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The present study investigates the efficiency of the forex market based on the theory of the Efficient Market Hypothesis in Mauritius, a well-diversified and emerging economy in the African region. Hence, this study considers the case of Mauritian forex market nominal spot rate daily data namely EUR/MUR, USD/ MUR, GBP/ MUR and JPY/ MUR over a time period of 5 years ranging from 2012 to 2016. The technique used for analysis is firstly concentrated on the use of Augmented-Dickey Fuller (ADF) and Philips Peron (PP) unit root to test the weak-form of efficiency and secondly, the Johansen Cointegration Test, the Granger Causality Test and Variance Decomposition are utilized to examine the existence of semi-strong form efficiency in the Mauritian foreign exchange market. Results indicated that the unit root test tested by ADF and PP unit root test support the weak form market as it follows a random walk process. Secondly, the Johansen Cointegration test reveals that there is no long run relationships among foreign exchange variables. However, the Granger causality test confirmed the existence of unidirectional and bidirectional relationships among the various exchange rates. Moreover, the Variance Decomposition confirmed the presence of long run co-movements among the exchange rates. Therefore, both tests fail to support the semi-strong form market. This means that one exchange rate can predict one or more exchange rates which is against the semi-strong form market hypothesis. Therefore, it is deduced that the foreign market is efficient in the weak-form but is inefficient in the semi-strong form in Mauritius.

In financial economics, the Efficient Market Hypothesis theory has been a great debate since its inception in the 1960s at the University of Chicago. At present, it is becoming more prominent as investors are more engaged in diversification of investment products worldwide. However, EMH was criticized because even though this theory was held by academics, it was a controversy in applied finance resulting to anomalies Le Baron [

Market efficiency plays a major role in the foreign exchange market for investors, financial analysts, financial managers and to all relevant stakeholders using foreign exchange. Fama [

The purpose of the study is to investigate the efficiency of the Mauritian forex market based on the theory of Efficient Market Hypothesis. As a developing country, Mauritius has become an emerging market with a lot of potential of investment that gets an attention for financial analysts, investors and financial managers need to rethink about their buying and selling recommendations in forex. In fact, Foreign Exchange Reserves in Mauritius increased to 5262.10 USD Million in June from 5158 USD Million in June of 2017. Mauritian Foreign Exchange Reserves averaged 2295.92USD Million from 1999 until 2017, reaching a high of 5262.62 USD Million in May of 2017 and a record low of 637.50 USD Million in October of 2000. In the long-term, the Mauritius Foreign Exchange Reserves is projected to trend around 4935.22 USD Million in 2020.Foreign Exchange Reserves in Mauritius is reported by the Bank of Mauritius. Hence, this study considers the case of the Mauritian forex market namely EUR/MUR, USD/ MUR, GBP/MUR, JPY/MUR and AUD/MUR over a time frame of 5 years ranging from 2012 to 2016 as they are more actively traded. The importance here is to understand the main theories of market efficiency related to foreign exchange and how it is applicable and predictable in Mauritius. Therefore, the technique used for analysis is concentrated on the use of Augmented-Fuller Test and Philips Peron Test to examine the existence of a weak form market efficiency in Mauritian forex. Secondly, the semi-strong form market efficiency is also tested by using the Granger causality test.

Another motive for conducting this study is that most research work performed on testing the efficiency of the markets was based mainly on the efficiency of stock and share prices. For instance, Fowdar [

Hence, the study to be analysed is concerned with the following objectives:-

➢ To investigate the existence of the weak-form method of efficiency in the Mauritian foreign exchange market

➢ To analyse the existence of the semi-strong form method of efficiency in the Mauritian foreign exchange market

The plan of the study is outlined as follows: Section II provides a review of previous research studies. The research methodology and data are discussed in Section III. Section IV presents the empirical results of this study in the light of literature review and researcher’s opinions. Subsequently, Section V summarizes the findings and presents the conclusion and policy implications.

