3. An Application to ADRs and Their Underlying Stocks
3.3. Data and Empirical Results
The ADR and UND series were tested for stationarity in this study using unit root tests;
followed by an examination of the cointegration test between the two series. If they were cointegrated, the threshold VECM was then applied to determine the short-run dynamics and the long-run equilibrium between the ADR and the UND markets.
The daily returns of three locally traded Argentinean firms provided the data for analysis in this study, with Table 1 providing the basic description of their respective New York Stock Exchange-traded ADRs. Although the ADRs are priced in US dollars, UNDs in the home stock market are priced in Argentinian pesos. The prices of ADRs are calculated into the Argentinian peso price using the daily closing exchange rate. ADRs prices, the prices of UNDs, and the exchange rates used in this study were obtained from Datastream.
Table 1. Data description
Symbol Company Industry Shares per DR
TGS TRANSPORTADORA DE GAS DEL SUR, S.A.
Oil and gas
operator 5 2 Jan 95
- 31 Jul 04 2,500
The log-price of the ADRs and the UNDs was used to carry out this empirical analysis, with the returns of ADRs and UNDs being calculated, first of all, by taking the difference in the log-price. Table 2 presents the results of the unit root and cointegration tests; the unit root test used the null hypothesis versus the alternative of stationarity in the variables for the results of the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests. The results thus cannot reject the null hypothesis of a unit root; the variables in the levels were I (1) for each ADR price and UND price. The variables in the first difference were integrated of order zero;
the null hypothesis of unit root was rejected at the 5% level for the price difference series.
These results indicate that the two price series are integrated in the first difference and thus validate the use of the cointegration test.
Table 2. Unit root and cointegration tests for log-prices of ADRs and UNDs
Augmented Dickey-Fuller Test Phillips-Perron Test Unit Root Test
Levels First
Differences Levels First Differences ADR -0.112758 -51.53653 ** -0.091492 -51.49286 **
YPF UND -0.138284 -48.78652 ** -0.126952 -48.83657 **
ADR -1.679652 -45.80010 ** -1.635612 45.39878 **
TEO UND -1.624543 -45.71221 ** -1.579939 -45.34922 **
ADR -2.256933 -38.23152 ** -1.811293 -51.83980 **
TGS UND -1.898783 -47.40127 ** -1.897981 -47.33906 **
Cointegration Tests Trace Test 5% CV Max-Eigenvalue Test 5% CV
None 78.15789 ** 15.41 78.15465 ** 14.07
YPF One at most 0.003231 3.76 0.003231 3.76
None 77.81962 ** 15.41 77.81962 ** 14.07
TEO One at most 2.827981 3.76 2.827981 3.76
None 111.4459 ** 15.41 107.8217 ** 14.07
TGS One at most 3.624222 3.76 3.624222 3.76
Notes:
1Total number of sample observations is 2,888 for YPF, 2,516 for TEO, and 2,500 for TGS. UND represents price of underlying stock.
** P < 0.05.
Given that all the variables of the same order were integrated, this study used two Johansen multivariate cointegration tests to determine whether the variables in each series were cointegrated. The maximum likelihood estimation procedure provided a likelihood ratio test, referred to as a trace test, with the likelihood ratio test being the test for maximum eigenvalue. The likelihood ratio statistic rejected the null hypothesis of no cointegration at the 5% level. A feature of this approach is that the VECM contains an error correction term that reflects the current error in achieving long-run equilibrium. Therefore, the VECM can be used to jointly estimate the long-run relationship with short-run dynamics, a process that has been proven to be more effective than Granger causality.
Table 3 provides the estimates of the linear model. To address the issue of linear, or nonlinear, adjustment to the long-run equilibrium, this study estimated a linear VECM, given by equation (11), with the selection of the lag length being based upon the AIC and BIC criteria. As a comparison, this study first of all estimated the linear VECM for the price series of the ADRs and UNDs, reporting the results of the linear VECM estimation in Table 3. The estimated coefficients of the error correction term on the equations of the UND were all significant at the 5% level.
Table 3. Linear VECM estimations for log-prices of ADRs and UNDs
AIC -22529.2 -4510.15 -18063.0
BIC -22505.9 -4487.76 -18046.2
Notes:
1Values in parentheses are Eicker-White standard errors.
***P < 0.01; **P < 0.05; * P < 0.10.
The estimation results of the threshold VECM, and the test for the hypothesis of linearity versus the threshold effect of nonlinearity, provided by equation (13), are presented in Tables 4, 5 and 6, under the application of the SupLM test for the complete bivariate specification.
