Data on the daily closing index of six ASEAN stock markets, including Indonesia, Malaysia, the Philippines, Singapore, Thailand, and Vietnam are used to calculate Shannon ent[r]
Trang 1INVESTIGATING THE RELATIONSHIPS BETWEEN ASEAN STOCK MARKETS: AN APPROACH USING
THE GRANGER CAUSALITY TEST OF TIME-VARYING INFORMATION EFFICIENCY
Tran Thi Tuan Anh a*
a University of Economics Ho Chi Minh City, Ho Chi Minh City, Vietnam
* Corresponding author: Email: anhttt@ueh.edu.vn
Article history
Abstract
The information efficiency and the relationships between ASEAN stock markets are two of the issues that are of great research interest However, these two issues were often investigated separately in previous studies Therefore, this paper combines these two issues
in the same analysis Data on the daily closing index of six ASEAN stock markets, including Indonesia, Malaysia, the Philippines, Singapore, Thailand, and Vietnam are used to calculate Shannon entropy to measure the stock market information efficiency In addition, this paper conducts the Granger causality test to reveal the relationships between the ASEAN stock markets The results show that all six stock markets are not in the state of information efficiency, which means the stock indices, stock returns, and volatility are not purely random, but patterned In addition, the Granger test results show that the ASEAN stock markets are logically correlated The two markets that are more integrated than the others are Indonesia and Malaysia Vietnam participates in regional economics in a passive way, while the Philippines is more proactive The Singapore stock market is also less integrated with the other ASEAN markets, although it is a mature stock market that outperforms the rest
Keywords: ASEAN stock markets; Efficient market hypothesis; Granger causality test;
Rolling window method; Shannon entropy
DOI: http://dx.doi.org/10.37569/DalatUniversity.10.4.614(2020)
Article type: (peer-reviewed) Full-length research article
Copyright © 2020 The author(s)
Licensing: This article is licensed under a CC BY-NC 4.0
Trang 2KHẢO SÁT MỐI LIÊN HỆ GIỮA CÁC THỊ TRƯỜNG CHỨNG KHOÁN ĐÔNG NAM Á: TIẾP CẬN BẰNG KIỂM ĐỊNH NHÂN QUẢ GRANGER TÍNH HIỆU QUẢ THÔNG TIN GIỮA
CÁC THỊ TRƯỜNG Trần Thị Tuấn Anh a*
a Trường Đại học Kinh tế TP Hồ Chí Minh, TP Hồ Chí Minh, Việt Nam
* Tác giả liên hệ: Email: anhttt@ueh.edu.vn
Lịch sử bài báo
Nhận ngày 04 tháng 11 năm 2019 Chỉnh sửa ngày 19 tháng 12 năm 2019 | Chấp nhận đăng ngày 06 tháng 01 năm 2020
Tóm tắt
Tính hiệu quả thông tin trên thị trường chứng khoán và mối liên hệ giữa các thị trường chứng khoán của các quốc gia Đông Nam Á là hai trong số những vấn đề rất được quan tâm nghiên cứu Tuy nhiên, hai vấn đề này thường được tách biệt trong nghiên cứu riêng trong các nghiên cứu trước Do vậy, bài viết này kết hợp nghiên cứu hai vấn đề này trong cùng một phân tích Dữ liệu về chỉ số chứng khoán đóng cửa hàng ngày của sáu thị trường chứng khoán Đông Nam Á, bao gồm Indonesia, Malaysia, Philippines, Singapore, Thái Lan, và Việt Nam được sử dụng để tính toán Shannon entropy nhằm đo lường tính hiệu quả của thị trường Bên cạnh đó, bài viết cũng đồng thời áp dụng kiểm định nhân quả Granger để khảo sát mối liên hệ giữa thị trường chứng khoán các quốc gia Đông Nam Á Kết quả nghiên cứu cho thấy
cả sáu thị trường chứng khoán đều không đạt trạng thái hiệu quả thông tin, điều đó có nghĩa
là biến động chỉ số chứng khoán và tỷ suất sinh lợi trên thị trường chưa phải hoàn toàn ngẫu nhiên Ngoài ra, kết quả kiểm định Granger cho thấy rằng các thị trường chứng khoán ở các quốc gia Đông Nam Á có mối liên hệ hợp lý với nhau Hai thị trường hội nhập tốt với khu vực bao gồm Indonesia và Malaysia Việt Nam tham gia vào các mối liên hệ trong kinh tế khu vực với vai trò thụ động hơn các quốc gia khác, còn Philippines, mặc dù có khuynh hướng suy giảm trong suốt thời gian dữ liệu được thu thập, nhưng lại đóng vai trò chủ động trong khu vực Thị trường chứng khoán Singapore cũng ít hội nhập với khu vực mặc dù đây
là thị trường chứng khoán phát triển và trưởng thành vượt trội hơn các quốc gia còn lại
Từ khóa: Kiểm định nhân quả Granger; Phương pháp cửa sổ cuộn; Shannon entropy; Thị
trường chứng khoán các nước Đông Nam Á; Thị trường hiệu quả thông tin
DOI: http://dx.doi.org/10.37569/DalatUniversity.10.4.614(2020)
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Bản quyền © 2020 (Các) Tác giả
Cấp phép: Bài báo này được cấp phép theo CC BY-NC 4.0
Trang 31 INTRODUCTION
The information efficiency in the stock market and the relationship among ASEAN’s stock markets are issues of great concern to researchers The information efficiency of stock markets originates as a concept from the efficient market hypothesis (EMH) of Fama (1970) According to the EMH, stock prices in an efficient market always reflect all relevant information As a result, an efficient market cannot be beaten because