The recent studies that were performed to indicate the efficiency of the foreign exchange market and the use of various types of econometric techniques and data frequencies are described to explain this theory.

Hakio [

[

Coleman [

Aron [

[

Aroskar et al. [

Cooray and Wickremasinghe [

Kuntara and Lee [

Ibrahim et al. [

[

Dinica et al. [

Sing and Sapna [

[

[

Sheefeeni et al. [

Makorvsky [

Mabakeng et al. [

Cicek [

Kumar et al. [

In order to determine the existence of weak-form and semi-strong form market efficiency in the Mauritian foreign market, this paper will use the Augmented- Dickey Fuller Test and Philips Peron Test to test the weak form market efficiency to determine if spot exchange rates in Mauritius behave as random walk patterns. Secondly, Johansen Cointegration Test, Granger Causality Test and Variance Decomposition is used to determine the existence of strong-form market efficiency by investigating the cointegrating relationship and non-existence of causal relationship among the spot exchange rates as adapted by [

The data sample in this study is made up of 5 set of official spot exchange rates namely EUR/MUR, USD/MUR, GBP/MUR and JPY/ MUR. All the data is secondary and are collected from the Mauritius Commercial Bank website [

As the objective is to investigate the efficiency of foreign exchange market in Mauritius, the following hypotheses for testing have been designed as follows:

Part 1: Weak-Form Market Hypothesis:

Augmented Dickey Fuller Test, Philips Peron Test

H_{1}-Unit Root exists in Mauritian FX time series (follows a random walk)

H_{2}-Unit Root does not exist in Mauritian FX time series (does not follow a random walk)

Part 2: Semi-Strong Form Market Hypothesis:

Granger Causality Test and Variance Decomposition

H_{1}-Granger causality does not exist in Mauritian FX time series

H_{2}-Granger causality exists in Mauritian FX time series

Exchange rates, in common with many financial variables, typically exhibit non-stationary time series processes: that is, they are series trending over time, rather than mean-reverting or stationary series Aron [

The ADF test was developed by Dickey and Fuller in 1984 which is an augmented version of the DF test. The augmented Dickey-Fuller (ADF) statistic, used in the test, should be a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence. It is also important that the error term should be correlated.

The ADF test is indicated as follows:-

Δ x t = a 0 + b 0 x t − 1 + Σ c 0 Δ x t − 1 + w t

where

Δ is the difference operator, a_{0}, b_{0}, c_{0} are coefficients to be estimated,

x is a variable whose unit roots are examined and w is the error term.

The null hypothesis for this is b_{0} = 0 (i.e. the series is non-stationary and a random walk with drift) against the alternative hypothesis b_{0} < 0 (i.e. the series is stationary).

Most time series in economics exhibit trend over time and when this is the case, it is usually said that these time series are not stationary (contain unit root). Being non-stationary implies that the mean, variance and covariance are not constant over time. In the context of this study, when data contains a unit root it means the data follows a random walk

The Phillips-Perron test [

γ i = α + p y t − 1 + ϵ t

where

y and p are parameters

ϵ is referred to as white noise

t is the transcript for time.

This study will use three econometric measures to test the semi-strong form of the EMH namely Johansen Cointegration Test, Granger Causality Test and Variance Decomposition Test.

Cointegration tests are carried out in order to see if the markets share a long run stochastic trend. The first step in the analysis tests for the order of integration of the variables. Order of integration refers to the number of times a variable is differenced before becoming stationary. One condition for the co-integration tests is that the variables in the co-integrating equation must be integrated of the same order. In this paper, ADF and PP tests are used to test the stationarity of the residuals obtained from the bivariate cointegration equations.

