Testing Forward Rate Unbiasedness in India an Econometric Analysis of Indo-US Forex Market

International Research Journal of Finance and Economics ISSN 1450-2887 Issue 12 (2007) EuroJournals Publishing, Inc. 2007 http://www.eurojournals.com/finance.htm Testing Forward Rate Unbiasedness in India an Econometric Analysis of Indo-US Forex Market Rohit Vishal Kumar Reader, Department of Marketing & Finance Xavier Institute of Social Service P.O. Box No: 7, Purulia Road Ranchi 834001, Jharkhand, India E-mail: rohitvishalkumar@yahoo.com Tel: (91-651) 220-4456 / 0873 Ext. 308, Tel: (91) 99341-11169 Soumya Mukherjee PGD (Finance) 4th Semester Student, Xavier Institute of Social Service Abstract The Unbiased Forward Rate Hypothesis (UFH) states that the forward exchange rate of any foreign currency must be an unbiased predictor of the future spot rate. In developed economies, considerable empirical work has been undertaken by researchers to test the validity of UFH; however the results have been quite mixed. In the Indian context, little empirical (or even theoretical) work has been undertaken to test/examine/investigate the validity of UFH in the Indian forex market. In this paper, we attempt to reexamine in Indian context the familiar relationship between forward and future spot rate. Using the rates for the US Dollar on a monthly basis, we use level specification to test for UFH in the Indo-US foreign exchange rate market. Cointegration tests are performed to confirm the legitimacy of forward rate and spot rate being included in regression. Evidence of serial correlation is found and models for correction of serial correlation are used. The data taken from the Reserve Bank of India covers a period from September 2000 to January 2007. Our investigations reveal that the Indian forex market does not fully support the UFH. For the entire sample period, the evidences indicate that even though the current forward rate has a significant impact in predicting the future spot rate, however, enough variability remain to make the predictions a suspect. Based on our evidences, we highlight some reasons as to why the UHF fails in the Indian forex market and suggest areas for further research. Keywords: Foreign Exchange (F31), Econometrics (C01), Financial Markets (D53) 1. Introduction There is a substantial empirical literature investigating what is called the forward exchange rate unbiasedness hypothesis, according to which forward exchange rates represent unbiased forecasts of future spot exchange rates. In this context the western world has developed significant theoretical model which uses various econometric techniques to test whether the Unbiased Forward Rate Hypothesis (UFH) holds in forex markets and whether forward exchange rate can predict future spot exchange rate in an unbiased manner. UFH argues that the forward rate fully reflects available

International Research Journal of Finance and Economics - Issue 12 (2007) 57 information about the exchange rate expectations (Bradford Cornell, 1977) which is a view also supported by market efficiency. Market efficiency states that the current prices reflect all available information. When this is applied to the foreign exchange market, it implies that expectation of the economic agents about future values of exchange rate determinants are fully reflected in the forward rates (Thomas C Chiang, 1988). In the Indian context little work has been done to test UFH and market efficiency. Madhu Vij (2002) used forward specification to test the UFH in Indian forex market for the period October 1997 to June 2001 and found out that forward rate is not an unbiased predictor of the future spot rate. Sharma & Mitra (2006) also tested the UFH in Indian forex market by using the forward specification. The results of their study do not support the hypothesis that forward rate is an unbiased predictor of future spot rate in Indian forex market. Results of another study done by Frankel and Poonawala (2006) using the forward specification for the period October 1997 to December 2004 shows a slope coefficient of 3.53, thereby rejecting UFH in Indian market. In this study presence of serial correlation was also found, thereby casting doubt on the efficiency of the results. Exchange rate of Indian Rupee (INR) is largely market determined. The intervention of the central bank of the country Reserve Bank of India (RBI) - in forex market does not make a significant impact in determination of forward premium and is only aimed at smoothing the volatility in foreign exchange market. Forward premium is more and more being influenced by demand and supply factors. Sharma and Mitra (2006) found out that the main determinants of forward premium of the US Dollar vis-à-vis Indian rupee are interest rate differential in the inter bank market of the two economies coupled with capital receipts and excess of current accounts payments on accounts of imports in relation to exports. Information regarding these three factors is normally available to the market players at the time of determining forward exchange rate. The forward exchange rate is determined by the market after taking into account all the information available at that time. Thus, it can be argued that the forward rate already contains information relating to these factors. If forward market in India is efficient in the sense that market players optimally process all available information at the time of determining the forward rate, then forward rate should be able to predict future spot rate with fair accuracy, if not perfectly. In the contrary, if there are deviations in future spot rate from forward rate, it can be attributed to a time varying risk premium, or to any other imperfection(s). The objective of this paper is to test UFH in Indian forex market for the US Dollar vis-à-vis Indian Rupee using detailed econometric techniques. In order the UFH to hold the market has to be efficient in the sense that the market participants are risk neutral (no risk premium) and form expectations in a "rational" manner; the expected values of exchange rate determinants are explicitly discounted to the present values; and all the information relevant for predicting future spot exchange rates is fully reflected in the current forward exchange rates. The paper is organized as follows: Section 2 reviews previous studies that have been conducted to test the validity of the UFH. Section 3 specifies the basic regression model and addresses the issues of serial correlation and cointegration in time series analysis. Section 4 reports the results from the regression analysis. Section 5 concludes the paper. 