it incorporates all important determining information into current share prices Therefore, stocks trade at a fair value and cannot be purchased undervalued or sold overvalued It is not possible to employ technical analysis, fundamental analysis, or find a pattern to forecast stock prices to obtain outstanding returns Many methods have been proposed to test market efficiency, such as testing for random walk, Monday effect, January effect, turn-of-the-month effect, holiday effect, variance ratio test, and other statistical techniques In addition to these traditional statistical tools, after the Shannon entropy concept was borrowed from thermodynamics and applied to finance, many financial researchers have been interested in using entropy to measure the efficiency of stock markets Some representative studies that can be mentioned include Mensi (2012), Risso (2009), and Zunino, Massimiliano, Tabak, Pérez, and Rosso (2009) These studies have achieved many interesting results However, measuring the stock market’s efficiency and measuring the relationship between stock markets have often been performed in separate studies Now, researchers have started to combine these issues together In line with this research trend, this article aims to provide more empirical evidence on information efficiency as well as the relationship among ASEAN stock markets Along with the above objectives, the following sections of this article are organized as follows: Section 2 summarizes some relevant previous studies; Section 3 introduces data and methodology; Section 4 represents the data analysis and discusses the results; and Section 5 concludes the main results of the article and proposes some implications
The efficient market hypothesis was proposed by Fama (1970) with the idea that the stock market will reach a state of information efficiency when stock prices reflect all available information on the market The efficiency of markets is considered in three forms: weak, semi-strong, and strong efficient markets If all past prices, historical values, and trends have been reflected in prices, then the market reaches the weak form efficiency state The semi-strong form efficiency theory states that all public information is used in the calculation of a stock's current price, so investors cannot utilize either technical or fundamental analysis to gain abnormal returns in the market And for the market to achieve a state of strong efficiency, stock prices must reflect not only the information available to the public but also any information not publicly known The strong and semi-strong forms of efficiency are difficult for markets to achieve in practice, so most research
on market efficiency focuses on testing the weak form of efficiency In the sense that, when the market is weakly efficient, investors cannot predict future stock prices with only the information of past stock prices This implies that historical data of stock prices do not help to predict future prices; there is no opportunity to discern patterns in stock time series Consequently, a common way to perform weak efficiency tests is to try to find the
Trang 4paradigm or pattern of the historical time series of a stock’s prices or returns If there exists any pattern in the historical data, it means that investors can also exploit past information to predict future stock prices to gain abnormal profits This is evidence against the efficiency of the market A variety of statistical tools are used to find empirical patterns, such as the calendar effect, seasonal effect, weekend effect, and others Most of these approaches are performed through statistical tests or regression techniques As opposed to traditional statistical approaches, the Shannon entropy approach is based on the randomness of the stock market time series The more efficient the market, the more random the stock price movement is, and all possible outcomes of stock prices or returns are equally probable This property is the basis for using entropy to measure the efficiency
of the market In the early studies of entropy, Shannon (1948) used entropy to measure the chaotic nature of a physical system When applying Shannon entropy in economics, researchers also considered the randomness of stock fluctuations to be similar to the disorder of a physical system, and thus it is reasonable to employ entropy to measure this randomness An efficient market implies that it is impossible to predict whether the next
day’s stock return will be higher or lower than the mean So, the probability p for a stock
return to be higher or lower than the mean is 0.5 for both outcomes Then Shannon entropy reaches its maximum value of 1 Based on this feature, there can be evidence for market inefficiency when the Shannon entropy of the stock series is less than 1 The larger the calculated Shannon entropy, the more efficient the market is, and vice versa
Among studies that apply Shannon entropy and extended forms of entropy in quantitative finance, some particularly relevant studies include Risso (2009), Zunino et
al (2009), and Mensi (2012) Risso (2009) applied a symbolic technique to transform a continuous return time series into a discrete form and then computed Shannon entropy to measure the efficiency of 20 stock markets His data were the daily stock indices from July 1997 to December 2007 of some developed countries, such as Japan and Singapore, and some emerging economies The results show that Taiwan (R.O.C), Japan, and Singapore had the highest levels of stock market efficiency, and that developed stock markets often had lower market efficiency levels than those of emerging stock markets Different from Risso (2009), Zunino et al (2009) proposed an extension of the Shannon entropy method, named permutation entropy, to quantify the degree of market inefficiency The common feature of both types of entropy is that prices are random for
an efficient market If there is a pattern that dominates the frequencies, the market is no longer random The results show that emerging markets, such as Greece, Hong Kong (P.R.C), Singapore, Taiwan (R.O.C), and Turkey, became more efficient over time from
1995 to 2007 Mensi (2012) evaluated the time-varying efficiency of crude oil markets
by using Shannon entropy and symbolic time series analysis (STSA) Mensi used daily price data from May 20th, 1987, to March 6th, 2012, for two worldwide crude oil benchmarks, West Texas Intermediate (WTI) and European Brent His work revealed that the weak market efficiency of both oil markets improved over time However, the WTI market appears to be less efficient than the European Brent market These results have many implications for market investors and policymakers of the countries concerned Lahmiri, Bekiros, and Avdoulas (2018) used daily data of stock markets in Asia, America, Europe, and Oceania to measure market information efficiency Their paper used Shannon entropy, the Hurst exponent, and the Lempel-Ziv index to conduct calculations
Trang 5The authors also used the Granger causality test to investigate the information flow among these markets The research results showed that the randomness and efficiency of information in these markets are transmitted to each other The Granger causality effect
is bidirectional between all pairs of stock markets except Oceania and Europe In general, these transmissions depend on the geographical locations of the markets Several studies
in Vietnam by Tran (2018a, 2018b, 2019) have used entropy to verify the information efficiency of the stock market, but these studies only deal with time-invariant Shannon entropy They do not test information transmission between markets by the Granger causality test on time-varying Shannon entropy series
3.1 Data
This paper uses daily closing prices collected from the website Investing.com for ASEAN-6 stock markets from March 2012 to October 2019 The six stock markets included in the sample are Vietnam, the Philippines, Malaysia, Indonesia, Thailand, and Singapore These six countries have jointly launched the ASEAN Trading Link, a gateway for securities brokers to offer investors easier access to connected exchanges This ASEAN exchange aims to promote growth in the ASEAN capital market and bring more investment opportunities for investors in ASEAN The stock indices used in this article are listed in Table 1
Table 1 List of stock market index of ASEAN countries
From the daily closing prices, the stock returns are calculated by a logarithmic formula as follows:
, 1
it
i t
P r
P −
where r it is the stock return of market i at day t, P it is the closing price of market i
at day t, and P i,t-1 is the closing price of market i at day t-1
Trang 6Figure 1 Daily closing price and return series of ASEAN-6 stock markets
from 2012 to 2019
Trang 7The daily returns along with daily closing prices of stock indices are plotted in Figure 1 The plots on the left side of Figure 1 show the trend of stock indices, while those
on the right show the return series of the ASEAN-6 markets, including Indonesia, Malaysia, Philippines, Singapore, Thailand, and Vietnam, respectively Each stock index has its own up and down movements, but their overall trends are increasing, except for the Philippine stock market which declined over time The graphs of the return series also show unequal variations over time of these six stock markets
3.2 Methodology
3.2.1 Shannon entropy
Shannon entropy was firstly introduced by Shannon (1948) as a quantity used to measure the level of randomness or complexity in a signal sequence The Shannon entropy concept was later used extensively in financial studies, especially to measure the
randomness in financial time series Suppose we consider a time series X t , t=1,2,3,… representing fluctuations in financial asset prices, X t can take discrete values x 1 , x 2 ,…, x n
with probabilities p(x 1 ), p(x 2 ),…, p(x n )which satisfy the condition
1
( ) 1
n i i
p x
=
=
entropy, H, is then calculated using Equation (2)
1
( ) log ( )
n
i
=
Shannon entropy takes the minimum value of 0 if there is a certain value x i that
will inevitably occur in all cases, meaning that the probability that X t equals x i is 1
Otherwise, Shannon entropy will be maximized when all possible values of x i have the same probability of occuring That is, all possible outcomes are equally likely to happen,
so the series is completely random
In the case that X t is a continuous random variable, the calculation of Shannon
entropy becomes more difficult than when X t is a discrete variable One of the simplest ways to calculate Shannon entropy for continuous random variables is to symbolize them into a discrete binary series and then compute the entropy The symbolization process is performed as follows:
1
1
1
0
t t t
t t
if X X S
if X X
−
−
That is, assume X t is the daily closing price P it of the i th stock index; it can be
