RDP 2003-06: The Characteristics and Trading Behaviour of Dual-Listed Companies 5. Testing for Excess Comovement
June 2003
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The phenomenon of assets with similar cash flows trading at quite different prices is interesting. While these differences do not provide an opportunity for pure riskless arbitrage, they are nonetheless an anomaly. Froot and Dabora (1999) find that the price differential is correlated with the relative performance of the markets in which the twins trade most. They propose that this comovement with the market index where most of a twin's trading occurs is a reflection of prices in each market being influenced by market sentiment.
Given the recent creation of three Anglo-Australian DLCs, this section tests whether the twins in these companies are also subject to excess comovement. Further, we also test whether the excess comovement for the longer-standing Anglo-Dutch DLCs has endured. In each case we apply Froot and Dabora's methodology and test the hypothesis that each twin's price comoves excessively with the market on which it trades most. For example, comovement would imply that positive market shocks in Australia are associated with an increase in the price of the Australian twin relative to the price of the UK twin.^{[19]} Accordingly, we regress the return differential between the two companies on the returns of the Australian and UK market indices plus the currency return:
where and are log returns on the Australian and UK twins in DLC i, and are the log returns on the Australian and UK stock market, and is the log return on the AUD/GBP exchange rate. We also run the corresponding regression for the Anglo-Dutch DLCs.
The use of standard market indices in such regressions potentially creates a bias when one of the companies is included in a market index. For example, each of the Australian and UK twins are included in the ASX 100 and FTSE 100, respectively. However, similar to the evidence in Froot and Dabora (1999), we find the effect of this bias is minor since each firm bears a relatively small weight in its index. However, in the case of the tests for the Anglo-Dutch DLCs, when we use the Dutch AEX 100 index we remove Royal Dutch due to its significant weight.
The null hypothesis is that changes in the price differential are uncorrelated with the performance of the two national markets on which the DLCs trade, but may be correlated with exchange rate movements since the dependent variable is the difference between price changes of assets traded in different currencies. Indeed, if the twins' prices (in a common currency) always moved together, we would expect a coefficient of minus unity on the exchange rate variable. For instance, an appreciation in the Australian dollar/pound sterling exchange rate should result in a relative increase (decrease) in the local-currency price of the UK (Australian) scrip.
The alternative hypothesis based on the comovement phenomenon is that β_{1} will be positive and β_{2} will be negative. For example, a shock to the overall Australian (UK) equity market is expected to be associated with an increase (decrease) in the local currency price of the Australian twin relative to the local currency price of the UK twin. The implication is that the price differential is being driven to an extent by market-specific liquidity shocks or relative market sentiment.
We have estimated Equation (1) using a wide range of return horizon, but for brevity, Table 3 presents results only for horizons of 2, 5, 10 and 20 days. The reason for presenting longer horizon returns is to ensure that any estimated excess comovement is not due to asynchronous trading effects or very short-term liquidity shocks, and also to get a sense of the persistence of such effects.^{[20]} These results all involve rolling regressions using overlapping data, so the statistical tests are based on Newey-West standard errors to account for the moving average error process that is introduced.^{[21]}
Rio Tinto | BHP Billiton | Brambles | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2-day | 5-day | 10-day | 20-day | 2-day | 5-day | 10-day | 20-day | 2-day | 5-day | 10-day | 20-day | |||
