“Test of capital market integration using Fama-French three-factor model: empirical evidence from India”

Integration or segmentation of markets determines whether substantial advantages in risk reduction can be attained through portfolio diversification in foreign securities. In an integrated market, investors face risk from country-specific factors and factors, which are common to all countries, but price only the later, as country-specific risk is diversifiable. The aim of this study is two-fold, firstly, investigating the superiority of the Fama-French three-factor model over Capital Asset Pricing Model (CAPM) and later using the superior model to test for integration of Indian and US equity markets (a proxy for global markets). Based on a sample of Bombay Stock Exchange 500 non-financial companies for the period 2003–2019, the data suggest the superiority of Fama-French three-factor model over CAPM. Using the Non-Linear Seemingly Unrelated Regression technique, the first half of the sample period (2003–2010) shows evidence of market segmentation; however, the second sub-period (2011–2019) shows weak signs of market integration, which is supported by the Johansen test of cointegration, suggesting that Indian market is gradually getting integrated with global markets.


INTRODUCTION
All sound investment and portfolio management decisions are guided by expected cash flows to secure maximum expected possible returns for a given amount of risk.The stock market returns in such a scenario are priced for the various systematic risk factors.CAPM showed that an efficient combination of various risky assets would demonstrate a linear relationship between risks and return (Sharpe, 1964).Followed by this, CAPM was independently developed by Lintner (1965) and Mossin (1966).While it can be argued that testing of CAPM is not empirically possible because of the absence of a good proxy for market portfolio (Roll, 1977), there is enough existing research to support that there are more factors than market volatility to explain the returns (Miller, 1999).Fama and French (1992) discovered the violation of a linear cross-sectional relationship between mean excess returns and exposures to the market factor (main prediction of the CAPM) for the US stock market.Then, a new asset pricing model, with two additional explanatory variables, size and book equity to market equity ratio, was developed (Fama & French, 1993).Chui and Wei (1998) did empirical testing on China, Taiwan, Malaysia, Korea, and Singapore equity markets and concluded a strong relationship between the expected stock returns and these three factors.Although there have been a plethora of empirical studies focused on CAPM and Fama-French three-factor model, only a few research studies have been conducted for Indian markets, notably Connor and Sehgal (2001), Sehgal and Tripathi (2006), and Taneja (2010).All of these findings suggest that Fama-French three-factor model explains excess returns better than CAPM.They concluded that to explain excess returns, the market factor is most important, and there are no conclusive remarks on which amongst the size and value factor explains excess return better.However, all three factors combined have a better adjusted Coefficient of determination (R 2 ) than the market factor alone.
However, there has been a considerable change since these studies were done.There are recent findings that suggest that the explanation of excess returns by Fama-French multifactor model has dwindled over time on Istanbul Stock Exchange (Eraslan, 2013).This raises an obvious question, is Fama-French still pervasive in the Indian context?This study tries to fill this gap by, first, empirically testing and comparing CAPM with Fama-French model.The study concludes that for all the six portfolios constructed, Fama-French explains excess returns better than CAPM, and it is still pervasive in the Indian context.This research also tried to find an answer to the question, which factor, size, or value is the second most important factor in explaining excess returns.
The Indian economy since the 1991 reforms has seen a high level of growth and economic prosperity.These reforms then coupled by many other financial sector reforms during 1998-2004 and the enactment of Financial Sector Legislative Reforms Commission (FSLRC) in 2011 were moves in the right direction, the importance of which will be felt for many years to come (Rajan, 2014).Subsequently, India has jumped 79 positions in the past five years in Ease of Doing Business ranking, coupled with political stability, the concept of universal and big banks, reduced taxes, and implementation of one nation one tax policy.All this contributed to the image of India as an attractive global destination for investment.
In this context, it was important to check whether the Indian stock market is segmented to global capital market or is it already integrated with global peers.The majority of such research testing market integration has been focused on developed markets like Canada and Australia.The study of market integration has widely applied CAPM, notable among these are Solnik (1974) for European stocks, Stehle (1976), Jorion and Schwartz (1986), and Mittoo (1992) in the Canadian market.
The use of Fama-French three-factor model to study market integration is limited.In developing markets, Brooks, Iorio, Faff, and Wang (2009) examined market integration in the Chinese market for the period 1995-2006, extending the work of Jorion and Schwartz (1986) to Fama-French threefactor model, and suggested that the Chinese stock market is segmented from the stock market of the United States and the government's restriction on capital movement is preventing integration of Chinese market with global peers.In the Indian context, it has not come to the knowledge of authors, any study that uses Fama-French three-factor model for testing the market integration.Through this work, attempts are made to fill this gap in the literature by empirically testing market integration using Fama-French three-factor model.Another contradiction to the proposed CAPM came from Bhandari (1988) who documented that expected stock returns are positively correlated with the level of debt to equity of common stocks.Fama and French (1992) researched for the addition of independent variables in the CAPM to improve upon its explanatory power, expanding CAPM, thus, developing an asset pricing model.They concluded that a significant portion of the cross-sectional dispersion in the mean returns could be explained by exposures to two factors other than the excess market returns, a "size" factor, and a "value" factor based on the BE/ME ratio.