2. Review of Literature There exists an enormous literature on whether the forward exchange rate is an unbiased predictor of future spot exchange rates. The earliest studies (Bradford Cornell, 1977, J A Frenkel, 1980, R M Levich, 1979) involves regression of the log of the future spot exchange rate, S t+1, on the log of the current forward exchange rate, F t. This has been referred to as the level specification. The results of these studies generally support the UFH in the sense that the regression typically yields a coefficient close to unity.

58 International Research Journal of Finance and Economics - Issue 12 (2007) Later studies (John Bilson, 1981, Eugene F Fama, 1984, J A Frenkel and K A Froot, 1989) tested UFH by running regression of the future change in the log of the spot exchange rate, S t+1, on the forward premium, F t S t that is on the log of the forward exchange rate minus the log of the spot exchange rate. This has been referred to as the forward premium specification. Such a test is expected to yield a coefficient of unity if markets are efficient. Instead, regression estimates of this forward premium specification yield a coefficient that is significantly less than unity and frequently negative. In econometrics this phenomenon has been termed as the "Forward Premium Puzzle". Those who followed the forward specification were of the view that since the forward premium form involves stationary I(0) variables, the resulting regression coefficient would be consistent (Peter Isard, 1995, Richard Meese, 1989, Richard Meese and K Singleton, 1982). They argued that since the variables in the level form the future spot and current forward exchange rates are non-stationary I(1) variables, they have unit roots and therefore the levels regression is not a valid regression equation because of the spurious regression problem as described in Granger and Newbold (1974) Subsequent theoretical development in the field of econometrics showed that even if the variables have unit roots, it will not lead to inconsistent parameter estimates provided the variables are cointegrated. In fact, the regression estimates would be super consistent (Robert F Engle and C W J Granger, 1987, James D Hamilton, 1994). Weike Hai et al. (1997) used dynamic OLS estimator on the levels regression to provide evidence that F t and S t+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 to evaluate market efficiency (Avik Chakraborty and Stephen E Haynes, 2005). Much of the literature attempting to find out the reason(s) for coefficient deviation from unity in both forward and level specification focused on explanations involving a risk premium in the forward exchange market. Fama (1984) argued that the negative slope coefficient was due to the existence of a time varying risk premium. Frenkel & Poonawala (2006) found that the bias in forward exchange rate were smaller for emerging currencies than for currencies of advanced country. They concluded that a time-varying exchange risk premium may not be the explanation for traditional findings of bias - because the currency of emerging markets are comparatively more risky than advanced country currencies and therefore would carry a higher risk premium. Froot and Frankel (1989), on the other hand, demonstrate empirically that the bias can be primarily attributed to the systematic forecast error, which is negatively correlated with the forward premium, rather than to a forward market risk premium. Another interpretation is given by Cornell (1989) who argued that the negative values of the slope coefficient are due to measurement errors in the data used to test the UFH. However, Bekaert and Hodrick (1993) demonstrate that Cornell s objections do not significantly affect the slope coefficient. Another study done by Baillie and Bollerslev (2000) suggest that the forward premium puzzle is due to small sample sizes and to very persistent autocorrelation of the forward premium. Chakraborty and Haynes (2005) suggested that the key reason for the coefficients in either form (forward and level specification) to deviate from unity is non-rationality of agents in the foreign exchange market. Their finding does not rule out the possibility of the existence of a risk premium, but does indicate that the puzzle is not solely a consequence of a risk premium. In the Indian context little work has been done to test UFH and market efficiency. Vij (2002) used forward premium specification to test the UFH in Indian forex market for the period October 1997 to June 2001 and found out that forward rate is not an unbiased predictor of the future spot rate. Sharma & Mitra (2006) tested the UFH in Indian forex market by using the forward premium specification over the period September 2000 to December 2005. They found out that UFH does not hold good for Indian market. The results of the study by Frankel and Poonawala (2006) using forward premium specification for the period October 1997 to December 2004 also rejects the UFH in India. In this paper we use the level specification to test the UHF in the Indian market.