The P values of the results supporting the threshold cointegration hypothesis were calculated using both the fixed repressor and a residual bootstrap experiment, with 1,000 simulation replications. The estimated threshold VECM was provided by equation (12), with the selection of the lag length being based upon the AIC and BIC criteria; it was also considered
in this study that the cointegrating vector should be estimated. Standard errors were calculated from the heteroskedasticity-robust covariance estimator, with the parameter estimates being calculated by the minimization of equation (8) over a 300 × 300 grid on the parameters (
βˆ
γ β, ).
Table 4 reports the threshold VECM results for ADR with ticker symbol ‘YPF’ along with UND. In this study, a lag length of l = 3 was selected, with the estimated cointegrating relationship being wt-1 = ADRt-1 −1.00123UNDt-1, quite close to a unit coefficient. This study also conducted analyses for the case where a unit coefficient is imposed, with the results being very similar. The estimated threshold parameter wasγ = 0.000368, indicating that the first regime corresponded to |ADRt-1 −1.00123UNDt-1|≤ 0.000368. This first regime, which comprised 78% of all of the observations in the sample, is referred to in this study as the
‘typical’ regime. Conversely, the second regime, which was |ADRt-1 −1.00123UNDt-1| >
0.000368, comprised 22% of all of the observations in the sample and is referred to here as the ‘extreme’ regime.
In the ‘typical’ regime specifically, both ∆ADRt and ∆UNDt had statistically insignificant error correction effects and minimal dynamics. They were close to white noise, which indicates that in this regime, ADRt and UNDt were close to random walks. In contrast, in the
‘extreme’ regime, the asymmetry of ∆ADRt and ∆UNDt was implied, in the sense that there was an error correction effect in the ADR and UND equation being statistically significant with dynamic coefficients. All in all, ADRt and UNDt were statistically significant in the error correction effects in the ‘extreme’ regime, but not in the ‘typical’ regime.
Table 4. Threshold VECM estimations of YPF for log-prices of ADR and UND
First Regime: |wt-1 |≤ 0.000368 Percentage of Obs = 0.783634
Second Regime: |wt-1 |> 0.000368 Percentage of Obs = 0.216366
Dep ∆ADRt ∆UNDt ∆ADRt ∆UNDt
Ind. Estimate Std Error Estimate Std Error Estimate Std Error Estimate Std Error wt-1 -0.032 0.027 0.015 0.016 -0.395 ** 0.200 0.442 *** 0.131 Constant (×10-3) 0.579 0.643 -0.774 0.478 -3.324 ** 1.572 2.064 1.563
∆ADRt-1 -0.005 0.039 0.144 *** 0.043 0.427 *** 0.138 0.217 ** 0.109
∆ADRt-2 0.078 0.049 -0.052 0.044 -0.257 * 0.141 0.106 0.115
∆ADRt-3 -0.017 0.056 0.057 * 0.034 0.241 * 0.133 0.054 0.113
∆UND t-1 -0.018 0.045 -0.016 0.037 -0.274 ** 0.127 -0.112 0.098
∆UND t-2 -0.015 0.038 0.018 0.027 0.197 *** 0.055 0.018 0.081
∆UND t-3 -0.018 0.036 0.009 0.037 -0.238 *** 0.086 -0.061 0.076 Threshold Estimate = 0.000368; Cointegrating Vector Estimate = 1.00123; AIC= -22653.1; BIC = -22606.4 Lagrange Multiplier Threshold Test
Fixed Regressor bootstrap = 84.114*** (P < 0.001) Residual bootstrap = 28.306*** (P < 0.001 ) Wald Test
Equality of Dynamic Coefficients = 34.188*** (P < 0.001) Equality of EC Coefficients = 24.911*** (P = 0.008) Note: ***P < 0.01; **P < 0.05; *P < 0.10.
The evidence of nonlinearity appeared to gain strength from the results of the Wald test diagnostics; thus, the null hypothesis of linearity in error correction terms was rejected.