LITERATURE REVIEW
There are many plausible explanations relating to why stocks with high BE/ME ratio (value stocks) outperform the growth stocks.Fama andFrench (1992, 1996)

Applicability of Fama-French model in India
In the Indian context, Connor and Sehgal (2001) constructed six equally weighted portfolios on common stocks between 1989 and 1998 and inferred that cross-sectional mean returns are explained by three factors and not just market beta alone.The results were consistent with Fama-French three-factor model.Mohanty (2002) used Fama-Macbeth regression 2 to verify whether the cross-sectional variations in stock returns could be explained by size, value, price earning ratio, and leverage.He found a negative correlation between "size" factor and returns and between "value" factor and returns.Sehgal and Tripathi (2006) also found Fama-French to be a superior model to CAPM in explaining stock returns.Taneja (2010) found high correlations between the size and value factors in the Indian market and concluded that any of the two factors could be used to improve the model.
Thus, based on these past studies, this study hypothesizes that: H1: Fama-French three-factor model is superior to the Capital Asset Pricing Model in explaining cross-sectional variations in the mean returns from the stocks.

Test of market integration using asset pricing models
For the test of capital market integration, the first empirical testing was of Solnik (1974) who, in a series of papers, argued that an investor should diversify internationally to reduce risk.His findings include that international diversification leads to greater risk reduction than domestic diversification in the US.He used Fama-Macbeth regression using Merton's International Asset Pricing Model (IAPM) and could not reject integration in seven European countries.Stehle (1977) did research on the US stocks and could not reject both integration and segmentation.In the Indian context, market integration was studied using price correlation by Mukherjee and Mishra (2007), whose study rejected market integration for the period 1990-2005 using pooled regression technique.Gupta and Guidi (2012) studied the integration of the Indian market and the Asian stock markets and suggested the presence of a short-run relationship between these markets, but the absence of a long-run relationship.
Therefore, the following hypotheses have been developed: H2a: Indian capital markets are integrated with global markets.H2b: Indian capital markets are segmented from global markets.

Data
Adjusted monthly closing prices, market capitalization, price to book ratio, index closing prices of 3 For the missing observations, where data points were missing for a day with available preceding and succeeding values, the arithmetic mean of the 2 was used as a replacement.Then, the gaps in our time series data were filled using the Stata's time-series operators.
the S&P BSE 500 Index and the stocks comprising this Index were obtained for 16 years starting from September 2003 to September 2019, from CMIE PROWESS IQ.The book equity to market equity ratio was obtained for the end of fiscal year along with market capitalization at the end of September for the sample companies.S&P BSE 500 Index is a free-float broad-based index, which covers 93% of total market capitalization of companies listed on Bombay Stock Exchange.These 500 listed companies in the Indian stock market comprise all major twenty industries of the economy.Only non-financial firms were incorporated in this analysis, reducing the number of firms from 500 to 398.The exclusion of financial firms can be attributed to differences in financial statements for financial firms.Further, the number of sample firms varied from 222 in 2003 to 362 in 2019 (Table A1) due to non-availability of data for all relevant companies throughout the entire sample period.For analysis, the monthly prices data were converted into percentage monthly return series, which had been calculated, taking into account only the component involving capital gain because of low dividend yields for Indian companies.The riskfree rate of return was derived from T-91 Bill implicit yields, determined by auctions, which were obtained from the Reserve Bank of India Database.
For the test of integration, additional data of the United States, which included market returns, risk-free rate, and their "size" and "value" factors for the period October 2003 -September 2019 were sourced from the Kenneth R French data library.
For Johansen cointegration test, daily stock price indices for S&P BSE 500 and S&P 500 (US) were obtained for 8 years starting from October 2011 to September 2019 3 .The US INR exchange rates were used to convert the price indices for the Indian market obtained in local currency into US dollars.