International Research Journal of Finance and Economics - Issue 12 (2007) 59 3. Model Specifications The level specification is the regression relationship of the log of the future spot exchange rate S t+1 on the log of the current forward exchange rate F t. The relationship is expressed as: S t = a + bf t+1 + e t+1 where a is the intercept, b is the slope coefficient, e and is a random error term. The equation expresses the notion of rational expectations with no risk premium. The assumption is, therefore, that market participants are risk neutral and form expectations in a rational manner or that the expected values of exchange rate determinants are explicitly discounted to the present values. The relevant information for predicting future spot exchange rates is fully reflected in the current forward exchange rate. Therefore, testing the hypothesis of forward market efficiency is equivalent to testing the joint hypothesis a = 0 and b = 1 and E[e t+1 ] = 0. Failure to reject the joint hypothesis implies that the forward rate determined at time t is an unbiased predictor of the spot rate for time t+k. However, statistical rejection of this joint hypothesis means either that the market is inefficient or that the specification of the model is incorrect, or both. For correct interpretation of time series data, it is required that the time series under consideration are stationary in nature or in other words, the time series should have a constant unconditional mean and variance over time. For many a years, econometricians achieved stationarity by simply removing drifts and trends from the data. However, this practice did not always achieve stationarity especially in the case of integrated variables where the presence of unit root grave rise to stochastic trends as opposed to pure deterministic trends leading to nonsense or spurious regression (C W J Granger and P Newbold, 1974, Charles R Nelson and Charles I Plosser, 1982). Later works or Granger (1981) and Engle & Granger (1987) formally established the idea that two random-walk and non-stationary economic series can have a linear combination which is stationary in nature which is termed as cointegration. Cointegrated series could be tested for existence of equilibrium relationships within a fully dynamic framework. Valid estimation of the level specification requires cointegration between the future spot and current forward exchange rates. To identify cointegration relationship between the future spot rate and the current forward rate we apply two cointegration tests, namely the Johansen Test (S Johansen, 1994, 1988) and the Engle-Granger Test (Robert F Engle and C W J Granger, 1987). While fitting a classical regression equation it is usual to assume that the disturbance term represents the net effect upon the dependent variable of a large number of subsidiary variables which, individually are of insufficient importance to be included in the systematic part of the model. The error terms are therefore assumed to be of independently distributed. However, while analyzing time series data, this assumption is frequently violated giving rise to the problem of serial correlation. In the presence of serial correlation, the OLS estimates will be inefficient, though they will still be unbiased and consistent. This consistency property does not hold, however, if lagged variables are included as explanatory variables. In such a case, OLS estimates of the parameters, and forecasts based on them, will be biased and consistent. In econometrics, the traditional means of representing the inertial properties of the disturbance process has been to adopt a first-order autoregressive model, or AR(1) model. The two common procedure that are followed are the Cochrance-Orcutt (1949) and the Hilderth Lu (1960) procedure. Some authors are of the opinion that Hilderth-Lu is more efficient than the Cochrane-Orcutt procedure as the former selects the global minima for ESS by searching for the value of r over the entire range -1 and +1, whereas, since the later iterates to a local minima for ESS (r), it might miss the global minima if there is more than one local minima. Ramanathan (1995) suggests that a more desirable procedure is to search in broader steps using the Hilderth Lu procedure and then fine-tune it using the Cochrane Orcutt technique. For the purpose of this paper we have used the suggestion as provided by Ramanathan. The estimates thus obtained are believed to be consistent and asymptotically more efficient than ordinary least square estimates.

