In the light of the discussion about the methodology of the research and the overview of the study this report performs the empherical analysis of the impact of introduction of currency futures on the volatility of exchange rates. The autoregressive model ARCH/GARCH is being used to determine the volatility of exchange rates. Then the two way relationship between exchange rates and volume of the contracts being traded on NSE is analysed and a comparison of volatility before the introduction of currency futures i.e. from Jan 2004 to August 2008 and after the introduction of currency futures from SEP.2008 to Dec. 2012 has been done.
5.2 SECONDARY DATA ANALYSIS:
The daily exchange rates from Jan 2004 to Dec. 2012 for USD, GBP, EURO and YEN have been taken and checked for the presence of unit roots with the help of Augmented-Dickey fuller test in STATA 12. The presence of unit root effect has been modified by taking the log of the exchange rates. Then returns of the exchange rate have been calculated to generate the GARCH (1, 1) model. The GARCH model is developed with the EVIEWS and STATA 12 softwares. Then Granger Causality test is performed in EVIEWS to analyse the two way effect between exchange rates and volumes by taking data on a monthly basis here the average monthly exchange rates and average volume of contracts has been taken. A one way ANOVA has been done in EXECL to analyse the difference in volatilities before and after the introduction of currency futures i.e. August 2008.
5.2.1 DESCRIPTIVE STATISTICS OF THE SECONDARY DATA:
The descriptive statistics of a time series data generally provided detailed information regarding the quantitative features of the data. The descriptive statistics time series data for daily exchange rates from Jan 2004 to Dec 2012 on a daily basis for all the rates i.e. USD, GBP, EURO and YEN has been estimated and the result is shown in the following table. Following information can be interpreted from the result:
Table 5.2.1.1
Descriptive Statistics
USD
GBP
EURO
YEN
Mean
45.95916
79.54261
61.08086
47.513
Median
45.35
80.12
59.61
42.62
Maximum
57.2165
89.5368
72.773
72.12
Minimum
39.27
65.6471
51.84
32.69
Std. Dev.
3.770361
5.444235
5.400598
10.36497
Skewness
0.760782
-0.360806
0.263162
0.688269
Kurtosis
3.643798
2.202811
1.811443
2.418986
Jarque-Bera
248.2826
105.1691
153.6909
203.0586
Probability
0
0
0
0
Sum
100328.8
173641.5
133339.5
103720.9
Sum Sq. Dev.
31018.49
64673.82
63641.22
234418.1
Observations
2182
2182
2182
2182
The mean and median generally tell us about the location of the centre of the data and what should be a typical value for the whole sample as in this case the mean and median of USD, GBP, EURO and YEN tell us that the typical exchange rate value for them over the time period of 9 years has been almost 45, 79, 60, and 45 respectively.
The standard deviation of USD is not very high i.e. 3.7 as compared to others means the rates very not very much far from the mean over the long period and is the same case for EURO and GBP, however for YEN its 10.3 which means there is a huge variation in the volatility from its typical value over a period of time.
As the mean and median for all the exchange rates are not equal hence certain amount if asymmetry is present in the data it means the data is skewed. The skewness is positive for all but negative for GBP meaning the long tail of data continues to the left right side of the mean. It is least for EURO which the rate has not been as volatile as in case of USD.
The USD rates and return follow a lognormal distribution as its kurtosis is more than 3, it will also be considered as a continuous distribution. EURO rates and return follow a uniform distribution having skewness of 1.8 and as mentioned above they are less volatile. However GBP and YEN rates and return data follow triangular distribution. This kind of distribution is very much helpful for risk analysts as it provide flexibility in shape and also a better understanding of the parameters.
The Jarque-Bera test is a goodness of fit test for skewness, kurtosis and normal distribution present in the data and with a p-value of 0 for all the rates implies that there residuals are not normally distributed.