Construction of the "size" and "value" sorted portfolios
In this study, two additional factors, one based on size and the other based on value, were used along with excess returns to the market portfolio.For the "size" factor, at the end of September of year t, These annual portfolios were formed at the end of September to account for the time lag between the time of financial closing and annual reports and board decision publications.Firms, which had been listed for less than two years, were excluded from the analysis.Finally, all these six portfolios were used to calculate the explanatory variables in the study, namely SMB (small minus big) and HML (high minus low).

Factor calculations
The market factor denoted as the risk premium was computed as an excess of monthly market returns (represented by S&P BSE 500 Index monthly returns) over risk-free monthly rate of return.SMB (small minus big), used as a proxy for size effect was obtained for each month of sample period using the difference between the equally-weighted average return of three portfolios comprising the small stocks over the equally-weighted average return of the three portfolios comprising the big stocks.This factor was devoid of BE/ME effects.Similarly, the HML (high minus low), used as a value proxy was calculated as the excess of equally-weighted average returns of two high BE/ME stock portfolios over the equally weighted mean returns of stocks with low book to market equity ratio for each month.This component of the model was calculated to be free of size effect.

Fama-French model estimation for the Indian stock market
Monthly excess mean returns for all the six portfolios were estimated.Finally, the excess returns on the portfolios were regressed using Fama-French three-factor time series regression estimation as follows: ( ) [ ] τ are sensitivities of the portfolio returns to "market" factor, "size" factor, and "value" factor, respectively, on portfolio .i Obtaining statistically significant results for values of the slope coefficients of three above factors would demonstrate that the respective factors explain cross-sectional variations in the portfolio returns.By adding and eliminating one of the explanatory variables at a time, the test variants of this model were obtained, and the obtained values of the adjusted R 2 were compared with each other.Ordinary least squares method of estimation was used for the analysis of this study.

Test of market integration using the Fama-French model
Following the test procedure used by Brooks et al. (2009) in the Chinese market to test integration vs segmentation and Beaulieu, Gagnon, and Khalaf (2009) to test integration in North American markets, the previously formed six portfolios were used as test assets.
An augmented model for asset pricing was constructed for Indian market securities.If the market is fully segmented, the only priced risk factor in the international version of Fama-French model is with respect to Indian index returns.If the market is fully integrated, the priced risk factor is with respect to this mean-variance efficient global index returns, which in case of this study was represented by US market index returns.Considering the markets to be fully integrated, the procedures are as follows.
In Fama-French model: where it R is the random return on stock i at time , t ( ) it ER is the rational expectation 5 To test the hypothesis of market integration, the above completely international version of Fama-French model was reformulated as follows: The parameters ij σ and , i δ where i, j = 1, 2, 3, 4, 5, and 6 in the system of equation ( 6) were jointly estimated using the technique of Nonlinear Seemingly Unrelated Regression (NSUR), which is a non-linear variant of the technique, which was described by Zellner (1962), based on the procedure followed by Brooks et al. (2009).Since the study needed joint estimation of the coefficients for six equations, NSUR was an efficient method and preferable over maximum likelihood in this case, as it did not require normality assumption of error terms to give unbiased results.

Johansen cointegration test
Johansen cointegration test was also conducted to further support this argument.To proceed with the cointegration test, it was necessary to ensure that both the time series variables were integrated at order one.To do so, the study used the Augmented Dickey-Fuller Unit Root Test on both the time series, the lag length for which was selected based on Schwarz Information Criterion.After establishing the series to be I(1), the common lag length for estimation of the Johansen cointegration test was selected based on Akaike Information Criteria, Hannan and Quinn Information Criteria, Swartz-Bayes Criteria, the Final Prediction Error Criteria, all of which suggested it to be 4 days by estimation of an unrestricted VAR model first.After ascertainment of lag length, the test was conducted, based on a linear deterministic trend (restricting the cointegrating equations to be stationary around constant means) on the stock price indices transformed in their natural logarithmic forms.

RESULTS
For the test of the applicability of Fama-French three-factor model in India, the ordinary least squares method was used with the six portfolios as response variables and MKT, SMB, and HML as three explanatory variables.Since the data were time series in nature, the stationarity of data was tested.Other tests like test for multicollinearity, autocorrelation, tests for heteroscedasticity were done to ensure the robustness of results.

Descriptive statistics
Table A2 represents the descriptive statistics for variables used in the analysis.As evident from the mean results, there existed an inverse relationship between the size of stocks and average returns as the mean returns for the portfolios were increasing as the size was decreasing, keeping the value constant.The small stocks supported the results that there exists a strong positive relationship between the average returns and the value of stocks.However, the big stocks failed to establish any such definite relationship as for big stocks, the mean re-6 P-values of 0.077 and 0.120, respectively.
turn of high-value stock was not maximum.The standard deviations for the excess returns of value stocks were higher in the case of both the small and big stocks, thus, re-establishing the intuitive fact that the value stocks are more volatile than their counterparts.