60 International Research Journal of Finance and Economics - Issue 12 (2007) 4. Empirical Results Monthly Indian exchange rate data on spot rate and forward rate over the period August of 2000 to January of 2007 are used to estimate the equation. Thus a total of 77 observations are used for the test. All tests are conducted over the full sample. Both spot rates and thirty-day forward rates are defined as the units of local currency per unit of US dollar and are expressed in terms of natural logarithms. All the data refer to the end of the month and are taken from the data bank of the Reserve Bank of India. We do find a few dates, for both the spot and forward exchange data, where the exchange rate is missing. In such cases we have taken the data available for the nearest date of the same month. The summary statistics of the dataset is provided in Table 1 and a plot of the spot vs. the forward rate is provided in Figure 1. Table 1: Summary Statistics of Dataset (Period: August 2000 to January 2007) Descriptive Statistics Spot Rate Forward Rate Number of Observations 77 77 Mean 46.17 46.28 Median 46.15 46.25 Minimum 43.48 43.522 Maximum 49.04 49.28 Standard Deviation 1.621 1.6685 Coefficient of Variation 0.03511 0.036053 Skewness 0.0068495 0.047162 Excess Kurtosis -1.0362-1.0459 Figure 1 : Spot Vs. Forward Rate Though it is generally accepted in the literature that both spot and forward exchange rates are indeed I(1), we started by performing the unit-root tests. Presence of unit root in In(S t+1 ) and In(F t ) was tested using the Augmented Dickey-Fuller test both with constant and with constant and trend

International Research Journal of Finance and Economics - Issue 12 (2007) 61 (1979, 1981a, 1981b), and the Phillips Perron Test both with stationarity and trend stationarity (1988). The null hypothesis for all these tests is that the time series is a unit root process (a = 1). The results of these tests are reported in Table 2 & 3 respectively. Selection of p values (for ADF) under the null hypothesis was done using the Akaike and the Hannan Quinn information criteria - both of which suggested the optimal p level as one. Table 2: Augmented Dickey Fuller Test Results Spot Rate Test Statistic 5% 10% Asymptotic p-value R-square Test with constant -1.44767-2.89-2.58 0.5603 0.07005 Test with constant and trend -2.37637-3.40-3.13 0.392 0.11514 Forward Rate Test Statistic 5% 10% Asymptotic p-value R-square Test with constant -1.50014-2.89-2.58 0.5338 0.09815 Test with constant and trend -2.61892-3.40-3.13` 0.2717 0.15583 Table 3: Phillips Perron Test Results Spot Rate Alpha Test Statistics 5% 10% p value Unit Root 0.9618-3.70-14.51-11.65 0.58 Unit Root With Drift 0.8933-9.58-21.78-18.42 0.47 Forward Rate Alpha Test Statistics 5% 10% p value Unit Root 0.9634-3.70-14.51-11.65 0.58 Unit Root With Drift 0.9022-8.97-21.78-18.42 0.52 In both the cases it was seen that the null hypothesis was accepted and as such the presence of unit root in both spot and forward rate was confirmed. In the presence of unit-root, the regression results will only be consistent and unbiased if there exists cointegration relationship between S t+1 and F t. To test the cointegration requirement, Johansen's test (1994, 1988) and Engle-Granger test (1987) are applied to the exchange rates in our sample. Results are presented in Table 4 for Johansen s test and Table 5 for Engle-Granger test. In Table 4, trace statistics indicate that cointegrating relations exist at the conventional level of significance between the future spot rate and the current forward rate. Table 4: Johansen Test Results (Cointegration between S t+1 and F t ) Rank Eigenvalue Trace test p-value Lmax test p-value 0 0.9860063985 326.57 [0.0000] 324.46 [0.0000] 1 0.0274527411 2.1156 [0.1458] 2.1156 [0.1458] Critical Values No restriction on Intercept R Test Statistic 20% 10% 5% H 0 : There are r cointegrated vector 0 324.50 10.10 12.10 14.00 H 1 : There are r+1 cointegrated vectors 1 2.1 1.7 2.8 4.00 H 0 : There are at most r cointegrated vector 0 326.60 11.20 13.30 15.20 H 1 : There are 2 cointegrated vectors 1 2.1 1.7 2.8 4.00 Restriction on Intercept R Test Statistic 20% 10% 5% H 0 : There are r cointegrated vector 0 324.50 10.70 12.80 14.60 H 1 : There are r+1 cointegrated vectors 1 2.1 4.9 6.7 8.1 H 0 : There are at most r cointegrated vector 0 326.60 13.00 15.60 17.80 H 1 : There are 2 cointegrated vectors 1 2.1 4.9 6.7 8.1

62 International Research Journal of Finance and Economics - Issue 12 (2007) In case of the Engle-Granger test there is evidence for a cointegrating relationship if the unitroot hypothesis is not rejected for the individual variables, and the unit-root hypothesis is rejected for the residuals from the cointegrating regression. It may be noted that from the Augmented Dickey- Fuller test previously conducted, the null hypothesis is rejected for the individual variables. Conducting Dickey-Fuller test on the residuals with the unit root null hypothesis led to the conclusion that the unit root hypothesis is rejected for the residuals from the cointegrating regression. Results of cointegration regression and Dickey-Fuller test on residuals are provided in Table 6. Table 5: Cointegrating Regression Variable Coefficient Standard Error T Statistics p-value Constant 0.237134 0.131724 1.80 0.07584 * Forward Rate 0.937433 0.0343509 27.29 <0.00001 *** Table 6: Dickey-Fuller Test on Residuals Test Statistics 5% 10% Test with constant -5.37878-2.89-2.58 Thus, the estimates in Tables 5 and 6 clearly indicate that cointegrating relations exist between S t+1 and F t, and the non-stationarity of the variables in the level specification does not lead to inconsistency in OLS estimation, but rather super consistency. As the specified model contains lagged variable, the Durbin-Watson statistics is not an efficient estimate for autocorrelations (Ramu Ramanathan, 1995). To test for autocorrelations we therefore apply the Breusch-Godfrey Langrange Multiplier Test (T Breusch, 1978, L G Godfrey, 1978) the results of which are presented in Table 7. Table 7: Breusch Godfrey Test for Autocorrelation Test for First Order Auto Correlation Variable Coefficient Standard Error T Statistics p Value Constant 0.089346 0.13384 0.668 0.50652 Forward Rate -0.02332 0.0349028-0.668 0.50614 uhat_1 0.282861 0.117656 2.404 0.01875 ** Unadjusted R-squared = 0.0733678 Test statistic: LMF = 5.779905, with p-value = P(F(1,73) > 5.77991) = 0.0187 Alternative statistic: TR 2 = 5.575950, with p-value = P(Chi-square(1) > 5.57595) = 0.0182 Table 7: Breusch Godfrey Test for Autocorrelation (Cont.) Test for autocorrelation up to order 2 Variable Coefficient Standard Error t Statistics P Value Constant 0.08627 0.139276 0.619 0.53762 Forward Rate -0.02257 0.0363221-0.621 0.53632 uhat 1 0.274981 0.119521 2.301 0.02435 ** uhat_2 0.001319 0.122479 0.011 0.99144 Unadjusted R-squared = 0.0715644 Test Statistic: LMF = 2.736360, with p-value = P(F(2,71) > 2.73636) = 0.0716 Alternative Statistic: TR 2 = 5.367327, with p-value = P(Chi-square(2) > 5.36733) = 0.0683 In the presence of autocorrelation, the values of t-statistics and that of R 2 as derived from OLS regression are inefficient. Since serial correlation is present, it is necessary to run the regression after correcting for serial correlation. For this purpose the Cochrane Orcutt procedure, the Hildreth Lu technique and a mixed Hildreth Lu and Cochrane Orcutt procedure are used (D Cochrane and J H

International Research Journal of Finance and Economics - Issue 12 (2007) 63 Orcutt, 1949, C Hilderth and J Y Lu, 1960, Ramu Ramanathan, 1995). The results are presented below (Table 8) along with the statistics based on rho-differences (Table 9). Table 8: Estimates between S t+1 and F t Procedure Variable Coefficient t Statistics Standard Error p Value Cochrane Orcutt Constant 0.35997 2.057 0.174969 0.04318 In(Ft) 0.905369 19.842 0.0456290 <0.00001 Hilderth-Lu Constant 0.359612 2.057 0.174863 0.04326 In(Ft) 0.905463 19.856 0.0456016 0.00001 Mixed Hi-Lu and Constant 0.359928 2.057 0.174956 0.04319 Cochrane-Orcutt In(Ft) 0.90538 19.844 0.0456259 0.00001 Table 9: Statistics Based on Rho Difference Cochrane-Orcutt Hilderth-Lu Modified HiLu & CO Observations: 76 76 76 Degrees of Freedom: 74 74 74 Sum of Squared Residuals: 0.00794452 0.00794452 0.00794452 Standard Error of Residuals: 0.0103614 0.0103614 0.0103614 R-Squared: 0.915333 0.915333 0.915333 Adjusted R-Squared: 0.914189 0.914189 0.914189 Durbin-Watson Statistic: 1.98134 1.98055 1.98125 First-order Autocorrelation Coefficient: -0.00658199-0.00618934-0.00653645 After correcting for serial correlation, the t-statistics for the constant term increases, while the t- statistics for the forward rate decreases. This is because serial correlation increases the variance, which decreases the computed standard error, which in turn increases the t-statistic of the independent variable. The critical value for Durbin Watson for a one-tailed test is dl=1.598 and du=1.652 for 77 observations and k=1. Therefore, the null hypothesis that there exists no serial correlation is not rejected in all the three methods at 5% level of significance. At 1% level of significance, the null hypothesis that the constant term is zero is not rejected. At 5% and 10% level of significance, the null hypothesis is rejected, and the alternative hypothesis is accepted, concluding that the constant term is significantly different from zero. Therefore, at 5% level we can conclude that the UFH does not hold, because a significant constant term may reflect the presence of a premium, or other factors, which affects the spot exchange rate. Therefore, the forward rate does not capture all available information. At 1%, 5% and 10% levels of significance, the null hypothesis that the coefficient is unity can be rejected, and the alternative hypothesis can be accepted, concluding that the estimated coefficient of the one-period lagged forward rate does not significantly differ from one, which is a criteria for the UFH to hold. Thus the results of the regression do not fully support the UFH. Results show that the constant term is significantly different from zero even after correcting for serial correlation. This means that the constant term is capturing information that is not captured in the forward rate, or that the forward rate does not fully reflect all information available to economic agents. 5. Conclusions In this paper, we attempted to investigate the empirical issue of market efficiency for the Indian Rupees vis-à-vis the US Dollar using the monthly data from August 2000 to January 2007. The empirical evidence for the entire sample period indicates that the current forward rate is significant in the prediction of the future spot rate. Regression results after correcting for serial correlation show that the estimated coefficient of the oneperiod lagged forward rate does not significantly differ from unity.

64 International Research Journal of Finance and Economics - Issue 12 (2007) However, the constant term is significantly different from zero. This means that the constant term is capturing information that is not captured in the forward rate, or that the forward rate does not fully reflect all information available to economic agents. Based on our observations we can therefore conclude that UFH does not hold in Indian forex market. In this paper, we make no conjecture about the source of the variation between future spot rate and current forward rate. Also, we do not explore whether or not structural changes over time has a bearing on Indian forex market for USD. This leaves further scope for exploratory analysis in this area. Since the one-period lagged forward rate does not seem to reflect all available information, which it should for exchange rate market efficiency to be possible, future researches can focus on the lagged effect of news in determining future spot rate in India. Empirical studies have been conducted in developed economies to determine the role that news plays in predicting the spot rate. These studies found out that exchange rate movements respond to new information that is available to economic agents in every period. Edwards (1982) expressed exchange rate as a function of factors known in advance, which are captured by the forward rate determined in the previous period, and news regarding changes in economic conditions like domestic and foreign quantities of money, real incomes and real interest rates, or even political stability. Therefore, it has been suggested that the forecasting error, S t+1 F t, is explained by the news captured in the future spot rate that was not available when the forward rate was determined.

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