5.2.2 Augmented Dickey Fuller test:
A stationary time series means that it is a stochastic process where probability distributions do not change with time, however this is not the case when the time-series data is non-stationary. Hence ADF test is conducted to check if the data set is Stationary or not by finding out the presence of unit root in the time series. The hypothesis tested for this process is:
H0: Time series Data set is non-stationary.
H1: Time series Data set is Stationary.
The null hypothesis is rejected if the Test-statistics value is less negative then the Critical value 95% level, which implies that the data is non-stationary and unit root is present.
Table 5.2.2.1: ADF Test for USDINR
Null hypothesis cannot be rejected, the series is non-stationary.
Table 5.2.2.2: ADF Test for GBPINR
Null hypothesis cannot be rejected, the series is non-stationary.
Table 5.2.2.3: ADF Test for EUROINR
Null hypothesis cannot be rejected, the series is non-stationary.
Table 5.2.2.4: ADF Test for YENINR
Null hypothesis cannot be rejected, the series is non-stationary.
The dickey fuller test tells us that the series for all the exchange rates is non-stationary. The unit root is also present with grit meaning that volatility is caused due to own lags of the independent variable which are the corresponding exchange rates and due to changes in other factors like changes in the government policies or regulatory policies and the unit root is absorbed by ARCH/GARCH model.
5.2.3 GARCH model:
Generalized Auto Regressive Conditional Heteroscedasticity is generally used for modelling the volatility present in the time series data the returns from the various exchange rates. As from the dickey fuller test is clear that the exchange rates are non-stationary and therefore in order to absorb the unit root or the arch effect present in the data it is modelled with the help of GARCH. The residuals of the return from all four exchange rates have been calculated by taking natural log of the exchange rate returns. In case of time series data these residual are auto correlated hence in order to deal with the arch effect GARCH model has been used to forecast the volatility and to ensure that no further arch effect is present.
There are two equations present in the GARCH model, in the first mean equation the mean equation in which the returns of exchange rates are taken as the dependent variable and there are no independent variables used in this model hence the Lags of the residuals of the exchange rate returns are responsible for the variation and volatility i.e. they are auto correlated and the lags of the residuals or return are taken as dependent variables to estimate the volatility and are calculated by squaring the residuals. And the other one is variance equation in which the ARCH-least square method is included to eliminate the arch effect.
In this case the baseline GARCH model GARCH (1, 1) is used which is a first order Garch model. The model is calculated with the help of EVIEWS 7 software and the Residuals and the Lags have been calculated in Excel for the USD, GBP, EURO and YEN from a period of Jan 2004 to Dec 2012 on a daily basis.
Table 5.2.3.1: GARCH model for USD exchange rate returns
Dependent Variable: USRD
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 02/22/13 Time: 20:12
Sample (adjusted): 1/02/2004 5/11/2012
Included observations: 2181 after adjustments
Convergence achieved after 13 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1)
Variable
Coefficient
Std. Error
z-Statistic
Prob.
C
-0.007650
0.005719
-1.337616
0.1810
LUSRD
0.056440
0.033739
1.672860
0.0944
Variance Equation
C
0.001715
0.000385
4.448900
0.0000
RESID(-1)^2
0.234786
0.017776
13.20800
0.0000
GARCH(-1)
0.792890
0.011948
66.35951
0.0000
R-squared
0.002043
Mean dependent var
0.008456
Adjusted R-squared
0.001585
S.D. dependent var
0.483572
S.E. of regression
0.483189
Akaike info criterion
0.939164
Sum squared resid
508.7348
Schwarz criterion
0.952203
Log likelihood
-1019.158
Hannan-Quinn criter.
0.943930
Durbin-Watson stat
1.960423
Table 5.2.3.2: GARCH model for GBP exchange rate returns
Dependent Variable: GBPR
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 02/18/13 Time: 12:58
Sample (adjusted): 1/02/2004 5/11/2012
Included observations: 2181 after adjustments
Convergence achieved after 9 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1)
Variable
Coefficient
Std. Error
z-Statistic
Prob.
C
-0.001085
0.013056
-0.083090
0.9338
LGBPR
0.015189
0.018998
0.799492
0.4240
Variance Equation
C
0.005253
0.001619
3.244272
0.0012
RESID(-1)^2
0.055017
0.008009
6.869118
0.0000
GARCH(-1)
0.932471
0.010121
92.13436
0.0000
R-squared
0.000503
Mean dependent var
0.003742
Adjusted R-squared
0.000045
S.D. dependent var
0.672547
S.E. of regression
0.672532
Akaike info criterion
1.820463
Sum squared resid
985.5602
Schwarz criterion
1.833502
Log likelihood
-1980.215
Hannan-Quinn criter.
1.825230
Durbin-Watson stat
1.946082
Table 5.2.3.3: GARCH model for EURO exchange rate returns
Dependent Variable: EUROR
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 02/18/13 Time: 15:56
Sample (adjusted): 1/02/2004 5/11/2012
Included observations: 2181 after adjustments
Convergence achieved after 12 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1)
Variable
Coefficient
Std. Error
z-Statistic
Prob.
C
-0.006329
0.013460
-0.470248
0.6382
LEUROR
0.031693
0.020531
1.543696
0.1227
Variance Equation
C
0.004710
0.001212
3.887403
0.0001
RESID(-1)^2
0.047687
0.007318
6.516317
0.0000
GARCH(-1)
0.942302
0.008241
114.3395
0.0000
R-squared
0.002795
Mean dependent var
0.010782
Adjusted R-squared
0.002338
S.D. dependent var
0.656001
S.E. of regression
0.655234
Akaike info criterion
1.866350
Sum squared resid
935.5143
Schwarz criterion
1.879388
Log likelihood
-2030.254
Hannan-Quinn criter.
1.871116
Durbin-Watson stat
1.964489
Table 5.2.3.4: GARCH model for YEN exchange rate returns
Dependent Variable: YENR
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 02/18/13 Time: 13:10
Sample (adjusted): 1/02/2004 5/11/2012
Included observations: 2181 after adjustments
Convergence achieved after 17 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1)
Variable
Coefficient
Std. Error
z-Statistic
Prob.
C
-0.016478
0.015593
-1.056773
0.2906
LYENR
0.020324
0.012942
1.570385
0.1163
Variance Equation
C
0.014631
0.002656
5.508414
0.0000
RESID(-1)^2
0.109463
0.010856
10.08305
0.0000
GARCH(-1)
0.875758
0.011262
77.76080
0.0000
R-squared
0.000567
Mean dependent var
0.018414
Adjusted R-squared
0.000108
S.D. dependent var
0.880534
S.E. of regression
0.880486
Akaike info criterion
2.330357
Sum squared resid
1689.282
Schwarz criterion
2.343396
Log likelihood
-2536.255
Hannan-Quinn criter.
2.335124
Durbin-Watson stat
2.090341
Interpretation of GARCH model:
The GARCH lag coeficients are more than 0.7 which is always possinle in fiancial markets hence laregr coeficients means thatvolatilty is not going to be continiusly present in the exchange rates it will be reduced slowly but however due to its nature it can again gain a high volaitlty with chnges the market.
The standard error in case of USD returns is less as compared to YEN returns which is highest, a low standard error means that the voality in USD exchange returns responses very less to the market and their volality is not goin to be very high however it can take backward trend.
The coeficients of ARCH and GARCH are postive and less than on for all the cases and are signifaicant at 95% confidence interval.
The sum of both the coeficients is nearly equal to 1 i.e. 0.99 hence it means that the shocks to volality will be very high which means rejection of null hypothesis i.e. introduction of currency futures have a great impact on the market.
The probability for all the cefficeints is less than 5 % it is 0.00 which means that all the exchange rate returns are have ARCH and GARCH effect and they are effected by their own shocks not other policies or regulations.
This also means that the previous day's volatility in return can effect current days volatility.
Then the values of Akaike info criterion, Schwarz criterion and Hannan-Quinn criter are postive and more than 1 which means that this model is best and apprioate for estimating the volatility in terms of acuuracy.
The pobability of almost 0 also indicates that there is no more autoregressiom present in the lagged residuals of returns which means the data has become statioanry now.
5.2.4 Granger Causality Tests:
Granger causality test tells us about the two way relationship between two variables unlike other linear tests which only estimates the their influential relationship but not the direction of influence and this is very important to determine in case of time-series variables to check for the exogenous nature between two time series variables. In this case the data from February 2010 to January 2012 has been taken for Volume of futures being traded and the exchange rate returns on daily basis for USD, GBP, EURO and YEN to see whether the volume of contracts is affecting the volatility in exchange rates or it is vice-versa. Hence Granger Causality test has been performed in EVIEWS 7 software. A lag diffrence of 4 has been taken the length of lag increases with increase in the obersvations, the test can be done by taking lags of 4, 6, 8, etc., depending upon data length and the users choice.
Table 5.2.4.1: Causality Test for USD rate returns and volume of USD futures contracts:
Pairwise Granger Causality Tests
Date: 02/18/13 Time: 05:06
Sample: 2/01/2010 12/30/2012
Lags: 4
Null Hypothesis:
Obs
F-Statistic
Prob.
FTRVOL does not Granger Cause USDR
496
0.46357
0.0617
USDR does not Granger Cause FTRVOL
1.90570
0.0236
Interpretation:
As the value of p < 0.05 hence the null hypothesis stating:
volume of USD futures contract being traded does not cause the USD exchnage rate returns, and
that volatility in returns does not effect the volume contract is rejected.
Hence there is a two way relationship between these two variables along with the proof of presence of autocorelation among the own lags of returns which is driving the volatility. Hence the volatilty in returns is also caused due to contracts of futures traded and cahnge is volume of contracts day by day is also efffcted due to the volatility in returns exogenously.
Table 5.2.4.1: Causality Test for GBP rate returns and volume of GBP futures contracts:
Pairwise Granger Causality Tests
Date: 02/18/13 Time: 05:09
Sample: 2/01/2010 12/30/2012
Lags: 4
Null Hypothesis:
Obs
F-Statistic
Prob.
FTRVOL does not Granger Cause GBPR
496
2.53887
0.0287
GBPR does not Granger Cause FTRVOL
1.45892
0.0500
Interpretation:
As the value of p < 0.05 hence the null hypothesis is rejected. Hence there is a two directional exogenous relationship between these two variables.
Table 5.2.4.1: Causality Test for EURO rate returns and volume of EURO futures contracts:
Pairwise Granger Causality Tests
Date: 02/18/13 Time: 05:10
Sample: 2/01/2010 12/30/2012
Lags: 4
Null Hypothesis:
Obs
F-Statistic
Prob.
FTRVOL does not Granger Cause EUROR
496
2.14729
0.0023
EUROR does not Granger Cause FTRVOL
1.69220
0.0249
Interpretation:
As the value of p < 0.05 at 95 % confidence interval hence the null hypothesis is rejected. Hence there is a two directional exogenous relationship between the Euro futures contract and Euro exchange returns.
Table 5.2.4.4: Causality Test for YEN rate returns and volume of YEN futures contracts:
Pairwise Granger Causality Tests
Date: 02/18/13 Time: 05:15
Sample: 2/01/2010 12/30/2012
Lags: 4
Null Hypothesis:
Obs
F-Statistic
Prob.
FTRVOL does not Granger Cause YENR
496
3.25895
0.0036
YENR does not Granger Cause FTRVOL
6.48890
0.0424
Interpretation:
As the value of p < 0.05 at 95 % confidence interval hence the null hypothesis is rejected. Hence there is a two way exogenous relationship between the YEN futures contract and YEN exchange returns.
However the Granger Causality test can not be allways rekied uponbecuase th eprobability chnges with increse in number of lags taken in the calculation if the same teast is rum at 6 or 8 or 12 lags the value of p can come more than 0.05 hence in that the null hypothesis cannot be rejected and thus the two way exogenous or derived realitionship cannot be established.
5.2.5 Analysis of change in the volatility before and after introduction of futures derivatives:
The currency futures for USD were introduced on 29 August 2008, however for GBP, EURO and YEN it was introduced in January 2010. Hence the daily returns have been divided into two parts from 2004 to 2012 as before and after the introduction of currency futures by adding a suffix of PRE and POST respectively to the variables all the exchange rates. Then in order to check whether there is any change in the volatility Analysis of variance has been done in Excel. In case of Anova test the two alternative hypothecs are:
Ho: there is no change in volatility after the introduction of currency futures.
H1: there is a change in volatility after the introduction of currency futures.
The test results are:
Table 5.2.5.1: ANOVA for difference in volatility of USD returns:
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
USD_PREFTR
1041
-3.85785
-0.00371
0.103156
USD_POSTFTR
1041
22.51475
0.021628
0.373119
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
0.33406
1
0.33406
1.402804
0.03639
3.845933
Within Groups
495.3261
2080
0.238138
Total
495.6601
2081
Interpretation of results:
As the value of F statistic < Fcritical and is very low i.e. 1.4 also the value of p < .05 at 95% confidence interval hence null hypothesis is rejected which means that there is a change in volatility after the introduction of futures.
As we can see that the variance of returns have been changed from 0.1 to 0.3 and hence become persistent with a growth of 20% which becomes that market have become mature after the introduction of futures in 2008 and this has a significant impact on market.
Table 5.2.5.2: ANOVA for difference in volatility of GBP returns:
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
GBP_PREFTR
1083
2.798909
0.002584
0.28076
GBP_POSTFTR
1083
2.550868
0.002355
0.620924
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
0.00284
1
0.28
0.630036
0.043668
3.84576
Within Groups
975.6217
2164
0.450842
Total
975.6217
2165
Interpretation of results:
Rejection of the null hypothesis as the value of F statistic < Fcritical and is very low i.e. 0.63 and the value of p < .05 which means that there is a change in volatility after the introduction of futures.
The variance of returns have been changed from 0.2 to 0.6 and hence become durable with a growth of 40% hence it can be said that market have become mature after the introduction of futures in 2010 and have has a significant impact on market.
Table 5.2.5.3: ANOVA for difference in volatility of EURO returns:
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
EURO_POSTFTR
708
11.15989
0.015763
0.420694
EURO_PREFTR
708
21.02286
0.029693
0.708376
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
0.068699
1
0.068699
0.121692
0.037259
3.848044
Within Groups
798.252
1414
0.564535
Total
798.3207
1415
Interpretation of results:
Rejection of the null hypothesis as the value of F statistic < Fcritical it is 0.12 and the value of p < .05.
The variance of returns have been changed from 0.4 to 0.7 with a growth of 30% which means that market have become mature and durable after the introduction of futures in 2010.
Table 5.2.5.4: ANOVA for difference in volatility of YEN returns:
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
YEN_PREFTR
709
33.53873
0.047304
1.309161
YEN_POSTFTR
709
20.59551
0.029049
0.70767
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
0.118143
1
0.118143
0.117157
0.032189
3.848034
Within Groups
1427.916
1416
1.008416
Total
1428.035
1417
Interpretation of results:
Rejection of the null hypothesis as the value of F statistic < Fcritical and is very low i.e. 0.11 and the value of p < .05 which means that there is a change in volatility after the introduction of futures.
The variance have been changed from 1.3 to 0.7 with a decrease in growth of 60% indicating that the market for YEN futures after introduction does not have a significant effect on the performance of the YEN exchange rates due to which the volatility in returns might have been increased, the market is still not durable and persistent after the introduction of futures in 2010.
