The Capital Asset Pricing Model and the Law of One Price for Cross-Listed Stocks on the NYSE and the Euronext
Lieselotte Bulsing 10266437
Universiteit van Amsterdam (UvA) Supervisor: Dhr. M. Kool
Abstract
This research investigates whether the Law of One Price and the Capital Asset Pricing Model are valid on stocks that are listed on more than one exchange. The cross-listed stocks that have been investigated were the ones listed on the NYSE and on the Euronext. The hypothesis in this research was that the CAP-Model would not hold, concerning the extra international factors that play a role in determining stock prices for stocks listed on more than one exchange, which are not taken into account in the CAPM regression equation. The Law of One Price was expected to hold; otherwise free arbitrage opportunities would have been left unused. 36 stocks were selected and for each stock was evaluated whether the CAPM applied and whether there were arbitrage opportunities, while taking into account transaction costs. The hypothesis was partly rejected: for 28 companies the CAPM does hold on both the NYSE market and the Euronext market, for 8 companies it only holds for one market.
However, the CAPM does not display high explanatory power. Besides, significant arbitrage opportunities were found for 33 out of the 36 stocks that were incorporated in this research. Therefore, the conclusion of this investigation was that the CAPM partly holds and that the Law of One Price does not hold for the majority of the cross-listed stocks on the NYSE and the Euronext.
1 Introduction
The main topic of this research is whether the Capital Asset Pricing Model and the Law of One Price hold for stocks that are traded on more than one exchange. The design was to choose two exchanges, from which all stocks that were listed on both exchanges were taken. For each individual stock the stock price returns were evaluated in order to check for CAPM. Then the arbitrage opportunities that were present for each stock were calculated, while taking into consideration the exchange rate movements that occurred simultaneously.
The two stock exchanges that have been used in this research were subject to two requirements. First of all, they had to operate in different currencies. This was necessary in order to fit the research question, because stocks that are listed in the same currency are not subject to underlying exchange rate movements. Furthermore, the Efficient Market
Hypothesis by Fama (1970) states that market prices reflect all current information, if many investors have information at their disposal (p. 388). From this can be inferred that the larger the market, the more investors there are that seek relevant information, the more investors that have the information at their disposal. Therefore, the second requirement was that the
exchange markets should be as large as possible.
The first exchange, which was used in this research, was the New York Stock
Exchange. This exchange was chosen, because it was the largest stock exchange in the world (World Federation of Exchanges). Market capitalization was used as a measure of active trading.
The second exchange that was used in this research was the Euronext. The reasoning behind choosing the Euronext as the second exchange was that it is integrated within the NYSE market. The NYSE and the Euronext were merged into NYSE Euronext in 2007. This merger took away inefficiencies that were present in cross-border trade (AEX 2014). From the Efficient Market Hypothesis by Fama (1970), which states that a market is more efficient
as more people have information at their disposal, can be inferred that higher integration increases efficiency.
The term Euronext represents the Euronext exchanges of Amsterdam, Brussels, Paris and Lisbon. Those exchanges were merged into the Euronext in 2000. Later, Euronext acquired the London International Financial Futures and Options Exchange (LIFFE) in 2002, but the LIFFE was not incorporated into this research, since it was acquired, not merged with the other Euronext exchanges (NYSE 2014). Nine years after NYSE group and Euronext’s merger, InterContinental Exchange, ICE, took over NYSE Euronext in 2013 (ICE 2014). This was also considered as a separate exchange, however, since it is a global exchange, it is not a separate market anymore.
Taking the factors previously mentioned into account, the following research question was formulated: To what extent do the Law of One Price and the Capital Asset Pricing model hold for cross-listed stocks on the NYSE and the Euronext? The hypothesis was that the law of one price would hold, otherwise free arbitrage opportunities would have been left unused. Investors who profit from those arbitrage opportunities would drive price discrepancies towards zero. The Capital Asset Pricing model, however, was expected not to hold. This was expected, because the capital asset pricing model is a linear relationship based on the return of the market and the risk-free rate in a specific country. However, when a stock is traded on different exchanges, international factors, such as the exchange rate, move stock prices in directions not defined in the Capital Asset Pricing model.
The motivation behind performing this research was that trading on a global scale becomes easier, since the usage of electronic devices is increasing and since the internet makes the world more interconnected. This raised questions on the validity of the Capital Asset Pricing Model for stocks that are listed on more than one exchange, since those are subject to international as well as national trading. Moreover, this also raised questions on the
validity of the Law of One Price, since one could expect that electronic trading could drive price discrepancies towards zero.
In order to answer the research question, first a literature review was done, which will be presented in section two. After this will be elaborated on the data and the method in section three. Next, in section four the results of this analysis are presented. Finally, based on those results, the conclusion is stated in section five. In that section also suggestions for further research on this topic are mentioned.
2 Literature Review
In this part, past research on cross-listed stocks will be addressed. First, the two economic models that this research investigates are presented: the Capital Asset Pricing Model in section 2.1 and the Law of One Price in section 2.2. Then, the cross-market premium is focused on in section 2.3. Next, efficiency-reducing factors are presented in section 2.4. Moreover, in section 2.5 will be enlarged on home market dominance. Finally, exchange trading hours are discussed in section 2.6.
2.1 Capital Asset Pricing Model
In their research paper, Fama and French (2004) describe the Capital Asset Pricing Model represented by the following equation by Sharpe and Lintner: E(Ri) = Rf + β*[E(Rm) –
Rf)], with i = 1, …, N and 𝛽! =!"#(!!!(!!!,!)!) . The first term represents the expected return on risk-free assets. The second term represents the risk premium (p. 28). The beta shows the assets reaction to a change in the market return premium, it is a measure of market risk. For time-series, this regression was adjusted to: E(Ri) - Rf = α +β*[E(Rm) – Rf)], with i = 1, …, N and 𝛽! = !"#(!!!(!!)!,!!). Sharpe and Lintner assume the alpha to be zero (p. 32).
Fama and French (2004) show that several empirical tests on the Capital Asset Pricing model show regression lines that are too flat when they are compared with the actual stock
performance, which rejects the CAPM model (p. 32). They also report that researchers have added variables to the CAPM-regression, in order to get a regression line that explains more of the data. Fama and French (2004) say: “We continue to teach the CAPM as an introduction to the fundamental concepts of portfolio theory and asset pricing, to be built on by more complicated models” (p. 44).
2.2 Law of One Price
Nicholson and Snyder (2010) explain the Law of One price as the law that states that prices are equal for homogeneous goods, when you are in a market in which there are no transaction costs and in which information is available to everyone (p. 409). When this is applied to stocks, a stock traded on two markets should have the same price on both markets, assuming transaction costs are zero, and assuming information is available. A stock traded on two markets is considered homogeneous here.
2.3 Cross market premium
According to Yeyati, Schmukler and van Horen (2009), the cross market premium is the percentage difference in price between the value of the stock traded on the foreign market (translated into home currency) and the value of the stock traded on the home market.
According to them, instead of the value of the stock on the home market, also the Depository Receipt value can be used. A Depository Receipt is a financial instrument that is traded in a foreign market, which is equivalent to a number of shares in the home market (p. 436). They find that in practice the cross market premium is close to zero (p. 434).
2.4 Efficiency reducing factors
As mentioned in the introduction, Fama’s Efficient Market Hypothesis (1970) argues that when there is more relevant information present in the market, the market is more efficient (p. 388). Yeyati, Schmukler and van Horen (2009) highlight that this efficiency could be reduced, when stocks are traded infrequently. This means that arbitrage opportunities
can only be taken advantage of, when trades take place in both markets where the price difference occurred (p. 433). This implies that there are arbitrage opportunities that exist for a longer period of time, since there is no continuous trading.
Moreover, Gagnon and Karolyi’s research (2010) shows that holding costs explain a significant part of arbitrage opportunities, which were already adjusted for transaction costs. The arbitrage opportunities that they found were small on average (4.9 basis points), but they did reach extreme values incidentally. They also found that restrictions on short selling increased deviations from price parity. Other factors that they found which could increase deviations from price parity are trading fees, high cost of capital, instability of the market and restricted home market accessibility. In their research they also found that arbitrage
movements were partly related to currency and market index returns. However, they say that the rest of the arbitrage is still explained by holding costs (p. 77).
2.5 Home market dominance
A research by Agerwal, Liu & Rhee (2007) on stocks, listed in home region Hong Kong and also in London, shows that the stock price movements in London are almost entirely explained by stock price movements in Hong Kong (p. 62). A research by Alhaj-Yaseen et al. (2014) on cross-listed Israeli stocks, that were first issued abroad, after which they were listed in Israel, also confirms the fact that the home market dominates in price determination (p. 86). The term used for this is home market dominance (p. 80).
On the other hand, Eun & Sabherwal (2003) found that for Canadian stocks that are cross-listed in the U.S., both the home and the foreign market have influence on price determination, although U.S. stock prices have less influence on Canadian stock prices than the other way around (p. 573). From this can be inferred that there still is some home market dominance.
2.6 Opening hours exchanges
The NYSE and the Euronext operate in different time zones. The NYSE trading hours are from Monday through Friday from 09.30 until 16.00 ‘o clock (NYSE 2014). The Euronext trading hours are from 09.00 until 17.30 on Monday through Friday (Euronext 2014). In New York it is 6 hours earlier, which means that both exchanges are open together during 2,5 hour per day, from 15.00 until 17.30 Dutch time, every day. A research by Kleidon & Werner (1996) on cross-listed stocks on exchanges in the United Stated and in the United Kingdom shows that the fact that the UK-exchange had been opened 6 hours before the US-exchange opened, did not influence trading (p. 657).
In conclusion, past literature highlighted several aspects of regular and cross-listed stocks. To start with, for stocks in general, there is the CAPM regression equation, which researchers view as a basic economic model. However, the regression line is sometimes contradictory to the stock behaviour in practice. Thus, researchers view the CAPM as a model to which other factors have to be added.
Secondly, the Law of One Price states that homogeneous goods should be sold for the same price if market conditions are perfect. In this research stocks traded on two markets are treated as homogeneous. This means that if the market conditions in this research are perfect, stock prices should be equal on both markets.
Thirdly, empirical evidence has shown that the premium on stocks listed on more than one exchange is close to zero. If the outcome of this research is in line with this, then the conclusion would be that the law of one price holds.
Fourthly, there are several factors that could decrease efficiency in the stock market and hence influence arbitrage profiting. Those facors are: infrequent trading, holding costs, transaction costs, restrictions on short selling, instability of the market and restricted home
market accessibility. This means that if the law of one price does not hold in this research, it could be that the market is not efficient due to one of the factors mentioned here.
Fifthly, several investigations were found that confirmed home country dominance in stock price determination. For this research this could mean that the CAPM regression equation could explain more of the stock price variance on the home market than on the foreign market.
Finally, research has shown that different opening hours for stock exchanges in the U.K. and the U.S. did not influence trading in stocks, which are cross-listed on those
exchanges. Therefore, different opening hours of the exchanges are expected not to influence this research.
3 Research Method
In this section the way this research was conducted is explained. First, the sources of the data will be addressed in section 3.1. Secondly, the stock selection procedure is explained in section 3.2. Thirdly, the procedures that were used in order to check whether the Capital Asset Pricing Model holds, are explained in section 3.3. Finally, the procedure in order to check whether the Law of One Price holds, is elaborated on in section 3.4.
3.1 Data sources
In order to select the stocks that were subject to this research, lists of stocks of both the NYSE and the Euronext were compared. For the Euronext, stocks traded on the Euronext itself, on the alternext and on the Marché Libre were included. This was done in order to incorporate as many stocks as possible. On the NYSE 3303 common stocks and on Euronext 1353 common stocks were listed on 27 May 2014 (Euronext 2014, NASDAQ 2014).
For the CAPM analysis of each stock on each market the following values were incorporated: stock market prices for all 36 stocks on both exchanges, values for the S&P500
as the market index, and values of the 30-year treasury bill as the risk-free rate. Those data were collected form Yahoo!Finance (2014). The values were taken from as far back as possible, in order to create a sample that is as large as possible.
The number of observations for the T-bill rate was 9343 (back to 15 February 1977) and the number of observations for the S&P500 was 16231 (back to 3 January 1950). Since both values had to be available on all dates that were incorporated into this research, 9343 values for both the S&P500 and the T-bill could be taken into account. This meant that for each stock also 9343 values could be taken into account at maximum, since the t-bill and S&P500 values had to be available for all stock prices incorporated in this research. The numbers of stock price values in the sample was dependent on the history of the stock: the longer a stock is traded on an exchange, the more stock price observations in the sample.
In order to evaluate whether the Law of One Price held, data on the Euro-Dollar exchange rate were collected from Quandl (2014). Since the Euro-Dollar exchange rate was used, this research was restricted to the lifetime of the Euro. The data from Quandl were from 6 September 1999 onwards, which were 3860 observations. This meant that at maximum the Law-Of-One-Price analysis could incorporate 3860 exchange rate observations for one stock.
Furthermore, for the Law-Of-One-Price analysis, the stock had to be listed simultaneously on both exchanges. This meant that the number of observations was also dependent on the presence of the stock on both markets simultaneously. If a stock had been listed on an exchange for a longer time than on the other exchange, the investigation was restricted to the time period when both stocks were listed simultaneously.
3.2 Stock Selection
The lists of the stocks traded on the NYSE and on the Euronext were compared, by checking for equal tickers and/or company names. The same company does not necessarily
have the same ticker on two exchanges. The 36 stocks that are listed on both the NYSE and the Euronext are presented in table 1:
*Table 1
Company Name Ticker NYSE Ticker Euronext
1 Anheiser-Busch Inbev BUD ABI
2 Abbvie ABBV ABBV
3 Aegon AEG AGN
4 Alcatel-Lucent ALU ALU
5 Arcelormittal MT MT
6 Brookfield Asset Management BAM BAMA
7 Caterpillar Inc CAT CATR
8 CGG CGG CGG
9 Coca-Cola Enterprise CCE CCE
10 Core Laboratories CLB CLB
11 Delhaize Group DEG DELB
12 Diageo DEO DGE
13 DRDGold Cert. Belg. DRD DRD
14 Du Pont de Nemours DD DUPP
15 Ford Motor Cert. F F
16 General Electric GE GNE
17 Harmony Cert. HMY HMY
18 Hexcel HXL HXL
19 HSBC Holdings HSBC HSB
20 Infosys Ltd ads INFY INFY
21 ING Groupe/Groep ING INGA
22 Lilly and Co LLY LLY
23 Merck and Co. Inc. MRK MRK
24 Orange ORAN ORA
25 Pfizer Cert. PFE PFEBC
26 Philip Morris PM PM
27 Proctor and Gamble PG PGP
28 Rio Tinto Cert. RIO RIOS
29 Royal Bank of Schotland RBS RBS
30 Royal Dutch Shell A RDS/A RDSA
31 Royal Dutch Shell B RDS/B RDSB
32 Schlumberger SLB SLB
33 STMicroelectronics STM STM
34 Vale VALE VALE3
35 Watsco WSO WSO
36 Weatherford WFT WFT
3.3 The Capital Asset Pricing Model
In order to check for the Capital Asset Pricing Model validity for each stock, the excess stock returns over the risk-free rates were regressed on the excess returns of the market over the risk-free rates by using the regression equation E(Ri) - Rf = α +β*[E(Rm) – Rf)], as mentioned in section section 2.1, in Stata. This was done in order to check whether the CAP-model held
for every stock within an exchange, so without taking into account the fact that it was also listed on another exchange.
The dependent variable (Ri - Rf ) was calculated for every date for which both values, the asset’s resturn and the risk-free rate, were available. The same was done for (Rm – Rf) for every date for which both values, the market return and the risk-free rate, were available. This was used as independent variable. Then all dates and values of the dependent and the
independent variable were compared. Only values of dates that were available for both the dependent and the independent variable were put into Stata. This procedure was executed for each of the 36 on stocks, on both exchanges.
Next, the regressions were run and the resulting alpha’s were analysed. The criterion that was used in order to check for CAPM was that alpha should not be significantly different from zero. For this a significance level of 5% was used, so for all alpha’s with a p-value lower than 0.05, the hypothesis that alpha equals zero was rejected. There was one adjustment made in the data: On 26-04-07 and 14-08-06 Aegon paid dividend to its shareholders, which caused large outliers in the outcomes. Those two values were removed, since they were not
representative for the rest of the sample. On other dividend dates the stock price returns were representative of the rest of the sample, so those were kept in the sample.
3.4 Law of One Price
Next, in order to check whether the Law of One Price held, each stock’s prices on both exchanges were analysed to check whether there had been any arbitrage opportunities over time. The stock prices were converted to dollar values, using the historical exchange rate over time. For each stock, all values were filtered in order to only incorporate dates for which the values of the stock on both exchanges and the exchange rate were available. Then, stock ratios had to be adjusted, using information from company websites. The following factors were corrected for:
-‐ 1 NYSE share of Delhaize is equal to 0.25 Euronext shares (Delhaize) -‐ 1 NYSE share of Diageo is equal to 4 Euronext shares (Diageo) -‐ 1 NYSE share of HSBC is equal to 5 Euronext shares (BSHC)
-‐ The stock split for Proctor and Gamble on 21 June 2004 (Proctor and Gamble) -‐ 1 NYSE share of Royal Bank of Scotland is equal to 2 Euronext shares (Royal Bank
of Scotland)
-‐ 1 share of Royal Dutch Shell A or B on the NYSE is equal to 2 Euronext A or B shares (Royal Dutch Shell)
All stock prices were adjusted in order to be equivalent to 1 NYSE share.
The formula that was used for the price difference was: 𝑃𝑟𝑖𝑐𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
𝑃! 𝑁𝑌𝑆𝐸 − 𝑆!𝑃!(𝐸𝑢𝑟𝑜𝑛𝑒𝑥𝑡). The price difference was calculated in dollars. For each stock, two one-sided tests were performed, in order to check whether any arbitrage opportunities were significantly present in either the dollar market or in the euro market. The hypothesis used in order to check for this was: 𝐻!: 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑔𝑒 > 0
𝐻!: 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑔𝑒 ≤ 0
At a significance level of 5%. The rejection region was: t < -1.645 (with df = ∞) And then: 𝐻!: 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑔𝑒 < 0
𝐻!: 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑔𝑒 ≥ 0
At a significance level of 5%. The rejection region was: t > 1.645 (with df = ∞)
The point here was not to check whether the arbitrage opportunities were significantly different from zero, because when a value is significantly different from zero, statistically seen it must be significant in one direction (rejection regions of a two-sided test at 5% would be t < -1.960 and t > 1.960). The fact that some arbitrage amounts are negative only points to the market where the arbitrage is to be gained. A negative arbitrage amount implies that the
Euronext price is higher than the NYSE price, a positive arbitrage amount implies that the NYSE price is higher than the Euronext price.
The next step was to correct for transaction costs, for those stocks for which was concluded that the arbitrage amounts are significantly different from zero. The transaction costs are equal to 0.0015 dollar per stock traded on the NYSE (NYSE 2014) and 0.05 euro on the Euronext (Euronext 2014), which is equal to 0.07 dollar on 30 june 2014 (Wisselkoers 2014). A total of 0.07+0.0015=0.0715 dollar was used as transaction costs in calculating the new t-statistic. The formula that was used for the new t-statistic was: 𝑡 = !±!
!/ ! with µ being equal to the transaction costs. Here was assumed that in order to take advantage of the price difference, two trades had to be made, so transaction costs had been paid on both markets.
The hypothesis of this test was whether the arbitrage amount was significantly larger than the transaction costs. In case of a positive arbitrage amount, the hypothesis was:
𝐻!: 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑔𝑒 > 𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡𝑠 𝐻!: 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑔𝑒 ≤ 𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡𝑠 In case of a negative arbitrage amount, the hypothesis was:
𝐻!: 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑔𝑒 < 𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡𝑠 𝐻!: 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑔𝑒 ≥ 𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡𝑠
In calculating the t-statistic, the transaction costs were added in case of a negative number for mean arbitrage, and subtracted in case of a positive number for mean arbitrage. Thus, the transaction costs lower the absolute value of the arbitrage profit. For this again a significance level of 5% was used, so the rejection regions were t < -1.645 and t > 1.645 (both with df = ∞).
4 Results
In this section the results of this research will be explained. First, the results of the research on the Capital Asset Pricing Model will be presented in section 4.1. In this section, the results on the tests on alpha are shown. Moreover, factors that could not be proven, but that do raise questions are highlighted. Finally, the findings on the law of one price are presented in section 4.2.
4.1 The Capital Asset Pricing Model
The first part of this research was to investigate whether CAPM holds. The linear regression presented in section 3.3 was performed for each stock: E(Ri) - Rf = α +β*[E(Rm) –
Rf)]. The results are presented in tables 2 and 3 on the next pages. Table 2 shows the results for the regression on NYSE stock values, table 3 shows the results for the regression on Euronext stock values. Graphs 2 until 37 in section 7.1 in Appendix A show scatter plots of each stock’s excess returns regressed on the excess market return.
4.1.1 Alpha. Column three in both tables represents the alpha’s estimated by the regression equation. Column four displays the p-values of those alpha’s. The fifth column tells whether CAPM holds within the separate exchange, based on the criterion that alpha is assumed to be zero for cases where CAPM holds. The hypothesis that alpha is not statistically different from zero, is rejected for alpha’s with a p-value lower than 0.05.
On the NYSE market, the hypothesis that alpha is zero is rejected for 7 stocks. For those 7 stocks the CAPM is assumed not to hold within the NYSE market. For the Euronext market for one alpha the hypothesis that alpha equals zero is rejected. The conclusion is that for 28 companies the Capital Asset Pricing Model holds on both exchanges and for 8
Table 2: Regression on the NYSE (1) Company Name (2) Home Country (3) Estimated alpha (4) P-value alpha (5) CAPM holds? (6) Estimated beta squared (7) R-(8) Adjusted R-square (9) Obs 1 Ab Inbev BE 0.0003768 0.256 yes 1.023866 0.5979 0.5976 1246 2 Abbvie US 0.0006476 0.352 yes 1.053697 0.4828 0.4814 364 3 Aegon NL 0.0003021 0.228 yes 0.9924501 0.3236 0.3235 7258 4 Alcatel-Lucent FR -0.0001675 0.664 yes 1.166287 0.259 0.2589 5537
5 ArcelorMittal UK&LUX 0.0003063 0.55 yes 1.07988 0.1958 0.1956 4230
6 Brookfield Asset Management Canada 0.0004038 0.028 No 0.8171802 0.3607 0.3606 7631
7 Caterpillar Inc US 0.0001989 0.219 yes 0.9852799 0.4595 0.4593 9342
8 CGG FR 0.0003727 0.434 yes 0.8680553 0.1516 0.1514 4294
9 Coca-Cola Enterprises US 0.0003183 0.156 yes 0.8693467 0.3255 0.3254 6909
10 Core Laboratories US 0.0010208 0.012 no 0.82386 0.1674 0.1672 4700
11 Delhaize Group BE 0.0002549 0.459 yes 0.8816073 0.3161 0.3159 3299
12 Diageo plc UK 0.0003544 0.114 yes 0.7394116 0.354 0.3538 4540
13 DRDGold Cert. Belg. South-A 0.0001119 0.188 yes 0.611772 0.0404 0.0402 4443
14 Du Pont de Nemours US 0.001875 0.162 yes 0.9901604 0.5552 0.5552 9342
15 Ford Motor Cert. US 0.0002618 0.209 yes 1.050991 0.3676 0.3676 9342
16 General Electric US 0.0002185 0.083 yes 1.077168 0.6265 0.6265 9342
17 Harmony Cert. South-A 0.0002858 0.61 yes 0.7107277 0.0769 0.0767 4443
18 Hexcel US 0.0003379 0.382 yes 0.9746419 0.1659 0.1658 6671
19 HSBC Holdings plc UK 0.0001456 0.488 yes 0.9323422 0.5521 0.552 3746
20 Infosys Ltd ads India 0.0009909 0.043 no 1.078505 0.2298 0.2296 3834
21 ING Groupe/Groep NL 0.0001825 0.624 yes 1.119628 0.3202 0.32 4410
22 Eli Lilly and Co US 0.0002471 0.102 yes 0.9498995 0.4758 0.4757 9342
23 Merck and Co. Inc. US 0.0002844 0.055 yes 0.9397419 0.48 0.48 9342
24 Orange FR 0.0001377 0.688 yes 1.060075 0.3457 0.3455 4180
25 Pfizer Cert. US 0.0003753 0.033 no 0.8650047 0.3557 0.3556 9341
26 Philip Morris US 0.0003096 0.332 yes 0.8912321 0.6088 0.6086 1571
27 Proctor and Gamble US 0.0002369 0.071 yes 0.9025261 0.5207 0.5207 9342
28 Rio Tinto Cert. UK 0.0004276 0.116 yes 0.8801147 0.2672 0.267 6010
29 Royal Bank of Schotland UK -0.0005772 0.566 yes 1.374319 0.2551 0.2547 1673
30 Royal Dutch Shell A NL 0.0001827 0.459 yes 1.015877 0.6613 0.6612 2236
31 Royal Dutch Shell B NL 0.0002503 0.115 yes 0.8681984 0.4819 0.4818 6635
32 Schlumberger FR 0.000194 0.341 yes 0.9866403 0.3878 0.3878 8130
33 STMicroelectronics Swiss 0.0002277 0.517 yes 1.192833 0.3437 0.3436 4898
34 Vale Brazil 0.0008023 0.046 no 1.155877 0.3842 0.384 3076
35 Watsco US 0.0005511 0.025 no 0.7462893 0.2101 0.21 7522
36 Weatherford Swiss 0.00006927 0.023 no 0.8074761 0.1383 0.1382 9342
* notes: The following cells were displayed in bold for clarity: US as home country in column (2), and where CAPM does not hold in column (5)
Table 3: Regression on the Euronext (1) Company Name (2) Home Country (3) Estimated alpha (4) P-value alpha (5) CAPM holds? (6) Estimated beta (7) R-squared (8)Adjusted R-squared (9) Obs 1 Ab Inbev BE 0.0003149 0.63 yes 0.5820538 0.1468 0.1462 1474 2 Abbvie US 0.0009679 0.455 yes 0.8127463 0.1432 0.1407 353 3 Aegon NL -0.0001661 0.731 yes 0.7402191 0.132 0.1318 3616 4 Alcatel-Lucent FR -0.000207 0.707 yes 0.8297333 0.1274 0.1272 3574
5 ArcelorMittal UK&LUX -0.0004419 0.64 yes 0.8110045 0.2002 0.1995 1060
6 Brookfield Asset Management Canada 0.0018363 0.053 yes -0.0511025 0.0002 -0.0001 2939
7 Caterpillar Inc US 0.021211 0.089 yes 0.7450793 0.031 0.0307 2729
8 CGG FR 0.0004098 0.401 yes 0.704602 0.1187 0.1185 3614
9 Coca-Cola Enterprises US 0.0004928 0.63 yes 1.132238 0.243 0.2419 693
10 Core Laboratories US -0.0007106 0.5 yes 0.8347478 0.1619 0.1602 520
11 Delhaize Group BE 0.0001478 0.665 yes 0.6382768 0.1837 0.1835 3624
12 Diageo plc UK 0.0010347 0.091 yes 0.6323528 0.0735 0.0732 3168
13 DRDGold Cert. Belg. Sth-Africa 0.0012291 0.869 yes 0.4653135 0.016 0.0158 3563
14 Du Pont de Nemours US 0.000304 0.515 yes 0.5818545 0.1059 0.1056 3085
15 Ford Motor Cert. US 0.0017077 0.218 yes 0.7204665 0.0196 0.0192 3122
16 General Electric US -0.0002948 0.738 yes 0.868368 0.2557 0.2539 409
17 Harmony Cert. South-A 0.0001846 0.743 yes 0.4903952 0.0474 0.0472 3575
18 Hexcel US 0.0007368 0.575 yes 0.8878823 0.1091 0.1077 642
19 HSBC Holdings plc UK 0.0011102 0.007 no 0.7222306 0.1874 0.1871 3182
20 Infosys Ltd ads India 0.0013119 0.551 yes 0.7569423 0.0646 0.061 261
21 ING Groupe/Groep NL -0.0002429 0.631 yes 0.7708937 0.1854 0.185 2475
22 Eli Lilly and Co US -0.0000328 0.988 yes 1.047684 0.1106 0.1055 178
23 Merck and Co. Inc. US 0.0000344 0.93 yes 0.634631 0.1658 0.1655 3151
24 Orange FR -0.0002209 0.58 yes 0.7286251 0.1766 0.1764 3624
25 Pfizer Cert. US 0.0001635 0.626 yes 0.5876857 0.167 0.1667 3588
26 Philip Morris US 0.0007811 0.224 yes 0.5889544 0.1448 0.1443 1542
27 Proctor and Gamble US 0.0000946 0.785 yes 0.5735864 0.1696 0.1694 3144
28 Rio Tinto Cert. UK 0.001042 0.119 yes 0.5563966 0.048 0.0477 3254
29 Royal Bank of Schotland UK 0.0000404 0.968 yes 0.7098101 0.0842 0.0837 1670
30 Royal Dutch Shell A NL 0.0001403 0.64 yes 0.7266922 0.4036 0.4033 2235
31 Royal Dutch Shell B NL 0.0003035 0.504 yes 0.7815721 0.3778 0.3773 1412
32 Schlumberger FR 0.0006069 0.248 yes 0.5233991 0.0685 0.0682 3182
33 STMicroelectronics Swiss -0.0002366 0.558 yes 0.7405825 0.199 0.1988 3182
34 Vale Brazil -0.000217 0.83 yes 0.7465494 0.103 0.1023 1373
35 Watsco US -0.000657 0.059 yes 0.8596647 0.6859 0.6851 406
36 Weatherford Swiss -0.0000418 0.966 yes 0.9787537 0.2088 0.2075 622
* notes: The following cells were displayed in bold for clarity: US as home country in column (2), and where CAPM does not hold in column (5)
4.1.2 Other findings which could not be proven. The CAPM regressions outcomes raised questions on the overall model. The beta, the R-squared and home market dominance are highlighted in the next sections.
Beta. The regressions on both exchanges resulted in two regression lines for one
individual company. As explained in section 2.1, the beta shows the asset’s reaction to a change in the market return premium. For 31 out of 36 companies the beta on the NYSE estimated by the regression was higher than the beta on the Euronext estimated by the
regression. Testing whether this result is significant is beyond the scope of this research, since testing a difference in beta’s essentially means testing a difference in market reactions. This would require adjusting the entire dataset in order to estimate both beta’s for the same time periods on both exchanges. Moreover, also other factors should be taken into account, like consumer confidence, market reactions to crises and all other factors that could be of influence in analysing the reaction of an asset to changes in market circumstances.
As mentioned in section 2.1, Fama and French showed regression lines where the CAPM was applied, which showed signs of being too flat, i.e. the beta was too low in comparison with reality. In this research no evidence for that is found.
R-squared. Considering the (adjusted) R-squares of all stocks in tables 2 and 3, the
regression lines do not seem to explain a lot of the variation in stock price returns, because the (adjusted) R-squared values are not very high. This could be in line with Fama and French’ theory, presented in section 2.1, which states that empirical research has shown that CAPM is not in line with stocks’ behaviour in practice. However, the fact that the (adjusted) R-squares are not very high could also be a confirmation of the hypothesis, which states that the CAP-model does not hold, due to the exchange rate influences and other international factors, which are not defined in the CAPM regression equation.
Home Market Dominance. As explained in the literature review, some researches
have shown presence of home country price determination dominance. In column 2 of tables 2 and 3 all the stocks’ home countries are listed. From the 8 companies for which the CAP-Model was not accepted in section 4.1.1, 4 were rejected on the foreign exchange, and 4 on the home exchange. Home market dominance cannot be confirmed nor rejected here.
4.1.3 Multi regression model. In section 4.1.2 was highlighted that the R-squared values of the regressions are not very high in most cases. As mentioned in section 2.1, Fama and French (2004) called the CAP-model a basic model to which other more complicating factors could be added (p. 44). In this analysis two variables were added to the regression equation: 1) Days until dividend payment and 2) the exchange rate. ‘Days until dividend payment’ was added because from the Dividend Discount Model by Berk and DeMarzo (2011) could be inferred that as a dividend date approaches, the stock price increases (p. 256). The logic behind this is that the present value of the dividend payment is higher as it
approaches the due date, since it is discounted over a shorter period of time. The exchange rate was added, because in this research the CAPM is analysed on stocks that are traded in different currencies, so the exchange rate was the factor that distinguished them.
When those variables were included in the regressions, the coefficients and the adjusted R-squares did not show any signs of those variables being of influence in
determining the excess return of the stocks. Therefore those two variables were left out of the analysis.
4.2 The Law of One Price
The next step in the investigation was to investigate whether the law of one price held. The formula mentioned in the method in section 3 was 𝑃𝑟𝑖𝑐𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑃! 𝑁𝑌𝑆𝐸 − 𝑆!𝑃!(𝐸𝑢𝑟𝑜𝑛𝑒𝑥𝑡). If this resulted in a positive amount, it meant that the price of the stock on the NYSE was higher than the price of the stock on the Euronext. If it resulted in a negative
amount, it meant that the NYSE-price was lower than the Euronext one. All the stocks’ arbitrage profits were plotted over time, while ignoring transaction costs, in order to get Graph 1 that is presented on page 22. In section 7.2 in Appendix B, graphs 38 until graph 73 present for each stock the individual arbitrage opportunities. The analysis of each stock’s arbitrage is presented in table 4:
*Table 4:
Variable (1) Obs (2) Mean ($) (3) Std. Dev (4) T-statistic (7) Sign? (8) * T-statistic (9) Sign? (10) *
1 AB Inbeb 1245 -1.515049 1.644672 -32.50364425 < 0 -30.96969349 < 0 2 Abbvie 353 -0.6171485 3.254937 -3.56233242 < 0 -3.149616894 < 0
3 Aegon 2151 1.648748 4.308036 17.74986945 > 0 16.98012437 > 0
4 Alcatel-Lucent 3575 0.1694576 0.9896945 10.23759436 > 0 5.918000568 > 0 5 ArcelorMittal 2472 5.58647 15.90682 17.4613709 > 0 17.23788666 > 0 6 Brookfield Asset Management 3366 -1.73865 2.788588 -36.17302817 < 0 -34.6854536 < 0 7 Caterpillar 2733 -0.21922 10.39724 -1.102254601 - applicable Not
8 Coca-Cola Enterprises 694 0.3518334 1.50382 6.163408373 > 0 4.910873228 > 0 9 CGG 3617 -0.5504779 0.6455264 -51.28615425 < 0 -44.62474236 < 0 10 Core Laborstories 521 -0.0701059 4.040767 -0.396013163 - applicable Not
11 Delhaize Group 3304 -0.3581142 0.3340786 -61.61591531 < 0 -49.31386768 < 0 12 Diageo 3174 10.19248 10.31411 55.67389042 > 0 55.28333943 > 0 13 DRD-Gold 3569 10.89693 8.493005 76.65068764 > 0 76.1477456 > 0 14 Du Pont de Nemours 3092 1.354384 1.795037 41.95542767 > 0 39.74053656 > 0 15 Ford Motor Company 3127 -8.718386 11.28854 -43.18791695 < 0 -42.83373029 < 0 16 General Electric 412 13.90105 1.51671 186.0345736 > 0 185.0777055 > 0 17 Harmony 3580 2.550836 1.422477 107.2948305 > 0 104.2873535 > 0 18 Hexcel 645 2.41568 4.091471 14.99476914 > 0 14.5509496 > 0 19 HSBC 3188 23.34291 19.89302 66.2542028 > 0 66.05126428 > 0 20 Infosys 264 5.457571 10.69599 8.290493241 > 0 8.181878939 > 0 21 ING Group 2480 -0.1472493 1.852274 -3.958893772 < 0 -2.036569492 < 0 22 Eli Lilly and Co. 181 0.8681757 3.62846 3.21902666 > 0 2.953918565 > 0 23 Merck and Co. Inc. 3157 1.195577 2.61272 25.71117787 > 0 24.17355276 > 0 24 Orange 3630 -1.105714 2.617339 -25.45283396 < 0 -23.80694938 < 0 25 Pfizer 3595 -0.2710072 1.412301 -11.50543412 < 0 -8.469948199 < 0 26 Philip Morris 1548 3.670929 1.28409 112.4775892 > 0 110.2868228 > 0 27 Proctor and Gamble 3152 2.300809 1.846893 69.94101598 > 0 67.76752716 > 0 28 Rio Tinto 3262 -4.588365 4.207473 -62.28430159 < 0 -61.31373199 < 0 29 Royal Bank of Schotland 1673 -1.080565 3.775872 -11.70527452 < 0 -10.93074718 < 0 30 Royal Dutch Shell - A 2242 -0.0186619 0.6590912 44.26783161 > 0 42.71354007 > 0 31 Royal Dutch Shell - B 1418 0.5534887 0.3866062 -1.340689317 - applicable Not
32 Schlumberger 3190 2.036394 2.598178 53.91108342 > 0 46.94681755 > 0 33 STMicroelectronics 3190 1.199213 0.8412583 80.5123137 > 0 75.71197346 > 0
34 Vale 1379 -0.0860014 0.9594175 -3.328741101 < 0 -0.561286284 -
35 Watsco 412 22.35372 8.165503 55.56681085 > 0 55.38907636 > 0
36 Weatherford 623 0.5157618 1.443801 8.916324339 > 0 7.680255304 > 0 * > 0 means the mean arbitrage is significantly larger than zero, < 0 means the mean arbitrage is significantly smaller than zero, - means the value is not significantly different from zero.
The average arbitrage values vary from -8.72 to +23.34. This meant that there was a stock for which the NYSE-value was on average 23.34 dollars higher than the Euronext value. There also was a stock for which the NYSE value was on average 8.72 dollar lower than the European counterpart. The lowest average arbitrage that was found was 0.1472493 dollar.
For each stock, an analysis was performed in order to test whether the arbitrage opportunities were significantly above or under zero, using the t-statistic presented in column 7. The results are displayed in column 8 in table 4. For 12 stocks the arbitrage opportunities were significantly smaller than zero, which meant that the NYSE-price was significantly smaller than the Euronext-price. For 21 stocks the arbitrage opportunities were significantly higher than zero, which meant that the Euronext-price was significantly smaller than the NYSE-price. 3 stocks’ arbitrage was not significantly different from zero.
For all the stocks whose arbitrage values were significantly different from zero, an adapted t-statistic was calculated presented in column 9 of table 4 in order to correct for transaction costs. For 32 out of the 33 stocks arbitrage would have been profitable. This is in contrast with Yeyati, Schmukler and van Horen’s findings, who found a cross market
premium of close to zero, as explained in section 2.3.
A possible explanation for the fact that profitable arbitrage opportunities were found in this research could be that markets are inefficient. In section 2.4, factors that could reduce market efficiency are named, such as market risk, the dividend yield on the stock and interest rates. Idiosyncratic risk could influence efficiency too. One of those factors could cause the market to be inefficient.
All in all, the CAPM model for cross–listed stocks on the NYSE and the Euronext is valid for 28 stocks on both stock exchanges, for the remaining 8 stocks it holds on one
exchange. There were findings which could not be proven, but that did raise questions. Such a finding was that the R-squared values of the CAPM regressions were not very high. This meant that the regression line did not explain much of the variation in stock price returns. Adding two variables to the regression equation did not improve this analysis.
Another finding, which could not be proven was that for 33 out of the 36 companies, the beta estimated by the regression equation was higher on the NYSE than on the Euronext. Investigating whether this is significant and what this would imply would require an entire new research. The fact that Fama and French (2004) stated that the regression lines estimated by the CAPM are too flat in comparison with reality (p. 32), cannot be confirmed nor rejected based on this research. Moreover, no signs of home dominance were found in this research.
In the Law of One Price analysis, significant arbitrage opportunities were found for 33 out of 36 stocks, when corrected for transaction costs. From this can be concluded that de Law of One Price is not valid for 33 out the 36 cross-listed stocks incorporated in this research, since parity deviations have been found for them. This could imply that stock markets are not efficient.
5 Conclusion
This research investigated whether the Capital Asset Pricing Model and the Law of One Price hold for cross-listed stocks that are traded on the New York Stock Exchange and the Euronext. Theory predicts stocks’ excess return over the risk-free rate to act according to the CAPM regression equation. Past research has shown that CAPM in practice does not seem to be in line with what the regression line equation predicts. Empirical research has shown that the regression line should be steeper in order to be in line with reality. Researchers therefore view the CAPM as a basic economic model, to which more complicating factors have to be added.
This investigation has shown that for 28 out of a total of 36 stocks, the CAPM is valid on both exchanges, when the assumption is used that alpha should be equal to zero. For the remaining 8 stocks, the CAPM is valid on one of the two exchanges. The stocks’ regression lines do not explain much of the variation in stocks’ excess return over the risk-free rate when looking at the R-squared values. This could be due to the fact that CAPM does not have high explanatory power itself, or due to the fact that, as the hypothesis stated, CAPM does not incorporate international factors that play a role when a stock price is determined on two markets simultaneously.
Furthermore, in this research, the Law of One Price for cross-listed stocks on the Euronext and on the NYSE is not valid. Theory predicted the Law of One Price to hold and past empirical investigations also confirmed that cross market premia are close to zero. In this research, however, was found that arbitrage opportunities are significantly present on either the NYSE or the Euronext for 33 out of the 36 stocks that were incorporated. This could imply that market inefficiencies are present on the stock market.
Possible room for improvement could entail taking the risk free rate and market returns of the specific country that the stock is traded in, in order to make the
CAPM-estimations more country specific. A research on stock market index behaviour by Roll (1992) has shown that there are differences in volatility on stock markets, due to differences in the size of the stock pool that is taken into account, due to an individual country’s risk, and the index’ sensitivity to exchange rates (p. 37). From this can be inferred that taking country specific market indexes, in order to represent market return, could improve the analysis.
Besides, a finding, which could not be proven in this research, was that the beta’s on the NYSE markets seem higher than the beta’s on the Euronext market. In order to investigate this, the dataset should be adjusted in order to incorporate values from simultaneous periods. Moreover, since the beta represents an asset’s reaction to changes in market circumstances, also crisis correction factors, consumer confidence on both markets, and all other factors that could be of importance, should be incorporated.
All in all, the hypothesis was partly rejected: The CAPM holds for most of the cross-listed stocks in this research. However, it does not reflect high explanatory power. Besides, the law of one price is also rejected, since arbitrage opportunities are significantly present for the majority of the stocks, when corrected for transaction costs.
6 References 6.1 Bibliography
Agarwal, S., Liu, C. & Rhee, G. (2007). Where does price discovery occur for stocks traded in multiple markets? Evidence from Hong Kong and London. Journal of International
Money and Finance, 26(1), p. 62.
Alhaj-Yaseen, Y.S., Lam, E. & Barkoulas, J.T. (2014). Price discovery for cross-listed firms with foreign IPOs. International Review of Financial analysis, 31, p. 86.
Berk, J. & DeMarzo, P. (2011). Corporate Finance. Essex: Pearson.
Eun, C. S. & Sabherwal, S. (2003). Cross-Border Listings and Price Discovery: Evidence from U.S.-Listed Canadian Stocks. The Journal of Finance, 58(2), pp. 549–576. Fama, E.F. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. The
Journal of Finance, 25(2), pp. 383-417.
Fama, E.F. & French, K.R. (2004). The Capital Asset Pricing Model: Theory and Evidence.
Journal of economic perspectives, 18(3), pp. 25-46.
Gagnon, L. & Karolyi, G.A. (2010). Multi-market trading and arbitrage. Journal of Financial
Kleidon, A.W. & Werner, I.M. (1996). U.K. and U.S. Trading of British Cross-Listed Stocks: An Intraday analysis of Market Integration. Review of Financial Studies, 9(2), pp. 619-664.
Nicholson, W. & Snyder, C. (2010). Microeconomic Theory: Basic Priciples and Extensions. Canada, Cengage Learning.
R. Roll (1992). Industrial Structure and the Comparative Behavior of International Stock Market Indices. The Journal of Finance, 47(1), pp. 3-41.
Yeyati, E.L., Schmukler, S.L. & van Horen, N. (2009). International financial integration through the law of one price: The role of liquidity and capital controls. Journal of
Financial Intermediation, 18(3), pp. 434-437.
6.2 Data sources
Abbvie. Home country. Retrieved from: http://www.abbvie.com/
Aegon. Home country. Retrieved from: http://www.aegon.com/en/Home/About/Contact-Us/Address-head-office/
Alcatel-Lucent. Home country. Retrieved from: http://www.alcatel-lucent.com/contact-us Anheiser-Busch Inbev. Home country. Retrieved from: http://www.ab-inbev.com/contact.cfm ArcerlorMittal. Home country. Retrieved from:
http://corporate.arcelormittal.com/who-we-are/contact-us
Caterprillar. Home country. Retrieved from:
http://www.caterpillar.com/nl/company/history.html
CGG. Home country. Retrieved from: http://www.cgg.com/Contact.aspx?cid=88 Coca-Cola Enterprises. Home country. Retrieved from:
http://www.cokecce.com/about-cce/our-story
Core Laboratories. Home country. Retrieved from: http://www.corelab.com/corporate/history Delhaize Group. Home country. Retrieved from:
http://delhaize.com/nl/Home/Onzehistoriek.aspx Delhaize. Ratio stocks NYSE-Euronext. Retrieved from:
http://www.delhaize.com/nl/BeleggersCenter/InformatieoverhetAandeel/ADRprogram ma.aspx
Diageo plc. Home country. Retrieved from: http://www.diageo.com/en-row/ourbusiness/Pages/History.aspx
Diageo. Ratio stocks NYSE-Euronext. Retrieved from: http://www.diageo.com/en-us/investor/Pages/FAQs.aspx#q28
DRD-Gold. Home country. Retrieved from: http://www.drd.co.za/contact-us Du Pont de Nemours. Home country. Retrieved from:
http://www2.dupont.com/Phoenix_Heritage/en_US/1802_a_detail.html
Eli Lilly and Co. Home country. Retrieved from: http://www.lilly.com/Pages/contact.aspx Euronext. (2014). Equities listings. Euronext. Retrieved from:
https://euronext.com/equities-directory.
Euronext. (2014). Trading fees. Retrieved from:
https://derivatives.euronext.com/sites/derivatives.euronext.com/files/euronext_derivati ves_trading_fee_guide_22_april_2014.pdf
Euronext. (2014). Trading hours. Retrieved from:
https://europeanequities.nyx.com/nl/trading/trading-hours-and-holidays Ford Motor Company. Home country. Retrieved from: http://corporate.ford.com/our-
company/heritage/company-milestones-news-detail/677-5-dollar-a-day General Electric. Home country. Retrieved from: http://www.ge.com/contact/general Harmony. Home country. Retrieved from: http://www.harmony.co.za/contact-us Hexcel. Home country. Retrieved from: http://www.hexcel.com/ourcompany/history HSBC. Home country. Retrieved from:
http://www.hsbc.com/about-hsbc/company-history/hsbc-history
HSBC. Ratio stocks NYSE-Euronext. Retrieved from: http://www.hsbc.com/investor-relations/share-information
Infosys. Home country. Retrieved from: http://www.infosys.com/about/Pages/history.aspx ING Group. Home country. Retrieved from:
http://www.ing.com/About-us/Our-stories/ING-Head-office.htm
Merck and Co. Home country. Retrieved from: http://www.merck.com/contact/home.html New York Stock Exchange. Merger NYSE and Euronext. Retrieved from:
https://www.intercontinentalexchange.com/about#growth NYSE (2014). Equities listings. [Data File]. NASDAQ. Retrieved from:
http://www.nasdaq.com/screening/company-list.aspx. NYSE. Trading fees. Retrieved from:
https://beta.nyse.com/publicdocs/nyse/markets/nyse/NYSE_Price_List_2040624.pdf NYSE. Trading hours. Retrieved from: https://beta.nyse.com/markets/hours-calendars Orange. Home country. Retrieved from: http://orange.com/sirius/histoire/en/home
Pfizer. Home country. Retrieved from: http://www.pfizer.com/contact/contact_us_support Philip Morris. Home country. Retrieved from:
http://www.pmi.com/nld/about_us/pages/our_history.aspx Proctor and Gamble. Home country. Retrieved from:
http://www.pg.com/en_US/company/heritage.shtml Proctor and Gamble. Stock split. Retrieved from:
http://www.pginvestor.com/divs.aspx?iid=4004124 Quandl. Exchange rate Euro-Dollar. Retrieved from:
http://www.quandl.com/QUANDL/EURUSD-Currency-Exchange-Rates-EUR-vs-USD
Rio Tinto. Home country. Retrieved from:
http://www.riotinto.com/annualreport2007/services/contactus/index.html
Royal Bank of Schotland. Home country. Retrieved from: http://www.rbs.com/faqs.html Royal Bank of Schotland. Ratio stocks NYSE-Euronext. Retrieved from:
http://www.rbs.com/faqs/investors.html Royal Dutch Shell. Home country. Retrieved from:
http://www.shell.com/global/aboutshell/contact-us.html Royal Dutch Shell. Ratio stocks NYSE-Euronext. Retrieved from:
http://www.shell.com/global/aboutshell/investor/shareholder-information/ads/ads-faq.html#textwithimage_3
STMicroelectronics. Home country. Retrieved from:
http://www.st.com/stonline/contactus/contacts/index.php?type=6
Vale. Home country. Retrieved from: http://www.vale.com/en/pages/contact.aspx Watsco. Home country. Retrieved from: http://www.watsco.com/contact-us/ Weatherford. Home country. Retrieved from:
http://www.weatherford.com/AboutWeatherford/InvestorRelations/InvestorFAQs/ World Federation of Exchanges. Market Capitalization Stock Exchanges. Retrieved from:
http://www.world-exchanges.org/statistics/time-series/market-capitalization
www.wisselkoers.nl. Exchange rate euro-dollar on 30 june 2014. Retrieved from:
http://www.wisselkoers.nl/
Yahoo!Finance. (2014). Stock prices, S&P500 values and 30-year Treasury bill values. [Data File]. Retrieved from: http://finance.yahoo.com/
7 Appendix 7.1 Appendix A
In Stata d + company ticker + first letter of exchange (n (NYSE) or e (Euronext)) was used as the name of the variable that represents the excess return of the stock over the risk free rate, f.e. dabbvn is the excess return of Abbvie (ABBV) on the NYSE over the risk free rate. The NYSE values were regressed on dmkt, and the Euronext values on dmkt2.
Graph 2 A and B: Anheiser-Busch Inbev:
Graph 4 A and B: Aegon:
Graph 5A and B: Alcatel-Lucent:
Graph 7 A and B: Brookfield Asset Management:
Graph 8 A and B: Caterpillar:
Graph 9 A and B: Coca-Cola Enterprises:
Graph 11 A and B: Core Laboratories:
Graph 12 A and B: Delhaize:
Graph 13 A and B: Diageo:
Graph 15 A and B: Du Pont de Nemours:
Graph 16 A and B: Ford Motor Company:
Graph 17 A and B: General Electric:
Graph 19 A and B: Hexcel:
Graph 20 A and B: HSBC:
Graph 21 A and B: Infosys:
Graph 23 A and B: Eli Lilly and Company:
Graph 24 A and B: Merck and Co.:
Graph 25 A and B: Orange:
Graph 27 A and B: Philip Morris:
Graph 28 A and B: Proctor and Gamble:
Graph 29 A and B: Royal Bank of Schotland:
Graph 31 A and B: Schlumberger:
Graph 32 A and B: Shell-A:
Graph 33 A and B: Shell-B:
Graph 35 A and B: Vale:
Graph 36 A and B: Watsco:
7.2 Appendix B
In this section graphs of the arbitrage opportunities per stock are presented. The A at the beginning of every variable name stands for Arbitrage, which is followed by the company name.
Graph 38: Anheiser-Busch Inbev:
Graph 39: Abbvie
Graph 41: Alcatel-Lucent
Graph 42: Arcelor-Mittal
Graph 44: Caterpillar
Graph 45: Coca-Cola Enterprises:
Graph 47: Core Laboratories:
Graph 48: Delhaize:
Graph 50: DRDGold:
Graph 51: Du Pont de Nemours:
Graph 53: General Electric:
Graph 54: Harmony:
Graph 56: HSBC:
Graph 57: Infosys:
Graph 59: Eli Lilly and Company:
Graph 60: Merck and Co.:
Graph 62: Pfizer:
Graph 63: Philip Morris:
Graph 65: Royal Bank of Schotland:
Graph 66: Rio Tinto:
Graph 68: Shell-A:
Graph 69: Shell-B:
Graph 71: Vale:
Graph 72: Watsco:
