Camilo Orejuela Mesa Student number: 10839526
Thesis Supervisor: Tomislav Ladika
Master in International Finance Amsterdam Business School
This study analyzes price discrepancies between American Depositary Receipts and their corresponding underlying stocks using high frequency data to capture the deviations and corrections of prices during the trading day. The research is performed over the year 2015 using firms from different countries including the Netherlands, France, Germany, Spain, Finland, United Kingdom and Brazil. Based on a multiple linear regression model I study the ADR spread and its correlation with market indexes and other proxies of demand/supply imbalances between ADRs and underlying stocks. The result of this research reveal that the demand/supply imbalance between the two assets driven by changes in the S&P500, the local stock market or the currency rate produce correlated changes on the ADR spread with a mean reverting effect. By sampling data every 10 seconds this study analyses the efficiency of the market and the role of arbitrageurs and high-frequency traders in bringing prices back to equilibrium and efficiently propagating information between the ADR market and the underlying stock market.
1. Introduction...1 2. Background...5 3. Methodology...11 4. Data...17 5. Results...21 6. Conclusions...27 7. Bibliography...29
1. Introduction
With the development of technology sophisticated traders are able to react to news and price changes within a fraction of a second. Even small private investors are now able to execute transaction in matter of minutes via their phones. These improvements in technology have changed the dynamics of trading activity in the market and researchers need to consider these changes and revise their research methods.
According to the efficient market hypothesis all public information gets reflected in asset prices immediately and any deviation from that price will present an arbitrage opportunity. Divergence in supply or demand in different markets could cause price deviations between cross-listed assets and arbitrageurs waiting for those opportunities react using the fastest technology available trying to profit from the mis-priced assets. This rapid trading activity pushes prices back to equilibrium and enforces an efficient market. It is also an essential mechanism through which information flows between markets. The speed at which this trading activity gets executed determines how long assets remain mis-priced in the market. When looking at asset mis-pricing in cross-listed markets the speed at which investors and arbitrageurs are able to react is a fundamental factor and therefore it will require a refined data sampling period to perform a realistic statistical study.
Akram et al (2009) provides evidence that there are numerous short-lived deviations from equilibrium within the trading day and that their duration is on average low enough to explain why such violations of the Law of One Price can be difficult to detect using data sampled at low frequencies. Price deviations between two assets will only exist for short periods because the fast reaction time of the market participants will bring the prices back
to parity in matter of seconds. For the daily observer, one who samples the market using the closing price of each day, it will appear as if there were no price deviations and the statistical attempt to explain the price discrepancies will not be realistic. Sampling at daily closing prices hides all the trading activity happening intra-day. Because of this reason the analysis of asset mis-pricing and the study of their possible causes and correlations requires a high-frequency data sampling to derive realistic conclusions.
One of the most common vehicles used by companies to cross-list their shares in the U.S is by the use of American Depositary Receipts. ADRs give the owner rights over shares in non-U.S companies and investors are entitled to all benefits granted by the underlying shares. When investors buy ADRs a custodian in the home country immobilizes the corresponding shares of the underlying stock and investors can, at any moment, exchange their ADRs for the underlying stocks. Investors can also exchange stocks for the corresponding ADRs, under exceptional cases this operation can be restricted but under normal circumstances it can also be done at any time. Because of these reasons ADRs are perfect candidates for research studies regarding price discrepancies since they should completely reflect the underlying share price at all times.
This study will analyze price discrepancies between ADRs and their corresponding underlying stocks using high frequency data to be able to capture the deviations and corrections of prices during the trading day. Alsayed and McGroarty (2011) found high incidence of small quickly-disappearing mispricings by performing their research constructing their data set sampling at 1 minute intervals. My study tries to explain the intra-day ADR spread deviations by taking data samples every 10 seconds and using a multiple linear regression model incorporating relevant explanatory variables.
There are several factors that could drive prices of the cross-listed assets out of line and they are mainly related to a skewed interest of investors towards one of the assets. The causes of these preferences could vary from trading restrictions for different kinds of investors, a home bias selection or the investor’s sentiment on the local economy. Deviations of ADR prices with respect to their underlying stocks are mainly attributed to differences in demand or supply in the corresponding markets. If there is any demand or supply change in the U.S market or in the underlying stock local market it will probably cause a price discrepancy between the two assets. Because U.S investors mainly trade ADRs and non-U.S investors mainly trade the local stocks, their behavioral difference driven by the returns of their home market are expected to have significant correlation with the ADR spread. The results of this study show a positive significant correlation of the S&P500 index returns with the ADR spread and negative significant correlation of the underlying stock market index returns with the ADR spread.
Since ADRs are traded in US dollars there is an intrinsic relationship between the price of the ADRs and the currency rate. ADR prices are adjusted to fluctuations in the currency rate at a very high speed due to arbitrage and high-frequency trading activity that tries to profit from incorrect priced assets. By incorporating currency rate returns in the linear regression model and given the high frequencies sample rate of the data, the results of this study show of a positive significant correlation of the currency rate with the ADR spread.
Previous similar studies used lower data sampling frequencies and their research methods are outdated and not appropriate to derive conclusion on the current market. Daily data sampling might have been a good approach in old days when technology didn't allow
traders to react as fast as they can do today and price discrepancies could last longer than a day. Gagnon and Karolyi (2004) performed a similar regression analysis including market indexes and currency rate but using daily closing prices. Their study found no significant correlation of the ADR spread with the U.S market index and no significant correlation to the currency rate. My research takes into account that current market data requires high frequency sampling to derive realistic conclusion and my results contradict Gagnons and Karolyi (2004).
In addition to the high-frequency sampling rate, this study expands the research analysis by including new factors in the linear regression model that act as proxies of demand or supply shocks by measuring volatility and liquidity in both markets. Demand/supply shocks that affect the price of the ADRs or underlying stocks independently generate an effect in volatility and/or liquidity in one of the assets without affecting the other. The arbitrageurs and high-frequency traders will propagate this effect from one market to the other but any imbalance will result in a price discrepancy between the assets. Based on the findings of this study I conclude that high-frequency traders are able to transmit volatility and liquidity across the markets efficiently and there should be no considerable difference between the volatility of the ADR and of the underlying stock to produce significant price deviations.
The findings of this research provide valuable contribution to traders building and improving strategies that profit from short lived discrepancies within the trading day.
2. Background
American Depositary Receipts (ADRs) give the owner rights over shares in non-U.S companies. These receipts can be traded in American exchanges like the New York Stock Exchange (NYSE) . ADRs are available in other American exchanges like the NASDAQ but this study will only consider ADRs listed on the NYSE. When an investor buys an ADR a custodian immobilize the underlying stock in the local market and the investor is entitled to all benefits granted by the underlying shares. Investors can exchange ADRs for their underlying shares or vice versa at any time. The ADR prices should completely reflect the underlying share price at all times. Nevertheless, there are market forces driving the prices of the ADRs differently than for the underlying stocks. Different types of investors, trading restriction or home market bias could cause asymmetry in the supply or demand of one of the assets which will be reflected in price a discrepancy between the two assets. These price discrepancies represent arbitrage opportunities and their exploitation creates an opposing force that brings the ADRs and the underlying stocks back to parity.
The price deviation between ADRs and the underlying stocks is referred as the ADR spread and it has very particular characteristics. Theoretically the ADR spread should be zero but when investors express a particular interest in one of the assets more than the other the spread will deviate from zero. Because of transaction costs and conversion fees (a fee charged by the ADR provider to convert ADRs into the underlying stock or the other way around) there is no arbitrage opportunity until the spread is big enough to compensate for those costs. When the spread breaches the arbitrage threshold arbitrageurs waiting for those opportunities will compete to capture a risk free profit. By buying the cheap asset and short selling the expensive asset the arbitrageurs can use the ADR conversion mechanism to close their positions and profit from the difference. With a long position in
the stocks and a short position in the ADR, arbitrageurs can request an ADR creation and they will receive a new ADR certificate in exchange for the underlying stocks closing their position. In a similar way, via an ADR redemption, the arbitrageur receives the underlying stocks in exchange for the ADR. Using this conversion mechanism traders can realize a profit at no risk when the price deviation between the two assets is large enough to cover the conversion costs. This behavior creates a contention barrier for the ADR spread. Price deviations over the arbitrage boundaries create risk-less opportunities that will be exploited holding the prices within the contention barrier.
Within the arbitrage threshold boundaries of the ADR spread there are other market participants that help keeping the spread even closer to zero. High frequency traders will take a position in the spread in the same way as arbitrageurs do but they will not close their position by creating or redeeming the ADRs; instead, they will hold to the assets hopping the spread will return to zero. If the spread actually returns to zero the traders will profit by closing their position reverting the trades. This requires very low transaction costs to be a profitable, since there are four transactions involved, but it can be cheaper compared with a full arbitrage strategy because it eliminates the conversion fees. Because these strategies bear the risk that the spread will not return to zero they are not considered a complete or pure arbitrage. These type of strategies are based on the assumption that the price differences will be corrected over time and are typically called 'pairs trading' strategies. They are mostly used between not interchangeable cross-listed assets or between highly correlated assets.
Since pairs trading strategies totally depend on asset prices converging back to parity the traders face several risks. Because ADRs are completely interchangeable with the
underlying stocks, using them in a pairs trading strategy carries a lower risk compare to other cross-listed asset that are not interchangeable. Hamad et al (2011) considers pairs trading as the main mechanism by which the law of one price is enforced between stocks and ADRs. Within the pure arbitrage boundaries of the ADR spread the traders using pairs trading strategies will be the main participants pushing the ADR spread towards zero and the limits they impose themselves, considering the risks they face, could be a major factor explaining price deviations from parity. Gromb and Vayanos (2010) describe how limits and constrains faced by pairs trading strategies can explain anomalies and price deviations from their fundamental values. The study establishes two building blocks by which anomalies can be explained, one is the demand shocks experienced by investors that will drive prices away from their fundamental values, and the second block is the limits of the traders that prevent those price anomalies to be corrected.
The trading limits described by Gromb and Vayanos (2010) include non-fundamental risk and short selling risk. These are some of the mosts important risks faced by real life arbitrage traders and it is essential to consider them when trying to explain price discrepancies. “Non-fundamental” risk, as is referred in Gromb's article, is the risk faced by demand shocks that affect prices. The same demand forces that drive prices out of parity imply a reduction in the correlation between the two assets and an increases in the volatility of one asset without affecting the other. This will also affect the volatility of the returns of pairs trading strategies that took a position in the ADR spread driven by the effects of a demand shock and therefore it will increase its risk. Another risk faced by arbitrageurs is given by the short selling costs. When investors get into a short position they usually need to borrow the asset and they will need to pay borrowing fees; the longer the investor leave the position open the borrowing fees will drain out the unrealized profits
of the original trade and eventually transforming it into a losing strategy. This means the traders face a risk based on how long the prices will remain out of line.
Several other risks mentioned by Gromb and Vayanos (2010) are related to arbitrageurs capital constrains. Their ability to raise capital, to obtain leverage or their margin constrains could affect the ability of the traders to enter or keep their positions. These imply that the ability of arbitrage traders to enforce the law of one prices will depend on their capital constrains. If their capital is large enough relative to the demand shock the price discrepancies will be absorbed by arbitrageurs taking the other side of shock, providing liquidity to the market and limiting the price change. If the demand shock if too big arbitrageurs will not be able to absorb the shock limiting their ability to take the other side of the possible transactions and therefore providing lower liquidity to the market and unable to contain the price impact.
Typical creation and redemption fees for ADRs are around 5 cents of a Dollar (0.05$), these fees can vary from different ADR providers and market makers can obtain significant discounts. This 5 cents theoretically represent the pure arbitrage boundaries of the ADR spread, meaning that if the ADR spread deviates for more than 5 cents arbitrageurs will be able to capture a risk less profit. In the U.K there is a Stamp Duty Tax of 1.5% investors have to pay extra to convert U.K stocks into ADRs. These extra tax payment creates a wider price band where the U.K stocks can move without causing a pure arbitrage opportunity with the ADR. Price discrepancies contained within the pure arbitrage band are exploited by the high-frequency pair trading strategies that, considering the risks mentioned before, must decide how large the ADR spread must be to take a position that will likely compensate for all the risks. The traders must decide if they will not lose other more profitable opportunities due to capital constrains if they enter a position at the current
ADR spread level. After establishing the initial position the traders must decide for how long they will be able to keep that position before the borrowing costs drain out the possible profits. On top of all these, if the ADR spread widens the traders faces a loss on their position.
The previous insight into arbitrage risks and trading strategies is essential to understand why price deviations could persist in the market. It is also important to analyze what produces the price deviations in the first place. The demand shocks in one of the assets could be caused by a preference of investors to trade one of the assets more than the other at a certain moment. Chakravarty et al (2007) show in their study that institutional investors choice of trading venue (ADR or local stock) depends on a variety of factors including firm size, the level of shareholder rights protection, the market design, etc. Most of these factors are not subject to sudden changes and are not likely to produce spontaneous shocks of demand or supply in one the the assets. Poshakwale et al (2008) investigates the dynamics of information flow between the ADR market and the underlying stock market. He focuses in volatility transmission and provides empirical evidence of a bidirectional transmission that suggest that information in the ADR could change the expectations in the underlying stock and vice versa. Similarly, Kim et al (2000) examined how a shock in one market is transmitted into the other and gave evidence that ADR returns under react to underlying security movements and over react to U.S market index. Using market indexes these studies show a good way to proxy demand/supply shocks that could affect one asset and not the other.
Gagnon and Karolyi (2004) provide a similar study where they analyze the differences in the prices of shares of stocks that trade simultaneously in different markets around the
world focusing on ADRs. Their study embraces 581 stocks in 39 countries during the periods between 1993 and 2002 and analyses returns differences of the ADRs with local stock returns. Using a linear regression approach they examined the magnitude of the deviations from parity and the systematic co-movements with market indexes and currencies. They concluded that on average there is a negative and significant mean reversion, negative and significant net exposure to the home market, positive and insignificant exposure to the U.S market and a positive but insignificant exposure to the currency rate differential. Gagnon and Karolyi (2004) based their study in data sets with a sampling period of one day. The study uses U.S closing prices and captures the bid ask midpoint on the home market at the U.S. closing time. I believe arbitrageurs and high frequency traders taking advantage of price discrepancies will react within the trading day pushing the prices back to parity and all the information embedded in this activity is lost when sampling closing day prices. Between 1993 and 2002 (data period used by Gagnon and Karolyi) investors didn't have the technology to react that fast to events and price movements, therefore, a sampling period of one day was probably good enough. Performing a similar research with current data will require high-frequency sampling to obtain realistic results.
While researching profitability of arbitrage strategies Alsayed and McGroarty (2011) criticize analogous studies that use daily closing prices and cannot find any exploitable price discrepancies between ADRs and their underlying shares. By using daily closing prices the researchers looking for arbitrage opportunities missed all the intra-day trading activity and therefore couldn't find any profitable price discrepancies. To address the problems surrounding daily sampling Alsayed and McGroarty (2011) constructed their data set sampling at 1 minute intervals through the period of January 1, 2007 to December 31,
2009 and found high incidence of small quickly-disappearing mispricings. In a similar study Suarez (2005) also states that exploitable price discrepancies only exist for very short periods and they are invisible to the daily observer.
Considering all the previews background knowledge the methodology for this research incorporates a high-frequency data sampling and proxies including market indexes, volatility and liquidity that capture the effect of demand/supply shocks in one of the assets.
3. Methodology
The main purpose of this research is to examine, at a high frequency level, the price discrepancies between ADRs and their underlying stocks. By sampling the data at periods of 10 seconds it is possible to capture occurrences of price deviations before arbitrageurs and high-frequency traders push the prices back to equilibrium. Using a multiple linear correlation analysis several explanatory variables are put to test to determine their significance correlation with the observed price discrepancies.
The dependent variable in the multiple linear regression model is the ADR spread return which is calculated as the difference between the ADR return and the underlying stock return over 10 seconds. Price discrepancies that last for more than 10 seconds will be reflected in the ADR spread returns deviating from zero. The hypothesis that the ADR spread return is zero can be rejected if significant correlation is found with the explanatory variables of the model. By finding significant factors that help explain the deviation from zero of ADR spread returns will provide empirical evidence of high-frequency price deviations.
Considering the different points described in the previous section of this research, 8 explanatory variables were chosen to capture demand/supply shocks that could be correlated with price differences.
Lagged ADR spread return:
The lagged measurement of the ADR spread returns means that for each sample of 10 seconds the previous recorded measurement is used as explanatory variable in the model. If the ADR spread returns deviates from zero the high frequency trading activity will push the prices back to equilibrium and the spread returns will go back to zero. With the intra-day sampling period of 10 seconds intervals it is possible to capture the effect of these forces. It is expected to find a negative significant correlation that describes the mean reverting behavior around zero.
U.S market index returns (S&P500 index):
By using the U.S market index as a possible correlated factor with the ADR spread it will be possible to incorporate the investor’s sentiment towards the U.S economy in the model. If we assume a perfect market then the ADRs and local stocks should move together within the 10 seconds sample period and the ADR spread returns should always be zero. Any increase/decrease in the ADR price while the stock remains unchanged will cause a positive/negative spread return. Since ADRs are mostly traded by American investors their sentiment about the economy could be propagated into the ADRs creating a shock in demand or supply. This imbalance of demand/supply between the ADR and underlying stock will take the prices out of balance.
expectations. Positive returns of the S&P500 index could lead to positive returns of the ADR spread if U.S investors generalize their expectations of the U.S economy into the rest of the world and assume foreign companies will be affected in the same way as U.S companies. The foreign investors, who mainly trade the underlying stock, might not react on information of the U.S economy by trading their local stocks. For example when the U.S economy is doing well and the S&P500 index increases its value, U.S investors will be more bullish on the ADRs than the foreign investors on their local stocks. Similarly when the U.S economy is not doing well and the S&P500 index goes down, the U.S investors generalize the negative expectation and sell their ADRs while the foreign investors will not behave the same way and will not sell their local stocks. This difference in the behavior of the U.S investors compared to the foreign investors is a main factor in the imbalance of supply and demand between ADRs and underlying stocks and it is a possible explanation of price discrepancies.
Local market index returns:
The same relationship done with S&P500 index and the U.S economy can be done with the market index of the local stock and the local economy. The returns are constructed by measuring Index futures returns over 10 seconds periods. The changes in the local market index will correlate with the local stock causing ADR prices to adjust accordingly. If this process takes longer than 10 seconds the ADR spread returns measured in our sample will deviate from zero.
Risk limits restricting high-frequency traders play an important role on how quickly the price discrepancy will disappear. For example, when the home market goes up and the local stock goes up with it, the high-frequency traders will start trading the mispriced ADRs that are not fast enough to update to the new local stock prices. The traders will start building
positions of ADRs and local stock pairs to try to profit when the prices go back to equilibrium. In the case of a big stock the demand/supply shock could be too big and the high-frequency traders will probably reach their limits. If after 10 seconds the shock persists and the high-frequency traders are already at their maximum limit, they will not propagate the shock to the ADR market. The prices will go back to equilibrium a bit slower as the rest of the market participants catch up. In my model, this scenario will be reflected in a negative correlation between the underlying home market returns and the ADR spread return. If the demand/supply shocks are not significant it is possible that high-frequency traders will quickly exhaust all possible price disparity opportunities and prices will adjust to their equilibrium point too fast to capture in discrepancies in the sampling.
Currency exchange rate returns:
Since the price of an ADR should exactly reflect the price of its underlying stock translated to USD, when assuming perfect market conditions any change in the currency rate should immediately cause a correction in the ADR prices. Because the sampling period is of just 10 seconds, the model is putting to the test the efficiency of the market. When the currency rate moves, all the active ADR orders in the market will need to be adjusted to reflect the new currency rate, if the best bid and best ask price of the ADR are not adjusted within 10 seconds our model will capture the price discrepancy.
Currency rates, especially big currency pairs as EUR/USD or GBP/USD, move constantly at high-frequency and with very fine tick sizes. These small price movement could cause small price discrepancies that are not significant enough to compensate for the costs and risks assumed by high-frequency traders and therefore these small price discrepancies will be left for longer periods in the market.
Volatility of the ADR and Volatility of the underlying stock:
Demand/supply shocks that affect the price of the ADR or underlying stock independently generate an increase in volatility in one of the assets without affecting the other. The arbitrageurs and high-frequency traders will propagate this volatility from one market to the other. It will be possible to capture these demand/supply shocks using their volatility effect on the assets as a proxy. By constantly measuring the volatility at a high-frequency in both assets and incorporating this measurements as explanatory variables in the linear regression model their correlation significance with the ADR spread will be tested. If no significant correlation is found it means that arbitrageurs and high-frequency traders are able to propagate the volatility from one market to the other very efficiently.
The volatility was measure using the standard deviation of the stocks and ADR returns every 10 seconds.
Traded volume of the ADR and traded volume of the underlying stock:
The magnitude of demand/supply shocks together with the capacity of the arbitrage activity to absorb that shock are fundamental factors that will determine possible price discrepancies. If the magnitude of a shock is too big for arbitrageurs they will not be able to provide liquidity. This will be reflected in a limitation on the traded volume observed during the shock period. Measuring the traded volume in both asses will act as a proxy for demand/supply shocks that affect liquidity of an asset. On a low liquidity period on the underlying stock will increase its price and will cause the ADR spread to go down; likewise on a low liquidity period on the ADR its price will increase causing the spread to go up. The traded volume is measure every 10 seconds.
dependent variable the model is defined with the flowing formulas: RtA D R=l o g( PtAD R Pt −1A D R); Rts to ck=lo g ( Pts to c k* Ct Pt −1 s t o c k * Ct −1 ) ; Rts p r e a d=RtAD R−Rts t o ck Rts p r ea d=β0+β1* Rt −1 s p re a d +β2* Rts n p 500+β3* Rth o m e+β4* Rtc ur r enc y+β5*V oltA D R+β6*V olts t o ck+β7* T VtA D R+β8* T Vts to ck+e
Rspread is the difference between the ADR return and the underlying stock returns corrected
by currency at period t, where Ct-1 is the currency rate at the beginning of the sample
period and Ct is the currency rate at the end of the sample period.
Rsnp500 is the return of the S&P500 index, Rhome the return of the local market index and
Rcurrency the return of the currency rate at period t.
VolADR and Volstock are the standard deviation of the returns of the ADR and local stock
respectively over the 10 seconds period. TVADR and TVstock are measurements of the traded
volume during the last 10 seconds. Volatility and liquidity (measured by traded volume) are part of the information being transmitted from one market to the other and any imbalance could be reflected in the ADR spread therefore a significant correlations is expected with these explanatory variables.
The regression analysis is performed for each firm individually, grouped by region (Europe and Brazil) and over the entire sample.
Using this model 4 hypothesis are formulated. Their validity or rejection will be determine by the results of the multiple linear regression and the significance of each of the explanatory variables.
• Hypothesis 1: The ADR return spread is zero.
• Hypothesis 2: There is no significant intra-day correlation between the ADR return spread and the U.S market index returns.
• Hypothesis 3: There is no significant intra-day correlation between the ADR return spread and the local market index return.
• Hypothesis 4: There is no significant intra-day correlation between the ADR return spread and the currency rate return.
4. Data
The data analyzed in this study was from Optiver's internal database and measured at a sample period of 10 seconds. It composes stocks from different countries in Europe including the Netherlands, France, Germany, Spain, Finland and the United Kingdom. To expand the research into emerging markets several Brazilian stocks were included in the analysis. The selection of stocks is presented in Table 1 with detailing ISIN codes, the listed market used to obtain the sample data and corresponding ADR details. The regression model includes the returns of the S&P500 index and the returns of the corresponding local market index. The FTSE, DAX, AEX, CAC, IBEX, OMX and IBOV indexes were used in the regressions for their corresponding local markets and the S&P500 index as the U.S market index. To measure the returns on these indexes future prices with the nearest expiration dates were used as proxies. For example, the analysis of German stocks between January and March 2015 used the DAX index future that expired in March 2015; after March I rolled over to the next future expiration so that from April until June 2015 the index future with expiration date of June 2015 was used. With this
methodology the nearest expiration future was always used through the whole year rolling over to next expiration when the future expires. The same future proxy and rolling approach was used to measure the currency returns (EUR/USD, GBP/USD and BRL/USD)
The 10 seconds sample period was chosen to capture the effect of the different explanatory variables in the model at a high-frequency. Every 10 seconds the returns of local stocks, the returns of the ADRs and the returns of the market indexes and currency exchange rate were calculated using the midpoint between the best bid and best ask at the beginning and end of the period. The ADR spread returns are the difference between the return of the ADR and the return of the local stock adjusted by currency. This measurement of ADR spread return was used as the dependent variable in the regression model. The measurements of volatility and traded volume used to proxy the demand/supply differences between ADRs and local stocks were also measured at 10 seconds interval. The volatility for the local stock and for the ADR were calculated by measuring the returns every one second and then calculating the standard deviation of those returns over the 10 seconds period. Within the same 10 seconds period the traded volume of the local stock and of the ADR were measure.
As a robustness check several regressions were repeated at different sampling periods. Focusing only the S&P500 index returns, the local market index returns and the currency rate returns I analyzed how the significance of these variables changed while increasing the sampling period to 30 seconds and 60 seconds. The results show that as the sample period is increased the p-values of the three explanatory variables also increase. While the S&P500 index returns is a significant variable at 0.001 level for 95% of the regression done at 10 seconds sampling period, the percentage drops to 86% at 30 seconds and to
79% at 60 seconds. Similar decrease occurred for the other two variables and the adjusted R-squared also drop from 0.08 when sampling at 10 seconds to 0.06 and 0.07 when sampling at 30 seconds and 60 seconds respectively. Table 7 presents a summary of these results.
The regression analysis was done using historical data captured during the complete calendar year of 2015. For all trading days during that year only the simultaneous trading hours were considered, only the hours where the U.S market and the local stock market were open simultaneously. For the European stocks only the last 2 trading hours of the day trade simultaneously with the US. For the Brazilian stocks 6 hours per day were available to capture the required data. Holidays where either the local stock or the ADR didn't not trade were excluded. For some illiquid stocks it is possible to find 10 seconds periods where there is no bids and asks available in the order book, these empty periods were also removed from the data set. This exclusion of data points is observed in the degrees of freedom of the regressions. Liquid stocks like Royal Dutch Shell present 108,862 degrees of freedom on its regression while illiquid stocks regressions as for Novartis present 4,530 degrees of freedom. The average degrees of freedom obtained from the whole set of regressions of 62,669.
Table 2a, 2b and 2c present a summary of the collected data used for the regression analysis. The tables present all variables mean, minimum and maximum values found in the data sample. To get a better view of the distribution of the values the 1st quantile and
3rd quantile are also presented. Since the minimum and maximum values could be driven
by outliers, looking at the values in the 1st and 3rd quantile provides a more reliable
are evident from the summary of the data. The 10 seconds ADR spread returns show variations from -1.2 to 1.2 basis points between the 1st and 3rd quantile for UK stocks, while
for Brazilian stocks it varies between -4.8 and 4.7. The minimum and maximum values of the ADR spread returns show extreme variations of up to 21% in Brazil while in the UK remain contained around 20 basis points (with the exception of Rio Tinto with a maximun spread return of 91 basis points). Figure 1 and Figure 2 show a plot of the ADR spread returns in basis points measured every 10 seconds for the whole year of 2015, Figure 1 presents the values for Royal Dutch Shell (Netherlands listing) and Figure 2 for Petroleo Brasileiro. The two figures allow us to get a better picture of the distribution of the ADR spread returns and compare a typical European stock against a typical Brazilian stock. In Figure 2, Petroleo Brasileiro, we can see huge magnitude outliers that reach thousands of basis points, while for Roya Dutch Shell in Figure 1 the ADR spread returns remain below an absolute value of 15 basis points. Similarly, within the Netherlands, a stock like Royal Dutch present an ADR spread return variation between -1 and 1 basis point while Arcelor Mittal ADR spread returns shows a variation between -4 and 4 basis points.
Other interesting characteristics shown in the sampled data is how the volatility differences between the local stock and the ADR fluctuate in the different regions. In Europe on average the volatility of local stocks is lower than for the corresponding ADRs. This implies that there is higher variation in the returns of the ADR compare to the variation of the returns of the local stock. In Brazil the markets behave in the opposite way and the local stock returns are more volatile than the ADRs.
The traded volume shows no surprising measurements, in all regions it is on average higher for local stocks compared to their corresponding ADRs.
5. Results
By analyzing the summary of the sampled data obtained during 2015 it is possible to observe the spread between the ADR returns and the local stock returns measured every 10 seconds. These measurements show that price discrepancies between the ADRs and the underlying stocks appear at a high frequency level. For all the firms in the study the ADR spread returns variate around zero and reach maximum absolute values of several hundreds of basis points and of tens of basis points within the 1st and 3rd quantile. These
measurements show that price discrepancies between the ADRs and the local stocks appear in the market within the trading day and even at 10 second intervals the difference in the returns can reach considerable levels.
Given that the ADR conversion fees are around 0.05$, ADR spread deviations that qualify as pure arbitrage will require hundreds of basis points for small size firms to cover those costs. Data summaries in Table 2a and 2c show the ADR spread return values between the 1st and 3rd quantile and we can observe that even the smaller size firms remain contained bellow 5 basis points. Table 2b shows the data summary for U.K stocks and presents the same behavior where ADR spread returns are caped bellow 5 basis points even though U.K firms require an extra Stamp Duty Tax. These means the ADR spread remains contained at levels well bellow the pure arbitrage boundaries. Since there is no risk-less arbitrage possibilities at the observed levels of the spread these observations reflect that other forces, mainly attributed to high-frequency traders using pairs trading strategies, keep the ADR spread closer to zero.
The results of the multiple linear regression model provided empirical evidence of the significance of some of the explanatory variables in the model and their correlation with the
ADR spread. Each regression analysis produced different results but there are commonalities and significant variables across all pairs of ADRs and local stocks. All the regressions produced significant P-values of the overall F-test. The adjusted R-squared values for European stocks regressions only reaches 0.05 and 0.237 for Brazilian stock regressions as shown in Table 3b. These adjusted R-squared results show that the model can only explain on average 5% of the variation of the ADR spread returns for European stocks and 24% for Brazilian stocks. The adjusted R-squared for regressions of big European stocks like Royal Dutch Shell (Netherlands listing), Unilever and Rio Tinto reached 0.12, 0.10 and 0.08 respectively. The model does a bit better explaining the variation for the Brazilian ADR spread returns reaching 55% for Brasil Foods. Table 3a presents details of the described adjusted R-squared results and other the statistical measurements from the multiple linear regression analysis per stock.
The results from the multiple linear regression analysis are presented in Table 4a, 4b and Table 5. Table 5 presets the standard errors for the 8 explanatory variables and Table 4a and 4b presents the coefficients with their corresponding significance levels. The coefficients marked with *** are significant at 0.001 level, marked with ** at 0.01 level, marked with * at 0.05 and with '.' at 0.1.
In the model the intercept represents the deviation from zero for the ADR spread return that is not explained by any of the selected independent variables. If our first hypothesis is true, which states that the ADR return spread is zero, then the intercept should not be a significant variable and in the absence of any demand/supply shock expressed by the model the ADR spread return should be zero. Table 4a shows the results for the regressions of each firm and we can see that the intercept coefficients are not significant
for the majority of the regressions. This result is reaffirmed by the regression performed for the whole sample which shows no significance of the intercept variable (results presented in Table 6) and not rejecting hypothesis 1.
By analyzing firm by firm we can see that 40% of the Brazilian firms used for this study show significance of the intercept variable. These results where reaffirmed by running the regression separating firms by region and showing that Brazil presents significance of the intercept variable (results presented in Table 6). If we only take into account Brazilian firms our first hypothesis is rejected. On the contrary, if only European firms are taken into account, the first hypothesis is not rejected. This suggests a lower integration of the Brazilian market with the U.S market compared to the European.
The significance and magnitude of the lagged ADR spread returns coefficient provides very interesting information since it determines a mean reverting behavior and its magnitude. For the European firms the coefficient corresponding to the lagged ADR spread returns shows a value of -0.20 while for the Brazilian firms of -0.13 (results presented in Table 6). These coefficients represent the magnitude of the mean reversion. It means that, keeping all the other variables constant, a change of 1 basis point in the previous 10 seconds ADR spread returns will result in a reduction of 0.20 basis points in the next 10 seconds returns for European ADR spread. For Brazilian ADR spreads will result in a reduction of 0.13 basis points. These results show that European markets are more integrated with the U.S market and the mean reversion of the ADR spread returns is higher than for the Brazilian market. The ADR spread will revert faster to its zero mean in European stocks that in Brazilian stocks.
The S&P500 index returns show a positive significant correlation with the ADR spread returns in all the regressions performed in this study. This rejects my second hypothesis which states that there is no significant intra-day correlation between the ADR spread returns and the U.S market index returns. Table 4a shows the regression results per firm and Table 6 the regression results over the whole sample. This shows that U.S investors overreact on the S&P500 returns by trading ADRs while foreign investors are more prudent trading the underlying stocks.
The local market index returns show that there is significant negative correlation with the ADR spread returns. This rejects my third hypothesis which states that there is no significant intra-day correlation between the ADR spread returns and the local market index returns. 7% of the regressions, mainly on the smaller stocks, show no significant correlations with the home market returns (results presented in Table 4b). This could be explained because the demand/supply shocks on smaller stocks are absorbed immediately (in less than 10 seconds) by the high-frequency traders without reaching their trading limits. The regression performed for the whole sample reaffirms the significant correlation with the home market returns and rejects hypothesis 3.
The currency exchange rate returns show a negative and significant correlation with the ADR spread returns. This result rejects hypothesis 4 which states that there is no significant intra-day correlation between the ADR spread returns and the currency rate returns. Upwards changes in the currencies rate returns that are not significant enough will not cause opportunities for high-frequency traders and therefore ADR prices will not be adjusted within the 10 second periods, this will cause the ADR spread to deviate from zero into negative values explaining the negative correlation with the currency rate returns.
The results of the regressions in Table 4a show that the majority of the firms present no significant correlation between the volatility of the ADR or the underlying stock with the ADR spread returns. Given that the sampling period is 10 seconds we can conclude that high-frequency traders are able to transmit the volatility across the markets efficiently and there should be no considerable difference between the volatility of the ADR and of the underlying stock.
In a similar way, Table 4a shows show that for the majority of European firms there was no significant correlation with the traded volume of the ADR or the traded volume of the local stock with the ADR spread returns. From these results I can conclude that liquidity is transmitted across the two assets at a high-frequency. By trading ADR and stock pairs the high-frequency traders will propagate the trading activity on one asset to the other keeping the liquidity of both assets in balance. At a sample period of 10 seconds any change in traded volume in the ADR or local stock affects both assets equally and there is no significant change in the ADR spread. For Brazilian stocks the regression results didn't show a generic pattern. On average there Brazilian firms present a positive significant correlation with the underlying stock traded volume and a negative significant correlation with the ADR traded volume. These results could be explained by the lower integration between the Brazilian and the U.S markets and the low activity of high-frequency traders that help to propagate liquidity between the two markets.
Comparing the magnitude of coefficient estimates for the S&P500 returns and for the home market index returns it is possible to derive interesting observations. In the regression of European firms (Table 6) the absolute value for the S&P500 returns coefficient is of 0.20
which means that, keeping all other variable constant, one basis point move in the S&P500 returns will correlate to 0.20 basis points change in the ADR spread returns. The average absolute value for the home market index coefficient is 0.12, meaning that for one basis point move in the home market index a correlated change of 0.12 basis points in the ADR spread will be observed. This means than when considering European stocks and their ADRs, investor give more importance (they react stronger) to movements of the S&P500 than to movements of the local market index of the stock in question. In the Brazilian market investor behave in the opposite way giving more importance to the IBOV index than to the S&P500. The absolute value for the S&P500 coefficient is of 0.13 and of the IBOV index is of 0.21.
In summary the regression results show that the model explains on average 16.9% of the variation of the ADR spread returns and that this variation should be zero in the absence of any demand/supply shocks represented by the explanatory variables in the model. That the demand/supply imbalance between the two assets driven by changes in the S&P500 returns, the local stock market returns or the currency rate returns produce correlated changes on the ADR spread returns with a mean reverting effect of higher magnitude in well integrated markets with the U.S. And, that high-frequency trading activity efficiently propagates information between the two markets making sure that the volatility and liquidity impacts affect both assets in the same way.
6. Conclusions
This study analyzes price discrepancies between ADRs and their corresponding underlying stocks using high frequency data to be able to capture the deviations and corrections of prices during the trading day. By taking data samples every 10 seconds and incorporating demand/supply proxies as explanatory variables in a multiple linear regression model I was able to provide empirical evidence of the correlation of these variable with the intra-day ADR spread deviations.
The results show empirical evidence of a zero mean reverting behavior of the ADR spread returns and that U.S investor react more aggressively to movements of the S&P500 than none U.S investors do to movements of their local market index. It was possible to observe that the mean reversion of the ADR spread returns is higher for European markets than for the Brazilian market providing evidence of a more integrated European market with higher arbitrage and high-frequency trading activity keeping prices in balance.
Given the sampling period of 10 seconds I concluded that high-frequency traders cannot absorb big shocks of demand/supply in the ADRs or underlying stocks allowing price differences to persist for longer than the sampling period. High-frequency traders will take positions on the ADR spread until they reach their risk limits leaving price discrepancies to persist for longer periods. The capacity of high-frequency traders to absorb those shocks was observed comparing regressions of big and small stocks. With smaller stocks the demand/supply shocks are absorbed immediately (in less than 10 seconds) and the significance of the ADR spread with the independent variables is lost.
volatility across the markets efficiently and there should be no considerable difference between the volatility of the ADR and of the underlying stock. They also propagate liquidity from on one asset to the other making both assets get affected equally and producing no significant change in the ADR spread.
7. Bibliography
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Table 1: Stock specifications for regression analysis.
This table presents the selection of stocks used for the regression analysis. It presents the ISIN code and market where the underlying stock is traded, its currency and home market index. It also shows the corresponding ADR ISIN code and its market.
Market ISIN Currency Home Market Index ADR ISIN ADR market Royal Duch Shell Liffe Amsterdam GB00B03MLX29 EUR AEX US7802592060 New York Stock Exchange Philips Electronics Liffe Amsterdam NL0000009538 EUR AEX US5004723038 New York Stock Exchange Unilever Liffe Amsterdam NL0000009355 EUR AEX US9047847093 New York Stock Exchange ING Bank Liffe Amsterdam NL0000303600 EUR AEX US4568371037 New York Stock Exchange Arcelor Mital Liffe Amsterdam LU0323134006 EUR AEX US03938L1044 New York Stock Exchange STMMicroelectronics Liffe Paris NL0000226223 EUR CAC US8610121027 New York Stock Exchange DeutcheBank Deutsche Borse Xetra DE0005140008 EUR DAX DE0005140008 New York Stock Exchange Novartis Deutsche Borse Xetra CH0012005267 EUR DAX US66987V1098 New York Stock Exchange SAP Deutsche Borse Xetra DE0007164600 EUR DAX US8030542042 New York Stock Exchange BBVA Bolsa de Madrid ES0113211835 EUR IBEX US05946K1016 New York Stock Exchange Santander Bolsa de Madrid ES0113900J37 EUR IBEX US05964H1059 New York Stock Exchange Nokia NASDAQ OMX, Helsinki FI0009000681 EUR OMX US6549022043 New York Stock Exchange Royal Duch Shell London Stock Exchange GB00B03MLX29 EUR FTSE US7802592060 New York Stock Exchange AstraZeneca London Stock Exchange GB0009895292 GBP FTSE US0463531089 New York Stock Exchange British Pretroleum London Stock Exchange GB0007980591 GBP FTSE US0556221044 New York Stock Exchange BT London Stock Exchange GB0030913577 GBP FTSE US05577E1010 New York Stock Exchange Glaxo SmithKline London Stock Exchange GB0009252882 GBP FTSE US37733W1053 New York Stock Exchange Pearson London Stock Exchange GB0006776081 GBP FTSE US7050151056 New York Stock Exchange Rio Tinto London Stock Exchange GB0007188757 GBP FTSE US7672041008 New York Stock Exchange Petroleo Brasileiro Bolsa de Sao Paulo BRPETRACNPR6 BRL IBOV US71654V1017 New York Stock Exchange AMBEV Bolsa de Sao Paulo BRABEVACNOR1 BRL IBOV US02319V1035 New York Stock Exchange Brasil Foods Bolsa de Sao Paulo BRBRFSACNOR8 BRL IBOV US10552T1079 New York Stock Exchange VALE Bolsa de Sao Paulo BRVALEACNPA3 BRL IBOV US91912E2046 New York Stock Exchange Tim Participacoes Bolsa de Sao Paulo BRTIMPACNOR1 BRL IBOV US88706P2056 New York Stock Exchange Telefonica Brasil Bolsa de Sao Paulo BRVIVTACNPR7 BRL IBOV US87936R1068 New York Stock Exchange Ultrapar Bolsa de Sao Paulo BRUGPAACNOR8 BRL IBOV US90400P1012 New York Stock Exchange Banco Santander Brasil Bolsa de Sao Paulo BRSANBCDAM13 BRL IBOV US05967A1079 New York Stock Exchange Fibria Celulose Bolsa de Sao Paulo BRFIBRACNOR9 BRL IBOV US31573A1097 New York Stock Exchange Gerdau Bolsa de Sao Paulo BRGGBRACNPR8 BRL IBOV US3737371050 New York Stock Exchange
Table 2a: Measurements of returns, volatility and trading volume (Europe)
This table presents the summary statistics of the 10 seconds ADR spread returns, S&P500 index returns, local market index returns, currency rate returns, volatility in the local stock and in the ADR, traded volume in the local stock and in the ADR. All the return calculations are done every 10 seconds using the midpoint between the best bid and best ask price in the order book. The volatilities are calculated as the standard deviation of the returns of the local stock and of the ADR. The home index variates depending on the country, the AEX, CAC, DAX, IBEX and OMX index are used for the Netherlands, France, Germany, Spain and Finland respectively.
volatility adr volatility traded volume
Netherlands
Royal Duch Shell
Min. -23.1 -50.6 -81.0 -18.1 0.0000 0.0000 66 25 1st Qu. -1.0 -1.2 -1.1 -0.9 0.2053 0.2915 1362 200 Mean 0.0 0.0 0.0 0.0 0.4601 0.4746 5111 775 3rd Qu. 1.0 1.2 1.1 0.9 0.6539 0.6406 6667 1000 Max. 25.0 44.6 31.7 28.9 1.5399 1.4974 31685 4675 Philips Electronics Min. -24.5 -35.0 -25.8 -17.0 0.0000 0.0000 43 4 1st Qu. -1.6 -1.2 -1.6 -0.9 0.1654 0.0000 755 100 Mean 0.0 0.0 0.0 0.0 0.3827 0.3577 3168 531 3rd Qu. 1.6 1.2 1.5 0.9 0.5669 0.6665 3977 637 Max. 26.2 30.0 31.7 28.9 1.6046 1.7162 21913 3923 Unilever Min. -21.5 -35.0 -25.8 -18.1 0.0000 0.0000 50 4 1st Qu. -1.1 -1.2 -1.2 -0.9 0.1669 0.0000 798 190 Mean 0.0 0.0 0.0 0.0 0.3819 0.4016 3311 715 3rd Qu. 1.1 1.2 1.2 0.9 0.5343 0.5985 4281 900 Max. 23.0 44.6 48.3 28.9 1.4198 1.4218 21663 5242 ING Bank Min. -18.0 -50.6 -81.0 -17.0 0.0000 0.0000 100 8 1st Qu. -2.8 -1.2 -1.6 -0.9 0.0000 0.0000 3776 200 Mean 0.1 0.0 0.0 0.0 0.5347 0.4364 15083 1260 3rd Qu. 2.9 1.2 1.6 0.9 0.8331 1.0837 19511 1500 Max. 26.7 44.6 31.7 28.9 2.0863 2.3968 95362 10800 Arcelor Mital Min. -53.5 -35.0 -49.1 -18.1 0.0000 0.0000 110 49 1st Qu. -4.0 -1.2 -1.2 -0.9 0.2115 0.0000 3068 316 Mean 0.0 0.0 0.0 0.0 0.6163 0.5126 11303 3363 3rd Qu. 4.1 1.2 1.1 0.9 0.8722 0.0000 14732 4200 Max. 47.9 30.0 48.3 28.9 2.7114 4.2888 70888 28300 France STMMicroelectronics Min. -28.8 -34.4 -28.2 -18.1 0.0000 0.0000 30 17 1st Qu. -4.8 -1.2 -1.6 -0.9 0.0000 0.0000 1000 200 Mean 0.0 0.0 0.0 0.0 0.4192 0.3683 4008 1431 3rd Qu. 4.8 1.2 1.5 0.9 0.6216 0.5360 5158 1700 Max. 26.3 44.6 29.8 28.9 2.3834 3.5405 27435 11602 Germany DeutcheBank Min. -19.7 -50.6 -109.1 -18.1 0.0000 0.0000 45 7 1st Qu. -1.4 -1.2 -1.7 -0.9 0.2721 0.0000 990 100 Mean 0.0 0.0 0.0 0.0 0.5032 0.5035 4175 501 3rd Qu. 1.4 1.2 1.7 0.9 0.6798 0.7497 5219 600 Max. 24.9 44.6 36.5 28.9 1.6958 1.8296 29496 4400 Novartis Min. -95.1 -13.1 -27.5 -14.7 0.0000 0.0000 1 5 1st Qu. -1.6 -1.2 -1.8 -0.9 0.0922 0.1124 30 190 Mean 0.2 0.0 -0.1 0.0 0.3680 0.3491 207 770 3rd Qu. 2.0 1.2 1.6 0.9 0.4991 0.4798 250 901 Max. 57.5 26.4 25.1 28.9 2.7760 1.7340 2000 5786 SAP Min. -18.0 -35.0 -34.0 -18.1 0.0000 0.0000 23 5 1st Qu. -0.9 -1.2 -1.6 -0.9 0.2141 0.2556 353 100 Mean 0.0 0.0 0.0 0.0 0.4037 0.4286 1564 328 3rd Qu. 0.9 1.2 1.6 0.9 0.5536 0.5656 1891 400 Max. 173.0 30.0 36.2 28.9 1.2957 1.3354 12009 2260 Spain BBVA Min. -27.4 -35.0 -73.1 -18.1 0.0000 0.0000 100 10 1st Qu. -4.1 -1.2 -1.8 -0.9 0.1903 0.0000 2480 200 Mean 0.0 0.0 0.0 0.0 0.4838 0.3166 12043 1832 3rd Qu. 4.2 1.2 1.8 0.9 0.6797 0.0000 14478 2300 Max. 27.9 44.6 37.3 28.9 2.0055 2.9316 96475 15922 Santander Min. -32.7 -35.0 -39.0 -17.0 0.0000 0.0000 120 20 1st Qu. -3.7 -1.2 -1.5 -0.9 0.1902 0.0000 4897 200 Mean 0.1 0.0 0.0 0.0 0.4735 0.2818 24825 4305 3rd Qu. 3.9 1.2 1.5 0.9 0.6713 0.0000 30446 4900 Max. 34.7 30.0 37.3 28.9 1.8935 3.5677 197937 42200 Sweden Nokia Min. -251.8 -19.7 -59.1 -18.1 0.0000 0.0000 56 67 1st Qu. -3.7 -1.2 -0.8 -0.9 0.1177 0.0000 3500 500 Mean 0.2 -0.1 0.0 0.0 0.4809 0.3569 22687 10657 3rd Qu. 3.8 1.2 0.8 0.9 0.7215 0.0000 29000 13800 Max. 897.4 17.4 28.0 9.2 2.4946 3.4040 176310 85453 Spread returns (bps) snp500
returns (bps) home returns (bps)
currency returns
Table 2b: Measurements of returns, volatility and trading volume (UK)
This table presents the summary statistics of the 10 seconds ADR spread returns, S&P500 index returns, local market index returns, currency rate returns, volatility in the local stock and in the ADR, traded volume in the local stock and in the ADR. The calculations use the same methods as for Table 1a. The home index is the FTSE index and the currency rate is GBP/USD.
volatility adr volatility traded volume
UK
Royal Duch Shell
Min. -29.4 -50.6 -26.4 -16.2 0.0000 0.0000 38 25 1st Qu. -1.2 -1.2 -1.1 -0.6 0.2235 0.2941 945 200 Mean 0.0 0.0 0.0 0.0 0.4600 0.4800 3614 789.6 3rd Qu. 1.2 1.2 1.1 0.6 0.6712 0.6463 4764 1005 Max. 43.7 44.6 28.4 12.5 1.5327 1.5228 21820 4792 AstraZeneca Min. -21.2 -35.0 -26.4 -16.2 0.0000 0.0000 26 4 1st Qu. -1.0 -1.2 -1.1 -0.6 0.1386 0.0000 375 100 Mean 0.0 0.0 0.0 0.0 0.3282 0.3484 1319 416.1 3rd Qu. 1.0 1.2 1.1 0.6 0.4518 0.5436 1656 500 Max. 16.0 44.6 20.6 12.5 1.3588 1.4873 9095 3000 British Pretroleum Min. -26.0 -50.6 -26.4 -16.2 0.0000 0.0000 274.5 33 1st Qu. -1.1 -1.2 -0.8 -0.6 0.2396 0.0000 4425.2 201 Mean 0.0 0.0 0.0 0.0 0.4724 0.4956 15362.8 1078 3rd Qu. 1.1 1.2 0.8 0.6 0.6366 0.7287 19797 1400 Max. 50.9 44.6 28.4 12.5 1.6413 1.7261 95343.6 7114 BT Min. -13.1 -19.7 -9.8 -7.2 0.0000 0.0000 128 2 1st Qu. -1.0 -1.2 -1.1 -0.6 0.0000 0.1362 3583 100 Mean 0.0 -0.1 0.0 0.0 0.2731 0.3373 13399 173.1 3rd Qu. 0.9 1.2 1.1 0.6 0.4386 0.4729 16971 200 Max. 9.9 17.4 11.7 10.9 1.3506 1.6093 80573 1097.4 Glaxo SmithKline Min. -20.5 -35.0 -21.0 -16.2 0.0000 0.0000 56 29 1st Qu. -1.2 -1.2 -1.1 -0.6 0.0000 0.0000 1317 200 Mean 0.0 0.0 0.0 0.0 0.3097 0.3194 5870 836.5 3rd Qu. 1.2 1.2 1.1 0.6 0.6089 0.4955 7670 1100 Max. 16.4 44.6 28.4 12.5 1.3443 1.2590 38740 5100 Pearson Min. -18.0 -35.0 -19.4 -13.0 0.0000 0.0000 66 7 1st Qu. -2.4 -1.2 -1.2 -0.6 0.0000 0.0000 1451 100 Mean 0.1 0.0 0.0 0.0 0.3232 0.3912 6118 490.2 3rd Qu. 2.5 1.2 1.2 0.6 0.5790 0.7071 8016 518 Max. 20.4 44.6 28.4 12.5 2.4092 2.4021 37365 4452.4 Rio Tinto Min. -32.3 -35.0 -21.0 -16.2 0.0000 0.0000 58 30 1st Qu. -1.2 -1.2 -0.8 -0.6 0.2728 0.3171 702 200 Mean 0.0 0.0 0.0 0.0 0.5433 0.5829 2327 597.6 3rd Qu. 1.2 1.2 0.8 0.6 0.7519 0.8104 3007 734 Max. 91.0 30.0 20.0 12.5 1.8410 1.8855 14194 3900 Spread returns (bps) snp500
returns (bps) home returns (bps)
currency returns
Table 2c: Measurements of returns, volatility and trading volume (Brazil)
This table presents the summary statistics of the 10 seconds ADR spread returns, S&P500 index returns, local market index returns, currency rate returns, volatility in the local stock and in the ADR, traded volume in the local stock and in the ADR. The calculations use the same methods as for Table 1a. The home index is the IBOV index and the currency rate is BRL/USD.
volatility adr volatility traded volume
Brasil Petroleo Brasileiro Min. -1986.7 -31.5 -4890.5 -76.7 0.0000 0.0000 100 50 1st Qu. -4.1 -1.2 -1.5 -0.8 0.0000 0.0000 3500 300 Mean 0.0 0.0 0.0 0.0 0.8090 0.6962 33209 4466 3rd Qu. 4.1 1.2 1.5 0.8 1.6960 0.0000 42400 5100 Max. 3120.3 44.6 401.7 124.6 4.3170 5.3435 260900 39633 AMBEV Min. -1000.0 -50.6 -169.7 -255.3 0.0000 0.0000 100 85 1st Qu. -2.6 -1.2 -1.5 -0.8 0.0000 0.0000 800 200 Mean 0.0 0.0 0.0 0.0 0.4302 0.2727 8090 5602 3rd Qu. 2.2 1.2 1.5 0.8 0.8884 0.0000 9600 5100 Max. 632.3 44.6 46.3 124.6 2.7812 3.9088 75897 68955 Brasil Foods Min. -1715.2 -50.6 -301.2 -255.3 0.0000 0.0000 100 20 1st Qu. -2.6 -1.2 -1.6 -0.8 0.0000 0.0000 300 100 Mean 0.0 0.0 0.0 0.0 0.3395 0.3825 1552 558 3rd Qu. 2.7 1.2 1.5 0.8 0.4730 0.8390 1900 700 Max. 1478.7 43.4 133.1 247.2 2.1391 2.1837 12500 3554 VALE Min. -2085.1 -50.6 -301.2 -255.3 0.0000 0.0000 100 58.57 1st Qu. -4.8 -1.2 -1.5 -0.8 0.0000 0.0000 2000 300 Mean -0.1 0.0 0.0 0.0 0.6726 0.5105 15983 5565.39 3rd Qu. 4.7 1.2 1.5 0.8 1.1668 0.0000 20500 6000 Max. 1099.8 44.6 535.5 124.6 3.4737 5.4827 119100 53266.58 Tim Particpacoes Min. -1223.2 -34.4 -137.4 -75.9 0.0000 0.0000 100 15 1st Qu. -3.9 -1.2 -1.6 -0.8 0.0000 0.0000 300 100 Mean -0.2 0.0 0.0 0.0 0.5791 0.5662 3474 495.3 3rd Qu. 3.4 1.2 1.5 0.8 1.0297 1.0351 4100 600 Max. 1046.3 28.3 103.3 124.6 4.2751 3.8778 33200 3400 Telefonica Brasil Min. -1221.5 -34.4 -111.2 -255.3 0.0000 0.0000 100 43 1st Qu. -2.7 -1.2 -1.5 -0.8 0.0000 0.0000 300 200 Mean 0.0 0.0 0.0 0.0 0.4743 0.4126 1451 831.9 3rd Qu. 2.7 1.2 1.5 0.8 0.6607 0.7158 1700 1000 Max. 897.5 28.3 44.2 124.6 2.8363 3.0415 12700 6139.8 Ultrapar Min. -1575.6 -31.5 -176.4 -255.3 0.0000 0.0000 100 3 1st Qu. -2.7 -1.2 -1.6 -0.8 0.1269 0.0000 200 100 Mean 0.0 0.0 0.0 0.0 0.4183 0.4115 945.7 368.9 3rd Qu. 2.7 1.2 1.6 0.8 0.5703 0.8721 1200 500 Max. 1030.5 28.3 112.1 124.6 2.4542 2.4073 7000 2200
Banco Santander Brasil
Min. -1195.8 -34.4 -99.5 -255.3 0.0000 0.0000 100 14 1st Qu. -4.7 -1.2 -1.9 -0.8 0.0000 0.0000 300 100 Mean 0.0 0.0 0.0 0.0 0.6724 0.5395 1706 894.2 3rd Qu. 4.4 1.2 1.8 0.8 0.9576 0.0000 2100 1000 Max. 972.3 26.4 182.5 124.6 5.0799 7.0519 13429 8300 Fibria Celulose Min. -2178.5 -31.5 -210.6 -255.3 0.0000 0.0000 100 55 1st Qu. -3.2 -1.2 -1.5 -0.8 0.0000 0.0000 300 100 Mean 0.0 0.0 0.0 0.0 0.4897 0.4436 1549 547.3 3rd Qu. 3.4 1.2 1.5 0.8 0.6792 0.9433 1900 700 Max. 840.9 44.6 166.0 247.2 3.0326 3.1066 12100 3880.6 Gerdau Min. -2068.0 -34.4 -176.4 -75.9 0.0000 0.0000 100 46 1st Qu. 0.0 -1.2 -1.4 -0.8 0.0000 0.0000 600 100 Mean -0.3 0.0 0.0 0.0 0.6530 0.4877 8700 3246 3rd Qu. 0.0 1.2 1.4 0.8 1.0190 0.0000 10000 2300 Max. 991.1 28.3 211.7 124.6 5.4410 11.2068 91200 43800 Spread returns (bps) snp500
returns (bps) home returns (bps)
currency returns
Table 3a: Regression statistical measurements per stock.
This table presents the statistical measurements from the multiple linear regression analysis. The regression analysis was performed for 29 stocks independently. The model defines the dependent variable as the ADR spread return and 8 explanatory variables including a one lagged value of the ADR spread returns, the S&P500 returns, the home market index returns, the currency rate returns, the volatility of the ADR, the volatility of the stock, trading volume of the ADR and trading volume of the ADR.
Rt spread =B0+B1∗Rt−1 spread +B2∗Rt snp 500 +B3∗Rt home +B4∗Rt currency +B5∗Volt ADR +B6∗Volt stock +B7∗Lt ADR +B8∗Lt stock +e
The table presents the adjusted R-squared, R-squared, the standard deviation of errors and the degrees of freedom.
R-Squared
Netherlands
Royal Duch Shell 0.1232 0.1232 1.23 108862 Philips Electronics 0.0608 0.0610 1.98 47114 Unilever 0.1069 0.1070 1.26 83008 ING Bank 0.0563 0.0565 3.51 45798 Arcelor Mital 0.0510 0.0512 6.39 46241 France STMMicroelectronics 0.0299 0.0305 6.39 14185 Germany DeutcheBank 0.0718 0.0719 1.74 63298 Novartis 0.0130 0.0147 3.67 4530 SAP 0.0884 0.0885 1.05 73827 Spain BBVA 0.0552 0.0554 5.61 27775 Santander 0.0560 0.0563 7.42 26593 Sweden Nokia 0.0684 0.0696 5.96 6514 UK
Royal Duch Shell 0.0872 0.0872 1.68 95442 AstraZeneca 0.0691 0.0692 1.29 64180 British Pretroleum 0.0552 0.0554 5.61 27775 BT 0.0415 0.0434 1.28 4023 Glaxo SmithKline 0.0802 0.0803 1.51 68752 Pearson 0.0138 0.0145 3.42 11184 Rio Tinto 0.0801 0.0801 1.56 99476 Brasil Petroleo Brasileiro 0.2091 0.2092 8.30 121425 AMBEV 0.2267 0.2268 6.59 76394 Brasil Foods 0.5554 0.5554 3.53 105941 VALE 0.1880 0.1881 9.07 76648 Tim Particpacoes 0.2769 0.2770 6.06 87305 Telefonica Brasil 0.3893 0.3894 4.62 100603 Ultrapar 0.5317 0.5317 3.66 87865 Banco Santander Brasil 0.1781 0.1783 9.53 33962 Fibria Celulose 0.4297 0.4298 4.60 81478 Gerdau 0.0775 0.0776 15.05 45583
Adjusted
Table 3b: Regression statistical measurements per regions.
This table presents the statistical measurements from the multiple linear regression analysis per region. The regression analysis was performed for the whole sample of 29 firms across different countries and regions. Two more regression grouping the firms per region (European firms and Brazilian firms) are presented in the table. The model defines the dependent variable as the ADR spread return and 8 explanatory variables including a one lagged value of the ADR spread returns, the S&P500 returns, the home market index returns, the currency rate returns, the volatility of the ADR, the volatility of the stock, trading volume of the ADR and trading volume of the ADR.
Rt spread =B0+B1∗Rt−1 spread +B2∗Rt snp 500 +B3∗Rt home +B4∗Rt currency +B5∗Volt ADR +B6∗Volt stock +B7∗Lt ADR +B8∗Lt stock +e
The table presents the adjusted R-squared, R-squared, the standard deviation of errors and the degrees of freedom.
R-Squared
All samples 0.1697 0.1697 5.32 1821503
Europe 0.0503 0.0503 2.76 1004209
Brazil 0.2375 0.2375 7.10 817285
Adjusted
