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An investigation of price discovery in informationally-linked markets: equity trading in Malaysia and Singapore
Journal of Multinational Financial Management 9 (1999) 317 – 329 www.elsevier.com/locate/econbase
An investigation of price discovery in informationally-linked markets: equity trading in Malaysia and Singapore David K. Ding a, Frederick H. deB. Harris b, Sie Ting Lau a, Thomas H. McInish c,* a Nanyang Technological Uni6ersity, Nanyang, Singapore 639798 Babcock Graduate School of Management, Wake Forest Uni6ersity, Winston-Salem, NC 27109, USA c The Uni6ersity of Memphis, Fogelman College of Business and Economics, Memphis, TN 38152, USA b
Received 15 July 1998; accepted 26 February 1999
Abstract Using transactions data for the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore (SES) for a major Malaysian conglomerate, Sime Darby Berhad, and intraday exchange rate data, we investigate whether and to what extent each exchange contributes to price discovery. Results indicate that the price series are cointegrated. The raw data appear to indicate the presence of arbitrage opportunities, but none exist after taking exchange rate changes into account. Using the common long-memory factors of Gonzalo and Granger (1995, Journal of Business and Economic Statistics 13, 1 – 9), we show that while the majority of the price discovery (approximately 70%) occurs in the home country (Malaysia), the 26– 32% of the price discovery attributable to the SES is statistically significant and exceeds Singapore’s share of the trading volume. Further, we find evidence of strong error correction of Singapore prices to Malaysian prices, but only weak error correction of Malaysian prices to Singapore prices. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Price discovery; Error correction; Common long memory components JEL classification: G15; F31
* Corresponding author. Tel.: +1-901-678-4662; fax: +1-901-678-3006. E-mail addresses: [email protected] (D.K. Ding), [email protected] (F.H.B. Harris), [email protected] (S.T. Lau), [email protected] (T.H. McInish) 1042-444X/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 1 0 4 2 - 4 4 4 X ( 9 9 ) 0 0 0 0 5 - 5
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1. Introduction. Financial assets are commonly traded in multiple market centers and trading of securities outside their home markets is likely to grow. The New York Stock Exchange (NYSE) is seeking to greatly expand its listings of non-US stocks. Many investors prefer to trade in their home market because they have a greater knowledge of local individuals and institutions. Further, trading in local markets typically facilitates clearing and settlement and reduces or eliminates foreign exchange difficulties. If market centers outside the home market also contribute to price discovery, this would provide an additional reason for encouraging such trading. There is evidence that when securities are traded in multiple venues each contributes to price discovery. In an early study, Garbade and Silber (1979) found that US regional exchanges contribute to price discovery. More recently, Harris et al. (1995) employed the error-correction model of Engle and Granger (1987) to identify the extent to which price discovery for International Business Machines occurs on the NYSE, Midwest and Pacific exchanges. The authors conclude that all three exchanges contribute to price discovery. Harris et al. (1997) applied the common-long-memory approach of Gonzalo and Granger (1995) to quantify the relative contribution of the NYSE to price discovery. The ability to identify the percentage of price discovery occurring on different exchanges is a unique feature of the application of Gonzalo and Granger (1995) methodology by Harris et al. (1997). In this paper, we extend the work described in the previous paragraph to international markets by examining whether, and to what extent, the Stock Exchange of Singapore (SES) and the Kuala Lumpur Stock Exchange (KLSE) contribute to price discovery for a stock traded on both exchanges. We examine trading in the common stock of Sime Darby Berhad, a Malaysian conglomerate with operations in 22 countries.1 Our study differs from previous work in several respects. Because the KLSE and SES are located in different countries, our study has a natural international dimension. Because Kuala Lumpur and Singapore are in the same time zone the trading day for the two exchanges overlaps almost entirely. In contrast, the trading days for the London and New York markets examined by Werner and Kleidon (1996) overlap for only 2 h each day.2 Since trading on each exchange is in each country’s domestic currency, we examine price discovery both before and after taking intraday exchange rates into account. 1 In September 1998 the Malaysian government instituted exchange controls that effectively prevented settlement of trades for Malaysian stocks in Singapore. The SES was forced to discontinue trading of Malaysian stocks. 2 Kasa (1992), Leachman and Francis (1995) examine cointegration relationships across index funds on international equity markets using monthly data. Although exchange rates and interest rates have been analyzed at monthly intervals, these observation intervals are too long to observe the partial adjustment associated with error correction in stock markets. For stock index funds, the adjustment to equilibrium errors will occur within the month and usually within the day rather than between monthly observations. The highly unusual contemporaneous effects in the error correction model of Francis and Leachman (1997) are consistent with this interpretation.
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2. Background on the stock exchanges in Malaysia and Singapore
2.1. History of the exchanges In May 1960 shares were publicly traded for the first time with the formation of the Malaysian Stock Exchange. In the following year, the board trading system was introduced with trading rooms in Kuala Lumpur and in Singapore, which at that time was part of Malaysia. The two trading rooms were linked directly by telephone and the same stocks were traded at both locations. In 1965, when Singapore became an independent country, the stock exchange continued functioning as a single entity as the Stock Exchange of Malaysia and Singapore. This was possible because of the interchangeability of the two countries’ currencies. In 1973, the currency interchangeability was terminated, leading to the formation of the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore as two separate entities. Stocks from each country, however, continued to be listed on both exchanges. In 1990, by order of the Malaysian government, all Malaysian stocks were delisted from the SES. On the same day, Singapore stocks were also delisted from the KLSE. Following the delisting of Singapore stocks on the KLSE, the SES immediately set up a board to permit continued trading of Malaysian stocks in Singapore, but in Singapore dollars. This new board was called the CLOB (Central Limit Order Book) International and traded primarily Malaysia and Hong Kong stocks. CLOB International trading accounted for as much as 50% of total daily turnover in these cross-listed stocks.
2.2. Trading on the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore Since 1992, the KLSE has operated a fully automated trading system. All buyins and odd lots trading are fully automated. Off-market and married deals are reported on-line. Orders may be entered between 09:00 and 12:30 h and between 14:00 and 17:00 h. However, all matching is done during the trading hours 09:30 – 12:30 h and 14:30–17:00 h. KLSE orders entered for each of the two trading sessions in a day are good for that session only. Unexecuted orders at the end of a trading session have to be re-entered into the system for execution. Since 1989, all trading on the SES has been conducted through the fully automated and floorless, screen-based computer system. Crossings and married deals may be carried out outside the bid and ask quotes on the board for transactions involving 50 000 shares or more. Quantities over the full range of prices are displayed so that the investor has a full picture of the demand and supply of a stock. The SES accepts orders and trades from 09:00 h to 12:30 h and from 14:00 to 17:00 h each trading day. Orders are good for the entire trading day.
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On the SES (as well as the KLSE), there is no batch trade at the open. Instead, the SES computer allows trading after 09:00 h each trading day as buy and sell orders arrive. A transaction occurs if the prices specified for a buy and sell match. For each price at which there is an open limit order, each member’s terminal displays the number of shares at that price. Partially hiding a trade size is not allowed. All trades are consummated through computer matching of buy and sell quotes by price and time priority, and all transactions occur at posted prices. There can be no difference between posted and effective spreads. A trader dealing directly with a Malaysian broker has to pay a minimum brokerage fee of 0.5% for deals exceeding M$2 million in value up to a maximum fee of 1%. Brokerage fees on SES stocks are a minimum of 0.5% for deals in excess of S$1 million up to a maximum fee of 1%. There are no mechanisms for executing short sales on the SES or KLSE. At the time of our study, the settlement period for the SES was T+ 5 trading days and for the KLSE it was T +7 trading days.
2.3. Arbitrage between the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore Arbitrage activities exist between the cross-listed stocks on the KLSE and the SES. Settlement practices make direct arbitrage difficult. Instead, an arbitrageur wanting to take advantage of a price discrepancy can buy on the SES and at the same time sell on the KLSE from an existing inventory. Or the arbitrageur could sell on the SES and buy on the KLSE. This indirect arbitrage requires long positions in both Singapore and Malaysia. Suppose that a Singapore trader buys on the KLSE through a Singapore broker, paying a 0.5% commission to the Singapore broker and a 0.5% commission to a Malaysian broker. Then a like number of shares of the same stock are sold in Singapore, incurring a commission of 0.5%. Hence, the minimum commission is 1.5%. Since maximum one-way commissions are 1% in both Singapore and Malaysia, the maximum commission would be 3%. Given these high transaction costs it seem likely that direct arbitrage would be undertaken only by dealers with memberships of both exchanges. Of course, investors could indirectly arbitrage through their decisions about where to place marginal orders.
3. Data description and preliminary analysis
3.1. Equity data collection Neither the KLSE nor SES archive transaction data. We downloaded the SES transaction data from a US commercial vendor so that SES data were available for all of the SES – KLSE cross-listed securities. For the KLSE we were only able to obtain a hard copy of transaction data for one cross-listed firm for the period May 22, 1996 – July 17, 1996. We entered these data manually. Fortunately, the
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Malaysian firm for which we obtained data, Sime Darby Berhad, was one of the most active stocks in both Singapore and Malaysia. Sime Darby Berhad is one of Southeast Asia’s leading conglomerates with business interests in 22 countries in a variety of economic sectors such as plantations, financial services, manufacturing, property development, and distribution.
3.2. Pairing the Stock Exchange of Singapore and the Kuala Lumpur Stock Exchange trades We formed synchronous pairs of data using the minspan procedure of Harris et al. (1995). First, we select the first observation of a trade on one exchange (trade 1 on exchange 1) that is followed by a trade on the other exchange (trade 1 on exchange 2). Span 1a is the time between these two trades. We check whether the next trade following trade 1 on exchange 2 is on exchange 1 or 2. If the next trade is on exchange 2, we save trade 1 on exchange 1 and trade 1 on exchange 2 and begin the search again. If the next trade is on exchange 1, we label this trade 2 on exchange 1 and calculate span 1b as the time between trade 1 on exchange 2 and trade 2 on exchange 1. If span 1a is less than span 1b, we save the two consecutive trades, trade 1 on exchange 1 and trade 1 on exchange 2, and begin the search for consecutive pairs again with trade 2 on exchange 2. Otherwise, we save trade 1 on exchange 2 and trade 2 on exchange 1 and begin the search for consecutive pairs with the next trade. We present statistics for the resulting samples in Table 1. When all of the data are used (SALL) there are 411 observations with a mean span of 14.5 min and a maximum span of 345 min. Limiting the maximum span reduces the number of Table 1 Pairing KLSE and SES tradesa Sample
Number of observations
Mean span (min) Standard deviation Maximum span (min)
SALL S30 S15 S10
411 392 372 345
14.5 4.6 3.7 3.0
39.17 5.07 3.44 2.38
345 30 15 10
a Our goal is to pair trades on the KLSE and the SES which follow each other chronologically. We begin by selecting the first trade on one of the exchanges (exchange 1) that is immediately followed by a trade on the other exchange (exchange 2). We call the length of time between these two trades the span. If the next trade chronologically is on exchange 2, we pair the first trade on exchange 1 with the first trade on exchange 2, add the pair to our sample, and begin the process again with the second trade on exchange 2. If the next trade is on exchange 1, we also compute the span between this trade and the first trade on exchange 2. If the first span is shorter than the second, we add the first pair to our sample and begin the process again with the second trade on exchange 1. But if the second span is shorter, we add that pair to our sample and begin the search again with the trade following the second trade on exchange 1. We report the mean span when all of the paired observations are used (SALL) and when the sample is restricted to spans of less than 30 (S30), 15 (S15), and 10 min (S10).
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observations slightly as follows: 30 min (S30), 392; 15 min (S15), 372; and 10 min (S10), 345.
3.3. Exchange rates Trading on the SES is in Singapore dollars and on the KLSE in Malaysian ringgit. There is nothing in the cointegration methodology that requires that the two series be in the same currency. Hence, we could proceed ignoring currency issues. But, if possible, we would like to explore how exchange rates affect our outcomes. Unfortunately, we were not able to obtain transaction data for currencies. We approached several investment bankers and asked them how they handled exchange rates in conducting their businesses. We were told that due to the stability of the Singapore dollar/Malaysian ringgit exchange rate during this period they generally updated their exchange rates only periodically through the day rather than trying to fine tune their calculations using real time exchange rate data. One brokerage firm agreed to supply the exchange rates that it had actually used in its arbitrage activities during this period. These comprised exchange rates at four times each day (09:00, 11:00, 14:00 and 16:00 h). The brokerage firm obtained its exchange rates from a bank. These are the only exchange rates used by the brokerage firm in its trading and settlement activities. We indicate price series that have been adjusted for exchange rates by an asterisk. We realize that these exchange rates are not ideal. Nevertheless, we believe that their use is worthwhile because they conform to the market practice of a large brokerage firm and allow one of the first examinations of how exchange rates affect cross-boarder price discovery. Hence, we replicate all analyses both with and without exchange rate adjustments.
3.4. Unit roots and optimal lags Cointegration testing requires that all of the variables exhibit unit roots with the same degree of integration. We test for the presence of a unit root in the individual series using the augmented Dickey and Fuller (1981) approach, which involves estimating the following regression models: DPt =rPt − 1 +% Bt DPt − 1 + mt (random walk), DPt =a + rPt − 1 +% Bt DPt − 1 + mt (random walk with drift). For our 12 price series (four Malaysian price series—MSALL, MS30, MS15, MS10 and four Singapore price series—SSALL, SS30, SS15, SS10 and four Singapore price series converted into Malaysian ringgit—SSALL*, SS30*, SS15*, SS10*) we estimate a random walk model and a random walk with drift. Results are reported in Table 2. Our estimation used six lags. Column 2 reports the lags that are found to be significant at the 5% level. The augmented Dickey–Fuller test
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Table 2 Unit root testsa r
t
Malaysia (ringgit) MSALL 1,2 1,2 MS30 1,2 1,2 MS15 1,2 1,2 MS10 1,2 1,2
0.000 −0.008 0.000 −0.008 0.000 −0.009 0.000 −0.009
0.77
Singapore (dollars) SSALL 1 1 SS30 1 1 SS15 3 3 SS10 1 1
0.000 −0.006 0.000 −0.006 0.000 −0.007 0.000 −0.086
0.91
Singapore (ringgit) SSALL* 1 1 SS30* 1,4 1,4 SS15* 1,3 1,3 SS10* 1 1
0.000 −0.006 0.000 −0.007 0.000 −0.008 0.000 −0.010
Price series
Identity of significant lags
tm
Conclusion
−1.09 0.67 −1.02 0.70 −1.01 0.61 −1.22
−0.99 0.93 −0.98 0.87 −0.99 0.85 1.58 0.79 −1.20 0.73 −0.99 0.66 −1.04 0.72 −1.19
I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1)
a This table reports the results of the unit root tests for twelve price series — four Malaysian price series (MSALL, MS30, MS15, MS10), four Singapore price series (SSALL, SS30, SS15, and SS10), and four Singapore price series converted into Malaysian ringgit (SSALL*, SS30*, SS15*, SS10*). For each price series we estimate a random walk model and a random walk with drift:
DPt =rPt−1+% Bt DPt−1+mt (random walk) DPt =a+rPt−1+% Bt DPt−1+mt (random walk with drift) In each case we begin with six lags and then drop the lags that are not significant at the 5% level. Column 3 presents the first order autocorrelation coefficients for each of the series. The critical values for the augmented Dickey-Fuller test statistics for the random walk test presented in column 4 and the random walk with drift test presented in column 5 are t=−1.62 and tm =−2.57, respectively. In every case we cannot reject the hypothesis that r =0 at the 10% level or better. Hence, all of the series are I(1). Further testing showed that no time trends are present for these series and successive differencing identified no additional unit roots.
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statistics reported in columns 4 and 5 fail to reject the hypothesis of r= 0 at the 10% level or better in every case. Hence, the series are I(1). Moreover, further testing (not shown) indicates that no time trends are present and that successive differencing does not produce additional unit roots. Having confirmed the presence of I(1) series, we use the multivariate extension of the Akaike Information Criterion to identify the optimal lag length for use in our cointegration testing. We tested longer lags against shorter lags as restrictions in a vector autoregression of the underlying price levels. The AIC is minimized at a system lag length of two.
3.5. Cointegration We use the reduced rank regression procedure of Johansen (1988) to test for possible cointegration. With two underlying price series there is at most one cointegrating vector (r= 1). We test the null hypothesis that r= 0 with maximum eigenvalue and trace tests. The critical values for these tests at the 1% level obtained from Enders (1995), (table B) are lmax = 18.78 and ltrace = 21.96. The results reported in Table 3 show that all of the series are cointegrated. If prices in Malaysia (Mt ) and Singapore (St ) are cointegrated of order (1,1), there must be nonzero values of B1 and B2 for which the linear combination B1Mt + B2St is stationary. The necessary and sufficient condition for Mt and St to be CI(1,1) is: Table 3 Cointegration testsa Price series
Johansen test Maximum eigenvalue
Trace
Cointegrating vectors
SALL*
41.95*
42.56*
−13.174 13.257 0.083
SALL
35.08*
35.77*
−12.802 11.654 −1.148
S10*
42.02*
42.90*
−14.458 14.472 0.014
S10
36.69*
37.51*
−14.180 12.823 −1.375
a We report results for SALL, SALL*, S10, and S10*. To save space we do not report S15, S15*, S30, and S30* which have results that are qualitatively identical to those reported. Columns 2 and 3 report the test statistics for Johansen’s reduced rank regression procedure. The critical values for r= 0 at the 1% level, taken from Enders (1995) (table B), are lmax =18.78 and ltrace =21.96. All of the statistics are significant at the1% level. Column 4 provides estimates of the cointegrating vectors for each time series. * Significant at the 0.01 level.
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B1mMt +B2mSt =0, where m represents the trend in the random walk processes M and S, respectively, in period t. If prices in Malaysia and Singapore are cointegrated I(1,1), then mMt must be identical to mSt up to the scalar −B2/B1. That is, any two series cointegrated (1,1) must have identical stochastic trends, so that some properly scaled linear combination of the trends vanishes. In the case of two stock price series, the law of one price maintained by arbitrage implies that the scalar − B2/B1 = − 1, i.e. − B2 +B1 =0. We use eigenvector subroutines and Johansen’s reduced rank techniques to estimate and test the cointegrating vectors. Brokerage firms in both Kuala Lumpur and Singapore regularly monitor KLSE and SES prices for arbitrage opportunities. Transaction costs can prevent arbitrage trades and introduce short run imperfections in the cointegration error-correction process. In addition, unstable dynamic relationships between the markets can prevent the predictability required to generate arbitrage profits on average. Our results are reported in the fourth column of Table 3. All of the series are cointegrated. Examining the quantity B1 − B2 for the SALL and S10 price series in rows 2 and 4 might lead to the conclusion that arbitrage opportunities were present. But comparing each of these to its comparable exchange rate adjusted series in rows 1 and 3 shows that arbitrage opportunities that seem to be present if exchange rates are not taken into account largely disappear when the price series are adjusted for these exchange rates. Once exchange rates are taken into account, the quantity B1 − B2 is greater for the SALL* price series compared with the S10* price series. For the longer spans of the SALL* series, there is more time for the occurrence of new information which could drive the price apart temporarily. On the other hand, transaction costs, technological constraints and the like are a greater obstacle to error-correcting adjustment as the span between trades becomes shorter. Our results provide some evidence that the former considerations are more important than the latter. A pricing disparity that does not persist implies arbitrage trading profits only if the short-term dynamics of the adjustment process are predictable.
4. Common-long-memory results Next, we explore the relative contributions of the KLSE and SES to price discovery. Arbitrage insures that prices on the KLSE and SES error correct. Anytime either exchange moves away from the law of one price, one of the two markets (or both) adjusts to restore arbitrage equilibrium. A price adjustment process involving equilibrium error correction is orthogonal to any common stochastic trend in the cointegrated data. In essence, our approach is to identify the relative contribution of each exchange to the common long-run trend of prices. We interpret an exchange’s relative contribution to the long-memory trend as its relative contribution to price discovery.
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Table 4 Common-long-memory factorsa Price series
Malaysia
Singapore
x2
SALL* S30* S15* S10*
0.743 0.724 0.684 0.741
0.257 0.276 0.36 0.259
22.57* 22.19* 19.20* 22.13*
a
We present the common-long-memory factors estimated using the approach of Gonzalo and Granger (1995). Note that for each row, columns 2 and 3 sum to 100%. * Significant at the 0.01 level.
Our approach is based on the methodology developed by Gonzalo and Granger (1995). Specifically, we estimate a linear combination of Mt and St such that the error-correction terms do not cause the common factors at low frequencies. These common long-memory components are the driving force that results in cointegration of the price series. For each pair of price series, we estimate the cointegration structure, sum the estimated common long-memory factors, divide each individual eigenvalue by this sum, and report the normalized results in Table 4. The percentages are the proportions of the normalized eigenvector orthogonal to the transitory adjustment vector of the error-correction model. With synchronous trades, this vector of common long-memory factors [ f1, f2] can be interpreted as the degree of permanent price movement (i.e. of price discovery) occurring in each trading venue. An asterisk on the chi-square test statistic indicates 99% significance in likelihood ratio tests of the null hypothesis H0:f= [1,0] against the one-tailed alternative Ha:f2 \0. See Gonzalo and Granger (1995) for more detailed explanations and multiple illustrations of these hypothesis tests. The chi-square tests show that the Singapore Stock Exchange contributes significantly to the long-run driving force establishing common trends in these price series. Approximately 68 – 74% of the price discovery occurs on the KLSE with the remaining 26 – 32% of the price discovery occurring on the SES. Since Sime Darby Berhad is a Malaysian company, it is not surprising that the majority of the price discovery occurs in Malaysia. But the fact that both exchanges contribute to price discovery indicates that in this case the international cross listing improves the price discovery process.
5. Error-correction results The results of the estimation of the VAR with and without error-correction terms are shown in Table 5. On balance, we find a strong error correction of Singapore prices to Malaysian prices and a weak correction of Malaysian prices to Singapore prices. In the Singapore error-correction equation, the error-correction process fully explains the price adjustment. In the Malaysian error-correction equation only the
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first order lags are significant at conventional levels and the coefficient of the error-correction term approaches significance. The significance of the first order lagged coefficients in the Malaysian equation mirror the results of Harris et al. (1995) for the NYSE. Inclusion of the error-correction term substantially increases the explanatory power of the Singapore equation, but not the Malaysian equation. Comparison of the size of the coefficients of z(t−1) in the two error-correction estimations also suggests that Singapore reacts more strongly to differences between prices on the two exchanges than does the KLSE. The t values on the error-correction terms and the changes in the statistical significance of the coefficients of the lagged price change terms demonstrate that the VAR without the error-correction term is misspecified. This conclusion is reinforced for the Singapore equations where there are sign changes for the lagged price change coefficients.
Table 5 Error-correction modela DP Malaysia
DP Singapore
Constant DP Malaysia (t−1) DP Malaysia (t−2) DP Malaysia (t−3) DP Singapore (t−1) DP Singapore (t−2) DP Singapore (t−3) z(t−1) R2 DW F
0.0001 (0.44) −0.226 (−3.06)* −0.101 (−1.54)
0.001 0.032 0.017 −0.069 −0.133 −0.066 0.033 0.023 0.108 2.00 7.75*
(0.87) (0.46) (0.25) (−0.12) (−1.84) (−0.98) (0.55) (5.76)*
Constant DP Malaysia (t−1) DP Malaysia (t−2) DP Malaysia (t−3) DP Singapore (t−1) DP Singapore (t−2) DP Singapore (t−3) R2 DW F
0.001 (0.49) −0.034 (−5.03) −0.150 (−2.51)
0.001 0.100 0.111 0.149 −0.154 −0.118 −0.153 0.041 2.00 2.34
(0.66) (1.75) (1.87) (2.64)* (−2.52) (−1.86) (−2.46)
0.173 (2.53)* 0.096 (1.38) −0.008 (−1.81) 0.089 2.00 6.51*
0.236 (3.62) 0.134 (2.03)* 0.081 2.00 7.26*
a These results show estimates of the vector autoregressions for log deviation price changes in the Malaysia and Singapore price series with and without error correction being specified. The error-correction term z= PMalaysia −PSingapore has the expected sign and is statistically significant at 93% in the DPMalaysia equation and at 99% in the DPSingapore equation. In Singapore, the error-correction process fully explains the price adjustment and misspecifying the vector autoregression to exclude error correction leads to sign-reversals on the own-price lags and cross-price lags and a three-fold decrease in explanatory power. * Significant at the 0.01 level.
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6. Summary and conclusions Using the error-correction model of Engle and Granger (1987), Harris et al. (1995) show that the NYSE, Midwest, and Pacific exchanges all contribute to price discovery for International Business Machines. Further, using the common-longmemory component approach of Gonzalo and Granger (1995), Harris et al. (1997) estimate the percentage contribution of the NYSE and regional exchanges to price discovery. We extend the work of these authors by investigating price discovery for the shares of a large Malaysian conglomerate traded on both the KLSE and the SES. Our data comprises transaction data for both the KLSE and the SES and Singapore dollar/Malaysian ringgit exchanges rates at four times during the trading day. Typically, trade-to-trade data, which is crucial for observation of the errorcorrection process in equity markets, is not readily available. We were the first to obtain such data for these two markets. Because both of these exchanges are screen-based limit order book systems, we can be sure that our results are not due to intervention of designated market makers. Moreover, both exchanges are in the same time zone so that trading is taking place contemporaneously. If this were not the case, study of synchronous trades would not be possible. We report a number of findings: 1. The price series for both Malaysia and Singapore are integrated of order I(1) and the results of the Johansen test indicate that the price series are cointegrated. 2. Arbitrage opportunities that appear to be present using unadjusted price series largely disappear when the price series are adjusted for exchange rates. Hence, it is essential that researchers who investigate cross-listed securities control for intraday movements in exchange rates.3 3. The common-long-memory results show that the majority of the price discovery occurs in the Kuala Lumpur home market. But a substantial and statistically significant amount of price discovery (i.e. 26–32%) also occurs in Singapore. Hence, we provide evidence that there may be substantial benefits to the cross listing of securities. 4. The error-correction results show that Singapore prices strongly error correct to discrepancies with Malaysian prices but that Malaysian prices only weakly error correct to discrepancies in Singapore prices. In summary, applying the error-correction approach of Engle and Granger (1987) and the common-long-memory approach of Gonzalo and Granger (1995), we find that exchanges outside the home country can contribute substantially to price discovery. The NYSE has been actively seeking exchange listings from outside the US and as part of that process has been lobbying for easing of accounting restrictions that hinder these cross-listings. Our results provide support for these efforts. 3 We find no evidence that either the timing of exchange rate updates or the timing of trades over the trading day affects our findings.
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Acknowledgements We wish to acknowledge the insightful comments and helpful advice of Jesus Gonzalo, Clive Granger, and Lori Leachman.
References Dickey, D., Fuller, W.A., 1981. Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49, 1057–1072. Enders, W., 1995. Applied Econometric Time Series. Wiley, New York. Engle, R.F., Granger, C.W.J., 1987. Co-integration and error correction: representation, estimation, and testing. Econometrica 55, 251–276. Francis, B.B., L. Leachman, 1997. Superexogeneity and the dynamic linkages among international equity markets. J. Intl. Money Finance, (in press). Garbade, K.D., Silber, W.L., 1979. Structural organization of secondary markets: clearing frequency, dealer activity and liquidity risk. J. Finance 34, 577 – 593. Gonzalo, J., Granger, C.W.J., 1995. Estimation of common long-memory components in cointegrated systems. J. Bus. Econ. Stat. 13, 1–9. Harris, F.H. deB., McInish, T.H., Wood, R.A., 1997. Common long-memory components of intraday stock prices: a measure of price discovery. Working paper, Wake Forest University. Harris, F.H. deB., McInish, T.H., Shoesmith, G., Wood, R.A., 1995. Cointegration, error correction and price discovery on informationally-linked security markets. J. Financial Quant. Anal. 30, 563–579. Johansen, S., 1988. Statistical analysis of cointegrated vectors. J. Econ. Dyn. Control 12, 231 – 254. Kasa, K., 1992. Common stochastic trends in international stock markets. J. Monetary Econ. 29, 95–124. Leachman, L., Francis, B.B., 1995. Long-run relations among the G-5 and G-7 equity markets: evidence on the Plaza and Louvre accords. J. Macroecon. 17, 551 – 578. Werner, I.M., Kleidon, A.W., 1996. UK and US trading of British cross-listed stocks: an intraday analysis of market integration. Rev. Financial Stud. 9, 619 – 664.
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An investigation of price discovery in informationally-linked markets: equity trading in Malaysia and Singapore David K. Ding a, Frederick H. deB. Harris b, Sie Ting Lau a, Thomas H. McInish c,* a Nanyang Technological Uni6ersity, Nanyang, Singapore 639798 Babcock Graduate School of Management, Wake Forest Uni6ersity, Winston-Salem, NC 27109, USA c The Uni6ersity of Memphis, Fogelman College of Business and Economics, Memphis, TN 38152, USA b
Received 15 July 1998; accepted 26 February 1999
Abstract Using transactions data for the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore (SES) for a major Malaysian conglomerate, Sime Darby Berhad, and intraday exchange rate data, we investigate whether and to what extent each exchange contributes to price discovery. Results indicate that the price series are cointegrated. The raw data appear to indicate the presence of arbitrage opportunities, but none exist after taking exchange rate changes into account. Using the common long-memory factors of Gonzalo and Granger (1995, Journal of Business and Economic Statistics 13, 1 – 9), we show that while the majority of the price discovery (approximately 70%) occurs in the home country (Malaysia), the 26– 32% of the price discovery attributable to the SES is statistically significant and exceeds Singapore’s share of the trading volume. Further, we find evidence of strong error correction of Singapore prices to Malaysian prices, but only weak error correction of Malaysian prices to Singapore prices. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Price discovery; Error correction; Common long memory components JEL classification: G15; F31
* Corresponding author. Tel.: +1-901-678-4662; fax: +1-901-678-3006. E-mail addresses: [email protected] (D.K. Ding), [email protected] (F.H.B. Harris), [email protected] (S.T. Lau), [email protected] (T.H. McInish) 1042-444X/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 1 0 4 2 - 4 4 4 X ( 9 9 ) 0 0 0 0 5 - 5
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1. Introduction. Financial assets are commonly traded in multiple market centers and trading of securities outside their home markets is likely to grow. The New York Stock Exchange (NYSE) is seeking to greatly expand its listings of non-US stocks. Many investors prefer to trade in their home market because they have a greater knowledge of local individuals and institutions. Further, trading in local markets typically facilitates clearing and settlement and reduces or eliminates foreign exchange difficulties. If market centers outside the home market also contribute to price discovery, this would provide an additional reason for encouraging such trading. There is evidence that when securities are traded in multiple venues each contributes to price discovery. In an early study, Garbade and Silber (1979) found that US regional exchanges contribute to price discovery. More recently, Harris et al. (1995) employed the error-correction model of Engle and Granger (1987) to identify the extent to which price discovery for International Business Machines occurs on the NYSE, Midwest and Pacific exchanges. The authors conclude that all three exchanges contribute to price discovery. Harris et al. (1997) applied the common-long-memory approach of Gonzalo and Granger (1995) to quantify the relative contribution of the NYSE to price discovery. The ability to identify the percentage of price discovery occurring on different exchanges is a unique feature of the application of Gonzalo and Granger (1995) methodology by Harris et al. (1997). In this paper, we extend the work described in the previous paragraph to international markets by examining whether, and to what extent, the Stock Exchange of Singapore (SES) and the Kuala Lumpur Stock Exchange (KLSE) contribute to price discovery for a stock traded on both exchanges. We examine trading in the common stock of Sime Darby Berhad, a Malaysian conglomerate with operations in 22 countries.1 Our study differs from previous work in several respects. Because the KLSE and SES are located in different countries, our study has a natural international dimension. Because Kuala Lumpur and Singapore are in the same time zone the trading day for the two exchanges overlaps almost entirely. In contrast, the trading days for the London and New York markets examined by Werner and Kleidon (1996) overlap for only 2 h each day.2 Since trading on each exchange is in each country’s domestic currency, we examine price discovery both before and after taking intraday exchange rates into account. 1 In September 1998 the Malaysian government instituted exchange controls that effectively prevented settlement of trades for Malaysian stocks in Singapore. The SES was forced to discontinue trading of Malaysian stocks. 2 Kasa (1992), Leachman and Francis (1995) examine cointegration relationships across index funds on international equity markets using monthly data. Although exchange rates and interest rates have been analyzed at monthly intervals, these observation intervals are too long to observe the partial adjustment associated with error correction in stock markets. For stock index funds, the adjustment to equilibrium errors will occur within the month and usually within the day rather than between monthly observations. The highly unusual contemporaneous effects in the error correction model of Francis and Leachman (1997) are consistent with this interpretation.
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2. Background on the stock exchanges in Malaysia and Singapore
2.1. History of the exchanges In May 1960 shares were publicly traded for the first time with the formation of the Malaysian Stock Exchange. In the following year, the board trading system was introduced with trading rooms in Kuala Lumpur and in Singapore, which at that time was part of Malaysia. The two trading rooms were linked directly by telephone and the same stocks were traded at both locations. In 1965, when Singapore became an independent country, the stock exchange continued functioning as a single entity as the Stock Exchange of Malaysia and Singapore. This was possible because of the interchangeability of the two countries’ currencies. In 1973, the currency interchangeability was terminated, leading to the formation of the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore as two separate entities. Stocks from each country, however, continued to be listed on both exchanges. In 1990, by order of the Malaysian government, all Malaysian stocks were delisted from the SES. On the same day, Singapore stocks were also delisted from the KLSE. Following the delisting of Singapore stocks on the KLSE, the SES immediately set up a board to permit continued trading of Malaysian stocks in Singapore, but in Singapore dollars. This new board was called the CLOB (Central Limit Order Book) International and traded primarily Malaysia and Hong Kong stocks. CLOB International trading accounted for as much as 50% of total daily turnover in these cross-listed stocks.
2.2. Trading on the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore Since 1992, the KLSE has operated a fully automated trading system. All buyins and odd lots trading are fully automated. Off-market and married deals are reported on-line. Orders may be entered between 09:00 and 12:30 h and between 14:00 and 17:00 h. However, all matching is done during the trading hours 09:30 – 12:30 h and 14:30–17:00 h. KLSE orders entered for each of the two trading sessions in a day are good for that session only. Unexecuted orders at the end of a trading session have to be re-entered into the system for execution. Since 1989, all trading on the SES has been conducted through the fully automated and floorless, screen-based computer system. Crossings and married deals may be carried out outside the bid and ask quotes on the board for transactions involving 50 000 shares or more. Quantities over the full range of prices are displayed so that the investor has a full picture of the demand and supply of a stock. The SES accepts orders and trades from 09:00 h to 12:30 h and from 14:00 to 17:00 h each trading day. Orders are good for the entire trading day.
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On the SES (as well as the KLSE), there is no batch trade at the open. Instead, the SES computer allows trading after 09:00 h each trading day as buy and sell orders arrive. A transaction occurs if the prices specified for a buy and sell match. For each price at which there is an open limit order, each member’s terminal displays the number of shares at that price. Partially hiding a trade size is not allowed. All trades are consummated through computer matching of buy and sell quotes by price and time priority, and all transactions occur at posted prices. There can be no difference between posted and effective spreads. A trader dealing directly with a Malaysian broker has to pay a minimum brokerage fee of 0.5% for deals exceeding M$2 million in value up to a maximum fee of 1%. Brokerage fees on SES stocks are a minimum of 0.5% for deals in excess of S$1 million up to a maximum fee of 1%. There are no mechanisms for executing short sales on the SES or KLSE. At the time of our study, the settlement period for the SES was T+ 5 trading days and for the KLSE it was T +7 trading days.
2.3. Arbitrage between the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore Arbitrage activities exist between the cross-listed stocks on the KLSE and the SES. Settlement practices make direct arbitrage difficult. Instead, an arbitrageur wanting to take advantage of a price discrepancy can buy on the SES and at the same time sell on the KLSE from an existing inventory. Or the arbitrageur could sell on the SES and buy on the KLSE. This indirect arbitrage requires long positions in both Singapore and Malaysia. Suppose that a Singapore trader buys on the KLSE through a Singapore broker, paying a 0.5% commission to the Singapore broker and a 0.5% commission to a Malaysian broker. Then a like number of shares of the same stock are sold in Singapore, incurring a commission of 0.5%. Hence, the minimum commission is 1.5%. Since maximum one-way commissions are 1% in both Singapore and Malaysia, the maximum commission would be 3%. Given these high transaction costs it seem likely that direct arbitrage would be undertaken only by dealers with memberships of both exchanges. Of course, investors could indirectly arbitrage through their decisions about where to place marginal orders.
3. Data description and preliminary analysis
3.1. Equity data collection Neither the KLSE nor SES archive transaction data. We downloaded the SES transaction data from a US commercial vendor so that SES data were available for all of the SES – KLSE cross-listed securities. For the KLSE we were only able to obtain a hard copy of transaction data for one cross-listed firm for the period May 22, 1996 – July 17, 1996. We entered these data manually. Fortunately, the
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Malaysian firm for which we obtained data, Sime Darby Berhad, was one of the most active stocks in both Singapore and Malaysia. Sime Darby Berhad is one of Southeast Asia’s leading conglomerates with business interests in 22 countries in a variety of economic sectors such as plantations, financial services, manufacturing, property development, and distribution.
3.2. Pairing the Stock Exchange of Singapore and the Kuala Lumpur Stock Exchange trades We formed synchronous pairs of data using the minspan procedure of Harris et al. (1995). First, we select the first observation of a trade on one exchange (trade 1 on exchange 1) that is followed by a trade on the other exchange (trade 1 on exchange 2). Span 1a is the time between these two trades. We check whether the next trade following trade 1 on exchange 2 is on exchange 1 or 2. If the next trade is on exchange 2, we save trade 1 on exchange 1 and trade 1 on exchange 2 and begin the search again. If the next trade is on exchange 1, we label this trade 2 on exchange 1 and calculate span 1b as the time between trade 1 on exchange 2 and trade 2 on exchange 1. If span 1a is less than span 1b, we save the two consecutive trades, trade 1 on exchange 1 and trade 1 on exchange 2, and begin the search for consecutive pairs again with trade 2 on exchange 2. Otherwise, we save trade 1 on exchange 2 and trade 2 on exchange 1 and begin the search for consecutive pairs with the next trade. We present statistics for the resulting samples in Table 1. When all of the data are used (SALL) there are 411 observations with a mean span of 14.5 min and a maximum span of 345 min. Limiting the maximum span reduces the number of Table 1 Pairing KLSE and SES tradesa Sample
Number of observations
Mean span (min) Standard deviation Maximum span (min)
SALL S30 S15 S10
411 392 372 345
14.5 4.6 3.7 3.0
39.17 5.07 3.44 2.38
345 30 15 10
a Our goal is to pair trades on the KLSE and the SES which follow each other chronologically. We begin by selecting the first trade on one of the exchanges (exchange 1) that is immediately followed by a trade on the other exchange (exchange 2). We call the length of time between these two trades the span. If the next trade chronologically is on exchange 2, we pair the first trade on exchange 1 with the first trade on exchange 2, add the pair to our sample, and begin the process again with the second trade on exchange 2. If the next trade is on exchange 1, we also compute the span between this trade and the first trade on exchange 2. If the first span is shorter than the second, we add the first pair to our sample and begin the process again with the second trade on exchange 1. But if the second span is shorter, we add that pair to our sample and begin the search again with the trade following the second trade on exchange 1. We report the mean span when all of the paired observations are used (SALL) and when the sample is restricted to spans of less than 30 (S30), 15 (S15), and 10 min (S10).
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observations slightly as follows: 30 min (S30), 392; 15 min (S15), 372; and 10 min (S10), 345.
3.3. Exchange rates Trading on the SES is in Singapore dollars and on the KLSE in Malaysian ringgit. There is nothing in the cointegration methodology that requires that the two series be in the same currency. Hence, we could proceed ignoring currency issues. But, if possible, we would like to explore how exchange rates affect our outcomes. Unfortunately, we were not able to obtain transaction data for currencies. We approached several investment bankers and asked them how they handled exchange rates in conducting their businesses. We were told that due to the stability of the Singapore dollar/Malaysian ringgit exchange rate during this period they generally updated their exchange rates only periodically through the day rather than trying to fine tune their calculations using real time exchange rate data. One brokerage firm agreed to supply the exchange rates that it had actually used in its arbitrage activities during this period. These comprised exchange rates at four times each day (09:00, 11:00, 14:00 and 16:00 h). The brokerage firm obtained its exchange rates from a bank. These are the only exchange rates used by the brokerage firm in its trading and settlement activities. We indicate price series that have been adjusted for exchange rates by an asterisk. We realize that these exchange rates are not ideal. Nevertheless, we believe that their use is worthwhile because they conform to the market practice of a large brokerage firm and allow one of the first examinations of how exchange rates affect cross-boarder price discovery. Hence, we replicate all analyses both with and without exchange rate adjustments.
3.4. Unit roots and optimal lags Cointegration testing requires that all of the variables exhibit unit roots with the same degree of integration. We test for the presence of a unit root in the individual series using the augmented Dickey and Fuller (1981) approach, which involves estimating the following regression models: DPt =rPt − 1 +% Bt DPt − 1 + mt (random walk), DPt =a + rPt − 1 +% Bt DPt − 1 + mt (random walk with drift). For our 12 price series (four Malaysian price series—MSALL, MS30, MS15, MS10 and four Singapore price series—SSALL, SS30, SS15, SS10 and four Singapore price series converted into Malaysian ringgit—SSALL*, SS30*, SS15*, SS10*) we estimate a random walk model and a random walk with drift. Results are reported in Table 2. Our estimation used six lags. Column 2 reports the lags that are found to be significant at the 5% level. The augmented Dickey–Fuller test
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Table 2 Unit root testsa r
t
Malaysia (ringgit) MSALL 1,2 1,2 MS30 1,2 1,2 MS15 1,2 1,2 MS10 1,2 1,2
0.000 −0.008 0.000 −0.008 0.000 −0.009 0.000 −0.009
0.77
Singapore (dollars) SSALL 1 1 SS30 1 1 SS15 3 3 SS10 1 1
0.000 −0.006 0.000 −0.006 0.000 −0.007 0.000 −0.086
0.91
Singapore (ringgit) SSALL* 1 1 SS30* 1,4 1,4 SS15* 1,3 1,3 SS10* 1 1
0.000 −0.006 0.000 −0.007 0.000 −0.008 0.000 −0.010
Price series
Identity of significant lags
tm
Conclusion
−1.09 0.67 −1.02 0.70 −1.01 0.61 −1.22
−0.99 0.93 −0.98 0.87 −0.99 0.85 1.58 0.79 −1.20 0.73 −0.99 0.66 −1.04 0.72 −1.19
I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1) I(1)
a This table reports the results of the unit root tests for twelve price series — four Malaysian price series (MSALL, MS30, MS15, MS10), four Singapore price series (SSALL, SS30, SS15, and SS10), and four Singapore price series converted into Malaysian ringgit (SSALL*, SS30*, SS15*, SS10*). For each price series we estimate a random walk model and a random walk with drift:
DPt =rPt−1+% Bt DPt−1+mt (random walk) DPt =a+rPt−1+% Bt DPt−1+mt (random walk with drift) In each case we begin with six lags and then drop the lags that are not significant at the 5% level. Column 3 presents the first order autocorrelation coefficients for each of the series. The critical values for the augmented Dickey-Fuller test statistics for the random walk test presented in column 4 and the random walk with drift test presented in column 5 are t=−1.62 and tm =−2.57, respectively. In every case we cannot reject the hypothesis that r =0 at the 10% level or better. Hence, all of the series are I(1). Further testing showed that no time trends are present for these series and successive differencing identified no additional unit roots.
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statistics reported in columns 4 and 5 fail to reject the hypothesis of r= 0 at the 10% level or better in every case. Hence, the series are I(1). Moreover, further testing (not shown) indicates that no time trends are present and that successive differencing does not produce additional unit roots. Having confirmed the presence of I(1) series, we use the multivariate extension of the Akaike Information Criterion to identify the optimal lag length for use in our cointegration testing. We tested longer lags against shorter lags as restrictions in a vector autoregression of the underlying price levels. The AIC is minimized at a system lag length of two.
3.5. Cointegration We use the reduced rank regression procedure of Johansen (1988) to test for possible cointegration. With two underlying price series there is at most one cointegrating vector (r= 1). We test the null hypothesis that r= 0 with maximum eigenvalue and trace tests. The critical values for these tests at the 1% level obtained from Enders (1995), (table B) are lmax = 18.78 and ltrace = 21.96. The results reported in Table 3 show that all of the series are cointegrated. If prices in Malaysia (Mt ) and Singapore (St ) are cointegrated of order (1,1), there must be nonzero values of B1 and B2 for which the linear combination B1Mt + B2St is stationary. The necessary and sufficient condition for Mt and St to be CI(1,1) is: Table 3 Cointegration testsa Price series
Johansen test Maximum eigenvalue
Trace
Cointegrating vectors
SALL*
41.95*
42.56*
−13.174 13.257 0.083
SALL
35.08*
35.77*
−12.802 11.654 −1.148
S10*
42.02*
42.90*
−14.458 14.472 0.014
S10
36.69*
37.51*
−14.180 12.823 −1.375
a We report results for SALL, SALL*, S10, and S10*. To save space we do not report S15, S15*, S30, and S30* which have results that are qualitatively identical to those reported. Columns 2 and 3 report the test statistics for Johansen’s reduced rank regression procedure. The critical values for r= 0 at the 1% level, taken from Enders (1995) (table B), are lmax =18.78 and ltrace =21.96. All of the statistics are significant at the1% level. Column 4 provides estimates of the cointegrating vectors for each time series. * Significant at the 0.01 level.
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B1mMt +B2mSt =0, where m represents the trend in the random walk processes M and S, respectively, in period t. If prices in Malaysia and Singapore are cointegrated I(1,1), then mMt must be identical to mSt up to the scalar −B2/B1. That is, any two series cointegrated (1,1) must have identical stochastic trends, so that some properly scaled linear combination of the trends vanishes. In the case of two stock price series, the law of one price maintained by arbitrage implies that the scalar − B2/B1 = − 1, i.e. − B2 +B1 =0. We use eigenvector subroutines and Johansen’s reduced rank techniques to estimate and test the cointegrating vectors. Brokerage firms in both Kuala Lumpur and Singapore regularly monitor KLSE and SES prices for arbitrage opportunities. Transaction costs can prevent arbitrage trades and introduce short run imperfections in the cointegration error-correction process. In addition, unstable dynamic relationships between the markets can prevent the predictability required to generate arbitrage profits on average. Our results are reported in the fourth column of Table 3. All of the series are cointegrated. Examining the quantity B1 − B2 for the SALL and S10 price series in rows 2 and 4 might lead to the conclusion that arbitrage opportunities were present. But comparing each of these to its comparable exchange rate adjusted series in rows 1 and 3 shows that arbitrage opportunities that seem to be present if exchange rates are not taken into account largely disappear when the price series are adjusted for these exchange rates. Once exchange rates are taken into account, the quantity B1 − B2 is greater for the SALL* price series compared with the S10* price series. For the longer spans of the SALL* series, there is more time for the occurrence of new information which could drive the price apart temporarily. On the other hand, transaction costs, technological constraints and the like are a greater obstacle to error-correcting adjustment as the span between trades becomes shorter. Our results provide some evidence that the former considerations are more important than the latter. A pricing disparity that does not persist implies arbitrage trading profits only if the short-term dynamics of the adjustment process are predictable.
4. Common-long-memory results Next, we explore the relative contributions of the KLSE and SES to price discovery. Arbitrage insures that prices on the KLSE and SES error correct. Anytime either exchange moves away from the law of one price, one of the two markets (or both) adjusts to restore arbitrage equilibrium. A price adjustment process involving equilibrium error correction is orthogonal to any common stochastic trend in the cointegrated data. In essence, our approach is to identify the relative contribution of each exchange to the common long-run trend of prices. We interpret an exchange’s relative contribution to the long-memory trend as its relative contribution to price discovery.
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Table 4 Common-long-memory factorsa Price series
Malaysia
Singapore
x2
SALL* S30* S15* S10*
0.743 0.724 0.684 0.741
0.257 0.276 0.36 0.259
22.57* 22.19* 19.20* 22.13*
a
We present the common-long-memory factors estimated using the approach of Gonzalo and Granger (1995). Note that for each row, columns 2 and 3 sum to 100%. * Significant at the 0.01 level.
Our approach is based on the methodology developed by Gonzalo and Granger (1995). Specifically, we estimate a linear combination of Mt and St such that the error-correction terms do not cause the common factors at low frequencies. These common long-memory components are the driving force that results in cointegration of the price series. For each pair of price series, we estimate the cointegration structure, sum the estimated common long-memory factors, divide each individual eigenvalue by this sum, and report the normalized results in Table 4. The percentages are the proportions of the normalized eigenvector orthogonal to the transitory adjustment vector of the error-correction model. With synchronous trades, this vector of common long-memory factors [ f1, f2] can be interpreted as the degree of permanent price movement (i.e. of price discovery) occurring in each trading venue. An asterisk on the chi-square test statistic indicates 99% significance in likelihood ratio tests of the null hypothesis H0:f= [1,0] against the one-tailed alternative Ha:f2 \0. See Gonzalo and Granger (1995) for more detailed explanations and multiple illustrations of these hypothesis tests. The chi-square tests show that the Singapore Stock Exchange contributes significantly to the long-run driving force establishing common trends in these price series. Approximately 68 – 74% of the price discovery occurs on the KLSE with the remaining 26 – 32% of the price discovery occurring on the SES. Since Sime Darby Berhad is a Malaysian company, it is not surprising that the majority of the price discovery occurs in Malaysia. But the fact that both exchanges contribute to price discovery indicates that in this case the international cross listing improves the price discovery process.
5. Error-correction results The results of the estimation of the VAR with and without error-correction terms are shown in Table 5. On balance, we find a strong error correction of Singapore prices to Malaysian prices and a weak correction of Malaysian prices to Singapore prices. In the Singapore error-correction equation, the error-correction process fully explains the price adjustment. In the Malaysian error-correction equation only the
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first order lags are significant at conventional levels and the coefficient of the error-correction term approaches significance. The significance of the first order lagged coefficients in the Malaysian equation mirror the results of Harris et al. (1995) for the NYSE. Inclusion of the error-correction term substantially increases the explanatory power of the Singapore equation, but not the Malaysian equation. Comparison of the size of the coefficients of z(t−1) in the two error-correction estimations also suggests that Singapore reacts more strongly to differences between prices on the two exchanges than does the KLSE. The t values on the error-correction terms and the changes in the statistical significance of the coefficients of the lagged price change terms demonstrate that the VAR without the error-correction term is misspecified. This conclusion is reinforced for the Singapore equations where there are sign changes for the lagged price change coefficients.
Table 5 Error-correction modela DP Malaysia
DP Singapore
Constant DP Malaysia (t−1) DP Malaysia (t−2) DP Malaysia (t−3) DP Singapore (t−1) DP Singapore (t−2) DP Singapore (t−3) z(t−1) R2 DW F
0.0001 (0.44) −0.226 (−3.06)* −0.101 (−1.54)
0.001 0.032 0.017 −0.069 −0.133 −0.066 0.033 0.023 0.108 2.00 7.75*
(0.87) (0.46) (0.25) (−0.12) (−1.84) (−0.98) (0.55) (5.76)*
Constant DP Malaysia (t−1) DP Malaysia (t−2) DP Malaysia (t−3) DP Singapore (t−1) DP Singapore (t−2) DP Singapore (t−3) R2 DW F
0.001 (0.49) −0.034 (−5.03) −0.150 (−2.51)
0.001 0.100 0.111 0.149 −0.154 −0.118 −0.153 0.041 2.00 2.34
(0.66) (1.75) (1.87) (2.64)* (−2.52) (−1.86) (−2.46)
0.173 (2.53)* 0.096 (1.38) −0.008 (−1.81) 0.089 2.00 6.51*
0.236 (3.62) 0.134 (2.03)* 0.081 2.00 7.26*
a These results show estimates of the vector autoregressions for log deviation price changes in the Malaysia and Singapore price series with and without error correction being specified. The error-correction term z= PMalaysia −PSingapore has the expected sign and is statistically significant at 93% in the DPMalaysia equation and at 99% in the DPSingapore equation. In Singapore, the error-correction process fully explains the price adjustment and misspecifying the vector autoregression to exclude error correction leads to sign-reversals on the own-price lags and cross-price lags and a three-fold decrease in explanatory power. * Significant at the 0.01 level.
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6. Summary and conclusions Using the error-correction model of Engle and Granger (1987), Harris et al. (1995) show that the NYSE, Midwest, and Pacific exchanges all contribute to price discovery for International Business Machines. Further, using the common-longmemory component approach of Gonzalo and Granger (1995), Harris et al. (1997) estimate the percentage contribution of the NYSE and regional exchanges to price discovery. We extend the work of these authors by investigating price discovery for the shares of a large Malaysian conglomerate traded on both the KLSE and the SES. Our data comprises transaction data for both the KLSE and the SES and Singapore dollar/Malaysian ringgit exchanges rates at four times during the trading day. Typically, trade-to-trade data, which is crucial for observation of the errorcorrection process in equity markets, is not readily available. We were the first to obtain such data for these two markets. Because both of these exchanges are screen-based limit order book systems, we can be sure that our results are not due to intervention of designated market makers. Moreover, both exchanges are in the same time zone so that trading is taking place contemporaneously. If this were not the case, study of synchronous trades would not be possible. We report a number of findings: 1. The price series for both Malaysia and Singapore are integrated of order I(1) and the results of the Johansen test indicate that the price series are cointegrated. 2. Arbitrage opportunities that appear to be present using unadjusted price series largely disappear when the price series are adjusted for exchange rates. Hence, it is essential that researchers who investigate cross-listed securities control for intraday movements in exchange rates.3 3. The common-long-memory results show that the majority of the price discovery occurs in the Kuala Lumpur home market. But a substantial and statistically significant amount of price discovery (i.e. 26–32%) also occurs in Singapore. Hence, we provide evidence that there may be substantial benefits to the cross listing of securities. 4. The error-correction results show that Singapore prices strongly error correct to discrepancies with Malaysian prices but that Malaysian prices only weakly error correct to discrepancies in Singapore prices. In summary, applying the error-correction approach of Engle and Granger (1987) and the common-long-memory approach of Gonzalo and Granger (1995), we find that exchanges outside the home country can contribute substantially to price discovery. The NYSE has been actively seeking exchange listings from outside the US and as part of that process has been lobbying for easing of accounting restrictions that hinder these cross-listings. Our results provide support for these efforts. 3 We find no evidence that either the timing of exchange rate updates or the timing of trades over the trading day affects our findings.
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Acknowledgements We wish to acknowledge the insightful comments and helpful advice of Jesus Gonzalo, Clive Granger, and Lori Leachman.
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