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The Limits of Arbitrage: Evidence from Dual-Listed Companies

Abe de Jong Erasmus University Rotterdam

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Leonard Rosenthal Bentley College

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Mathijs A. van Dijk Erasmus University Rotterdam

[email protected]

May 2003 Correspondence Mathijs A. van Dijk Department of Financial Management (Room F4-21) Erasmus University Rotterdam PO Box 1738 3000 DR Rotterdam THE NETHERLANDS Phone: +31 10 408 2748 Fax : +31 10 408 9017

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The Limits of Arbitrage: Evidence from Dual-Listed Companies

Abstract

We study the limits of arbitrage in international equity markets by examining a sample of

dual-listed companies (DLCs). DLCs are the result of a merger in which both companies

remain incorporated independently. DLCs have structured corporate agreements that allocate

current and future equity cash flows to the shareholders of the parent companies according to

a fixed ratio. This implies that in integrated and efficient financial markets, the stock prices of

the parent companies will move together perfectly. Therefore, DLCs offer a unique

opportunity to study market efficiency and the roles of noise traders and arbitrageurs in equity

markets. We examine all 13 known DLCs that currently exist or have existed. We show that

for all DLCs large deviations from the theoretical price ratio occur. The difference between

the relative price of a DLC and the theoretical ratio is often larger than 10 percent in absolute

value and occasionally reaches levels of 20 to 50 percent. Moreover, deviations from parity

vary considerably over time for all DLCs. We find that return differentials between the DLC

parent companies can to a large extent be attributed to co-movement with domestic stock

market indices, consistent with Froot and Dabora (1999). These findings are evidence of

inefficiencies in financial markets that seem to be driven by noise trading. Our findings have

important implications for the effectiveness of arbitrage in international financial markets.

Keywords

Market efficiency, arbitrage, anomalies, international finance

JEL subject codes

F30, G14, G15

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1. Introduction

In recent years, there has been increased debate between those who believe that stock markets

in developed countries are efficient and those who believe that there are behavioral reasons

which interfere with rational pricing by investors.1 Shleifer and Vishny (1997) make a

convincing argument for the limits of arbitrage, and in particular risk arbitrage. As early as

1986, Black described the effects of noise on financial markets. Noise trading is defined as

trading on noise as if it were information. According to Black, noise traders make markets

possible. On the other hand, the noise that these traders put in stock prices is cumulative and

without a counter-force prices will drift away from their underlying value. However,

information traders are able to benefit from deviations caused by noise traders and in an

arbitraging process the prices will move back to the fundamental value. Black (1986, p. 533)

asserts that: �All estimates of value are noisy, so we can never know how far away price is

from value.�

Subsequent studies have modeled the effects of noise trader risk on arbitrage (see De

Long, Shleifer, Summers, and Waldmann, 1990 and Shleifer and Vishny, 1997). In these

models, arbitrageurs may be driven out of the market by the possibility of adverse price

movements in the short-run, even though it is known that prices will converge eventually.

Recent studies argue that other impediments to textbook arbitrage exist in financial markets.

First, two traded assets may be similar, but are hardly ever perfect substitutes in the real

world. Second, arbitrage requires capital. This results in opportunity costs as well as holding

costs. Moreover, dedicating capital to a specific arbitrage position may induce unhedgeable

fundamental risk. Third, transaction costs (such as bid-ask spreads, commissions, and market

impact) are incurred in the set-up of an arbitrage position.

This paper studies the limits of arbitrage in real-world equity markets by looking at

mispricing in a sample of dual-listed companies (also referred to as Siamese twins). A dual-

listed company (DLC) structure involves two companies contractually agreeing to operate

their businesses as if they were a unified enterprise, while retaining their separate legal

identity and existing stock exchange listings. Well-known examples of DLCs are the Anglo-

Dutch combinations Royal Dutch/Shell and Unilever NV/PLC. In integrated and efficient

financial markets, stock prices of the twin pair should move together perfectly. DLCs offer a

unique opportunity to analyze market efficiency and the roles of noise traders and

1 See e.g. Rubinstein (2001) and Thaler (1999).

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arbitrageurs, because the stocks of the twin pair are close substitutes. According to Black

(1986), we cannot measure the underlying value of a traded asset. However, DLCs provide an

excellent vehicle for examining the behavior of two assets of which the fundamental value

should be exactly the same.

Previous studies by Rosenthal and Young (1990) and Froot and Dabora (1999) have

shown that significant mispricing in three DLCs has existed over a long period of time.

Rosenthal and Young assert that no satisfactory explanation can be found for the price

disparity of the Royal Dutch/Shell and Unilever twins. Froot and Dabora also investigate the

Anglo-American corporation Smithkline Beecham and show that the prices of twin stocks are

correlated with the stock indices of the markets on which each of the twins has its main

listing. They conclude that the location of the trade matters for the pricing of DLCs.

We examine all 13 DLCs that exist or have existed to our knowledge. The motivation

for our study is three-fold. First, since the two previous papers were written, 10 additional

DLCs have been established, without any research on their structure, pricing and other issues

related to it.2 There have been no academic research papers which have examined all 13, their

similarities and differences, and their pricing patterns. Recent DLCs may have learned from

the older twins and the mispricing may be reduced. Moreover, equity markets may have

operated more efficiently in the 1990s than in the 1980s. Our second motivation is that 6 of

the 13 twins studied in this paper have unified the DLC into a single structure. The transition

from DLC to regular stock allows us to measure the effects in the market and the persistence

of mispricing. Third, we expect that more DLCs will be established in the future.

Understanding the pricing behavior is therefore not only important from the perspective of

arbitrage in equity markets, but also from a corporate finance viewpoint (e.g. the optimal legal

structure in cross-border mergers and problems in cost of capital estimation for twins with

unequal returns).

The issues involved in DLCs bear some resemblance to the closed-end fund puzzle.

Closed-end funds are traded mutual funds that hold a portfolio of other publicly traded funds.

The puzzling anomaly is that closed-end funds typically exhibit discounts of 10 to 20 percent

relative to their net asset value. Explanations offered in the literature stem from agency costs,

tax liabilities, asset illiquidity, and investor sentiment (see Lee, Shleifer, and Thaler, 1991).