Notes: This table provides tests of whether the three recent Anglo-Australian DLCs also demonstrate the excess comovement phenomenon identified by Froot and Dabora (1999). It reports estimates of Equation (1): where and are the log returns on the Australian and UK twins, respectively, and are the log returns on the Australian and UK stock markets, respectively, is the log return on the AUD/GBP exchange rate, and all log-difference returns are multiplied by 100. To take account of asynchronous trading, the Australian returns are measured to day t and the UK returns are measured to day t−1. Newey-West standard errors are shown in parentheses. Rejections of the null hypothesis at the 10, 5 and 1 per cent levels are denoted by *, ** and ***, respectively. The sample period is January 1996-December 2002 for Rio Tinto, July 2001-December 2002 for BHP Billiton, and August 2001-December 2002 for Brambles Industries. |
||||||||||||||
β_{1} | 0.65*** (0.06) |
0.45*** (0.06) |
0.41*** (0.06) |
0.42*** (0.03) |
0.77*** (0.14) |
0.41*** (0.14) |
0.28** (0.11) |
0.42*** (0.07) |
0.65*** (0.19) |
0.29** (0.14) |
0.24** (0.11) |
0.02 (0.11) |
||
β_{2} | −0.55*** (0.04) |
−0.45*** (0.04) |
−0.38*** (0.04) |
−0.34*** (0.02) |
−0.40*** (0.08) |
−0.23*** (0.08) |
−0.22*** (0.07) |
−0.29*** (0.04) |
−0.33*** (0.11) |
−0.22*** (0.07) |
−0.15** (0.07) |
−0.07 (0.06) |
||
δ | −0.35*** (0.06) |
−0.56*** (0.06) |
−0.71*** (0.06) |
−0.85*** (0.03) |
−0.71** (0.12) |
−0.86 (0.13) |
−0.76** (0.09) |
−0.91 (0.06) |
−0.73* (0.16) |
−0.97 (0.11) |
−1.07 (0.11) |
−1.05 (0.10) |
||
β_{0} | −0.01 (0.04) |
−0.02 (0.08) |
−0.05 (0.13) |
−0.15** (0.08) |
−0.02 (0.09) |
−0.03 (0.16) |
−0.08 (0.18) |
−0.39 (0.24) |
−0.01 (0.12) |
−0.04 (0.19) |
−0.04 (0.24) |
−0.06 (0.23) |
||
Adjusted R^{2} | 0.22 | 0.27 | 0.37 | 0.49 | 0.22 | 0.28 | 0.43 | 0.66 | 0.06 | 0.19 | 0.32 | 0.49 | ||
Observations | 1,824 | 1,821 | 1,816 | 1,806 | 389 | 386 | 381 | 381 | 364 | 361 | 356 | 356 |
Our results confirm the excess comovement findings of Froot and Dabora. Almost all coefficients are significantly different from zero at the 1 per cent level and of the expected sign. At the 2-day horizon, it may not be surprising that β_{1} is strongly positive and that β_{2} is strongly negative, i.e., that the relative price of the twins is very substantially affected by the relative performance of their national markets. However, any short-term effects from liquidity shocks should be largely absent in longer-term returns. Yet at the 10-day horizon, for example, the estimates for β_{1} and β_{2} and of around 0.30 and −0.25, respectively, imply that a 10 per cent increase in the Australian (UK) benchmark index is associated with an increase in the relative price of the Australian (UK) twin of around 3 (2½) per cent.
Furthermore, it may not be surprising that the exchange rate coefficient δ is typically substantially less than −1 at the 2-day horizon, so that exchange rate changes in the very short-term have significant effects on the price differential. However, at longer horizons it also remains less than −1. For example, estimates for β_{3} of around −0.8 at the 10-day horizon imply that a 10 per cent change in the Australian dollar/pound sterling exchange rate would tend to be associated with a 2 per cent increase in the (common currency) relative price of the twin from the country that has seen an appreciation.^{[22]}
The observation that the magnitude of the coefficients on the two market indices falls (and that on the exchange rate coefficient rises) as the return horizon lengthens, suggests that excess comovement may be largely a short-run phenomenon. However, results from regressions using 50-day returns (available upon request) continue to show excess comovement for Rio Tinto and BHP Billiton, suggesting that the comovement is still present at fairly long horizons.
Given that Froot and Dabora's finding of excess comovement was based on data only up to 1995, it may be of interest to see if this phenomenon has continued more recently. Accordingly, we estimated versions of Equation (1) for Royal Dutch/Shell, Unilever and Reed Elsevier for 1996–2002, and also for 1989–1995, the previous seven-year period. In the case of the first two DLCs, we follow Froot and Dabora and include the return on the S&P 500 index and the change in the US dollar/pound sterling exchange rate to reflect the significant share of trading of the Dutch twin that occurs in the US market. In all three cases, the dependent variable is defined as the return on the Dutch twin less the return on the UK twin, so the alternate hypothesis of excess comovement would suggest that the sum of the coefficients on the Dutch and US market indices will be positive, and the sign of the coefficient on the UK market index will be negative.
