996; LeBaron, 1992). Clarida, Sarno, Taylor & Valente (2003)applied vector equilibrium correction models (VECM) and showed an improvement in prediction rates ofstandard models.

2.2 Explanations for the Forward Premium Puzzle

Much of the literature attempting to find out the reason(s) for coefficient deviation from unity — inboth forward and level specification — focused on explanations involving a risk premium in the forwardexchange market. Fama (1984) argued that the negative slope coefficient was due to the existence of atime varying risk premium. Froot and Frankel (1989), on the other hand, demonstrate that the bias is



primarily attributed to the systematic forecast error, which is negatively correlated with the forwardpremium, rather than to a forward market risk premium.

Cornell (1989) argued that the negative values of the slope are due to measurement errors in the dataused to test the FRUH. However, Bekaert and Hodrick (1993) demonstrated that Cornell’s objections donot significantly affect the slope coefficient. Hai, Mark and Wu (1997) tried to explain the negativeestimates of the slope coefficient by using a permanent-transitory component for spot and forwardexchange rates and concluded that the transitory component (consisting of risk premium) wasresponsible for the negative sign of the slope coefficient.

Baillie and Bollerslev (2000) suggested that the forward premium puzzle is due to small sample sizes andto very persistent autocorrelation of the forward premium. Chakraborty and Haynes (2005) suggestedthat the key reason for the coefficients, in either form (forward and level specification), to deviate fromunity is non-rationality of agents in the foreign exchange market. Their finding does not rule out thepossibility of the existence of a risk premium, but does indicate that the puzzle is not solely aconsequence of a risk premium.

The work of Frenkel & Poonawala (2006) created another milestone in the literature of exchange rateswhen they found that the bias in forward exchange rates were smaller for emerging currencies than foradvanced countries. They concluded that a time-varying risk premium may not be the explanation fortraditional findings of bias — because the currencies of emerging markets are comparatively riskier thanadvanced country currencies and therefore would carry a higher risk premium.

Work has been undertaken on country specific basis by many authors to approve or disprove the FRUHin their countries. Studies in the Indian foreign exchange markets concluded that the FRUH does nothold in the Indian foreign exchange markets (Kumar & Mukherjee, 2007; Vij, 2002). Wesso (1999)analyzed the South African Foreign Markets and also rejected the FRUH. Kan & O’Collaghan (2007)studied the FRUH for ten post-crisis Asian and Australian countries for the period from December 1996to May 2003 and found that the hypothesis is rejected for all countries except for Thailand. Bonga-Bonga (2009) used Smooth Transition Regression to assess the relationship between the Rand and USDollar and found that FRUH holds in the South African Markets for the period of January 1994 andNovember 2006.

Thus, as can be seen, comprehensive work has been done on FRUH, both at the various levels –international and country specific. However, in the Tunisian Markets, no work of significance has beenundertaken to understand the FRUH. In the next section, we present a brief overview of the TunisianForeign Exchange Markets.

3. OVERVIEW OF TUNISIAN FOREIGN EXCHANGE SYSTEM

Situated on the northernmost tip of the African continent, Tunisia obtained independence from Francein 1956 and became a republic in 1957. Today, Tunisia is an export –oriented country, in the process ofliberalizing its economy. Tunisia has close relations with the European Union – with whom it hasassociation agreement – and with the Arab world. It is also a member of Arab League and the AfricanUnion. It also maintains close economic ties with its former protector France. Tunisia has a diverseeconomy, with agriculture, mining, manufacturing, petroleum and tourism being the mainstay. Thegross domestic product, in 2009, was $ 49 Billion (official exchange rate) or $ 83 Billion (Purchasing



Power Parity). It has the highest per capita GDP amongst the African and the Middle-East countries. Itwas ranked the most competitive economy in Africa and 40th in the world by the World EconomicForum.

The European Union remains the largest trading partner of Tunisia accounting for 73% of TunisianImports and 75% of Tunisian Exports. This huge reliance on European Union has significant impacts onTunisian foreign exchange policy. Since 2002, the Central Bank of Tunisia has been intervening bydepreciating the Tunisian real effective exchange rate. The beginning of 2005 was marked by a giantstep toward trade liberalization interesting especially resident exporting companies which must alwaysrepatriate all the cash flows generated by the exports but which have been, since that date, able tomaintain 100% of these cash flows in foreign currency accounts. Banks have been also allowed tocontract unlimited sums of foreign currency loans.