Correlation analysis
Table A3 shows the correlation between the explanatory variables.As evident from the results, all the explanatory variables were weakly correlated.Hence, having these independent variables in the model did not lead to the origination of the problem of multicollinearity.

Test of Fama-French model in India
Firstly, coefficients of CAPM were estimated by taking only the market factor as an independent variable, the results for which are reported in Table 1.These results showed that market factor is by far the most important factor in explaining stock returns.Table 2 includes the results of estimating Fama-French three-factor model and its variants.On adding "value" factor or "size" factor to this market factor, the adjusted R 2 increased and, hence, the two-factor model explained asset returns better than a single factor.It was an interesting observation that in general, small stocks had a better adjusted R 2 than big stocks on adding "size" factor as compared to "value" factor in explanatory variables.This suggested that the size effect is stronger in small stocks.This effect, though present in big stocks, was often overruled by adding "value" factor as stocks, which were bigger in size, showed better adjusted R 2 values by adding HML (value) rather than SMB factor (size).
The results for the CAPM had a better adjusted R 2 value than the variant of Fama-French model having the combination of the SMB and HML factor as the explanatory variable.This proved that the market factor is the most important in explaining excess returns.By adding all three factors together, it appeared that values for adjusted R 2 were more than CAPM in all cases, and all factors were statistically significant, except SMB factor in case of B/M & B/H 6 .These results proved that Fama- Note: This table presents the results obtained on estimation of CAPM.The values for the coefficients are mentioned along with their standard errors in the parentheses.Significance at 0.1% level is denoted by **.These results have been estimated based on the equation: French three-factor model is more pervasive in the Indian context than CAPM and, hence, this model was used in the further study of market integration for the Indian stock market.

Test of market integration using Fama-French three-factor model
The estimated premia z values and their standard errors obtained from NSUR method on equation ( 6) are mentioned in Table 3.In the test of market integration, the study used excess returns for the same six size and value sorted portfolios as dependent variables.Independent varia-bles were US "market", "size" and "value" factors along with corresponding orthogonalized domestic factors.For complete integration, at least one of the US risk premium ( ) 123 ,, δδδ should be statistically different from zero, and none of the domestic risk premiums must be different from zero ( ) 456 ,, .

δδδ
In the complete period of 16 years, none of the US factor, as well as the domestic factor, was statistically significant.For integration, one of the US factors should have been significantly priced, whereas none of the domestic factors should have been statistically priced.To gain more insights into these results, the complete sample period was broken into two subparts of 8 years each, i.e., from October 2003 to September 2011 and from October 2011 to September 2019.For the sub-period, October 2003 -September 2011, none of the US factors was statistically significant, whereas the domestic orthogonalized factor nt SMB′ was significant at 5% level.Hence, the integration hypothesis in which at least one US factor is statistically significant, whereas none of the domestic factors is statistically significant, was rejected in favor of market segmentation.
In the sub-period October 2011 -September 2019, again, none of the US factors was statistically significant, and none of the domestic factors was statistically significant at 5% level of significance.However, nt SMB′ was statistically significant at 10% level, but not at 5% level, suggesting that there is a movement from market segmentation towards market integration in the second sub-period.

Johansen cointegration test
Since the results for the second sub-period were suggestive of weak integration of the Indian and global markets (indicated by US markets), Johansen cointegration test was employed to further verify these results.The results of the stationarity test in Table A4 suggest that the indicative stock price indices in their natural logarithmic level are non-stationary series.On the other hand, the two series were stationary in their first difference form, which suggested that the series for the representative indices in the study were integrated at first order.
As shown in the output in Table 4, when the number of cointegrating equations was hypothesized to be 0, the study strongly rejected the null hypothesis of no cointegration because the trace statistic at r = 0, 37.4922 exceeded its critical value of 15.41.On the other hand, the trace statistic at r = 1 of 2.5485 was less than the critical value of 3.76; hence, it failed to reject the null hypothesis of at most one integrating equation.Thus, the number of cointegrating equations in the bivariate model of the natural logarithm transformed the Indian and US stock price indices estimated to be 1.Hence, in the second sub-period, statistical evidence was found for the cointegration among the two markets.
Thus, the results obtained from Johansen cointegration test further supported the results of the augmented Fama-French three-factor model, which suggested a weak integration of the global and Indian stock markets in the second sub-period.Note: This table reports the results obtained from Johansen cointegration test, performed in the second sub-period.The trace statistic has been computed using the eigenvalue in the line below it.* indicates that Johansen multiple-trace test procedure has been used to select the corresponding value of LL: Likelihood.