Comparing the estimated coefficients of the error correction terms in Tables 3 and 4 shows that the linear error correction models imply very slow speed of adjustment, a result consistent with that reported in Enders and Chumrusphonlert (2004). Since the null hypothesis is of equality of the coefficients on the error correction terms and of the dynamic coefficients across the two regimes, an important finding of the estimated linear VECM and threshold VECM is that the error correction term for the ADR was negative; this result is consistent with the error correction terms. This implies specifically that from the long-run equilibrium, the ADR adjusts to any short-run deviations. Furthermore, the negative sign of the error
correction term implies that if the ADR premium is above its equilibrium level, the ADR will decline. This was as predicted in the model when the ADR overshot its long-run equilibrium;
the result is therefore just as expected.
Details of the procedures and analyses provided above are also presented in Tables 5 and 6. The error correction term appeared to be significant only in the ‘extreme’ regime. The estimated coefficients of the error correction terms in the ‘extreme’ regime appeared to be larger than those in the linear VECM. The short-run dynamic effects of ADRs and UNDs showed significant differences between ‘typical’ and ‘extreme’ regimes.
Table 5. Threshold VECM estimations of TEO for log-prices of ADR and UND
First Regime: |wt-1 |≤ 0.439982 Percentage of Obs = 0.926693
Second Regime: |wt-1 | > 0.439982 Percentage of Obs = 0.073307
Dep ∆ADRt ∆UNDt ∆ADRt ∆UNDt
Ind. Estimate Std Error Estimate Std Error Estimate Std Error Estimate Std Error wt-1 -0.138 0.109 0.006 0.045 0.031 * 0.018 1.069 *** 0.188 Constant (×10-3) 28.461 29.030 -21.562 * 12.326 -71.085 * 40.829 -139.86 *** 349.526
∆ADRt-1 -0.669 *** 0.157 -0.018 0.072 -0.207 *** 0.056 0.317 *** 0.080
∆ADRt-2 0.014 * 0.008 -0.748 *** 0.079 0.011 ** 0.005 -0.052 0.121
∆ADRt-3 -0.466 *** 0.163 -0.024 0.086 -0.565 *** 0.100 0.102 0.074
∆UND t-1 -0.002 0.011 -0.501 *** 0.086 0.004 0.004 -0.079 0.098
∆UND t-2 -0.197 * 0.118 -0.073 0.104 -0.970 *** 0.117 0.369 *** 0.142
∆UND t-3 -0.001 0.010 -0.353 *** 0.078 0.003 0.002 0.001 0.069 Threshold Estimate = 0.439982; Cointegrating Vector Estimate = 0.789472; AIC = -4740.20; BIC= -4695.41 Lagrange Multiplier Threshold Test
Fixed Regressor bootstrap = 103.117*** (P < 0.001) Residual bootstrap = 34.232*** (P < 0.001 )
Wald Test
Equality of Dynamic Coefficients = 24.806*** (P < 0.001) Equality of EC Coefficients = 26.127*** (P < 0.001) Note: ***P < 0.01; **P < 0.05; *P < 0.10.
Table 6. Threshold VECM estimations of TGS for log-prices of ADR and UND
First Regime: |wt-1 |≤ 0.000323 Percentage of Obs = 0.456548
Second Regime: |wt-1 | > 0.000323 Percentage of Obs = 0.543452
Dep ∆ADRt ∆UNDt ∆ADRt ∆UNDt
Ind. Estimate Std Error Estimate Std Error Estimate Std Error Estimate Std Error wt-1 -0.056 0.043 -0.004 0.016 -0.265 *** 0.090 0.374 *** 0.083 Constant (×10-3) 3.095 ** 1.483 -2.837 *** 0.920 0.705 1.247 -2.619 ** 1.075
∆ADRt-1 -0.009 0.054 0.029 0.034 -0.095 0.070 -0.046 0.057
∆ADRt-2 0.167 ** 0.073 0.094 * 0.051 0.148 ** 0.075 0.060 0.063
∆UND t-1 -0.016 0.052 0.105 *** 0.032 -0.213 *** 0.053 -0.102 ** 0.043
∆UND t-2 0.009 0.065 -0.081 * 0.046 0.108 * 0.063 0.018 0.051 Threshold Estimate = 0.000323; Cointegrating Vector Estimate = 0.993680
AIC = -18146. 3; BIC = -18112.8 Lagrange Multiplier Threshold Test
Fixed Regressor bootstrap = 20.910*** (P < 0.001) Residual bootstrap = 17.305*** (P < 0.001 ) Wald Test
Equality of Dynamic Coefficients = 20.772*** (P = 0.008) Equality of EC Coefficients = 49.256*** (P < 0.001) Note: ***P < 0.01; **P < 0.05; *P < 0.10.