Since the collapse of the Bretton Woods system (1973), Tunisia has adopted fixed or intermediaryexchange rate policy. However, the Tunisian foreign exchange policy can be broadly divided into fiveperiods (Safra & Ben-Marzouka, 1987). From 1973 to 1978, the Tunisian Dinar (TND) was pegged to theFrench Franc. This era was marked by a huge instability in the foreign exchange markets which ledTunisian authorities to use the Deutsch Mark as a benchmark currency (Sfaxi-Benhaji, 2008). From 1978to 1981, the Tunisian Dinar was pegged to a currency basket consisting of French Franc, the DeutschMark and the Dollar. From 1981 to 1986, the Tunisian central bank has been enlarging its currencybasket to provide more stability to the foreign exchange volatility. In 1986, recession and balance ofpayment crisis forced the authorities to devalue the domestic currency by 10% (Hanna, 2001). From1986 to 1989, the Central Bank of Tunisia has lowered the nominal effective exchange rate till the realeffective exchange rate achieved equilibrium. In the decade of the 90’s, the efforts of authorities werefocused on maintaining the stability of the real effective exchange rate. This period was marked by thedevelopment of the financial market in Tunisia. Since 2001 till date, Tunisia has enlarged the band offluctuation of the nominal exchange rate according to FMI's recommendations.

Given the above changes in the Tunisian Foreign Exchange markets and policies, it becomes necessary tounderstand the fluctuations in a better manner. Lack of any major study in Tunisia regarding the foreignexchange fluctuations, prompted us to study the subject of FRUH in the Tunisian Markets.

4. DATASET AND ANALYSIS

4.1. Traditional regressions

The dataset used in this study consists of 238 weekly observations of the TND-USD spot exchange rates,one-month, three-month, six-month and one-year forward exchange rates for the four-year span from01 April 2004 to 16 October 2008, yielding hence a total of 1190 observations. The series are expressedin logarithmic form to avoid the Siegel’s paradox (Baillie and McMahon, 1989). This dataset wasobtained from DataStreamTM, known by its important financial content of developed and emergingcountries. It is worthy of note that the Tunisian forward exchange market had been so rudimentarybefore 2004 and the decision to enlarge the scope of this market to cover financial transactions hasbeen taken in 2001 which has led trading in financial derivatives to be active three years later. Thesummary statistics of the dataset are provided, thanks to Gretl, in Table 1 which shows that the spot andforward exchange rates’ behavior is not anomalous since there is no evidence of skewness and/orexcess kurtosis. A plot of the spot versus one-month, three-month, six-month and one-year forward



rates is provided in Figures 1 to 4 witnessing that there is a turbulent behavior coupled with a markednegative trend particularly during two periods: from mid-2004 to 2005 and from 2006 to mid-2008 inthese TND/USD spot and forward exchange rates with no signal toward “mean reversion”. The mostsalient feature highlighted by figures 1 to 4 is the FRUH which appears a priori satisfied since there is aclear co-movement between spot and forward exchange rates, particularly at short term.

Table 1: Summary Statistics of Dataset:Weekly TND/USD spot and 1, 3, 6, and 12-month forward rates,

(April 2004 — October 2008, n = 238)

Forward rate(12 months)

Forward rate (6months)

Forward rate (3months)

Forward rate(1month)

Spot rateDescriptive Statistics

238

0.254570.262790.163990.32183

0.036594

0.14375

-0.59042

-0.36583

238

0.24897

0.256580.150230.32190

0.0398110.1599

-0.54765

-0.42148

238

0.245880.25152

0.143450.32100

0.0416410.16936

-0.51377

-0.48802

238

0.24363

0.24805

0.13920

0.32020

0.0429380.17624

-0.48688

-0.54952

238

0.24244

0.24659

0.13711

0.31954

0.043602

0.17984

-0.47589

-0.58203

Number of Observations

Mean

Median

Minimum

Maximum

Standard Deviation

Coefficient of Variation

Skewness

Excess Kurtosis

Based on the evolution of research in this field, the first step is to estimate equation (1) using theOrdinary Least Squares Method (OLS) which guarantees the Best Linear Unbiased Estimator (BLUE). Theresults of this regression are summarized in Table 2 below.



Table 2: Estimates of Level Specification

Horizon ̂ ̂ R² D-W

Waldstatistic

One month 0.0137771

(2.188)

(0.02967)

0.939473

(36.91)

(<0.00001)

0.854484 0.485117 3.21552

Three months 0.0363147

(3.1484)

(0.00187)

0.834159

(18.1531)

(<0.00001)

0.596406 0.141041 9.6307

Six months 0.0782997

(3.8970)

(0.00013)

0.64682

(8.2995)

(<0.00001)

0.246994 0.062030 19.6376

Twelve months 0.268926

(7.2521)

(<0.00001)

— 0.0764766

(— 0.5554)

(0.57933)

0.001673 0.034228 46.9562

Note: The numbers in parentheses are respectively t-statistics and p-values.

At the 5% level significance and for the one-month horizon, estimators are significantly very close totheir theoretical values with a high degree of fit and a Wald statistic lower than its critical value (5.99)indicating that the joint hypothesis α=0 and β=1 can not be rejected and proving hence that the FRUH is satisfied. For three and six month horizons, constant and slope estimators remain significantly close to 0and 1, respectively but the R² is decreasing and the Wald statistic is no longer adding a proof to acceptthe FRUH. However, for the longest horizon, the slope coefficient estimate is becoming negative, thevalue of R² tiny, which accuses equation 1 of bad specification, and all related digits contribute to rejectthe FRUH. These results reveal that there is a clear empirical support for the FRUH at the shortesthorizon and fall in line with the study run by Yang and Shintani (2006).



Figure 1: Spot versus Forward Rates (1 month horizon)

Figure 2: Spot versus Forward Rates (3 months horizon)





These figures demonstrate clearly that the spot exchange rate is well forecasted by the forwardexchange rates particularly at short horizons (1 month horizon) as it is shown in figure 1 since the twocurves are superimposed. A glance thrown on these four plots allows us to conclude that the path



drawn by future spot exchange rates begins to diverge from the other traced by the forward exchangerates from the forecast horizon of three months and the gap between these two variables is widen aslong as the horizon is increasing (Figures 2, 3 and 4).

To describe the spot and forward exchange rate behavior, a test for serial correlations is becomingcompulsory: the Durbin-Watson test is employed which shows that, for all horizons, there is evidence ofa positive serial correlation throwing doubts on the inconsistency of equation 1. It is also clear fromTable 2 that these regressions are spurious (Granger and Newbold, 1974) since a high degree of fit(R²=0.854484) is reported simultaneously with a low value of the Durbin-Watson statistic (d=0.48).These findings stress the importance of studying stationarity as a preliminary step in testing the FRUH.

For achieving that aim and after choosing, based on the Akaike’s Information criterion (AIC), an optimallag order of 2; three tests are used: the Augmented Dickey-Fuller (ADF, 1981), the ADF-GLS of Eliot,Rottenberg and Stock (1996) and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS, 1992) tests which applyto the constant-trend model and yield the results are displayed in Table 3.

Table 3: ADF, ADF-GLS and KPSS tests results

TND/USDSpot rate

ADF test

0H : Unit Root

ADF-GLS test

0H : Unit Root

KPSS test

0H : Stationarity

ADF level ADF firstdifference



Test statistic

5% criticalvalue

-1.40524

-2.873543

-7.83843

-2.873543

-1.3501

-2.89

-3.90241

-2.89

1.50581

0.146

0.14227

0.146

TND/USDone-monthforward rate

ADF test

0H : Unit Root

ADF-GLS test

0H : Unit Root

KPSS test

0H : Stationarity






Test statistic

5% criticalvalue

-1.42249

-2.873543

-7.90575

-2.873543

-1.37101

-2.89

-3.90747

-2.89

1.48895

0.146

0.138093

0.146

TND/USDthree-monthforward rate

ADF test

0H : Unit Root

ADF-GLS test

0H : Unit Root

KPSS test

0H : Stationarity




Test statistic

5% criticalvalue

-1.44555

-2.873543

-7.97275

-2.873543

-1.42425

-2.89

-3.95023

-2.89

1.44486

0.146

0.133314

0.146

TND/USD six-monthforward rate

ADF test

0H : Unit Root

ADF-GLS test

0H : Unit Root

KPSS test

0H : Stationarity

ADF first ADF first ADF first



These features approve the common result always revealed in previous studies: all the spot and forwardexchange rates are first difference stationary at 5% confidence level. This stationarity explains clearlywhy the one-month level specification has amazing outputs and does not contribute to hold the FRUH.To take into account this finding, we move to test equation 2, which results are portrayed in Table 4, as atrial looking for better ways to study the FRUH.

ADF level difference ADF level difference ADF level difference

Test statistic

5% criticalvalue

-1.44769

-2.873543

-8.02667

-2.873543

-1.50281

-2.89

-3.86226

-2.89

1.36622

0.146

0.130229

0.146

TND/USDtwelve-monthforward rate

ADF test

0H : Unit Root

ADF-GLS test

0H : Unit Root

KPSS test

0H : Stationarity




Test statistic

5% criticalvalue

-1.47492

-2.873543

-8.43421

-2.873543

-1.67011

-2.89

-4.17549

-2.89

1.15837

0.146

0.121978

0.146



Table 4: Estimates of equation 2

Horizon ̂ ̂ Waldstatistic

AdjustedR²

One month -0.00218197 (-1.424)

(0.1556)

2.01288(2.282)

(0.0234)

1.04045 0.017740

Three months -0.0093386

(-3.607)

(0.0004)

2.37086(4.587)

(<0.00001)

6.5557 0.082110

Six months -0.020149

(-5.522)

(<0.00001)

2.39324(6.053)

(<0.00001)

15.2484 0.144510

Twelve months -0.0402081

(-9.534)

(<0.00001)

3.09222

(12.125)

(<0.00001)

50.4702 0.441119

Note: The numbers in parentheses are respectively t-statistics and p-values.

In none of these four cases, the estimated slope is statistically or economically corroborating thetheoretical value; they are all significantly different from unity, the adjusted R² is very weak for the fourhorizons showing that this model is misspecified and Wald Statistic is in favor of the FRUH only for theone-month horizon. In other words, the forward exchange premium plays a crucial role as an unbiasedpredictor of the subsequent change of spot exchange rates, only at short term. For three, six and twelve-month horizons, the Wald test results reject strongly the possibility of using the forward premium toforecast the future fluctuation on spot rates. It is also worthy of note that the sign of these estimators isnot negative as it was frequently mentioned in literature, it is never significantly less than unity, itdeviates from unity without moving to the wrong direction. So, the forward premium puzzle persists butwith a new facet: the slope is upward-biased.

This stunning result has been reported recently by Frankel & Poonawala (2010, p. 595) who found thisbias less pronounced in emerging countries than in industrialized ones: the slope coefficients arepositive for 8 of 14 emerging countries (Czech Republic, Hungary, Indonesia, Kuwait, Philippines,Singapore, Taiwan and Thailand); these two researchers added that the average coefficient for emergingmarket economies is positive (0.0033) to emphasize their conclusion. Kan (2007, p. 309) has alsoobtained slope coefficients that are positive for the Asian post-crisis countries except for New Zealandand Australia. A glance thrown on constant coefficients reveals that they are all near zero.



To summarize, neither the naïve regression nor the forward specification are able to hold the FRUH andto forecast the future change of spot exchange rates. The promising means for improving chances ofsuccess in extracting useful information contained in forward premiums in order to find the optimalunbiased predictor of subsequent spot exchange rates and determine the path that they will takeconsist on estimating a Vector Error Correction Model (VECM) known as the natural extension of theVAR.

4.2. The term structure of the forward premium:

Based on the seminal work of Clarida & Taylor (1997), this VECM representation can be written as:

∆ (3)

where ty is a vector composed of the four TND/USD one, three, six and twelve-month forward rates

and the TND/USD spot rate and is the first-difference operator. According to Clarida & Taylor (1997),this specification can also be written as it follows:

+ (4)

where µ is a vector of constants, k is the lag order and is a vector of white noise error terms. is the

short-term adjustments’ matrix, is the cointegrating vectors’ matrix and is the matrix thatsummarizes the speed of adjustment parameters (Johansen, 1988).

The first step in the VECM estimation stage is to identify the number of cointegration relationships inthe system. In order to run the cointegration relationship, the number of lag order was determinedusing Akaike’s Information Criterion (AIC), Schwarz Information Criterion (SC) and Hannan-QuinnInformation Criterion (HIC). All the three criterion indicated that the lag order is two (2) in the system.

To determine whether cointegration was present in the system, we used the Engle-Granger test. Resultsof cointegration regression and Dickey-Fuller test on residuals are provided in Table 5.

Table 5: Engle-Granger cointegration results

Coefficient Standard error T statistics p-value

Constant -0.000154376 0.000135207 -1.142 0.2547

One-month



forward rate 1.67630 0.0332368 50.44 2.30e-127 ***

Three-monthforward rate

-0.783006 0.0627256 -12.48 1.01e-027 ***

Six-month forwardrate

0.0938222 0.0362321 2.589 0.0102 **

Twelve-monthforward rate

0.0132467 0.00749296 1.768 0.0784 *

Dickey-Fuller Test on Residuals

Test statistics Critical value 5% p-value

Test with constant -5.48844 -2.89 0.001454

The scrutiny of Table 5 indicates that there are cointegrating relationships present in the systembetween the TND/USD spot exchange rate and the one, three, six and twelve-month forward exchangerates.

In order to check for the cointegration rank we used both the Trace Test and the Maximum EigenvalueTest and both these test indicated that two (2) co-integrating equations are present in the system at 5%level of significance. Table 6, presents the results of the test.

Table 6: Cointegration rank test

Rank Eigenvalue Trace test p-value max test p-value

0 0.151695 93.17080

(69.81889)

0.0002 * 38.33192

( 33.87687)

0.0137 *



Note: numbers in parentheses are the corresponding critical values at 5% confidence level.

At this stage, it becomes possible to answer to the crucial question focusing on whether the termstructure of forward premiums is informative i.e. if it contains so valuable information that can be usedto predict the future fluctuation of the spot exchange rate thanks to the VECM estimation.

The unrestricted adjustment coefficients and the normalized cointegration vector matrix arerepresented in table 7 and 8 respectively.

Table 7: Unrestricted Adjustment Coefficients (Alpha)D(Spot Rate) - 0.000685 - 0.000229 0.000220 - 0.001303 0.000000

D(1 Month Forward Rate) - 0.000679 - 0.000262 0.000252 - 0.001301 0.000000

D(3 Months Forward Rate) - 0.000719 -0.000233 0.000303 - 0.001299 0.000000

D(6 Months Forward Rate) - 0.000828 - 0.000284 0.000352 - 0.001287 0.000000

D(12 Months Forward Rate) - 0.000480 - 0.000250 0.000676 - 0.001286 -0.000004

D indicates the first difference.

Table 8: Unrestricted Cointegrating Coefficients Normalized (Beta)

Spot Rate

1 Month

Forward Rate

3 Months

Forward Rate

6 Months

Forward Rate

12 Months

Forward Rate

1544.222 1333.5880 - 2552.786 3214.099 - 868.8094

- 4661.281 10196.44 - 8215.903 2812.749 - 115.3909

- 1347.114 27.90096 - 3089.394 2079.039 - 323.2004

1 0.116995 54.83888

(47.85613)

0.0096 * 28.98041

(27.58434)

0.0329 *

2 0.081097 25.85848

(29.79709)

0.1330 19.70587

(21.13162)

0.0782

3 0.026054 6.152601

(15.49471)

0.6775 6.151157

( 14.26460)

0.5939

4 6.20E-06 0.001444

( 3.841466)

0.9681 0.001444

(3.841466)

0.9681



- 2783.167 3034.097 - 533.1622 733.5367 82.6483

2874.308 - 3127.136 - 906.5622 1176.002 - 11.33893

The product of these two matrix ∏ generates the long-run cointegrating matrix able to capturethe information about long-run relationships existing between the different variables.The VECM estimation results performed thanks to Eviews 6 are presented in table 9.

Table 9: VECM (k=2, g=5, r=2) estimation result, unrestricted, unconstrained,(Sample: 1 April 2004 – 16 October 2008, weekly TND/USD spot and 1, 3, 6,

cand 12-month forward rate)Standard errors in ( ) &tstatistics in [ ]

Error Correction: D(ST) D(FWD1) D(FWD3) D(FWD6) D(FWD12)

CointEq1 -0.825903 -0.710139 -0.970169 -0.966274 0.468724

(2.38282) (2.38276) (2.38883) (2.39871) (2.47458)

[-0.34661] [-0.29803] [-0.40613] [-0.40283] [ 0.18942]

CointEq2 1.447082 1.249258 1.856694 1.609498 0.174998

(4.90366) (4.90355) (4.91604) (4.93637) (5.09251)

[ 0.29510] [ 0.25477] [ 0.37768] [ 0.32605] [ 0.03436]

D(ST(-1)) 4.621687 4.413470 4.297900 4.101666 2.913420

(3.60456) (3.60447) (3.61366) (3.62860) (3.74337)

[ 1.28218] [ 1.22444] [ 1.18935] [ 1.13037] [ 0.77829]

D(ST(-2)) 7.682531 7.749136 7.710633 7.732709 5.684712

(3.77446) (3.77437) (3.78398) (3.79963) (3.91982)

[ 2.03540] [ 2.05309] [ 2.03770] [ 2.03512] [ 1.45025]

D(FWD1(-1)) -5.494600 -5.365428 -5.462634 -5.382084 -4.936838

(5.57363) (5.57350) (5.58770) (5.61080) (5.78828)

[-0.98582] [-0.96267] [-0.97762] [-0.95924] [-0.85290]



D(FWD1(-2)) -9.239348 -9.394856 -9.403448 -9.380762 -6.672687

(5.37790) (5.37777) (5.39147) (5.41377) (5.58501)

[-1.71802] [-1.74698] [-1.74413] [-1.73276] [-1.19475]

D(FWD3(-1)) 1.510055 1.660324 1.939037 2.030136 2.828119

(4.06620) (4.06610) (4.07646) (4.09331) (4.22279)

[ 0.37137] [ 0.40833] [ 0.47567] [ 0.49596] [ 0.66973]

D(FWD3(-2)) 2.429742 2.473568 2.496624 2.270773 1.714696

(3.64834) (3.64826) (3.65755) (3.67267) (3.78884)

[ 0.66599] [ 0.67801] [ 0.68259] [ 0.61829] [ 0.45256]

D(FWD6(-1)) -0.709210 -0.797794 -0.873670 -0.791664 -0.504260

(2.02507) (2.02503) (2.03018) (2.03858) (2.10306)

[-0.35021] [-0.39397] [-0.43034] [-0.38834] [-0.23977]

D(FWD6(-2)) -0.822586 -0.777697 -0.751908 -0.531774 -0.486507

(1.70244) (1.70240) (1.70674) (1.71380) (1.76801)

[-0.48318] [-0.45682] [-0.44055] [-0.31029] [-0.27517]

D(FWD12(-1)) 0.068901 0.084216 0.091297 0.037921 -0.292882

(0.37721) (0.37720) (0.37816) (0.37972) (0.39173)

[ 0.18266] [ 0.22327] [ 0.24143] [ 0.09986] [-0.74766]

D(FWD12(-2)) -0.094761 -0.094170 -0.096993 -0.139958 -0.280980

(0.28354) (0.28353) (0.28426) (0.28543) (0.29446)

[-0.33421] [-0.33213] [-0.34122] [-0.49034] [-0.95422]

C -1.66E-05 -2.76E-05 -4.05E-05 -4.87E-05 -2.16E-05



(0.00057) (0.00057) (0.00058) (0.00058) (0.00060)

[-0.02898] [-0.04805] [-0.07035] [-0.08419] [-0.03617]

By looking at the first two lines of the table 9 which report the estimated coefficients of the errorcorrection terms in the VECM equations, it appears that they are not statistically significant. So, thesevariables are weakly exogenous and no adjustment of the disequilibrium towards the long-runequilibrium state is possible: the term structure of forward premium does not contribute to explain thedeviations of spot exchange rates at the level of 10%.

Throwing a glance on the coefficients of the first difference, only ST and FWD1 lagged two-period arestatistically significant, respectively, in FWD1, FWD3 and FWD6 equations and ST, FWD3, FWD6 andFWD12 equations. Hence, there is a short-run causality between all these variables. To give more proofto this finding, we suggest performing a standard Granger causality test as it is shown in Table 10.

Table 10: Granger Causality Test(4 lags)

Null Hypothesis: F-Statistic Prob.

FWD12 does not Granger Cause FWD1 0.72601 0.5750






ST does not Granger Cause FWD1 2.30417 0.0593

FWD1 does not Granger Cause ST 2.35053 0.0551








Table 4 reveals that at the 10% level of significance, there is a bi-directional short-run causality betweenthe spot and the one month horizon forward exchange rates. Besides, the null hypotheses of “FWD1does not Granger Cause FWD12”, “FWD3 does not Granger Cause FWD12”, “FWD6 does not GrangerCause FWD12”, “ST does not Granger Cause FWD12” are rejected at the same level of significance.These results confirm partly the VECM’s findings about the existence of short-run causality at the 10%level of significance.

To check the validity of the VEC specification, we choose to report some diagnostic tests in Table 11.Table 11: The VECM diagnostic checks








Type of Test p-value

Equation 1 Equation 2 Equation 3 Equation 4 Equation 5

R² 0.040431 0.039972 0.037424 0.037368 0.049072

LM Autocorrelation Test (4 lags) 0.3640

Normality test :

Jarque-Bera (Lütkepohl, 1993) 0.0037 0.0000 0.0000 0.0000 0.0000

ARCH 0.0000

ADF on residuals 0.0000 0.0000 0.0000 0.0000 0.0000



The first remark concerns the R² which is very small reflecting the fact that the exchange rates cannot bepredicted corroborating hence, a priori, the “holy” Random Walk always fiercely defended by Meeseand Rogoff (1983) and their disciples. The residual heteroskedasticity test on the levels and squares ofthe residuals indicate that the system has heteroskedasticity. Further test of normality on the residualsshowed that the residuals are not normally distributed. This does lead us to question the stability of thesystem. However, we turn our focus on to stationarity of residuals and find that the Augmented Dickey-Fuller Test rejects the hypothesis of unit root on the residuals. This leads to the conclusion that theseries are stationary and convergent in nature. Analysis of partial autocorrelation and correlation run onthe residuals of the system, thanks to the LM autocorrelation test, lead to the conclusion that theresiduals are all white-noise process. The BDS test is approving this finding since the null hypothesis of“Residuals are independent and identically distributed” is not rejected at the 5% level of significance.This clearly indicates that the system is stable in spite of some issues with normality andheteroskedasticity being present.

It is also worthy to note that the estimated system is stationary since all the roots of the characteristicpolynomial lie inside the unit circle.

BDS test:Bootstrapprob.

(Epsilon=0.7)

Dimension

2

3

4

5

6

0.5912

0.1480

0.2808

0.1136

0.1632

0.6152

0.1632

0.2592

0.1176

0.1576

0.6888

0.1816

0.3224

0.1552

0.2304

0.4600

0.1040

0.1968

0.1168

0.2000

0.5504

0.0904

0.1760

0.0656

0.0904

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Inverse Roots of AR Characteristic Polynomial



Finally, we mention that the stability of the system is apparent when we look at the impulse responsegraphs presented in the appendix. The impulse response graphs have been developed by providing a 1s.d. Cholesky Innovation Shock on each of the variables. As can be seen from the graphs, the systemreturns to a stable state, albeit the speed of adjustment leads a lot to be desired.