Johansen’s co-integration is based on the following vector auto regression equation:

y t = A t y t − 1 + ⋯ + A t y t − p + β x t + ε t

where:-

y_{t} is a k-vector of non-stationary I(1) variables,

x_{t} is a vector of deterministic variables

ε_{t} is a vector of innovations

In making inferences about the number of cointegrating relations, two statistics known as trace statistic and maximal eigenvalue statistic are used. The trace statistic analysed the null hypothesis that there are at most r cointegrating vectors against the alternative hypothesis of r or more cointegrating vectors. Meanwhile, in the maximal eigenvalue statistic test the null hypothesis of r cointegrating vectors is tested against the alternative of r + 1 cointegrating vectors [

The vector error correction (VEC) is also estimated to investigate weak exogeneity and to do hypothesis testing since VEC is applied only if there is a long run cointegrated relationship among the series. To be able to run Johansen cointegrating test the data must be nonstationary. If there is no long run cointegrated relationship among the variables, a VAR model specification is estimated.

Granger Causality TestBrooks [

The Granger causality test is useful in finding whether one time-series (x_{t}) can be predicted by another time-series (y_{t}). The test is carried out by regressing x_{t} on its lagged values and the lagged values of y_{t}. If the results indicate that x_{t} can be predicted by y_{t}, it is said that y_{t} Granger causes x_{t}. However, the

Granger causality implies a correlation between the current value of one variable and the past values of others; it does not mean changes in one variable cause changes in another. If there are two series Y_{t} & X_{t}, then it is said that X_{t} doesn’t granger cause Y_{t} if all lagged coefficients for X_{t} are zero, that is:

Y t = α 0 + α 1 Y t − 1 + ⋯ + β 1 X t − 1 + ⋯ + β p X t − p + ϵ t

Then, β 1 = β 2 = ⋯ = β p = 0 that is lagged of Xt has no effect on Y_{t}.

Note that model selection criteria, such as the Bayesian Information Criterion (BIC, Schwartz (1978)) or the Akaike Information Criterion (AIC, Akaike (1974)), can be used to determine the appropriate model order p.

Variance Decomposition indicate the proportion of the movements in the dependent variables that are due to their “own” shocks, versus shocks to the other variables [

A shock to the ith variable will directly affect that variable of course, but it will also be transmitted to all of the other variables in the system through the dynamic structure of the VAR. Variance decompositions determine how much of the s-step-ahead forecast error variance of a given variable is explained by innovations to each explanatory variable for s = 1, 2, ∙∙∙ [

We started our investigation with some basic descriptive statistics of the foreign exchange data for Mauritius focusing on the mean, standard deviation as a measure of volatility, skewness and kurtosis. The descriptive statistics are represented in

EUR_MUR | GBP_MUR | USD_MUR | JPY_MUR | |
---|---|---|---|---|

Mean | 1.5912 | 1.6875 | 1.5025 | 1.4931 |

Median | 1.5922 | 1.6865 | 1.4846 | 1.4815 |

Maximum | 1.6144 | 1.7398 | 1.5545 | 1.5888 |

Minimum | 1.5560 | 1.6309 | 1.4493 | 1.4049 |

Std. Dev | 0.0136 | 0.0261 | 0.0344 | 0.0453 |

Skewness | −0.3588 | 0.1989 | 0.3284 | 0.5366 |

Kurtosis | 2.3003 | 2.3286 | 1.4424 | 2.2680 |

Jarque-Bera | 52.1983 | 31.6445 | 148.4635 | 87.6912 |

Probalility | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

Observations | 1247 | 1247 | 1247 | 1247 |

In this paper, the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) were used to examine for the unit root. Here, the unit root tests are conducted at level and first difference.

Level | First Differences | |||||||
---|---|---|---|---|---|---|---|---|

Currency | Intercept | LAG | Intercept & Trend | LAG | Intercept | LAG | Intercept & Trend | LAG |

EURO | −2.3816 | 1 | −2.4079 | 1 | −37.3551* | 0 | −10.92158* | 15 |

GBP | −1.3743 | 12 | −2.3051 | 12 | −10.6374* | 11 | −10.80607* | 11 |

USD | −0.8640 | 4 | −1.7783 | 4 | −12.08791* | 3 | −12.08343* | 3 |

JPY | −0.7595 | 10 | −1.2844 | 10 | −10.27241* | 8 | −10.32014* | 8 |

(Author’s Computation) |

Notes for the above table: * denotes significance at 1% level; Mackinnon (1996) one-sided p-values.

