International Transmission Of Stock Prices Movements Finance Essay
This study uses a Cointegration analysis and Vector autogressive models to investigate the transmission of stock price movements among U.S, Japan and India. The results of Johansen cointegration test indicate that stock price indices of the three countries are not cointegrated, thus suggesting that there is not long run relationship between the three markets. The results from Pair-wise granger causality suggest the important and dominating role of the two developed markets of U.S and Japan over the developing markets of India and the existence of two way causation between the U.S and Japan. In contrast Indian stock markets have very little influence on both the U.S and Japanese stock market. The relative leading role of the U.S and Japanese markets are further supported by the variance decompositions and impulse response functions indicators.
Globalization of international stock markets and the day to day interdependence between them has to led to many studies over the last two decades especially after the October crash of 1987. With globalization playing its part there is a growing volume of cross –border transactions, in terms of goods and services as well as financial flows, the main reasons behind such turn of events if lifting of restrictions on capital flows and relaxation of exchange controls in many countries. President Obama in its recent visit to India had mentioned to lifting of more restrictions on capital flows and services both ways which again is a sign of advancement and an integration of world economies. Also recently there has also been an advance in technology, telecommunications and transport which has also helped financial flows. As a consequence of such advancements, investment opportunities are no longer restricted to domestic markets; investors are now also looking to invest in upcoming emerging markets of developing countries seeking profitable opportunities overseas. A portfolio that has financial assets in it reduces their risk by a considerable amount if there is negative or weakly correlated between the financial assets or simply by diversifying across different nations whose economic cycle as no coherent with each other thus the relationship among different stock markets has a great influence on the investment. Correlation between the stock markets is an important factor in determining the benefits of diversification. Besides helping in portfolio diversification relationships between stock markets help in macroeconomic policies, for example international portfolio investment can influence the exchange rate and could lead to appreciation of currency (local) , potential to destabilize an economy ( Mexican and East Asian financial crisis in 1990s). Over time the economies of the world become more closely integrated with each other which means that the stock markets of one country will surely affect the stock markets of the other countries i.e. stock markets become more correlated which reduces the benefits of international diversification. Again due to globalization the fluctuations in the economies of one country contribute into pricing of the domestic securities.
Since India’s independence, a lot of social and political problems have always stood in the way of progress thus not letting India realize its true economic potential. But recently a lot of economic and political reforms have been made which have been great for India’s growth. The most important policy change was opening of the economy to foreign investments. Since its inception the industrial export and foreign investment today are growing at the fastest rate ever (foreign exchange reserve rose to US $51 billion in March 2002 from less than US $1 billion in June 1991).Reform of the Indian stock market began with the establishment of Securities Exchange Board of India (SEBI) in 1988 to setup rules and regulations for operations of stock exchange in India. This paper is very timely as India has transformed during the past two decades especially in the last decade (1999- 2009) and also there is a lot effort made by the Indian Government to join ranks of other open economies of the world, the most important change being the installation of BPO’s which has been a game changer for the Indian economy beside IT sector. We are looking at how much India market is interdependent with the Stock market of U.S (world’s most dominant stock market) and Japan (Asia’s most dominant stock market) and how is has increased over time. Most of the studies were done in the period of 1987 – 1999 but out study re- investigates the transmission of stock price movements among India, U.S and Japan over an more recent set of data sample (1999- 2009). Regulations towards Foreign Institutional Investors (FIIs) investment are put in by the Government with caps of 10 percent by an FII in a single company and 20 percent in public sector (PSU) banks. FIIs are also not allowed to invest in print media. In the past few decades all the foreign investments in India by FIIs from U.S and Japan seems to have been increasing thus bring in more investments to the Indian market. India is one of the few markets where a lot of FII investments have been attracted due to the enormity of the returns. FIIs have started to invest through the equity and derivatives market, pension’s funds, mutual funds, investments trusts, asset management companies, nominee companies. As of now FIIs are allowed to invest in all categories of securities traded in the primary and secondary segments and in the derivatives segment. The decision to analyze the linkages between the Indian, U.S and Japanese stock markets is due to their large economy and market capitalization and also due to the find of affect they have on each other’s economy. Both U.S and Japan are developed markets and have a lot of investments in the India market especially in the industrial sector. Lately, Indian companies have successfully raised capital in world markets more so in U.S market due to IT companies like Infosys and Satyam Infoways.