5. CONCLUSION

The forward premium anomaly has been the hard core of a tremendous number of studies whichfocused in demystifying this puzzle and resolving its mysterious facts particularly in developed countriesforgetting hence to run similar researches in emergent countries. It is only recently that researchershave been inclined toward these countries; such a situation leads us to devote this paper not only todetect this famous bias in Tunisia but also to check if the term structure of the forward premiumcontains valuable information useful to forecast the future path of subsequent spot rates. To achievethese aims, this study uses weekly USD-TND data over the period spanning from the 1st April, 2004 tothe 16th October, 2008 for forecasting horizons ranging from one to twelve months and it employstraditional regressions (“naïve regressions” and “forward regressions”) and the Vector Error CorrectionModel (VECM) thanks to Gretl 1.8.7 and Eviews 6.

Built in a linear framework, this study reconfirms the results obtained previously in anterior researchesand adds proof to the quasi unanimity rejecting the Forward Rate Unbiasedness Hypothesis (FRUH). Bygoing through the VECM, there is econometric evidence showing that, at short-run, the term structureof forward exchange premium contains precious information useful to forecast the subsequentfluctuations of the spot foreign exchange rates. But, at long-run, there is no causality between variablesand consequently no adjustment of disequilibria to the equilibrium state.

However, it is judicious to mention that to control for possible non linearity in the foreign exchangerates, a similar study based on a non linear framework would take place and enrich the whole body ofstudies focusing on the forward premium anomaly in emergent countries.



.0084

.0085

.0086

.0087

5 10 15 20 25 30 35 40 45 50

Response of F1M to SPOT

.0083

.0084

.0085

.0086

.0087

.0088

5 10 15 20 25 30 35 40 45 50


.0083

.0084

.0085

.0086

.0087

.0088

5 10 15 20 25 30 35 40 45 50


.0084

.0085

.0086

.0087

.0088

.0089

5 10 15 20 25 30 35 40 45 50

Response of F1Y to SPOT

Response to Shock in Spot Rate



-.0024

-.0020

-.0016

-.0012

-.0008

-.0004

.0000

5 10 15 20 25 30 35 40 45 50

Response of SPOT to F1M

-.0020

-.0016

-.0012

-.0008

-.0004

.0000

.0004

5 10 15 20 25 30 35 40 45 50

Response of F3M to F1M

-.0016

-.0012

-.0008

-.0004

.0000

.0004

5 10 15 20 25 30 35 40 45 50


-.0016

-.0012

-.0008

-.0004

.0000

.0004

5 10 15 20 25 30 35 40 45 50

Response of F1Y to F1M

Response to Shock in 1 Month Forward Rate

-.0012

-.0010

-.0008

-.0006

-.0004

-.0002

.0000

5 10 15 20 25 30 35 40 45 50


-.0010

-.0008

-.0006

-.0004

-.0002

.0000

.0002

5 10 15 20 25 30 35 40 45 50


-.0006

-.0004

-.0002

.0000

.0002

.0004

.0006

5 10 15 20 25 30 35 40 45 50


-.0002

.0000

.0002

.0004

.0006

.0008

.0010

5 10 15 20 25 30 35 40 45 50


Response to Shock in 3 Months Forward Rate



-.0004

-.0003

-.0002

-.0001

.0000

5 10 15 20 25 30 35 40 45 50


-.0004

-.0003

-.0002

-.0001

.0000

5 10 15 20 25 30 35 40 45 50


-.0003

-.0002

-.0001

.0000

.0001

.0002

5 10 15 20 25 30 35 40 45 50


.0007

.0008

.0009

.0010

.0011

.0012

.0013

.0014

5 10 15 20 25 30 35 40 45 50


Response to Shock in 6 Months Forward Rate



.0000

.0001

.0002

.0003

.0004

.0005

.0006

.0007

.0008

.0009

5 10 15 20 25 30 35 40 45 50

Response of SPOT to F1Y

.0000

.0001

.0002

.0003

.0004

.0005

.0006

.0007

.0008

5 10 15 20 25 30 35 40 45 50

Response of F1M to F1Y

.0000

.0002

.0004

.0006

.0008

5 10 15 20 25 30 35 40 45 50


.0000

.0001

.0002

.0003

.0004

.0005

.0006

.0007

.0008

.0009

5 10 15 20 25 30 35 40 45 50


Response to Shock in 1 Year Forward Rate



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