The results for the Anglo-Dutch DLCs tell a similar story to the tests for the Anglo-Australian DLCs. Table 4 shows the results from the 10-day return specification (results for other horizons are available from the authors). In almost all cases, we reject the null hypothesis concerning the market indices at the 1 per cent level. Comparing the results of the two periods, there is some indication that the degree of excess comovement has lessened somewhat since the end of Froot and Dabora's sample. However, we hesitate to cite this result as evidence of a reduction in the degree of the anomalous return behaviour of these DLCs, since the earlier data on the mean absolute price differential in Table 2 would not really support such a conclusion.
Company | Constant | AEX | FTSE | S&P | EUR/GBP | EUR/USD | Adjusted R^{2} |
---|---|---|---|---|---|---|---|
Sample period: January 1989-December 1995 | |||||||
Royal Dutch Shell | 0.03 (0.08) |
0.15*** (0.04) |
−0.33*** (0.03) |
0.10*** (0.04) |
−0.67 (0.06) |
−0.12 (0.04) |
0.40 |
Unilever | −0.01 (0.10) |
0.19*** (0.04) |
−0.41*** (0.04) |
0.03 (0.05) |
−0.54 (0.07) |
−0.15 (0.05) |
0.28 |
Reed Elsevier^{(a)} | 0.37*** (0.07) |
0.26*** (0.04) |
−0.53*** (0.04) |
– | −0.75*** (0.05) |
– | 0.39 |
Sample period: January 1996-December 2002 | |||||||
Royal Dutch Shell | −0.07 (0.08) |
0.18*** (0.03) |
−0.27*** (0.04) |
0.00 (0.03) |
−0.67 (0.07) |
−0.09 (0.06) |
0.40 |
Unilever | −0.06 (0.10) |
0.14*** (0.05) |
−0.21*** (0.06) |
0.10*** (0.04) |
−0.82 (0.09) |
0.02 (0.07) |
0.25 |
Reed Elsevier | −0.10 (0.09) |
0.14*** (0.04) |
−0.18*** (0.05) |
– | −0.78*** (0.06) |
– | 0.28 |
Notes: This table provides tests of whether the excess comovement phenomenon
identified by Froot and Dabora (1999) has persisted beyond their sample period.
It uses 10-day returns and shows estimates from the equation: where: and are the log returns on the Dutch and UK twins,
respectively; , and
are the log returns on the Dutch, UK and US stock
markets, respectively; and are the log returns on the EUR/GBP and EUR/USD
exchange rates, respectively; and all log-differenced returns are multiplied by
100. In the case of the Dutch exchange rate, the guilder is used in place of the
euro prior to 1999. Newey-West standard errors are shown in parentheses.
Rejections of the null hypothesis at the 10, 5 and 1 per cent levels are denoted
by *, ** and ***, respectively, except in the case of the regression
coefficients for the exchange rate variables in the Royal Dutch/Shell and
Unilever equations, where there is no prediction about the size of the parameter
estimates. |
The results for both the Anglo-Dutch and Anglo-Australian DLCs therefore imply that excess comovement with aggregate market indices is a pervasive feature of the pricing of DLCs. In addition, the results consistently suggest a less-than-unit response of the relative valuation of the twins to movements in the exchange rate. In a sense, it appears that the market pays too much attention to one type of information (overall market indices) that should be irrelevant to the relative valuation of the twins but pays too little attention to information (exchange rates) that is relevant to their relative valuation.
Footnotes
For all three Australian-UK DLCs, the Australian and UK arms trade mostly on the Australian Stock Exchange and London Stock Exchange, respectively. [19]
In the case of the Anglo-Australian DLCs there is typically an eleven-hour difference between UK and Australian market closing times. One possible approach to minimise the problems of asynchronous trading would be to use Australian closing prices and UK opening prices (approximately a three-hour time difference). Unfortunately, data problems with opening prices precluded this approach. Instead, we conduct the regressions under the implicit assumption that most global equity price discovery occurs during Northern Hemisphere trading hours, so that a majority of price discovery for the Anglo-Australian DLCs also occurs during London trading. Hence, the regressions actually use Australian returns to day t and UK returns to day t−1. However, the results from an estimation using day t returns for both markets are similar, especially for longer-horizon returns. [20]
Although the standard errors are corrected by the Newey-West procedure, there is no similar adjustment to the adjusted R^{2}, which is biased upwards, especially as the extent of overlap increases. [21]
When we impose the restriction that β_{3} is equal to −1, the finding that β_{1} and β_{2} are significantly different to zero remains robust. [22]