2 Recently, the DLC structure was selected in the merger between U.S. cruise company Carnival Corporation and U.K. firm P&O Princess (Financial Times, October 27, 2002). In merger negotiations of Abbey National (U.K.) with National Australian Bank and Bank of Ireland with Alliance & Leicester (U.K.) the DLC structure was proposed, but both merger plans were abandoned (Financial Times, May 25, 1999 and July 8, 2002).

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Brauer (1984) and Brickley and Schallheim (1985) show that the ending of a closed-end fund

leads to an immediate disappearance of the discount. Pontiff (1996) provides evidence that

there is a relation between the discounts of closed-end funds and the costs of arbitrage.

Although studying closed-end funds yields several interesting insights in the mechanics of

arbitrage in equity markets, an analysis of DLCs is a much more straightforward way to

investigate this issue. In the case of closed-end funds, the price of the fund is compared with

the net asset value. A major problem in this literature is the determination of the asset value

which is hampered by e.g. agency costs, taxation, and liquidity. In contrast, the security prices

of DLCs are derived from one and the same underlying value. Therefore, we do not need to

construct and apply a subjective estimate of value.

Our results show that for each of the 13 DLCs large deviations from the theoretical

price are present. The maximum absolute deviations range from 15 percent to almost 50

percent. We also find that the deviations are time-varying. To a large extent, the variations can

be explained by co-movement with domestic stock market indices. These findings are

evidence of inefficiencies in financial markets that may well be driven by noise trading.

Moreover, the limitations of arbitrage are clearly illustrated by the obvious mispricing of

DLCs.

Our results imply that noise trader risk may lead to significant deviations of the prices

of two assets that are close perfect substitutes. First, this evidence suggests that sizeable

mispricing may well exist for common stocks. While investors in DLCs have the price of the

other twin as a point of reference, investors in regular stocks lack such guidance. As a result,

mispricing of regular stocks could be even more pronounced than mispricing in DLCs.

Second, the results are evidence of inefficient markets in which adverse effects of noise

trading are not eliminated by arbitrage. Welch (2000) surveyed 226 academic financial

economists and reported that 79 percent of the finance professors agreed with the statement

that, by and large, public securities markets are efficient. A second statement, that financial

markets offer no arbitrage opportunities, is agreed upon by 75 percent of the economists. Our

paper shows that reasonable doubt can be casted on the first statement. While the second

statement about arbitraging is more in line with our results, we argue that limitations to

arbitrage are a more likely reason than the absence of inefficiencies.

The remainder of the paper is structured as follows. In section 2 we describe the

structure of dual-listed companies. Section 3 provides the data description. We examine the

magnitude of the deviations of the twin prices from theoretical parity in section 4. Our testing

methodology and the empirical results are presented in section 5. Section 6 concludes.

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2. The structure of dual-listed companies

Dual-listed companies are the result of a merger between two firms in which the firms agree

to combine their activities and cash flows, but the corporations keep separate shareholder

registries and identities. In this section, we briefly explain the structure of a DLC based on an

example from our data set, Reed Elsevier. Subsequently, we discuss structures as well as

motives for a DLC structure and introduce the 13 DLCs in our data set.

On January 1, 1993, Elsevier NV (Elsevier) and Reed International PLC (Reed)

merged their businesses. (See Reed Elsevier Form 20-F for 1998). Under the merger, almost

all of the operating activities of both firms were put into Reed Elsevier PLC, a U.K.

corporation. Most of the treasury and related finance functions were put into Elsevier Reed

Finance B.V., which is incorporated in the Netherlands. The operations of the businesses have

been managed on unified basis, but both Reed and Elsevier retain their separate identities.

Their shares trade on the London, Amsterdam, and New York Stock Exchange. Reed and

Elsevier each holds a 50 percent interest in Reed Elsevier PLC. Reed International holds a 46

percent interest in Elsevier Reed Finance BV, while Elsevier holds the remaining 54 percent.

In addition, Reed holds a 5.8 percent indirect interest in Elsevier, which reflects the higher

market capitalization of Reed compared with Elsevier just prior to the merger. Elsevier also

owns shares in certain of the Dutch subsidiaries of Reed Elsevier PLC, which enables Elsevier

to receive dividends within its own tax jurisdiction. The effect is to mitigate potential tax costs

for Reed Elsevier. With respect to the latter, the companies have indicated the combination

was expected to cut the combined companies� effective tax rate by up to one percentage point

per year.3 The deal was structured so that there was no exchange of cash and therefore no

capital gains tax. Taking all of this into account, Reed International shareholders have a 52.9

percent economic interest in the net income of Reed Elsevier combined, and Elsevier

shareholders have a 47.1 percent economic interest. In the case of Reed and Elsevier, the

boards of director of both Elsevier and Reed each manage their shareholdings in Reed

Elsevier and Reed Finance BV. Elsevier and Reed are each entitled to appoint ten directors

and decisions of the board of directors of Reed Elsevier requires a two-thirds majority. As part

of the merger, Reed and Elsevier set up an equalization agreement to insure that the ordinary

shareholders of both firms have equivalent dividend and capital rights in the net income and

3 See Financial Times, February 18, 1993. Two partners at Price Waterhouse who worked on the deal pointed out to us that this arrangement allows Reed Elsevier to earn interest on its funds without taxes by legally investing it in a tax haven.

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net assets of the combined businesses. Given the significant effect of differences in taxation of

dividends in the U.K. and the Netherlands, Reed�s direct and indirect interest of 52.9 percent

in Reed International, Elsevier�s 54 percent interest in Elsevier Reed Finance, dividends and

capital rights are set such that one Elsevier ordinary share provides the economic equivalent

of 1.538 Reed ordinary shares in May 1997.4 The primary market for Reed shares is the

London Stock Exchange (LSE). Shares also trade the New York Stock Exchange (NYSE) as

ADRs, where each ADR equals four Reed ordinary shares. In addition, Reed shares trade in

Amsterdam (ASX). Elsevier ordinary shares trade primarily on the Amsterdam Stock

Exchange. They also trade on the NYSE as ADRs where each ADR equals two ordinary

shares. Elsevier shares trade as well on the London Stock Exchange.

DLCs can be structured in three alternative ways. The DLC structure of Elsevier/Reed

International is a combined entities structure.5 The key characteristic is that the assets of the

two companies are held by one or more jointly-owned holding companies. The latter pays

dividends to the two companies, which then distributes them to the shareholders using a

predetermined ratio as outlined in an equalization agreement. The two companies each have

their own shareholder base, domiciles and listings. Alternatively, in the separate entities

structure, the operating activities remain fully owned by each of the two merged companies.

The companies also retain their domiciles, listings and shareholders. The equalization

agreement is set up to insure that there is equal treatment of both companies� shareholders in

voting and economic terms. There are cross-holdings of special dividend access shares or

contractual payments to provide for equalization payments to shareholders. Finally, in the

stapled stock structure, shares in each firm are �stapled� to each other, so they cannot be

traded separately. The idea is to minimize the likelihood of the share of one company from

trading at a discount to the other.

Table 1 describes the types of structure used by each DLC as well as their date of

merger. The two eldest twins are the Anglo-Dutch combinations Royal Dutch/Shell and

Unilever. Extensive descriptions of these twins can be found in Rosenthal and Young (1990)

and Froot and Dabora (1999). In 1988, almost fifty years after the previous DLC, ABB, a

Swiss-Swedish engineering group was created. This DLC set the stage for a flow of DLCs,

4 See Reed Elsevier 20-F for 1998. There is an elaborate discussion of the differences in the tax treatment of dividends in the U.K. vs. the Netherlands, and how dividend decisions are made so as to take them into account with respect to making the distribution of cash flows economically equivalent. The so-called equalization ratio has changed over time to reflect stock splits for both companies. 5 See �Dual-Listed Company Transactions and Frustrating Action,� issued by the Panel on Takeovers and Mergers, April 26, 2002.

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from Eurotunnel in 1989 to Brambles Industries in 2001. It is clear that the combined entities

structure predominates occurring in 7 (14 of the companies) of the 13 pairs (26 companies),

with the separate entities structure occurring 5 times and the stapled structure twice.

Interestingly, the country most often involved by far is the U.K. with 8 individual companies,

followed by the Netherlands with 4 and Australia, Sweden and Switzerland with 3 each. In the

newest transaction, whose completion is pending, one of the firms is also domiciled in the

U.K.. When the structure is broken down by country, the combined structure dominates for

Dutch, Swiss and Swedish firms, while the separate entity structure dominates in Australia.

What are the motivations for firms to adopt a DLC structure, instead of a regular

merger where a single share is created? The first motivation is taxation. A capital gains tax

could be owed if an outright merger took place, but no such tax consequence would arise with

a DLC deal. Differences in tax regimes may also favor the DLC, because cross-border

dividend payments are minimized. In addition, there may be favorable tax consequences for

the companies.6 A second motivation is the preservation of the (national) identity of each of

the twins. This is a political reason, because by maintaining separate firms, any problems with

an important local company being taken over by a foreign firm would be eliminated. The third

motive is the reduction of investor flow-back, which would depress the price of the stock of

one of the firms in their own market if the merger route were used instead. The thought

behind this is that some institutional investors cannot own the shares of firms domiciled

outside the home country or can only own such shares in limited quantity. In addition, in a

merger, the non-surviving firm would be removed from any indexes that exist. Index tracking

funds would then have to sell the shares of the surviving company. With the DLC structure,

all of this would be avoided.7 A fourth motive is that DLCs do not necessarily require

regulatory (anti-trust) consent and are not constrained by foreign investment approvals.8

Finally, the access to capital markets may be reduced when in a regular merger a quotation

disappears. Keeping a separate stock exchange listing which may allow each of the firms to

have better access to capital in their local market. This is based on the idea that local

investors are already familiar with the company (from the pre-DLC period). The DLC

structure also has disadvantages. The structure may hamper transparency for investors. In

6 See Reserve Bank of Australia Bulletin, October 2002, p. 7-13. 7 See Baker & McKenzie newsletter on DLCs of July 2001. 8 In the U.K., the DLC structure was brought within the City Code on Takeovers and Acquisitions in 2002. See �Dual-Listed Company Transactions and Frustrating Action,� issued by the U.K. Panel on Takeovers and Mergers, April 26, 2002.

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addition, future capital market transactions (such as share repurchases and stock splits) are

more complex under the DLC structure.

3. Data

We collect daily stock prices, total returns in local currency, bid and ask prices, trading

volume, and the number of shares outstanding from Datastream. Bid and ask prices and

trading volume are generally not available in the first years of the sample. Datastream does

not supply bid-ask prices for Nordbanken AB and bid-ask prices and volume data for ABB

AB, the Swedish part of the ABB twin. For ABB AB, daily bid-ask prices and volume data

are obtained from Bloomberg. As no data on the Smithkline Beecham Equity Units (class E

shares) are available in Datastream, we use daily data from Bloomberg for the Smithkline

Beecham H and E shares.

We extract information about the theoretical price ratio of the twin prices from

corporate annual reports, the merger prospectus, and/or the unification prospectus. For seven

out of 13 twins, the theoretical price ratio is equal to 1:1. For the other six twins, we apply the

procedure outlined in Rosenthal and Young (1990) for the calculation of the theoretical price

ratio. This involves taking account of the number of shares outstanding for both parts of the

twin, as the current and future equity flows of these twin pairs are fixed at a specified ratio.

Daily exchange rates are obtained from Datastream. As domestic stock market indices

we use the ASX All Ordinaries index for Australia, the Brussels Allshare index for Belgium,

the SBF 250 index for France, the Helsinki HEX index for Finland, the CBS Allshare index

for the Netherlands, the Stockholmbörsen Allshare index for Sweden, the Swiss Performance

index for Switzerland, the FTSE Allshare index for the U.K., and the S&P 500 index for the

U.S. All indices are from Datastream, except for the FTSE and the S&P indices employed for

the Smithkline Beecham twin, which are taken from Bloomberg. Following Froot and Dabora

(1999), we measure the location of the trade effect using broad equity indices. Froot and

Dabora point out that the inclusion of several of the twins in the respective indices leads to a

bias in the estimated coefficients. They show that this bias is too small to affect the regression

results. As Royal Dutch forms a considerable part of the Dutch market index, however, we

remove Royal Dutch from the CBS Allshare index. The sample period for Royal Dutch/Shell

and Unilever is January 1, 1980 to October 3, 2002. The sample period for all other twins

starts at the date of the merger and ends either 20 trading days before the announcement date

of the share unification or at the last date in our full sample period. All returns are expressed

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in log form. In line with Froot and Dabora, we leave all variables in local currencies and

include log returns on the relevant exchange rate on the right hand side of the regression when

explaining return differences.

4. Deviations from theoretical parity

Figure 1 depicts graphs of the log deviations of the relative price of all 13 twins from

theoretical parity. It is obvious from the graphs that log deviations from parity are often

staggeringly large. Moreover, they fluctuate considerably over time. These observations are

supported by the summary statistics of the price differentials for each twin as reflected in

Table 2. The mean absolute price differential ranges from 2.60 percent (Eurotunnel) to 11.94

percent (ABB), which is very large in economic terms. For all of the twins, the deviation from

theoretical parity exceeds 15 percent in absolute value at some point in time. For 5 out of 13

twins, absolute price gaps amounting to 20 percent or more occur, while 3 of the twins have

an absolute price differential of more than 35 percent at some point during the sample period.

An extreme example of price disparity is provided by ABB AG, which traded at a near 50

percent discount relative to the theoretical price ratio with ABB AB on January 13, 1988.

Log deviations from parity exhibit great variation over time for most twins. Mean

disparities are negative for 5 twins and positive for 8 twins. For all twins but BHP Billiton and

Zürich Allied/Allied Zürich, however, the deviation from theoretical parity assumes both

positive and negative values over the sample period. As can be observed from the graphs in

Figure 1, the disparity changes from negative to positive (or vice versa) frequently for many

twins. The substantial time-series variation in the price differential is reflected in the estimates

of the standard deviation depicted in the third column of Table 2, which range from 2.8

percent for Eurotunnel to 14.2 percent for ABB. There does not seem to be any indication that

the price gap is smaller (or larger) for twins that were established later in the sample period.

Price differentials are highly correlated for several twins, however. The correlation between

the log deviations from parity of Anglo-Dutch twins Royal Dutch/Shell and Unilever amounts

to 0.86, while the correlation between the Royal Dutch/Shell and Reed Elsevier price

differentials is equal to 0.71. Disparities of the Anglo-Australian twins Rio Tinto and BHP

Billiton show a correlation of 0.57, but neither moves together with the price gap of Brambles

Industries. The substantial correlations suggest that common factors may drive the price

differentials of dual-listed companies from specific countries. This supposition will be borne

out in section 5 of this paper.

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Table 3 presents the test results of three different t-tests. The first column presents the

test statistic of a test of the null-hypothesis that the mean deviations from parity (in log-form)

are equal to zero for each individual twin. This hypothesis is strongly rejected for all 13 dual-

listed companies. Column 2 depicts test statistics of the null-hypothesis that mean daily

returns of the twin pairs are equal over the sample period when expressed in local currency.

The t-test fails to reject this hypothesis for all twins. Column 3 displays similar results for the

test for equality of mean returns when expressed in common currency. Table 4 investigates

whether the price differentials contain unit roots. We apply the augmented Dickey-Fuller tests

and include a trend and four lags of the first difference of the price differentials in the

regression. The results are mixed. For 6 out of 13 twins, we cannot reject the null-hypothesis

that price differentials contain a unit root at the 5 percent level. This signifies that the

hypothesis that the price ratio of these twins reverts toward theoretical parity in the long run is

not supported by the data. For the other 7 twins, the unit root hypothesis is rejected, indicating

that their price differentials at least exhibit some mean reversion. In the next section we

investigate whether relative movements in the stock market indices of the home countries of

the twin have an effect on the price differentials.

5. Empirical hypotheses and test results

This section examines whether the result of Froot and Dabora (1999) that the pricing of twin

stocks is affected by the location of the trade in the cases of Royal Dutch/Shell, Unilever, and

Smithkline Beecham can be confirmed in a sample that has been extended to include data on

all known dual-listed companies. We run the following regression for each twin9:

( ) tk

ktkj

jtji

ititBtAtBtA reIndexIndexrrrr εδγγβα ++++−+=− ∑∑∑−=

+−=

+=

+−−

1

1

0

1

1

01,1,,, ..21 , (1)

where A and B represent the twin pair, rA,t and rB,t are the log returns at time t of the first and

the second part of the twin in their local currencies, respectively (Table 1 defines what the

first and the second part is), Index1 and Index2 denote the log returns of the domestic market

indices corresponding to home country of twin A and twin B, and e.r. represents the log

9 Note that our specification differs from the basic Froot and Dabora (1999) regression framework in three ways. First, we do not include the S&P and the exchange rate of the U.S. dollar for all twins (except for Smithkline Beecham). Second, Froot and Dabora include a lead and a lag for all variables, while our set of leads and lags is based on the actual time differential. Third, we incorporate a lagged dependent variable in the regression, as the Durbin-Watson statistic indicates substantial autocorrelation in the error term. Neither of these methodological differences materially affects our results. The regression results of the basic Froot and Dabora regression are available from the authors on request.

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changes in the exchange rate between the home currencies of twin A and twin B. As all twins

are defined in such a way that the country of twin B is in an earlier time zone than the country

of twin A, we include a lead of Index1 and a lag of Index2. Our null-hypothesis is that the

return difference of the twin should be uncorrelated with the right hand side variables. In

absence of non-synchronous measurement of currency returns and stock returns, we expect

the coefficient on the exchange rate to equal �1, and the coefficients of the lead and lag of the

exchange rate returns to be equal to 0. Under the alternative hypothesis, stock markets are

segmented and the return differential of a twin is positively affected by a shock in the Index1

and negatively affected by a shock in Index2.

Table 5 reports estimation results of equation (1) for all 13 twins in the sample. We

employ Newey-West standard errors in order to correct for heteroskedasticity and auto-

correlation. The reported coefficients represent the sum of the coefficients on the lead, lag,

and current independent variable. The null hypothesis of perfect market integration is strongly

rejected for all the twins in the sample. The cumulative coefficient on Index1, the domestic

market index of the country of the first part of the twin is highly statistically significant for 11

out of 13 twins, while the market index of the country of the second part of the twin, Index2,

shows up significantly for every single twin. All signs of the domestic market indices are as

predicted by the location of the trade effect reported by Froot and Dabora (1999). A positive

shock in the market index of country 1 leads to an increase in the relative price of twin A.

Whether this implies that the deviation from theoretical parity increases or decreases depends

on whether the price differential was positive or negative. A positive shock in the market

index of country 2 leads to an increase of the relative stock return of twin B.

The economic importance of the market index effect is considerable, as the

coefficients on the domestic market indices are remarkably high. The coefficient on Index1

varies between 0.071 for Smithkline Beecham and 0.667 for ABB. The coefficient on Index2

ranges from �0.145 for Eurotunnel to �0.866 for Brambles. This implies, for example, that an

one-percent increase in the Swiss Performance index increases the relative return of ABB AG

versus ABB AB with 67 basis points and an one-percent increase in the FTSE Allshare index

decreases the relative return of Brambles Industries Ltd versus Brambles Industries PLC by

more than 85 basis points. The coefficients on the domestic stock market indices are similar to

those reported by Froot and Dabora. The location of the trade effect is able to explain a

considerable part of the daily variation of relative twin returns. The R2 indicates that 10 to 40

percent of daily return differentials can be explained by the lagged dependent variable, the

local stock market indices, and the exchange rate.

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The log deviations from parity of all twins (except Brambles) exhibit a statistically

significant first-order autoregressive component. The coefficient on the lagged dependent

variable is substantial and remarkably similar across twins. The fact that the coefficient is

negative suggests that return differentials display some kind of mean reversion. A positive

shock in the return deviation at date t will lead to a decline in the return differential at date t+1

of 5 to 40 basis points. This implies that the long-run sensitivities of the return differentials to

shocks in the local market indices are 5 to 40 percent smaller that the short-run sensitivities

presented in Table 5. Consequently, the location of the trade effect detected at the daily

frequency seems to persist over longer return horizons. Again, our results resemble the

findings of Froot and Dabora, who estimate the first-order autocorrelation of the return

differential to be approximately -0.20. The Durbin-Watson statistic is very close to 2 for all

twins, indicating that there is no significant serial correlation in the error term. This signifies

that the autoregressive model specification is correct. The estimated coefficient on exchange

rate changes is large and highly significant for most twins.10

6. Conclusions

Dual-listed companies (or Siamese twins) have been around for almost a century, starting with

Royal Dutch Petroleum and Shell Transport and Trading in 1907. In 1930, Unilever NV and

Unilever PLC were created. They remained the only two such firms until ABB AB and ABB

AG were formed in 1988, followed by the public offering of shares in Eurotunnel as well as

the creation of Smithkline Beecham in 1989. The 1990s saw the creation six more DLCs. In

the 21st century, there have been two, with one more near completion. In total, 13 DLCs have

been created. Interestingly enough, six have been collapsed into a single corporate structure.

A DLC is created by the de facto merger of two firms with different countries of

incorporation. Each firm retains its own separate legal identity and its own set of shareholders,

but is able to use the DLC structure to combine their operations. This is done by a set of

arrangements that are designed to insure that the business is operated as if were a single

company. As part of the legal contracts, the shareholders of each company will get dividends

based on a prescribed sharing of the cash flows created by the whole enterprise. In integrated

and efficient equity markets, the stock prices of the twins should move together perfectly, as

the stocks of both parent companies are perfect substitutes.

10 The small coefficient on the log returns of the exchange rate between British pound and the U.S. dollar for Smithkline Beecham can be explained by the fact the both the H and the E shares are traded in dollars.

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This paper studies the mispricing of all 13 known DLCs. We find that the relative

prices of all twins exhibit statistically significant and economically substantial deviations

from theoretical parity. Average absolute price differentials range from around 2.5 to almost

12 percent, while maximum deviations reach values of 15 to nearly 50 percent. The deviations

from parity show substantial deviation over time, assuming both negative and positive values

for 11 out of 13 twins. Standard deviations are very high for all twins. This indicates that

important mispricing exists in DLCs, suggesting that arbitrage may be hampered due to noise

trader risk.

We show that while relative twin prices seem to display some mean reversion, we

cannot reject the hypothesis that price disparities follow a random walk for 6 DLCs in the

sample. Following Froot and Dabora (1999), we analyze whether return differentials can be

explained by movements in the domestic market indices of the countries of domicile of the

twins. We find that the relative return of a twin is strongly affected by fluctuations in the

domestic market indices. The magnitude and sign of the coefficients on broad market indices

are remarkably consistent across twins and generally highly statistically significant. 10 to 40

percent of the historical variation in daily return differentials can be explained by the lagged

dependent variable, the local stock market indices, and the relevant exchange rate. This

suggests that the location of the trade matters for the pricing of DLCs, which is at variance

with integrated and efficient stock markets.

In the next draft of this paper we will include an analysis of the unification of six

DLCs. In case of unification, the firm obtains a single main listing and eliminates the DLC

structure. Unifications are recent phenomena and have not been investigated in previous

studies. The first unification took place in 1996, while the 5 other twins have been collapsed

into a single corporate structure after 1999. At the announcement of the unification the

horizon for arbitraging is no longer infinite. This implies that noise trader risk is less likely to

obstruct arbitrage. Therefore, we expect that prices will converge to the theoretical price

ratio very rapidly. We investigate prices and returns, as well as volumes and bid-ask spreads

in these events. Preliminary work shows that convergence to parity occurs rapidly. This

suggests that the mispricing before the announcement of the unification persisted because

arbitrageurs faced an infinite horizon. Our analysis corroborates Shleifer and Vishny�s

(1997) model of limited arbitrage.

14

References

Black, Fisher, 1986, Noise, Journal of Finance 41, 529-543.

Brauer, Greggory A., 1984, �Open-ending� closed-end funds, Journal of Financial Economics

13, 491-507.

Brickley, James A., and James S. Schallheim, 1985, Lifting the lid on closed-end investment

companies: a case of abnormal returns, Journal of Financial and Quantitative Analysis

20, 107-117.

De Long, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldmann,

1990, Noise trader risk in financial markets, Journal of Political Economy 98, 703-

738.

Froot, Kenneth A., and Emil M. Dabora, 1999, How are stock prices affected by the location

of trade?, Journal of Financial Economics 53, 189-216.

Lee, Charles, Andrei Shleifer, and Richard Thaler, 1991, Investor sentiment and the closed-

end fund puzzle, Journal of Finance 46, 75-110.

Pontiff, Jeffrey, 1996, Costly arbitrage: evidence from closed-end funds, Quarterly Journal of

Economics 111, 1135-1152.

Rosenthal, Leonard, and Colin Young, 1990, The seemingly anomalous price behavior of

Royal Dutch/Shell and Unilever N.V./PLC, Journal of Financial Economics 26, 123-

141.

Rubinstein, Mark, 2001, Rational markets, yes or no? The affirmative case, Financial

Analysts Journal, 15-29.

Thaler, Richard H., 1999, The end of behavioral finance, Financial Analysts Journal, 12-17.

Shleifer, Andrei, and Robert W. Vishny, 1997, The limits of arbitrage, Journal of Finance 52,

35-55.

Welch, Ivo, 2000, Views of financial economists on the equity premium and on professional

controversies, Journal of Business 73, 501-537.

15

Table 1 Description of the twins

DLC Country 1 / Country 2 (time diff.1)

DLC type

Merger Date

Unification Announced

Unification Date2

Royal Dutch / Shell Netherlands / United Kingdom (-1)

Combined Entities Structure 02.15.1907 − −

Unilever Netherlands / United Kingdom (-1)

Separate Entities Structure ??.??.1930 − −

ABB Switzerland / Sweden (0)

Combined Entities Structure 01.01.1988 02.04.1999 06.25.1999

Eurotunnel France / United Kingdom (-1)

Stapled Stock Structure 04.18.1989 − −

Smithkline Beecham United Kingdom / United States (-6)

Stapled Stock Structure 07.26.1989 02.20.1996 04.12.1996

Fortis Netherlands / Belgium (0)


Elsevier / Reed International Netherlands / United Kingdom (-1)

Combined Entities Structure 01.01.1993 − −

Rio Tinto Australia / United Kingdom (-10)

Separate Entities Structure 12.21.1995 − −

Dexia France / Belgium (0)


Merita / Nordbanken Finland / Sweden (-1)


Zürich Allied / Allied Zürich Switzerland / United Kingdom (-1)


BHP Billiton Australia / United Kingdom (-10)


Brambles Industries Australia / United Kingdom (-10)


1 Time differential between the two countries in hours. 2 Last trading day before unification.

16

Table 2 Summary Statistics of the log deviations from parity (in %)

This table shows summary statistics of the log deviations from parity for all 13 dual-listed companies (DLCs) in the sample. The columns present the mean, the mean of the absolute value, the standard deviation, the minimum, and the maximum value of the log deviations from parity (expressed in %) as well as the percentage of days in the sample period on which the log deviation was positive. For the unified DLCs the sample period ends 20 trading days before the unification announcement.

DLC Mean Abs StDv Min Max % pos

Royal Dutch / Shell 01.01.80−10.03.02 0.86 10.04 12.71 -36.22 19.83 68.5

Unilever 01.01.80−10.03.02 1.16 8.99 11.41 -39.07 29.10 62.2

ABB 01.01.88−01.07.99 -4.20 11.94 14.20 -48.77 17.77 45.2

Eurotunnel 04.18.89−10.03.02 -1.65 2.60 2.78 -10.87 17.67 25.7

Smithkline Beecham 07.26.89−01.22.96 7.94 8.10 4.09 -2.22 15.97 92.8

Fortis 12.12.90−07.31.00 -2.64 4.56 4.90 -17.10 13.79 30.5

Elsevier / Reed International 01.01.93−10.03.02 2.15 8.88 9.20 -14.73 17.58 55.6

Rio Tinto 12.21.95−10.03.02 1.90 4.11 4.76 -16.42 11.31 37.5

Dexia 11.19.96−08.20.99 -9.22 9.33 3.67 -17.66 5.15 1.8

Merita / Nordbanken 12.15.97−08.23.99 -7.01 7.07 3.19 -15.11 2.03 3.2

Zürich Allied / Allied Zürich 09.07.98−03.20.00 11.93 11.93 3.47 1.36 21.00 100

BHP Billiton 06.29.01−10.03.02 7.09 7.09 2.26 1.14 18.45 100

Brambles Industries 08.07.01−10.03.02 8.45 11.32 11.32 -18.62 29.15 74.3

17

Table 3 Test statistics

This table shows test results of three different t-tests for all 13 dual-listed companies (DLCs) in the sample. The first column reflects test statistics for the test that the mean the log deviation from parity equals zero over the sample period. The second column shows test statistics for the test that the mean total returns of both twins in local currency are equal over the sample period. The third column depicts tests statistics of the test that mean total returns are equal when expressed in a common currency. For the unified DLCs the sample period ends 20 trading days before the unification announcement. The 95% 2-tail critical value of the t-tests is equal to 1.96

DLC T-Test: Mean Log

Deviation from Parity Equal to Zero

T-Test: Equality of Mean Returns local currency

T-Test: Equality of Mean Returns

common currency Royal Dutch / Shell 01.01.80−10.03.02 5.24 -0.20 0.028

Unilever 01.01.80−10.03.02 7.83 -0.15 -0.011

ABB 01.01.88−01.07.99 -15.86 0.19 0.451

Eurotunnel 04.18.89−10.03.02 -35.16 -0.0034 0.018

Smithkline Beecham 07.26.89−01.22.96 78.63 0.074 −

Fortis 12.12.90−07.31.00 -26.99 0.36 0.44

Elsevier / Reed International 01.01.93−10.03.02 11.80 0.41 0.045

Rio Tinto 12.21.95−10.03.02 -16.76 0.26 -0.074

Dexia 11.19.96−08.20.99 -67.37 -0.13 -0.10

Merita / Nordbanken 12.15.97−08.23.99 -46.17 -0.088 -0.056

Zürich Allied / Allied Zürich 09.07.98−03.20.00 68.88 0.61 0.32

BHP Billiton 06.29.01−10.03.02 56.89 0.14 0.065

Brambles Industries 08.07.01−10.03.02 13.00 -0.63 -0.70

18

Table 4 Unit root tests

This table shows Augmented Dickey-Fuller test results for a unit root in the log deviations from parity for all 13 dual-listed companies (DLCs) in the sample. The augmented Dickey-Fuller regression includes a trend and four lags of the first difference of the log deviations from parity. The final column reflects whether the coefficient of the lagged log deviations from parity is statistically significance at the 5% level (based on the MacKinnon critical value of -3.413).

DLC Coefficient ADF Test Statistic Result

Royal Dutch / Shell 01.01.80−10.03.02 -0.0042 -2.726 Fail to reject unit root

Unilever 01.01.80−10.03.02 -0.0120 -4.711 Reject unit root

ABB 01.01.88−01.07.99 -0.0145 -3.956 Reject unit root

Eurotunnel 04.18.89−10.03.02 -0.1303 -10.35 Reject unit root

Smithkline Beecham 07.26.89−01.22.96 -0.0238 -3.244 Fail to reject unit root

Fortis 12.12.90−07.31.00 -0.0376 -5.839 Reject unit root

Elsevier / Reed International 01.01.93−10.03.02 -0.0060 -2.188 Fail to reject unit root

Rio Tinto 12.21.95−10.03.02 -0.0498 -4.565 Reject unit root

Dexia 11.19.96−08.20.99 -0.1035 -5.156 Reject unit root

Merita / Nordbanken 12.15.97−08.23.99 -0.0078 -2.903 Fail to reject unit root

Zürich Allied / Allied Zürich 09.07.98−03.20.00 -0.0762 -3.017 Fail to reject unit root

BHP Billiton 06.29.01−10.03.02 -0.4073 -5.679 Reject unit root

Brambles Industries 08.07.01−10.03.02 -0.0865 -3.070 Fail to reject unit root

19

Tab

le 5

L

og d

evia

tions

from

par

ity a

nd m

arke

t mov

emen

ts

This

tabl

e re

ports

regr

essi

on e

stim

ates

of t

he e

quat

ion:

()

tk

kt

kj

jt

ji

it

it

Bt

At

Bt

Are

Inde

xIn

dex

rr

rr

εδ

γγ

βα

++

++

−+

=−

∑∑

∑−

=+

−=

+=

+−

−

1

1

0

1

1 01

,1

,,

,..

21

,

whe

re A

and

B r

epre

sent

the

twin

pai

r, r A

,t an

d r B

,t ar

e th

e lo

g re

turn

s at

tim

e t o

f the

firs

t and

the

seco

nd p

art o

f the

DLC

in th

eir

loca

l cur

renc

ies,

resp

ectiv

ely

(Tab

le 1

�D

escr

iptio

n of

the

DLC

s� d

efin

es w

hat t

he fi

rst a

nd th

e se

cond

par

t is)

, Ind

ex1

and

Inde

x2 d

enot

e th

e lo

g re

turn

s of t

he d

omes

tic m

arke

t ind

ices

cor

resp

ondi

ng to

the

twin

A

and

twin

B, a

nd e

.r. re

pres

ents

the

log

chan

ges i

n th

e ex

chan

ge ra

te b

etw

een

the

curr

enci

es o

f the

firs

t par

t en

the

seco

nd p

art o

f the

twin

. Col

umns

dep

ict t

he tw

in, t

he sa

mpl

e pe

riod,

the

adju

sted

R2 , t

he D

urbi

n-W

atso

n sta

tistic

, the

deg

rees

of f

reed

om a

nd th

e cu

mul

ativ

e co

effic

ient

s on

all f

our i

ndep

ende

nt v

aria

bles

in th

e re

gres

sion

. For

the

unifi

ed

DLC

s th

e sa

mpl

e pe

riod

ends

20

tradi

ng d

ays

befo

re th

e un

ifica

tion

anno

unce

men

t. Fr

eque

ncy

is d

aily

. For

the

unifi

ed D

LCs

the

sam

ple

perio

d en

ds 2

0 tra

ding

day

s be

fore

th

e un

ifica

tion

anno

unce

men

t. a , b , c , r

efle

ct si

gnifi

canc

e at

the

10%

, 5%

and

1%

leve

l for

Wal

d te

sts t

hat t

he su

m o

f all

coef

ficie

nts (

lead

/lag

and

curr

ent v

alue

) equ

als z

ero.

D

LC

Sa

mpl

e pe

riod

R

2 D

W

DO

F L

agge

d de

p. v

ar.

Inde

x1

Inde

x2

e.r.

Roy

al D

utch

/ Sh

ell

01.0

1.80−1

0.03

.02

0.24

2 2.

03

5927

-0

.231

c 0.

346c

-0.5

01c

-0.8

06c

Uni

leve

r 01

.01.

80−1

0.03

.02

0.14

6 2.

06

5927

-0

.216

c 0.

170c

-0.5

60c

-0.5

95c

AB

B

01.0

1.88−0

1.07

.99

0.12

7 2.

02

2867

-0

.059

c 0.

667c

-0.4

84c

-0.4

30c

Eur

otun

nel

04.1

8.89−1

0.03

.02

0.13

7 2.

15

3501

-0

.329

c 0.

285c

-0.1

45b

-0.9

16c

Smith

klin

e B

eech

am

07.2

6.89−0

1.22

.96

0.13

2 2.

13

1527

-0

.296

c 0.

071b

-0.2

30c

0.03

8 Fo

rtis

12.1

2.90−0

7.31

.00

0.10

4 1.

99

2506

-0

.163

c 0.

476c

-0.5

37c

-0.5

80b

Else

vier

/ R

eed

Inte

rnat

iona

l 01

.01.

93−1

0.03

.02

0.19

7 2.

14

2534

-0

.319

c 0.

331c

-0.4

17c

-0.7

72c

Rio

Tin

to

12.2

1.95−1

0.03

.02

0.27

2 2.

15

1760

-0

.296

c 0.

431c

-0.7

41c

-0.5

24c

Dex

ia

11.1

9.96−0

8.20

.99

0.10

0 2.

18

708

-0.2

16c

0.29

0c -0

.324

c -0

.319

M

erita

/ N

ordb

anke

n 12

.15.

97−0

8.23

.99

0.24

6 2.

09

431

-0.3

71c

0.46

3c -0

.445

c -0

.139

Z

üric

h A

llied

/ A

llied

Zür

ich

09.0

7.98−0

3.20

.00

0.09

1 2.

03

390

-0.1

53c

0.15

5 -0

.354

b -0

.928

c B

HP

Bill

iton

06.2

9.01−1

0.03

.02

0.39

7 2.

21

319

-0.2

80c

0.45

9b -0

.709

c -0

.647

b B

ram

bles

Indu

stri

es

08.0

7.01−1

0.03

.02

0.28

8 2.

00

293

-0.0

05

0.34

3 -0

.866

c -0

.567

20

Figu

re 1

L

og d

evia

tions

from

par

ity

This

figu

re s

how

s on

a p

erce

ntag

e ba

sis

the

log

devi

atio

ns fr

om th

eore

tical

par

ity f

or a

ll 13

dua

l-lis

ted

com

pani

es (

DLC

s) in

the

sam

ple.

For

the

unifi

ed D

LCs

the

sam

ple

perio

d en

ds 2

0 tra

ding

day

s be

fore

the

unifi

catio

n an

noun

cem

ent.

Roy

al D

utch

/ Sh

ell

-50%

-40%

-30%

-20%

-10%0%10

%

20%

30% 1/

1/80

1/1/

831/

1/86

1/1/

891/

1/92

1/1/

951/

1/98

1/1/

01

Percent Deviation

Uni

leve

r

-50%

-40%

-30%

-20%

-10%0%10%

20%

30% 1/

1/80

1/1/

831/

1/86

1/1/

891/

1/92

1/1/

951/

1/98

1/1/

01

Percent Deviation

AB

B

-50%

-40%

-30%

-20%

-10%0%10%

20%

30% 1/

1/88

1/1/

901/

1/92

1/1/

941/

1/96

1/1/

98

Percent Deviation

Euro

tunn

el

-50%

-40%

-30%

-20%

-10%0%10

%

20%

30% 4/

18/8

94/

18/9

14/

18/9

34/

18/9

54/

18/9

74/

18/9

94/

18/0

1

Percent Deviation

21

Figu

re 1

− c

ontin

ued

Log

dev

iatio

ns fr

om p

arity

Th

is fig

ure

show

s on

a pe

rcen

tage

bas

is th

e lo

g de

viat

ions

from

theo

retic

al p

arity

for a

ll 13

dua

l-lis

ted

com

pani

es (D

LCs)

in th

e sa

mpl

e. F

or th

e un

ified

DLC

s the

sam

ple

perio

d en

ds 2

0 tra

ding

day

s be

fore

the

unifi

catio

n an

noun

cem

ent.

Smith

klin

e B

eech

am

-50%

-40%

-30%

-20%

-10%0%10

%

20%

30% 7/26

/198

98/

7/19

908/

19/1

991

8/28

/199

29/

10/1

993

9/22

/199

410

/4/1

995

Perecnt Deviation

Fort

is

-50%

-40%

-30%

-20%

-10%0%10

%

20%

30% 12

/12/

9012

/12/

9212

/12/

9412

/12/

9612

/12/

98

Percent Deviation

El

sevi

er /

Ree

d In

tern

atio

nal

-50%

-40%

-30%

-20%

-10%0%10

%

20%

30% 1/

1/93

1/1/

951/

1/97

1/1/

991/

1/01

Percent Deviation

Rio

Tin

to

-50%

-40%

-30%

-20%

-10%0%10%

20%

30% 12

/21/

9512

/21/

9712

/21/

9912

/21/

01

Percent Deviation

22

Figu

re 1

− c

ontin

ued

Log

dev

iatio

ns fr

om p

arity

Th

is fig

ure

show

s on

a pe

rcen

tage

bas

is th

e lo

g de

viat

ions

from

theo

retic

al p

arity

for a

ll 13

dua

l-lis

ted

com

pani

es (D

LCs)

in th

e sa

mpl

e. F

or th

e un

ified

DLC

s the

sam

ple

perio

d en

ds 2

0 tra

ding

day

s be

fore

the

unifi

catio

n an

noun

cem

ent.

Dexi

a

-50%

-40%

-30%

-20%

-10%0%10

%

20%

30% 11

/19/

965/

19/9

711

/19/

975/

19/9

811

/19/

985/

19/9

9

Percent Deviation

Mer

ita /

Nord

bank

en

-50%

-40%

-30%

-20%

-10%0%10

%

20%

30% 12

/15/

976/

15/9

812

/15/

986/

15/9

9

Percent Deviation

Zü

rich

Alli

ed /

Alli

ed Z

üric

h

-50%

-40%

-30%

-20%

-10%0%10%

20%

30% 9/

7/98

12/7

/98

3/7/

996/

7/99

9/7/

9912

/7/9

93/

7/00

Percent Deviation

BH

P B

illito

n

-50%

-40%

-30%

-20%

-10%0%10%

20%

30% 6/

29/0

19/

29/0

112

/29/

013/

29/0

26/

29/0

29/

29/0

2

Percent Deviation

23

Figu

re 1

− c

ontin

ued

Log

dev

iatio

ns fr

om p

arity

Th

is fig

ure

show

s on

a pe

rcen

tage

bas

is th

e lo

g de

viat

ions

from

theo

retic

al p

arity

for a

ll 13

dua

l-lis

ted

com

pani

es (D

LCs)

in th

e sa

mpl

e. F

or th

e un

ified

DLC

s the

sam

ple

perio

d en

ds 2

0 tra

ding

day

s be

fore

the

unifi

catio

n an

noun

cem

ent.

Bra

mbl

es

-50%

-40%

-30%

-20%

-10%0%10%

20%

30% 8/

7/01

11/7

/01

2/7/

025/

7/02

8/7/

02

Percent Deviation

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