easily interpreted that S t will receive value 1 if the stock index stays the same or goes up,
and S t will receive value 0 if the stock price falls The symbolization rules for the i th stock index will be:
, 1
, 1
1 0
it i t it
it i t
if P P S
if P P
−
−
Trang 8Equivalently, the stock price stays the same or increases ( P it P i t,−1 ) corresponding to a zero or positive rate of return, while a stock price decrease (P it P i t,−1 ) corresponds to a negative rate of return Thus, the binary series can also be made by using returns instead of prices:
it it
it
if r S
if r
and the Shannon entropy formula for the symbolized binary series is
1
0
i it it
i
H p S i p S i
=
The maximum value of Shannon entropy of the symbolized binary series is 1, which occurs when the two nondecreasing and decreasing states of the return series have equal probabilities, and the minimum value is 0, when the stock return is always at the same state The closer the calculated Shannon entropy value is to 1, the more purely random and less patterned the stock returns are, and the more difficult to predict because
of the high complexity Therefore, the market is more efficient Conversely, the further Shannon entropy is from 1, the more the series has more patterns because there will be one state that has a higher probability than the others It can be said that the market has not reached the state of information efficiency
In this paper, the calculation of Shannon entropy will be performed by the rolling
window technique with window length W = 250 After finishing the windowing process,
we will have a time-varying Shannon entropy series that shows changes in the randomness level of the stock index and changes in the efficiency level of the stock market The length of the rolling window is 250, corresponding to the average of 250 trading days per year on these stock markets Data samples for six stock index series will
be symbolized and then Shannon entropy series will be computed The Shannon entropy series of each market is used to examine market-to-market linkages through the Granger causality test
3.2.2 Granger causality test
The Granger causality test is used to test the empirical relationship between two
time series, X t and Y t The X t series has a Granger effect on Y t if past values of X contain information useful to explain or predict the current and future value of Y This test is
performed through the regression function
0
where α 0 is the intercept, β j is the slope of Y t-j , α j is the slope of X t-j , and ε t is the error
Trang 9If the hypothesis H0:1= = p =0 is rejected, there is sufficient statistical
evidence to conclude that X t has a Granger effect on Y t at lag p To ensure that the Granger
causality test results do not suffer from spurious regression, this article conducts a stationarity test for time-varying Shannon entropy series of all markets Calculations are performed by using Python software
4.1 Descriptive statistics
Table 2 presents descriptive statistics of the daily closing prices of ASEAN-6 stock markets This table shows the mean, standard deviation, maximum and minimum value of stock indices and does not reveal significant information about the efficiency of these stock markets
Table 2 Descriptive statistics of ASEAN stock indices
Table 3 shows descriptive statistics of the daily returns of ASEAN-6 stock indices Among these, the Philippines stock market has a negative average return over the period
of 2012-2019 This is quite reasonable because of the general declining trend of the Philippines market, as seen in Figure 1 The Philippines is also the market with the largest standard deviation while Vietnam is the market with the highest average return, Malaysia
is the market with the lowest standard deviation and lowest range of return
Table 3 Descriptive statistics of ASEAN stock returns
Trang 104.2 Shannon entropy results
The article applies the symbolizing technique to the stock return series of the ASEAN-6 markets according to Equation (5) and the rolling window method with a window size of 250 transaction days In each window frame, the Shannon entropy of the symbolized data series is calculated using Equation (6) Figure 2 shows a graph of the time-varying Shannon entropy series for each market, and Table 4 gives their stationarity test results
Figure 2 Time-varying Shannon entropy series for ASEAN-6 stock markets
The Shannon entropy series of the six markets shown in Figure 2 are all quite far from the maximum possible value of Shannon entropy This represents quantitative evidence of market inefficiency Therefore, all six ASEAN-6 stock markets do not achieve information efficiency This result is consistent with Tran (2018a); that study also concludes that the ASEAN-6 stock markets are inefficient, using data from 2010 to 2016 However, Tran (2018a) applied Shannon entropy for the whole sample, which treats Shannon entropy as time-invariant This paper, using the rolling window technique, shows the variation in inefficiency over time with the visualization in Figure 2
4.3 Granger causality results
Table 4 gives the stationary test results of the Shannon entropy series representing the six markets Among them, the entropy series of Vietnam and the Philippines are not