The Cross-Market Premium and Financial Integration

In this section, we study the behavior of the cross-market premium during “tranquil” (noncrisis) times, in the absence of capital controls. The Appendix explains the methodology used to identify crisis episodes. The results using just the crisis periods are reported in the working paper version of this paper, Levy Yeyati et al. (2006), since those merit a separate analysis. Capital control periods are easier to single out, and are described in the next section.

Table 1 [ PDF 42.9KB | 1 page ] presents a first glance at the data, where we show summary statistics of the simple average of the cross-market premium of the stocks in each country’s portfolio. A positive premium implies that the price of the underlying stock is higher than the DR price. The upper panel shows the summary statistics of the premium calculated for all days in the sample period. The bottom panel shows summary statistics of the cross-market premium based on days for which there is contemporaneous trading in both markets. The table shows that the country average premium is in general close to zero. The largest average premium is in Korea, with 1.69 percent followed by Mexico with 1.23; in all other cases, this number is below one percent. The summary statistics of all stocks shows a mean premium of 0.53 percent, with a standard deviation of 0.74.

Naturally, the premium when all days are included should be higher than the one when only days with contemporaneous trading are taken into account, as the former includes observations when we know that active arbitrage does not take place. Table 1 [ PDF 42.9KB | 1 page ] shows that, for contemporaneous trading days, the premium is on average 0.12 percent for all stocks and the standard deviation is 0.73 percent.²² Especially in countries where a relative large part of the stocks are characterized by limited trading in either the domestic market and/or in the United States, like Mexico and Brazil, we see a sharp decrease in the average premium and its standard deviation when only contemporaneous trading days are included in the sample. In other words, the summary statistics suggest that including information based on non-contemporaneous trading day activity creates a downward bias in the magnitude of financial integration.

To complement the evidence presented in Table 1 [ PDF 42.9KB | 1 page ], Figure 1 [ PDF 44.6KB | 1 page ] displays the difference in the behavior of the premium of a firm with several days without contemporaneous trading and that of a firm with only contemporaneous trading days. In the first case, the premium oscillates around zero but with a wide standard deviation (top panel). Due to the infrequency of trading in either stock or both stocks, there are periods with no arbitrage pressure, in which the premium can diverge from zero for a long time. In the second case, the premium oscillates around zero with a small standard deviation (bottom panel).

5.1. AR and TAR Estimates

To formally examine the extent of financial market integration through LOOP, we estimate AR models for each stock, both using only contemporaneous trading days and all days in the sample period. Table 2 [ PDF 35.6KB | 1 page ] provides the country averages of these results. Taking both contemporaneous and non-contemporaneous trading days into account the average half-life ranges from 0.73 in Argentina to 2.70 in Mexico. Including only contemporaneous trading days, the average half-lives tend to be substantially lower in the majority of countries. These results show again that including non-contemporaneous trading days in the estimations produces a downward bias in the magnitude of financial integration.

We next estimate the TAR model using a grid-search on the threshold, as described in Section 4. In Table 3 [ PDF 32.8KB | 1 page ], we provide a summary of our findings. The table provides the country average of the estimated TAR thresholds and the implied half-life associated with β_out . For comparison, we also show the implied half-life for the standard AR model. Both models are estimated using only contemporaneous trading days. The estimates for the individual stocks are reported in Appendix Table 2.²³

The results confirm our priors. The average band of no-arbitrage ranges from 0.11 percent in Russia to 0.68 percent in Venezuela. This implies, in particular, that the cross-market premium in Venezuela can move, on average, between –0.68 and 0.68 percent without arbitrage taking place in the market. Once outside the inaction-band, arbitrage takes place very rapidly: the typical half-life is less than a day. It is important to note that these results do not imply that Russia is more integrated with the U.S. than Venezuela. As shown in the next section, deviations from the law of one price are affected by stock liquidity. Thus, to study the relative integration of different countries one has to compare stocks with similar liquidity, a comparison difficult to make with our sample.²⁴

If non-linearities are present in the evolution of the cross-market premium, convergence speeds should be slower when estimated by a linear (AR) model than those obtained from the TAR model, as is indeed the case. Moreover, the wider the band-width, the higher the persistence estimated by the linear model, as Figure 2 [ PDF 42.2KB | 1 page ] shows. Additionally, the difference between the half-life estimated by the AR, and that obtained from TAR models outside the band, is itself proportional to the linear half-life. These results, which provide further evidence of how the presence of non-linearities influences the results from a linear estimation, are consistent with similar tests reported by Imbs et al. (2003) for goods markets. Appendix Table 2 (last column) shows, at the stock level, the results of the significance tests of the TAR versus the AR model. The P-values of the LLR suggest that in 31 percent of the cases the TAR is the preferred model. However, as explained in the previous section, this test has low power, so it is difficult to conclude that the TAR model should not be used.²⁵ In fact, the evidence from Figure 2 [ PDF 42.2KB | 1 page ] suggests how the presence of non-linearities might affect linear estimations.

5.2. Integration and Liquidity

One would expect the bands of no-arbitrage to widen as liquidity declines, to the extent that investors incorporate a liquidity risk premium as an additional transaction cost.²⁶ To see whether this is indeed the case, we examine how the AR half-lives and the TAR band-width and half-lives are associated with the liquidity of the stock. We use two measures of liquidity, one based on trading value, the other one on trading frequency.²⁷ In the first case, liquidity is measured as the log of the average of the mean value traded of the underlying stock and the DR. The second measure defines liquidity as the number of contemporaneous trading days (i.e. the number of days both the underlying stock and the DR were traded) over all days during the sample period.

Figure 3 [ PDF 65.8KB | 1 page ] reports the regression results and the partial regression plots of regressing the halflife estimates by the AR model on liquidity. In the top panel, we show the regression based on half-lives estimated using the cross-market premium for all days. In the lower panel, the regression results are based on the cross-market premium using only information from contemporaneous trading days. In all regressions we control for country-specific fixed effects and a constant. The results indicate that a significant negative correlation between AR halflives and liquidity exists; illiquid stocks, as characterized by a low trading value or infrequent trading, are associated with more persistent price deviations.²⁸ This relation is stronger when all trading days are included, suggestion that including non-contemporaneous trading days in the estimation leads to an overestimation of the trading costs.

Figure 4 [ PDF 71.8KB | 1 page ] shows the regression results and partial regression plots for the same regression using the estimated TAR band-width and half-life. The upper panels reveal the presence of a significant negative correlation between band-width and liquidity.²⁹ Furthermore, the lower panels show that band reversion, once outside the no-arbitrage regime, takes place more slowly (half-lives are longer) for illiquid stocks.³⁰ In sum, the size and persistence of the deviations from LOOP appear to be higher (integration appears to be weaker) as the liquidity of the stock declines: illiquidity adds to transaction costs and weakens financial integration.

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