Thus it is interesting to examine the possible relationship of Indian stock markets with U.S and Japanese markets. To understand the recent relationship between the three markets and study the underlying mechanism the stock prices indices of the three countries were taken for the time period of 1999 – 2009 and an empirical analysis was done using multivariate cointegration. Cointegration helps in identifying any long run relationship between the three stock markets .After that pair – wise Granger causality test is done to identify any short run relationships. The estimated coefficients of VAR are difficult to interpret, thus we need to look at the impulse response and variance decomposition of the system for conclusions.
Empirical results of study indicate that since there three markets are not cointegrated, the combination of these markets yields portfolio diversification in the long run. Granger causality suggests that the Indian stock markets in more influenced by the U.S as compared to Japan stock markets. There exists two- way causation between the U.S and Japanese stock markets. In contrast the Indian stock market has very little influence on both the U.S and Japanese stock market thus still not being able to dominate those two develop markets. The relative leading role of the U.S and Japanese markets are further supported by the variance decompositions and impulse response functions indicators.
2. Literature review
There was a lot of research that was done to understand the international market linkages and co – movements of stock markets for portfolio diversification. Despite these markets being totally different from each other in every sense the markets of the developed (US and Japan) and developing (India) are more closely interlinked with each other in recent times. If the fund manager knows how one stock market is related to the stock market of the other country it benefits him as he can strategize accordingly thus having an opportunity for portfolio diversification. The model used is cointegration analysis and vector autogressive models to investigate the interdependence.
Early studies by Ripley (1973), Lessard(1976) found there wasn’t any Linkages between national stock markets thus the correlation between was found to be very low, thus supporting the portfolio diversification. After the crash of October 1987 people realized that the national stock markets are very closely related to each other and U.S market has an influence on stock markets of almost every country. Lee and Kim examined the effect of crash and suggested that the national stock market became more interrelated after the crash and find that the co – movements among national stock markets and become stronger when the US stock market is more volatile. Jeon and Von- Furstenberg (1990) used VAR approach and impulse response function analysis again suggesting that the co – movements have become greater and stronger after the crash.
Sharma and Kennedy (1977) examined the price movements of Indian market with the US and UK stock to find that there is no evidence of any interdependence between the two markets. Bala Arshanapalli and Mukund S. Kulkarni used cointegration analysis and pair wise granger causality tests to conclude that pre - 1998 period India stock market has very little interdependence with the US Market which was surprising as during that time US markets were dominating the whole European and Asian markets. However post 1998 there was a evidence that the interdependence between the two markets existed which makes sense cause of a lot of companies particularly technology companies investing in NYSE. It is also clear that BSE is integrated with the NYSE but does not influence the markets hence from a Indian investors point of view investing in NYSE would results in increasingly less gains.
Wong ,Agarwal ,Du in the working paper use cointegration analysis and pair wise Granger causality to empirically investigate the long run equilibrium relationships and short run dynamic linkages between the Indian stock market and the stock markets of major countries (US , UK and Japan) after 1990. They concluded that Indian stock market is integrated with the mature markets in the long run and in the short run US and Japan Granger cause Indian stock markets but Indian stock markets were not to explain the stock markets of US, UK and Japan. In addition it was also concluded that these indices form fractionally cointegrated relationship in the long run.
Narayan, Smyth,Nadha examined the dynamic linkages of the emerging stock markets of South Asia (Bangladesh, India, Pakistan and Sri Lanka). It was found that there is a long run relationship between the four stock markets. The stock markets of India, Bangladesh and Sri lanka influence the Pakistan stock market in the long run. Using Impulse response they found that Bangladesh is the most exogenous of the four South Asian markets and then next India followed by Sri Lanka and Pakistan. In Short run there is unidirectional Granger Causality from stock prices in Pakistan to India, Sri Lanka to India and Pakistan to Sri Lanka.
Eun and Shim utilized the VAR approach to understand the interdependence between the developed national stock markets (US, UK, Japan, Switzerland, France, Australia, Canada, Germany and Hong Kong). It was again found that the US stock market influences the markets of these other developed countries thus have a strong hold on them dictating how these stock markets move while none of them where able to explain the US stock market. Cheung and Ng (1992) investigated the dynamic properties of stock returns in Japan and US market and found that the US market is an important global factor from January 1985 to December 1989. Also, Corhay, et al (1995) study the stock markets of Australia, Japan, Hong Kong, New Zealand and Singapore and find no evidence of a single stochastic trend for these countries.
Chan, Benton, Gup and Pan (1997) used cointegration for examining co-movement of eighteen stock markets of Pakistan, Australia, Europe and US for time period from 1961 to 1992 and it was concluded that regional factors does not always guarantee long- term relationship between stock markets. Since the cointegrating vectors after the October crisis were not more than before the crisis the hypothesis of contagion effect among stock markets was rejected.
Asim Ghosh, Reza Saidi and Keith H Johnson utilized the theory of cointegration to investigate which developing markets are moved by Japanese and United States Markets (developed). It was found that stock markets of Hong Kong, India, Korea and Malaysia share a long run relationship with the stock market of US which makes sense cause of the presence of large number of investments by multinational national companies in the respective countries. As for the stock markets of Indonesia, Philippines and Singapore, they share a long run relationship with Japan cause of the economic relationships and regulatory structure which is very closely related to that of Japan. The stock markets of Taiwan and Thailand are neither influenced by US or Japanese stock markets. Cointegration implied the existence of ECM which was utilized to forecast stock markets thus helping in portfolio diversification.
Chen, Firth and Rui (2002) used cointegration analysis in addition to the VAR model to examine dynamic linkage and long-term relationship of six major stock market indices of Latin America.The study was conducted in the time frame from 1995 – 2000. It was found that up until 1999 the six stock markets have a long run relationship but an investor did not have many opportunities to benefit from investing in stock of Latin America while from 1999- 2000 no cointegrating vector was found. So basically the investor after 1999 can diversify their portfolios by buying stocks in the six countries. Another important implication of the work is that financial crisis of Asia in 1997 and financial crisis of Russia in 1998 did not significantly affect interdependence of the markets that can be considered as a sign of the isolation from the world markets.
Chang and Nieh examined the stock prices of Taiwan with its trading partners (Hong Kong, Japan and the United States). The correlation between the Hong Kong and Japanese markets was the highest while the lowest was by the Taiwan and U.S. markets which can be explained by the economic relationship between the two stock markets. An important result was that the four stock markets are cointegrated thus the combination of these stock markets cannot yield portfolio diversification. Another important outcome was that U.S and Japanese markets play an important and leading role in driving and influencing the other two stock markets. At the same time, it was found that US stock crash of 1997 has influence only on US market while Asian financial crisis influenced both the U.S. and Japanese stock market. From VDC analysis it was found that the fluctuation in the Taiwan’s stock market is not significantly described by any of the major markets reason being because of cross country restrictions still existing and the Taiwan and Hong Kong markets are affected more by regional countries (Japan). IRF diagrams indicated that the Taiwan and Hong Kong are again affected more by regional country such as Japan than by US.
The paper is described as follows. Section 3 gives an overview of the three stock markets including information about the indices being used. Section 4 describes the data used in the analysis. Section 5 will describe the methodology, while empirical results are given in section 6. Section 7 gives the conclusion.
3. Overview of the Stock Markets
3.1 The Japanese Stock Market
Japan was the first country in Asia and one of the few countries in the world where a securities system was introduced in 1870. With a popularity of the securities system a request for a public trading institution was laid down which resulted in the Stock Exchange Ordinance in 1878. With this Ordinance in place the Tokyo Stock Exchange Co. Ltd. Was established on May 15, 1878 and the trading there began on June 1st in the same year
With the world war having affected Japan a lot with of structural damages and worsening of the economy, something had to be done to control the damages. In March 1943 Japanese Securities Law was forced which reorganized the stock exchange, on June 1930 all the stock exchanges throughout Japan was unified in one corporation which was called the Japan Securities Exchange but this was dissolved in April 1947. Among other steps that were taken one was that the securities market had to suspend all trading sessions from August 10, 1945. Opening of this securities market again after the war was over was proving to be very difficult but some sort of trading had again restarted unofficially in December of 1945.
The Securities and Exchange law was completely revised in April of 1948. Exactly a year later, three stock exchanges were established in Japan in Tokyo, Osaka and Nagoya and there after trading began on May 16th of the same year. The growth of these stock markets was very fast and in the very same year five new stock markets were established in Kyoto (merged into Osaka Securities Exchange in March 2001), Kobe (dissolved in October 1967), Hiroshima (merged in to Tokyo Stock in March 2000), Fukuota, and Niigoata (Merged with Tokyo Stock Exchange in March 2000). In April of 1950 Sapporo Securities Exchange was also formed which proved essential for the Japanese markets. As of today there are five stock exchanges in Japan, out of which the most important and influential stock market with dominance over the world stock market in the Tokyo Stock Exchange.
It is the second largest stock market in the world after the NYSE by aggregate market capitalization of its listed companies. TSE has 2414 listed companies with a combined market capitalization of US $3.1 trillion as of May 2010.
The stocks which are listed on the TSE are separated into three sections:
The First Section: Section is for large companies and as of 31 October 2010 there are 1675 First Section Companies.
The Second Section: Section is for mid-sized companies and as of 31st October there are 437 Second Sections Companies.
The Mothers: Sections is for high growth startup companies and as of 31st October 2010 there are 182 Mothers companies.
The main indices tracking the TSE are the Nikkei 225 index and the TOPIX index based on the share prices of the first section companies and the J30 index of large industrial companies maintained by Japan’s major broadsheet newspapers. As of today 89 domestic and 19 foreign securities companies participate in the TSE trading making is
3.2 The Indian Stock Market
There are 22 stock exchanges in India but only two of them account for most of the trading in the shares in India. They are Bombay Stock Exchange (BSE) and National Stock Exchange (NSE).
The BSE is the oldest stock exchange in Asia which began formal trading in 1875 and has the largest number of listed companies in the world with 4990 listed as of august 2010. On August the equity market capitalization of companies listed on BSE was US $1.39 trillion making it the 4th largest stock market in Asia and the 11th largest in the world
In 1956, the BSE became the first stock to be recognized by the Indian government under the Securities Contracts Regulation Act. There are three main Indices used in exchange, the BSE SENSEX or BSE-30, Economics Times Ordinary Share Price Index (ET) and Bombay Stock Exchange National Index (BSENI). It is the Value – Weighted index composed of 30 stocks and it started on the 1st of January 1986. The index is calculated based on a free float capitalization method.
Recently another share index, BSE 200 has been launched by Bombay Stock Exchange for exclusive use of the brokers who deal in Bombay only. The BSENI is the most commonly used index and considered as the most representative of all the three indices.
Effects of the Subprime Crisis in the U.S
On Monday July 23, 2007, the Sensex touched a new height of 15,733 points. On July 27, 2007 the Sensex witnessed a huge correction because of selling by Foreign Institutional Investor and global cues to come back to 15,160 points by noon. Following global cues and heavy selling in the international markets, the BSE Sensex fell by 615 points in a single day on Wednesday August 1, 2007.
The National Stock Exchange (NSE) is the largest stock exchange in terms of daily turnover and number of trades, for both equities and derivative trading. NSE has a market capitalization of around US $1,451.31 billion (August 2010) and was expected to become the biggest stock exchange in India in terms of market capitalization by 2009 end. NSE is mutually owned by a set of leading financial institutions, banks, insurance companies and other financial intermediaries in India. Two foreign investors NYSE Euronext and Goldman Sachs have taken a stake in the NSE .In October 2007, the equity market capitalization of the companies listed on the NSE was US $ 1.46 trillion making it the second largest stock exchange in South Asia.NSE is the third largest Stock Exchange in the world in terms of the number of trades in equities It is the second fastest growing stock exchange in the world with a recorded growth of 16.6%.
The main indices tracking the NSE are S&P CNX Nifty, CNX Nifty Junior, and S&P CNX 500.
The S&P CNX Nifty is the leading index for large companies on the National Stock Exchange of India. The Nifty is a well diversified 50 stock index accounting for 21 sectors of the economy. It is used for a variety of purposes such as benchmarking fund portfolios, index based derivatives and index funds. Nifty is owned and managed by India Index Services and Products Ltd , which is a joint venture between NSE and CRISIL. IISL is India's first specialized company focused upon the index as a core product. IISL has a marketing and licensing agreement with Standard & Poor's. The S&P CNX Nifty covers 22 sectors of the Indian economy and offers investment managers exposure to the Indian market in one portfolio. The S&P CNX Nifty stocks represent about 60% of the total market capitalization of the National Stock Exchange (NSE). The base period for the S&P CNX Nifty index is November 3, 1995, which marked the completion of one year of operations of NSE's Capital Market Segment. The base value of the index has been set at 1000, and a base capital of Rs 2.06 trillion.
3.3 The US Stock market
The Two major stock markets in the US is New York Stock Exchange (NYSE) and NASDAQ.
The NYSE can be traced back to 1792 when 24 New York City stockbrokers and merchants signed the buttonwood agreement.
The NYSE is the world largest stock market with a market capitalization of its listed companies at US $ 11.92 trillion as of august 2010. A merger took place between NYSE and Euronext and since then the NYSE is operated by NYSE Euronext.
The notable events that took place in the exchange include the exchange being closed shortly after the World War 2, the black Thursday crash in 1929 and the Black Tuesday which was due to the sell off panic which consequently led to the Great Depression of 1929. In 1934 the exchange was finally registered as the national securities exchange with the U.S Securities and Exchange Commission. Other notable events include Asian financial crisis, the mini- crash of 1989 and the flash crash.
The NYSE trades in a continuous auction format, where the traders are allowed to make stock transactions on behalf of the investors
The indices of used in the exchange are NYSE composite and Dow Jones Industrial Average. The NYSE Composite covers more than 2000 stocks in which 1600 or so is from United States and 360 are foreign listings. The index was introduced in 1965 since then it has outperformed all the other indices like the Dow Jones Industrial Average, the NASDAQ Composite and S&P 500.
The Dow Jones Industrial or simply Dow is owned by the CME group was founded in 1896 and represented 12 stocks at that time. Since then it is one of the most closely watched indices. It currently consists of 30 publicly owned companies. It is the second largest U.S market index after Dow Jones transportation Average. The value of Dow is not the actual average of the prices of its stocks but the sum components prices divided by a divisor.
The NASDAQ began trading in 1971 since then the stock market has 3200 companies from 37 countries from across all industrial sectors, it has a market capitalization of US$ 3.08 trillion. NASDAQ is essential to the American stock market because of the number of the companies it has on the list and the no. of shares it trades per day which is more than any others stock market in the world. In 1992 it joined the London Stock Exchange to form the first intercontinental linkage of securities market. The NASDAQ merger with the American Stock Exchange formed the NASDAQ-Amex Market Group and by beginning of the 21st century the NASDAQ Stock market is the largest U.S electronic stock market and the fastest growing market model.
The Indices used the Stock market are NASDAQ Composite, NASDAQ 100 and NASDAQ Biotechnology index.
4. Data Description
The data used in this study is a daily price of stock markets at the closing time. The indices used are NIKKEI 225 for Japan, BSE SENSEX for India and Dow Jones Industrial Average for the U.S.The period chosen for the study is from 1st January 1999 to 31st December 2009.Figure 1 contains the plots of the observed stock prices indices for these 3 countries. The total number of observations for each country is 2870. Data for all the indices is obtained from DataStream information system. In order to take of the data gap caused by public holiday and other non working days, Following Cheung and Ng (1992), missing data while is replaced by index value from previous day. All the series was measured in natural logs. The daily returns used in the econometrics model described in the following section are calculated as follows.
5.1 Unit root tests
The series have to be carefully be examined for stationary for 2 important reasons
The stationarity of a series can strongly influence its behavior and properties. For instance a stock to the system of a stationary series will gradually die away, which means that the effect of the shock will be small in t+1 and even smaller in t+2. If the shock is applied to the system to the a non-stationary series the persistence of shocks will always be infinite thus the effect of a shock during time t will not have a smaller effect in time t+1 and t+2 and so on .Thus it is important to know if the series is stationary or otherwise.
The use of non – stationarity can lead to “spurious regressions”. What is basically means is that if two stationary variables are generated as independent random series and when one is regressed over the other the t ratio on the slope ad the value of R2 would be expected to be low. However if the variables are trending over time a regression of one on the other could have a high R2. If normal regression techniques are applied to non – stationary data the end result could be a regression which only looks good under standard measures which is of no use.
To test for Stationarity of time series we use the “Unit Root “test. During my research several tests appeared for the presence of unit roots in time data series like Dickey Fuller, Augmented Dickey Fuller Test, Phillips and Perron(1988) and Kwiatowski (1992). Further research showed that Schwert (1989) after comparing all the unit root test suggested that ADF test with long lags is the most superior thus in my paper I will be using ADF test for testing if the time series is stationary or not. After reading the paper on procedure of selecting models by Doldado, Jenkinson and Sosvilla- Rivero(1990) ,I agreed the most appropriate model to use for all series is the one including a drift and a time trend which is as follows :
The null hypothesis of ADF test is:
Ho: del = 0
H1 : -2< del<0
Even though we know the most superior test for Unit root is ADF, we will be also performing Phillips Perron test for the three series being considered. The test is very much similar to the ADF test, but they incorporate an automatic correction to the DF procedure to allow for autocorrelated residuals. The results of both the tests are often very similar.
We will use information criteria to choose the appropriate lag length. An appropriate length has to be pre designated .This paper follows the suggestion by Reimers(1992) using Schwartz Bayesian Criterion (SBC) to choose the appropriate lag length.
5.2 Cointegration tests
Cointegration is a relatively a new statistical concept which was introduced by Granger (1983) and Engle and Granger (1987). The definition as given by Engle and Granger (1987) a set of variables ,Yt is said to be cointegrated of order (d,b) if :
All components of Yt are I (d)
There is at least one vector of coefficients , del, such that beta’Yt ~ I(d-b)
If two variables are said to be cointegrated when a linear combination of the two variables is stationary implying that there is a long run relationships between the variables. In contrast, if the two variables are not cointegrated then there is no such long run relation.
When the concept of non- stationarity was introduced the first response was to independently take first difference of the I(1) variables and then use the first difference in any modeling process. But it was quickly realized that when we are trying to find out any relation between two variables such a procedure is inadvisable. The problem was that the pure difference models have no long run relationship. Engle and Granger suggest an ECM instead of a first differencing VAR model to get the right results.
Gonzalo(1994) compared several methods for estimating cointegration and out of which the methodology of Johansen maximum likelihood was choose to be the most apt and powerful. We construct a p- dimensional (3 x 1) VAR model with Gaussian errors, which can be expressed by its first – differenced ECM as:
where Yt are stock prices series , et is a white – noise disturbance ~ N(0, sigma). Here the testing hypothesis is, Ho (r): = pie = alpha beta ‘. The pie matrix can be interpreted as a long – run coefficient matrix which conveys information about long- run relationship between Yt variables. The matrix beta gives the cointegrating vectors, while alpha gives the amount of each cointegrating vector entering each equation of VECM , also known as the ‘ adjustment parameters’. The rank of a matrix is equal to the number of its characteristic roots (eigen values), rank of pie is the number of linearly independent and stationary linear combination of stock prices studied.
The Likelihood ratio test statistic for the hypothesis with at most r cointegrating vector is:
Again according to Reimers (1992) we will use SBC to select the number of lags required in the cointegration test.
5.3 Granger Causality test
If there exists a cointegration vector among stock prices i.e. there exists a long- run relationships then there must be causality among these stock price series, in one direction or in both the directions i.e. we are testing the relationship between the three the stock markets in the short run. Granger (1998) provides a test of causality which takes in to account the information provided by the cointegration properties of variables. The model is:
Here Yit denotes the stocks prices of the 3 different series.
Since the granger causality tests are very sensitive to the lag length selection we use a procedure based on granger definition of causality and akaike’s (1974) minimum final prediction error (FPE) criterion of determine the lag lengths. This procedure is known as the stepwise Granger-causality technique, which provides a statistical criterion for choosing the optimum lag length using past information. The FPE criterion is specified as follows:
where T is the number of observations, k is the number of parameters estimated and SSR is the sum of squared residuals.
However, if these three stock price series are found to hold no cointegration, we should analyze the causality among these three stock markets without the error-correction term thus we use pair – wise Granger Causality.
5.4 Impulse Response function and variance decomposition
The estimated coefficients of VAR are difficult to interpret, thus we need to look at the impulse response and variance decomposition of the system for conclusions.
Impulse response traces out the responsiveness of the dependent variable in the VAR to shocks to each of the variables. Basically for each variable from the each equation separately, a unit shock is applied to the error and the effects upon the VAR system over time are noted.
Variance decomposition measures the percentage of a market’s forecast error variance that occurs as a result of a shock from a market in the system, it shows the fraction of s-step ahead forecast error variance of a given variable explained by the innovations to other variable.
. For calculating impulse responses and variance decomposition, the ordering of the variables is important.
6. Empirical Results
6.1 Preliminary data analysis
Table 1 presents a descriptive statistic of daily returns for each of the three stock markets. The reason why this is done as it enables us to compare statistical parameters of each stock. The market’s average daily index returns are .060 %, .004 % and -.008 % for India, U.S. and Japan. Returns on BSE SENSEX showed the highest mean is .060% while the NIKKEI 225 showed the lowest mean. We will now look at the standard deviation because it gives a sense of volatility of
the stock index. The standard deviation of BSE SENSEX is the highest at 1.75 thus making it the most volatile hence the most risky market out of the three. The U.S stock market is the most secure as it has a standard deviation of 1.26 over the sample period. We will now talk about the Skewness, Kutosis and Jarque-Bera Statistic. Table 1 also shows that return index of each country are leptokurtic, since the relatively large value of the Kurtosis statistic suggesting that the data is heavily tailed and sharply peaked about the mean. Skewness in all the three series is different from zero which is not specific for a normal distribution. Stock indices of Japan and India have negative skewness indicating it’s heavy on the right side while Stock Index return of U.S is positive thus indicating heaviness on the left side. This abnormal distribution of the data is supported by Jarque – Bera statistic as the null hypothesis is rejected.
We now look at the correlation matrix of the three stocks. By looking at table 2 we observe that the correlations between all the three stock market indices are positive and significant. The highest correlation is between the U.S. and Japanese stock market which the lowest is between Indian and U.S markets.
6.2 Unit root tests of stock price indices.
A necessary but not sufficient condition for contegration between the different stock prices index should be integrated of the same order. According to the test statistic non – stationarity cannot be rejected for the levels of each stock price series at 5% significance level based on ADF test. But when the data is differenced once the non- stationarity can be rejected. We use ADF and PP test to test for unit root. Looking at table 3 we see that both ADF and PP clearly reject the null hypothesis of the presence of a unit root for the first difference but doesn’t reject the null hypothesis for the index levels. Thus we conclude the stock indices are I (1) for all indices.
The number in the brackets indicates the appropriate lag length of the model
The number in the bracket indicates the lag truncation for Bartlett kernel suggested by Newey- West (1987).
6.3 Cointegration Tests.
Now that we know that the three stock price index series are integrated of order one or simply put has unit root, we now tested for the presence of cointegration between the 3 stock markets. As discussed before cointegration helps in identifying if there is any long – run equilibrium relationship between the data. We use cointegration methodology developed by Johansen (1988) and Johansen and Juselius (1990) multivariate cointegration tests. In order to see the estimated models, an option of intercept (no trend) in CE and test VAR, changing the Lag Interval to 1 3.Trace test suggested that there is no cointegrating relationship between the stock price indices of India, U.S and Japan. Not being able to find any even one cointegrating vector among the three stock markets suggest that there is not long- run relationship. This also explains the loose co- movements of stock price in fig 1. One important implication is that since there three markets are not cointegrated, the combination of these markets yields portfolio diversification in the long run. Thus investing in combination of these stocks can yield good returns for the investor. However cointegration does not rule out the short run relationships. To check for short run relationships, we proceed to implement bivariate Granger causation methodology.
6.4 Granger Causality test
Since we did not find any cointegrating vector among the three stock price indices instead of using causality test based on ECM, pair- wise granger causality was done to find out the short run relationships between the stock price indices. First step is to choose an appropriate number of lags which is based on the belief that I wanted to do a weekly assessment, thus the lag chosen is seven. Literature also suggests that having more lags is better than fewer lags. Null hypothesis is that there is no granger causation for each pair of the stock markets. The test suggests that U.S dominates and influence both the Indian markets heavily with coefficient of approx 20 .The Indian stock markets in more influenced by the U.S (coefficient of approx 20) as compared to Japan (coefficient of approx 11) stock markets. There exists two- way causation between the U.S and Japanese stock markets and this relationship is very strong with coefficients of approx 8 and 14. In contrast the Indian stock market has very little influence on both the U.S and Japanese stock market thus still not being able to dominate those two develop markets. Both U.S and Japanese are very dominating stock markets
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