Nonlinear interrelations between ADRs and their underlying stocks revisited: application of threshold VECM

Abstract

This study examines the dynamic interrelations between American depository receipts (ADRs) and their underlying stocks (UNDs) by using the threshold vector error correction model. In contrast to prior studies focusing on examining the effects of arbitrage threshold on stock return means, this study not only analyse the dynamics of return means but also return volatilities. Moreover, this article adopts two representative ADR issuers: UK VOD and Brazil CVDO and compares the differences between them. The empirical findings of this study are consistent with the following notions. First, for both of the case of UK VOD and Brazil CVDO, once the price relationship of ADRs and UNDs deviates away from the long-run cointegrated equilibrium, the re-establishing equilibrium process is more/less remarkable when the price deviations do (do not) exceed a critical threshold. However, for the case of UK VOD (Brazil CVDO), the tendency to adjust to correct a disequilibrium situation mostly depends on the UND (ADR) markets. Furthermore, this article denotes the threshold estimate in the case of UK VOD (Brazil CVDO) as an unusual (extreme) condition. Last, the arbitrage behaviours between the ADR and UND markets will increase the volatility in these two markets and reduce the correlation between them.

Notes

¹ADRs represent ownerships of foreign claims on multinational corporations (MNCs) incorporated outside the US There are several advantages for MNC to issue ADRs in the US market. For example, issuing ADRs can help MNC increase firms' exposure to the global markets, broaden the investors' base to raise more foreign capital without depressing their stock prices in the domestic markets, and reduce their costs of capitals. For investors, ADRs can provide gains from global diversification without trading abroad and hedge the investment opportunities in foreign equity markets as well as foreign exchange markets.

²Balke and Formby (1997) represent one of the first studies to introduce the threshold cointegration model for capturing the nonlinear adjustment behaviours in spot-futures markets. The concept of combining nonlinearity and cointegration has generated considerable applied interest, including the following applications: Martens et al. (1998) etc. dealing with the spot-futures relationship; Michael et al. (1997), Kilian and Taylor (2003) etc. focusing on the exchange rates; Balke and Wohar (1998), Peel and Taylor (2002) examining interest rate parity; Obstfeld and Taylor (1997), Taylor (2001) etc. focusing on purchasing power parity; Gallagher and Taylor (2001), Li (2006) analysing stock markets; analysing stock markets.

³The procedures are presented as follows: (1) ADR_t is regressed on UND_t and then the observations of equilibrium error, Z_t are obtained (2) a series of arranged error term is established that orders the observations of Z_t according to the value of Z_{t − 1} , rather than according to time. (3) by assigning two small numbers to serve as the initial value of θ and − θ, for example 0.005 and − 0.005, the series of arranged error terms can be split into two different regime areas: inside/outside the thresholds. (4) the regressions of Equation 1(1) are estimated for each regime area and the residual sum of square RSS is calculated and saves. (5) the values of θ and −θ are increased using one grid with very small values of 0.0001 and − 0.0001, and the above fourth procedure is then repeated for the new values of θ and −θ. (6) Procedures 4 and 5 are then repeated and the RSS value is derived for each value of θ and choose the value of θ for which the RSS is minimum.

⁴Although both of the and estimates are insignificant for the case of Brazil CVDO, however, the estimate (0.036) is greater than (0.004). This present finding still presents that the disequilibrium adjustment process is more remarkable in the outer regime.

Table 2. Parameter estimates of threshold VECM

⁵See Li (2005a) for the related discussions.

⁶See Li (2005b) for the related discussions.