According to the study, both tests confirm that the data become non-stationary at first level and become stationary when they are tested at the First difference which support the existence of the weak form efficiency. In other words, the Mauritian foreign exchange market is efficient in the weak form. The results of the study are consistent with a number of studies^{1}.

Level | First Differences | |||||||
---|---|---|---|---|---|---|---|---|

Currency | Intercept | LAG | Intercept & Trend | LAG | Intercept | LAG | Intercept & Trend | LAG |

EURO | −2.2584 | 8 | −2.3435 | 9 | −37.46186* | 11 | −37.50921* | 11 |

GBP | −1.6873 | 6 | −2.5881 | 8 | −34.47336* | 8 | −34.56479* | 10 |

USD | −0.8796 | 20 | −1.7004 | 20 | −28.77068* | 17 | −28.76248* | 17 |

JPY | −0.4059 | 6 | −1.0434 | 6 | −34.54471* | 5 | −34.57147* | 5 |

(Author’s Computation) |

Notes for the above table: * denotes significance at 1% level; Mackinnon (1996) one-sided p-values.

Null Hypothesis | Trace Statistics | 5% Critical Value | 1% Critical Value | Maximum Eigen Value Statistics | 5% Critical Value | 1% Critical Value |
---|---|---|---|---|---|---|

r = 0 | 38.658 | 47.21 | 54.46 | 22.010 | 27.07 | 32.24 |

r < 1 | 16.648 | 29.68 | 35.65 | 10.293 | 20.97 | 25.52 |

r < 2 | 6.355 | 15.41 | 20.04 | 6.297 | 14.07 | 18.63 |

r < 3 | 0.058 | 3.76 | 6.65 | 0.058 | 3.76 | 6.65 |

(Author’s Calculation) |

Notes for the above table: 1) EURO, GBP, USD and JPY denote the nominal exchange rates for EURO, British Pound, US Dollar and Japanese Yen respectively. 2) a and b imply significance at the 1% and 5% level, respectively. 3) Lag lengths in Vector Autogression were selected using Likelihood Ratio Test. 4) Critical Values for the Trace and Maximal Eigen Value Test are obtained from Osterwald Lenum (1992).

critical values in columns three and four, respectively. Similarly, the values of maximum Eigen value are shown in column five, with five and one percent critical values in columns six and seven, respectively.

According to the study, the result shows that around 100% of the exchange rate pairs are not cointegrated. Therefore, there is no long run relationship among the exchange rate variables. As a result, we can say that the Mauritian foreign exchange market is efficient in the semi-strong form which is consistent with the study a number of studies^{2}.

However, the results are still not conclusive. Therefore, to further verify and confirm the presence of any relationship between the variables, we proceed to carry out the Granger Causality test. The results of which are tabulated

Based on the given results, it is seen that there are unidirectional causal relationships between the various foreign exchange data namely GBP to EUR, GBP to USD, GBP to JPY and USD to JPY. All the results are statistically significant at 1% respectively. However, there is one bidirectional causal relationships namely USD to EUR and vice-versa. Therefore, the null hypothesis that there is no granger causality relationship among the Mauritian foreign exchange market will have to be rejected. The results conquer with a number of findings^{3}.

The basic requirement of the semi-strong form market efficiency is that there should be no granger causality relationships among the foreign exchange data. However, the empirical results clearly indicate the presence of causal relationships which states that one exchange rate can predict one or more exchange rates which is contradictory to the semi-strong form market efficiency. Therefore, it can be deduced that the Mauritian foreign market is not efficient in a semi- strong form. However, another test that is Variance Decomposition will have to be further performed to confirm the results of Granger Causality test.

Null Hypothesis | F-Statistics | Probality |
---|---|---|

GBP_MUR does not Granger Cause EUR_MUR | 15.7862 | 0.00* |

EUR_MUR does not Granger Cause GBP_MUR | 1.28634 | 0.2534 |

USD_MUR does not Granger Cause EUR_MUR | 74.6328 | 0.00* |

EUR_MUR does not Granger Cause USD_MUR | 3.7302 | 0.0005* |

JPY_MUR does not Granger Cause EUR_MUR | 1.29828 | 0.2475 |

EUR_MUR does not Granger Cause JPY_MUR | 0.83613 | 0.5573 |

USD_MUR does not Granger Cause GBP_MUR | 1.30408 | 0.2446 |

GBP_MUR does not Granger Cause USD_MUR | 9.0612 | 0.00* |

JPY_MUR does not Granger Cause GBP_MUR | 1.262 | 0.2658 |

GBP_MUR does not Granger Cause JPY_MUR | 5.73899 | 0.00* |

JPY_MUR does not Granger Cause USD_MUR | 1.59979 | 0.1314 |

USD_MUR does not Granger Cause JPY_MUR | 2.94586 | 0.0046* |

(Author’s Computation) |

Notes for the above table: 1) EUR, USD, GBP and JPY denote the spot exchange rates for Euro, US dollar, British Pound and Japanese yen and US dollar respectively. 2) * and ** implies significance at 1% and 5% respectively. 3) Implies the rejection of the null hypothesis. 4) Seven lags included in the vector auto regressions are determined using the Likelihood (LR) test.

According to the results reported in

When the GBP exchange rate is considered, most of its variance is explained by itself. About 99.78% of the variability of the GBP exchange rate in the first month is explained by itself. At this time horizon, EUR exchange rate explains most of the remaining variability (around 0.22%) of the GBP exchange rate. The higher the time horizon, the more is the variability of the GBP explained by the EURO and US dollar exchange rate. At longer time period that is 48 months, USD and the EUR account 1.22% and 0.82 % respectively of the variability of the GBP exchange rate.

Period Relative Variance | Percentage of Forecast Variance Explained by shocks in | ||||
---|---|---|---|---|---|

EUR | GBP | USD | JPY | ||

1 | EUR | 100.00 | 0.00 | 0.00 | 0.00 |

12 | 97.52 | 0.83 | 1.30 | 0.35 | |

24 | 97.04 | 0.66 | 1.25 | 1.04 | |

36 | 96.23 | 0.54 | 1.13 | 2.10 | |

48 | 95.02 | 0.46 | 1.02 | 3.50 | |

1 | GBP | 0.22 | 99.78 | 0.00 | 0.00 |

12 | 0.56 | 99.21 | 0.23 | 0.00 | |

24 | 0.90 | 98.61 | 0.48 | 0.01 | |

36 | 1.32 | 97.83 | 0.81 | 0.04 | |

48 | 0.82 | 96.88 | 1.22 | 0.08 | |

1 | USD | 0.01 | 1.27 | 98.71 | 0.00 |

12 | 2.57 | 0.84 | 96.51 | 0.02 | |

24 | 6.06 | 0.79 | 93.07 | 0.08 | |

36 | 10.00 | 0.67 | 89.19 | 0.14 | |

48 | 13.93 | 0.54 | 85.35 | 0.17 | |

1 | JPY | 1.83 | 0.04 | 0.01 | 98.13 |

12 | 3.03 | 1.63 | 0.89 | 94.45 | |

24 | 3.26 | 2.77 | 0.87 | 93.10 | |

36 | 3.37 | 4.11 | 0.78 | 91.74 | |

48 | 3.40 | 5.60 | 0.68 | 90.32 |

Notes: 1) Variance decompositions for the months 1, 12, 24, 36, and 48 only are reported. All figures have been rounded to two decimal places. 2) EUR, GBP, USD and JPY denote the nominal exchange rates for Euro, British Pound, US Dollar and Japanese yen. 3) Figures in column 1 refer to months after a once-only shock. Cholesky ordering for the variance decomposition was log(EUR), log(GBP), log(USD) and log(JPY).

Regarding USD exchange rate, 98.13% of its variance is explained by itself. At this same period, GBP accounts for 1.27%. However, the influence of the EUR is more prominent at all time horizons. When compared to the influence of the US dollar and the EURO at long time horizons which are 85.35% and 13.93% respectively, the impact on GBP and Japanese yen on Mauritian rupee is not so prominent at longer time horizons.

As far as JPY exchange rate is concerned, it seems that the variance is explained by 98.13% by itself in the first month. Moreover, EUR explains most of remaining variability that is 1.83% of the JPY exchange rate. At longer time horizons that is 48 months, JPY stands for 90.32% by itself and GBP exchange rate seems to be the most prominent exchange rate (5.60%) followed by the EUR exchange rate (3.40%). However, USD explains a very low influence on JPY that is 0.68% respectively.

The above results stated that the variance of one exchange rate is explained by others revealing causal relationships between currencies. Hence, these results do not support the semi-strong form of the EMH to the Mauritian foreign exchange market. Such causal relationships can be used to predict the future value of one currency from the past values of one or more of the other currencies.

In this study, it has been noted that the results of the Johansen cointegration test state that there is no co-integration relationship among the foreign exchange variables. However, the Granger Causality Test and variance decomposition analysis confirm the contrary and therefore indicate that the movement in one or more of the currencies can be predicted using the other exchange rates. These results are inconsistent with the efficient market hypothesis in its semi-strong form. Hence, the results conquer with a number of studies^{4}.

The foreign exchange market is one of the main important financial aspect of any economy of a country. The study was concerned with the investigation of the efficiency of the Mauritian foreign exchange market based on the theory of the EMH concentrating on the weak form and semi-strong market hypothesis. The study used daily spot rates data for a period of 5 years ranging from 2012 and 2016 with a total number of 1247 observations.

Firstly, the empirical results indicated that the Augmented Dicker Fuller and Phillips Perron unit root test conclude that the foreign exchange market is efficient in the weak-form market hypothesis. Therefore, the results are strictly consistent with the number of studies^{5}.

Moreover, the Johansen cointegration test was also examined and confirmed that there were no long-run relationships among the foreign exchange variables. However, when the Granger causality test was performed, it stated that there was the presence of unidirectional and bidirectional causal relationships between the various spot rates tested. Variance Decomposition analysis was also utilized to confirm the existence of long run comovements among the variables and concluded that there was the presence of innovations and shocks in the long run among the foreign exchange data. The findings conquer with the number of studies^{6}.

Based on the given results, it is concluded that the foreign exchange market in Mauritius is efficient in the weak form. These results indicate that the participants in the foreign exchange market in Mauritius cannot sub-divide some rule or technique that can be utilized to forecast future movements of an exchange rate from its past values.

However, when the Johansen Cointegration test is performed, the semi- strong form efficiency was supported but when the Granger Causality test and Variance Decomposition were used, the results showed that there were long run relationships among the various foreign exchange rates which is not in accordance with the semi-strong form. In other words, one exchange rate can predict one or more exchange rates and that exchange rate traders and market players can make returns on speculation through public information.

The results of the present research have important implications for the Mauritian government policy-making institutions as well as for the participants of the foreign exchange markets. The government will have to take action so as to reduce the exchange rate volatility and instability and appraise the effects of different economic policies on the behaviour of exchange rates. The participants of the foreign exchange market can benefit by devising trading rules or strategies to make profits from transactions in the foreign exchange market.

Amelot, L.M.M., Ushad, S.A. and Lamport, M. (2017) Testing the Efficient Market Hypothesis in an Emerging Market: Evidence from Forex Market in Mauritius. Theoretical Economics Letters, 7, 2104-2122. https://doi.org/10.4236/tel.2017.77143