DISCUSSION
Integration is when investors earn the same risk-adjusted expected return on similar financial instruments in different national markets.Risk, which is non-diversifiable in international capital market, demands higher returns, whereas internationally diversifiable risk, not capable of being diversified domestically, does not involve positive premiums (Stehle, 1976).The present study, when compared to the existing literature, yields similar results as obtained by Mittoo (1992) for the Canadian stock market for the period 1977-1986.This can be a result of reducing or eliminating many regulatory restrictions in early 1974 such as removal of capital flow restrictions by the United States.However, the findings of this study contradict the analysis of Brooks, Iorio, Faff, and Wang (2009), which suggested a complete segmentation of the Chinese and US markets, with no statistical evidence of movement towards the integration between two markets.This hampering in the integration of the markets can be attributed to the control over the capital flows exercised by the Chinese government.The Indian government, on the other hand, is progressively relaxing its capital flow restrictions, though still making attempts to discourage the capital flow instability.

CONCLUSION
The results of this study are consistent with previous empirical studies, which have advocated a superiority of three-factor model over CAPM.After establishing this superiority, this study showed that using Fama-French three-factor model, it cannot be still inferred that markets are integrated for the entire sample period.This suggests that there still exist barriers to entry and exit, capital outflow restrictions, and some undeveloped markets evidence.The past two decades have seen a remarkable improvement in the financial sector of the country; however, the scope of these reforms and approaches may have to be revisited in the current time period (Bhattacharya & Patel, 2003).
In the later sub-period, it could be inferred that there is movement from market segmentation to market integration; however, this movement is slow, and it would take yet another decade or two to support integration on a statistical basis.Indian capital market has increased in both depth and breadth in the last decade.Political stability, various government measures to increase transparency, efficiency by reducing bottlenecks have started to show the results.The implementation of Goods and Services Tax one nation and one tax policy is a serious step to move towards market economy.Merging several banks to make stronger and larger banks are all efforts to make the Indian market ready for integration with global markets.
Jorion and Schwartz (1986) consumption-based asset pricing model and predicted an asset pricing line using monthly data in the US between January 1960-1985 and could not accept that market integration holds.Jorion and Schwartz (1986)examined the Canadian market integration with North American Market between 1963 and 1982 using both domestic and international versions of CAPM to reject the hypothesis of integration, i.e., no evidence of a mean-variance efficient global market portfolio.Errunza, Losq, and Padmanabhan (1992) used Non-Linear Seemingly Unrelated Regression (NSUR) to deduce that for emerging markets, the markets are neither fully integrated nor fully segmented.
Brooks et al. (2009).21511/imfi.17(2).2020.10Mittoo(1992)usedCAPM and APT on the Canadian stocks to conclude segmentation for the period 1977-1981 and integration for the period 1982-1986.Brooks et al. (2009)suggested that the Chinese stock market is segmented from the US market, and the government's restriction on capital flows is preventing the integration of the Chinese market with global peers.

Table 1 .
Test results for the capital asset pricing model in the Indian stock market Source: Calculated by the authors based on the data available on Prowess IQ database.

Table 2 .
Test results for Fama-French three-factor model in the Indian stock market Source: Calculated by the authors based on the data available on Prowess IQ database.

Table 2 (
cont.).Test results for Fama-French three-factor model in the Indian stock market This table reports the coefficients of Fama-French three-factor model.The standard errors for these estimates are mentioned in the parentheses.Significance at 1% and 0.1% levels are denoted by * and **, respectively.The test variants for the model were estimated by eliminating the explanatory variables in the equation: (2)e:http://dx.doi.org/10.21511/imfi.17(2).2020.10

Table 4 .
Johansen cointegration test resultsSource: Calculated by authors based on the stock price indices for the two countries.

Table A2 .
Descriptive statisticsSource: Calculated by the authors based on the data available on Prowess IQ database.This table presents the summary statistics for the variables used in the estimation of Fama-French model in this study.S/L-R f , S/M-R f , S/H-R f , B/L-R f , B/M-R f ,and B/H-R f : the excess returns for the portfolios S/L, S/M, S/H, B/L, B/M, and B/H, respectively, over the risk free return, MKT: market risk premium, SMB: size premium, HML: value premium. Note: