Superiority of six factor model in Indian stock market

Prasad, Saroj S.; Verma, Ashutosh; Bakhshi, Priti; Prasad, Shantanu Article Superiority of six factor model in Indian stock market Cogent Economics & Finance Provided in Cooperation with: Taylor & Francis Group Suggested Citation: Prasad, Saroj S.; Verma, Ashutosh; Bakhshi, Priti; Prasad, Shantanu (2024) : Superiority of six factor model in Indian stock market, Cogent Economics & Finance, ISSN 2332-2039, Taylor & Francis, Abingdon, Vol. 12, Iss. 1, pp. 1-14, https://doi.org/10.1080/23322039.2024.2411567 This Version is available at: https://hdl.handle.net/10419/321625 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Cogent Economics & Finance ISSN: 2332-2039 (Online) Journal homepage: www.tandfonline.com/journals/oaef20 Superiority of six factor model in Indian stock market Saroj S. Prasad, Ashutosh Verma, Priti Bakhshi & Shantanu Prasad To cite this article: Saroj S. Prasad, Ashutosh Verma, Priti Bakhshi & Shantanu Prasad (2024) Superiority of six factor model in Indian stock market, Cogent Economics & Finance, 12:1, 2411567, DOI: 10.1080/23322039.2024.2411567 To link to this article: https://doi.org/10.1080/23322039.2024.2411567 © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group Published online: 08 Oct 2024. Submit your article to this journal Article views: 1131 View related articles View Crossmark data Citing articles: 2 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=oaef20 FINANCIAL ECONOMICS | RESEARCH ARTICLE Superiority of six factor model in Indian stock market Saroj S. Prasad a , Ashutosh Verma b , Priti Bakhshi c and Shantanu Prasad d a Department of Economics & Finance, Birla Institute of Technology & Science, Goa, India; b Indian Institute of Forest Management (IIFM), Bhopal, India; c S P Jain School of Global Management, Mumbai, India; d Goa Institute of Management (GIM), Goa, India ABSTRACT This novel work is the first study in India to incorporate the Human capital (HC) factor as a six-factor asset-pricing model and presents a robust methodology. The aim of this work is to examine the ability of the six-factor model to capture excess returns using a GMM framework with time periods that were missing in previous studies. Therefore, data for this study were collected using the BSE 500 index. Building on this insight, this study attempts to explain the inherent risk factors (firms and markets) that predict returns over a period of time, considering the dynamics of the Indian market. The GRS test also confirms the superiority of the six-factor model for the Indian equity market. The study asserts that the Instrumental variableGeneralized method of moments (IVGMM) is a robust model over OLS in explaining portfolio returns (single and bivariate), which implies that OLS in the asset pricing model is exaggerated in the Indian context. Single portfolios are constructed based on the factors of size, value, ROE, INV and human capital, while bivariate portfolios are constructed based on the intersection of any these two factors. This study confirms the significant role of HC (wealth) in describing the stock returns of an economy. This study contributes to the ongoing discourse on asset pricing models and offers valuable implications for investment decisions, risk management, and portfolio construction in one of the most attractive global financial markets. IMPACT STATEMENT This novel work is the first study in India to incorporate the Human capital (HC) factor as a six-factor asset-pricing model and presents a robust methodology. The aim of this work is to examine the ability of the six-factor model to capture excess returns using a GMM framework with time periods that were missing in previous studies. The study asserts that the Instrumental variableGeneralized method of moments (IVGMM) is a robust model over OLS in explaining portfolio returns (single and bivariate), which implies that OLS in the asset pricing model is exaggerated in the Indian context. Single portfolios are constructed based on the factors of size, value, ROE, INV and human capital, while bivariate portfolios are constructed based on the intersection of any these two factors. This study confirms the significant role of HC (wealth) in describing the stock returns of an economy. This study contributes to the ongoing discourse on asset pricing models and offers valuable implications for investment decisions, risk management, and portfolio construction in one of the most attractive global financial markets. ARTICLE HISTORY Received 17 April 2024 Revised 16 September 2024 Accepted 27 September 2024 KEYWORDS Asset pricing model; Human capital; Indian market; GMM; GRS; Financial market SUBJECTS Investment & Securities; Mathematical Finance; Quantitative Finance; Statistics for Business, Finance & Economics JEL CLASSIFICATION G120 1. Introduction Substantial empirical finance research addresses the correct valuation of financial assets (Santoni & Salerno, 2023). While the CAPM (Sharpe, 1965; Lintner, 1965) explains the linear risk-reward relationship, the identification of various factors that significantly contradict the model has called into question its global validity. Fabozzi and Francis (1978) conclude that the beta coefficient of the stock varies randomly over time and contradicts the basic assumptions of the CAPM. Therefore, the above discussion sheds CONTACT Priti Bakhshi [email protected] S P Jain School of Global Management, Mumbai, India ß2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. COGENT ECONOMICS & FINANCE 2024, VOL. 12, NO. 1, 2411567 https://doi.org/10.1080/23322039.2024.2411567 light on the limitation of CAPM beta in capturing other inherent market risks, and its stability has challenged the asset pricing framework globally (Sharpe, 1965). According to Bos and Newbold (1984), microeconomic variables such as the phase of the country’s business cycle, inflation rate, and the company’s business environment determine the beta of stocks. Fama and French (1993) extend CAPM by adding value (HML) and size (SMB) as key factors in explaining the excess returns of stocks. Carhart (1997) extends the Fama-French three-factor model by adding a momentum factor to the model and reports that this improves the explanatory power of the model for mutual fund performance. Following the approach of Miller and Modigliani (1961), Fama and French (2015) subsequently proposed profitability (RMW) and investment (CMA) as two additional factors that provide a better R2 (71% and 94%) in achieving excess returns. Chronologically, Chiah et al. (2016) also proposed the FF five-factor model as a better asset pricing model in international stock markets. However, both assumptions that only the beta factor influences asset pricing and market is efficient are contradicted by market anomalies reported in the literature, such as the size effect (Banz, 1981), value effect (Stattman, 1980), price-earnings ratio (Basu, 1983), firm leverage (Bhandari, 1988) and high dividend yield (Fama, 1998). As anomalies have no theoretical basis and cannot be explained by economic theories, this has led to the development of empirical, research-based factor models. This shows that the asset pricing model has always been expanded into a multifactor model with a new significant factor, whereby these multifactor models mimic the risk factor differently. Fama and French (1992) best-known three factors aim to provide a more comprehensive explanation of stock returns relative to CAPM, particularly in explaining the returns of small-cap and value stocks. The model was then transformed into a five-factor model by including profitability and investment factors to capture the variation in the average returns of diversified stock portfolios (Fama and French 2015). Despite their popularity, these models have conflicting results in markets and limitations in studies worldwide, which has always been a source for exploring a robust model. Looking at a broader market for ten countries, Lalwani and Chakraborty, (2020) find that the Fama-French five-factor model using GRS statistics and average absolute intercepts fits stock pricing for four countries well. However, the study may have relied on the cross-sectional data. Khudoykulov (2020) pointed out the crucial performance of the threeand five-factor models over the CAPM beta model while explaining portfolio returns in the Indian market from 2009 to 2018. In their study, Bhatti and Khan (2022) take a large sample of 25 emerging economies covering a sample period of 21 years, further divided into pre-crisis, crisis and post-crisis periods, and find that the performance of the three-factor model in the Asian region. The authors also introduce the 10-factor asset pricing model and confirm its applicability to the American market. However, the study lacks consistency in the proxies used for profitability, investments, liquidity and leverage. Recently, a new factor proposed by Park et al. (2024) tests the asset pricing model and simultaneously introduces COVID-19 as a pricing factor in the asset pricing model. The study uses the two-step GMM model and examines the relationship between the COVID-19 factor measured as pandemic risk and stock returns, indicating that it has a significant positive risk premium. Although the study is the first to propose COVID-19 as a factor in asset pricing, its applicability in different countries needs to be empirically tested. Apparently, the Fama-French models in India also have different results and are inconclusive. Therefore, various other factors have been identified for constructing an optimal portfolio. One of the risk-mimicking factors ignored by asset pricing models is human capital (HC). Mayers (1972)pointsout that individuals may hold significant portions of their wealth in non-marketable assets (HC), which cannot be easily traded in financial markets. Consequently, the existence of these non-marketable assets affects individuals’portfolio selection and investment strategies. Similarly, Kim et al. (2011) suggested that HC has predictive value in explaining asset returns. However, HC is gaining popularity (Campbell, 1996) and is recognized as an important factor in the asset pricing model. This study measures HC as an asset of the company and has an additive effect with regard to size and value factors. Campbell (1996) emphasized that human capital reflects the true wealth of the economy and should, therefore, be part of the asset pricing framework. Jagannathan and Wang (1996) find that CAPM can better explain more than 50% of the differences in cross-sectional returns when market returns are replaced by human capital. Later, Belo et al. (2017), Kuehn et al. (2017) confirm that human capital is an important determinant in measuring cross-sectional stock returns. The HC multifactor model is later referred to as the six-factor asset pricing model. Therefore, the above studies in various international markets support the HC-based multifactor model and 2 S.S. PRASAD ET AL. confirm its superior performance in global markets. Several studies have demonstrated the presence of human capital in the multifactor model in the international market (Belo et al., 2017; Kim et al., 2011; Kuehn et al., 2017; Lettau, & et al., 2019). Similarly, Maharani and Narsa (2023) found that intellectual capital plays a role in explaining asset returns in the Indonesian stock market for the period 2012–2022. Khan et al. (2023) highlights the importance of human capital in investment decisions and recommends investors consider the size, value and human capital while valuing the firms. The study extends the Fama-French three-factor by including human capital as the fourth factor and has shown its validity for Pakistani firms. However, the study uses a smaller number of portfolios for analysis. Anuno et al. (2023) note the applicability of the Fama-French five-factor model in Timor-Leste and emphasize that the SMB and HML factor contribute negatively to the excess returns, while the profitability factor contributes positively to explaining the returns. Since Timor-Leste is a low-income country, the study can use human capital as a sixth factor in asset pricing as the country has the growth potential of human capital. Although the HC-based multifactor model is widely accepted worldwide, its validity must be tested in emerging markets. Among the emerging markets, the Indian economy has witnessed tremendous growth across all sectors over the last decade. India ranks fifth among the top ten countries in terms of gross domestic product (GDP) in the world, India 1 ranks fifth among the top 10 countries and is expected to be the third 2 most powerful country by 2030. India’s exponential growth was the original motivation for research in the Indian market. Ironically, two studies on the six-factor asset pricing model also motivate us to investigate its existence in the Indian market. Some of the notable contributions to the six-factor multifactor model are from Shijin et al. (2012), who state that the HC-based multifactor model offers more predictive returns than the single-index model for the Indian market for 1996–2006. The authors exclusively used Granger causality tests, OLS regression, and impulse response functions for the Nifty 50 index. Maiti and Balakrishnan (2018) also report that the six-factor model reflects return patterns better than the threeand five-factor Fama-French models. This study uses GRS tests, 3D graphs, regression models, and residual graphs for BSE-500 index companies for the period 2004–2016 to examine HC in capturing returns on assets. It is pertinent to note here that the human factor as the sixth asset pricing model has received significant attention in the global market but has not received significant attention in the Indian market in recent times after 2017. India, with its vibrant and rapidly evolving stock market and diverse offerings of stocks from various sectors and industries, requires an investigation of the effectiveness and superiority of the six-factor model. Therefore, our study extends previous work in the context of a competent asset-pricing framework in the Indian market. This novel work is the first study in India to incorporate the HC factor as a six-factor asset-pricing model and presents a robust methodology. The two previous studies in this area are very limited and are, therefore, looking for methods that demonstrate agreement between them. The available literature on the six-factor model in India is limited to the study period of 6–7 years ago. There is a need for a study to propose a benchmark model for pricing assets in the Indian stock market while covering the pandemic (COVID-19) period, as there is no analysis in this area covering the period before, during and post-COVID-19. The aim of this work is to examine the ability of the six-factor model to capture excess returns using a GMM framework with time periods that were missing in previous studies. Since, GMM shows its potential when the cross-sectional heteroscedasticity of the data exists and the collected time series data is small (Kiviet et al., 2017). Furthermore, GMM provides a framework for addressing endogeneity issues by using instrumental variables or moment conditions to identify and estimate causal relationships between variables. Additionally, the conventional static approach of the Fama-French model may be mis-specified mis specified because its parameters have time-varying properties (Racicot et al. (2019). 2. Data For the Indian market, the BSE 500 is one of the best choices for all equity indices, as it has a strong relationship with all macroeconomic variables (Chaudhary & Bakhshi, 2021). Therefore, for this study, data was collected for companies listed in the BSE 500 index. The BSE 500 index covers the top 20 sectors of the Indian economy and represents 93% of the total BSE market capitalization 3 . Of the 500 companies listed on the BSE 500 Index, the data include only 280 4 companies for the 19-year study COGENT ECONOMICS & FINANCE 3 period, that is, from June 2002 to July 2021 (Maiti & Balakrishnan 2018), from the CMIE Prowess database. From the initial sample of BSE 500 listed companies, we removed companies whose market capitalization (MC) for size factor data for a period of 19 years are inadequate or irregular. This process is repeated for other factors: BM ratio (book value to price ratio) for value, ROE (return on equity) for profitability, INV (annual growth in total assets) for investments, and HC (salaries and wages) for human capital for the study period. As the list of companies has changed due to further incorporations and; Mergers and amalgamations of companies. Likewise, companies with irregularities in their closing prices are removed from the sample. In the end, we left with 280 companies for which the data is complete for all factors and for each year. The data is secondary in nature. Although the study uses a rigorous data collection methodology, the analysis conducted in the study acknowledges the possibility of survival bias, which can be considered as one of the limitations. Selection bias, also known as survivorship bias, is the tendency to include survivors in an analysis and those who failed, dropped out, or were otherwise removed are omitted. This is called ‘survivorship bias,’a type of selection bias. Failure to consider all available data, particularly those lost during the investigative process, could lead to overly optimistic conclusions. Elfakhani and Wei (2003) examined the survivorship bias, the stock price effect, and the small firm effect in Canadian financial markets. The study found evidence of survival bias in Canadian stock returns, with the returns of surviving companies being higher than the returns of the entire sample of companies. Previous studies by (Brown & Goetzmann, 1995; Grinblatt & Titman, 1993; and Malkiel, 1995) emphasized the existence of survivorship bias when examining the performance of mutual funds. In the Indian context, Agarwalla, et al. (2013) argued that the survival bias found in their study is negligible since the sample is from the Bombay Stock Exchange (BSE), which is similar to our sample. Therefore, the results of our study may also be negligible or overestimate the presence of survival bias. Hence, for the robustness of results, we recommend that subsequent studies, when conducted in the same area, should aim to include comprehensive data from all subjects, including those who do not survive the study. Employing techniques such as survival analysis or multiple imputation for missing data can help mitigate this bias and provide a more accurate representation. The motivation of the study is to take a long period of time for the robustness of the result. Both the initial and final periods of the study show stability in the Indian stock market after the global crisis, which is considered a normal period for conducting the analysis. The Indian stock market seems to be recovering since March 2002 after a massive terrorist attack (September 11) and is showing momentum after the global COVID-19 crisis. However, this period also includes a global recession in 2008. 3. Methodology The proxies for measuring the six factors are market capitalization (MC) for size, BM ratio (book-to-price ratio) for value, ROE (return on equity) for profitability, INV (annual growth in total assets) for investments, and HC (salaries and wages) for human capital. However, while operating profit measures the overall profitability of the company, analysts and investors critically examine ROE to estimate the return on the amount of money they have invested in the company. Additionally, people are more likely to buy shares in a company with a high ROE ratio. Furthermore, existing literature also confirms that ROE is a proxy for profitability (Haugen & Baker, 1996; Maiti & Balakrishnan, 2018). The sample companies were ranked each year in March based on the selected factors, for which monthly log returns were calculated from July 2002 to June 2021. We maintained the standard practice followed by (Prasad & Verma, 2013; Maiti & Balakrishnan, 2018), as it is the most popular practice. To construct five portfolios (P1, P2, P3, P4, and P5), equally weighted portfolios are used for each factor, with P1 representing the lowest rank and P5 the highest rank. The following portfolios were constructed by continuing the existing methodology. 3.1. Single sorted portfolios Single-sorted portfolios for each factor replicate five equally weighted portfolios consisting of 56 stocks each. These are referred to as P1 (the smallest stocks) and P5 (the largest stocks) based on MC, P1 as growth stocks, P5 as value stocks based on the BM ratio, P1 as weak stocks, P5 as robust stocks based 4 S.S. PRASAD ET AL. on ROE, P1 as conservative stocks, P5 as aggressive stocks based on investment, P1 as low compensation stocks, and P5 as high compensation stocks based on salaries and wages. 3.2. Bivariate portfolios Bivariate portfolios are constructed from the intersection of two factors, keeping the size of each factor the same. To construct portfolios based on the MC and BM ratio, companies are divided into two small and large companies based on MC, while companies are divided into Low, Medium and High companies based on the BM ratio. Six portfolios were then formed, referred to as SL, SM, SH, BL, BM, and BH. The same process was expanded to build six portfolios at the intersection of Small and Large (MC) and Robust, Neutral and Weak (ROE), referred to as SR, SN, SW, BR, BN, and BW. The other six portfolios are SC, SN, SA, BC, BN, and BA and are formed by the intersection of MC (Small and Large) and INV (Conservative, Neutral and Aggressive). The final set of six portfolios formed by combining Small and Big (MC) and lower compensation and higher compensation (HC) are SLc, SN, SHc, BLc, BN, and BHc. For each portfolio, excess returns were calculated by subtracting the RBI’s 91-day T-bill risk-free rate from the portfolios’monthly mean returns. This study uses 91-dayT-bills as a proxy for the risk-free rate, and BSE Sensex is selected as a market proxy. This study examines the six-factor model for which the portfolios constructed above are regressed using the six independent variables (SMB, HML, RMW, CMA, and LcMHc) 5 calculated as follows: SMB ¼1=3SLþSMþSH ðÞ −1=3BLþBMþBH ðÞ (1) Where SMB stands for Small minus Big and represents the size risk. HML ¼1=2SHþBH ðÞ −1=2SLþBL ðÞ (2) Where HML stands for High minus Low and represents the value risk. RMW ¼1=2SRþBR ðÞ −1=2SWþBW ðÞ (3) Where RMW stands for Robust minus Weak and represents the profitability risk. CMA ¼1=2SCþBC ðÞ −1=2SAþBA ðÞ (4) Where CMA stands for Conservative minus Aggressive and represents the investment risk. LcMHc ¼1=2 SLcþBLc ðÞ −1=2 SHc þBHc ðÞ (5) Where LcMHc stands for lower compensation minus higher compensation and represents the human capital risk. 3.3. Empirical tests A few recent studies in the field of asset pricing models (Keshari & Gautam, 2022) have used methodologies that still necessitate a comprehensive asset pricing study in the Indian market. Therefore, we used two different statistical methods to ensure the robustness of the model and reveal its applicability. First, we use a joint F-test for a set of portfolios using GRS (Gibbons, Ross and Shanken, 1989). We assume that returns are homoscedastic and not autocorrelated. The GRS test provides F-statistics to test whether the joint absolute value of the intercept is equal to zero, which is based on the following OLS equation: Rit –RFt¼aiþb1i RMt–RFt ðÞ þb2iSMBtþb3iHMLtþb4iRMWt þb5iCMAtþb6iLcMHc þeit (6) However, studies on the Indian market by Maiti and Balakrishnan (2018) and Shijin et al. (2010) require a robust methodology, as there is empirical evidence that the parameter estimates of the sixfactor framework using the IVGMM approach outperform traditional OLS because of specification and measurement errors (Roy, 2020). IVGMM is a stronger model for testing the asset pricing model over Fama Macbeth’s two-pass regression due to its efficiency, robustness, flexibility and ability to address complex econometric issues such as efficiency, endogeneity correction, handling measurement error and robust statistical inference. Moreover, in such complex issues two-pass time series leads to biased results. (Horv ath & Wang, 2021; Jagannathan et al., 2002). In this study, we adopted generalized COGENT ECONOMICS & FINANCE 5 methods of moments, a robust form of the methodology in the asset pricing framework that assumes a minimum standard error and does not require stationary variables. This can be expressed by the following equation: Rit –RFt ¼aGMMi þbGMM1i RMt–RFt ðÞ þbGMM2iSMBtþbGMM3iHMLtþbGMM4iRMWt þbGMM5iCMAtþbGMM6iLcMHc þeit (7) The results of the tests carried out using the Stata statistical software are further explained. 4. Results Table 1 shows that the average excess returns of the P1 portfolios are higher than those of the P5 portfolios for single-sorted portfolios based on six factors (size, value, RMW, CMA, and HC), and the risk associated Table 1. Descriptive statistics for single-sorted portfolios. Portfolios p1p2p3p4p5 MC Returns 0.024 0.010 0.008 0.008 0.005 Risk 0.096 0.093 0.084 0.077 0.073 BV Returns 0.018 0.013 0.011 0.006 0.006 Risk 0.091 0.083 0.081 0.086 0.080 ROE Returns 0.010 0.010 0.012 0.012 0.011 Risk 0.099 0.086 0.082 0.075 0.076 INV Returns 0.014 0.011 0.010 0.010 0.010 Risk 0.092 0.087 0.081 0.078 0.086 HC Returns 0.016 0.013 0.010 0.009 0.006 Risk 0.094 0.085 0.082 0.080 0.078 Note. Return and risk are the mean and standard deviation of the portfolios. Table 2. Correlation matrix of independent variables. Sensex SMB HML RMW CMA LcMHc Sensex 1 SMB −0.030 1.000 HML 0.036 −0.433 1.000 RMW 0.033 0.648 −0.142 1.000 CMA −0.018 0.206 0.447 0.073 1.000 LcMHc 0.020 0.147 −0.085 −0.010 −0.004 1 Note. Computed by authors. Table 3. Descriptive statistics for double-sorted portfolios. MC/BV Portfolios SL SM SH BL BM BH Returns 0.201 0.022 0.104 0.042 0.092 0.165 Risk 1.077 0.125 0.556 0.284 0.469 1.021 MC/ROE Portfolios SR SN SW BR BN BW Returns 0.174 0.207 0.111 0.078 0.108 0.166 Risk 0.901 1.097 0.556 0.373 0.561 1.003 MC/INV Portfolios SC SN SA BC BN BA Returns 0.097 0.128 0.104 0.103 0.085 0.097 Risk 0.571 0.736 0.523 0.546 0.515 0.537 MC/HC Portfolios SLc SN SHc BLc BN BHC Returns 1.056 −0.577 0.737 −0.470 0.902 −0.385 Risk 6.177 3.005 4.281 3.383 6.014 2.426 Note. Return and risk are the mean and standard deviation of the portfolios. 6 S.S. PRASAD ET AL. with the portfolio is also higher. This implies historical outperformance of (small-cap stocks relative to large-cap stocks, value stocks relative to growth stocks, high profitability ratio stocks relative to low profitability ratio stocks, and conservative investment stocks over aggressive investment stocks low compensation stocks over high compensation stocks). Based on ROE, the average return of the P5 portfolio is slightly higher than that of the P1 portfolio, indicating that investors prefer to invest in stocks that offer higher returns on the investments they make. Additionally, the risk associated with the P1 portfolios is higher across all factors, indicating higher volatility in market movements. Before proceeding with the GRS statistics, we determine the correlation between the independent variables to check for the presence of multicollinearity. Table 2 shows that the correlation between the variables is less than 0.50 in all cases, indicating that none of the independent variables are correlated with each other and therefore there is no multicollinearity between them. Table 3 presents that the average excess returns of small portfolios (SL, SR, SC and SLc) are higher than those of large portfolios (BH, BW, BA and BHc) for bivariate sorted portfolios. The risk associated with the portfolios is also higher, which suggesting a risk-reward ratio. Table 4 shows the results of the GRS tests of the six-factor model for the single-sorted portfolio based on size, value, RMW, CMA, and HC with the null hypothesis that the mean absolute alpha is zero. The rejection of the null hypothesis and the fact that the mean absolute alpha is closer to zero demonstrate the ineffectiveness of the factor model in explaining returns. These results clearly show that all single portfolios sorted by size and value are rejected, while the RMW, CMA, and HC sorted portfolios are accepted by the GRS test, suggesting the superiority of the six-factor model. Table 5; on the contrary, the six-factor model was found to be under-specified in explaining the returns, showing that the joint Table 4. GRS test results for single-sorted portfolios. Portfolios GRS pValue Mean absolute alpha AR 2 Size P1-P5 7.474 0.0000.004 0.107 Value P1-P5 3.793 0.0030.004 0.123 ROE P1-P5 0.547 0.740 0.004 0.113 INV P1-P5 0.547 0.740 0.004 0.113 HC P1-P5 1.330 0.253 0.004 0.120 Note. GRS statistic with the corresponding p-value at the 5% significance level. Table 5. GRS test results for bivariate portfolios. Portfolios GRS pValue Mean absolute alpha AR 2 MC/BV 0.380 0.891 0.005 0.840 MC/ROE 0.597 0.733 0.010 0.896 MC/INV 0.265 0.953 0.005 0.900 MC/HC 562.925 0.0000.317 0.265 Note. GRS statistic with the corresponding p-value at the 5% significance level. Table 6. Relevance test results for robust instruments. Alpha Sensex SMB HML RMW CMA HC F-Statistics Sensex 0.007 –−0.028 0.007 0.016 −0.006 0.001 0.326 1.467 −0.636 0.293 0.931 −0.246 0.500 SMB −0.005 −0.062 –−0.334 0.272 0.291 0.012 94.660 −0.800 −0.640 −12.050 14.090 9.300 2.890 HML −0.007 −0.054 −1.181 –0.237 0.661 0.005 52.190 −0.590 0.290 −12.050 5.020 12.420 0.670 RMW 0.042 0.231 1.734 0.429 –−0.370 −0.024 43.730 2.390 0.930 14.090 5.020 −4.130 −2.280 CMA 0.011 −0.044 0.963 0.619 −0.192 –−0.007 34.870 0.890 −0.250 9.300 12.420 −4.130 −0.980 HC 0.325 0.755 2.914 0.368 −0.919 −0.549 –2.130 3.010 0.500 2.890 0.670 −2.280 −0.980 Note. Regression results for each explanatory variable for all instruments with their corresponding F-statistics. COGENT ECONOMICS & FINANCE 7 Keshari, A., & Gautam, A. (2022). Asset pricing in global scenario: A bibliometric analysis. IIM Ranchi Journal of Management Studies,2(1), 48–69. https://doi.org/10.1108/IRJMS-02-2022-0025 Khan, N., Zada, H., Ahmed, S., Shah, F. A., & Jan, S. (2023). Human capital-based four-factor asset pricing model: An empirical study from Pakistan. Heliyon,9(5), e16328 10.1016/j.heliyon.2023.e16328 Khudoykulov, K. (2020). Asset-pricing models: A case of Indian capital market. Cogent Economics & Finance,8(1), 1832732. https://doi.org/10.1080/23322039.2020.1832732 Kim, D., Kim, T. S., & Min, B. K. (2011). Future labor income growth and the cross-section of equity returns. Journal of Banking & Finance,35(1), 67e81–67e81. https://doi.org/10.1016/j.jbankfin.2010.07.014 Kiviet, J., Pleus, M., & Poldermans, R. (2017). Accuracy and efficiency of various GMM inference techniques in dynamic micro panel data models. Econometrics,5(1), 14. https://doi.org/10.3390/econometrics5010014 Kuehn, L., Simutin, M., & Wang, J. J. (2017). A labor capital asset pricing model. The Journal of Finance,72(5), 2131– 2178. https://doi.org/10.1111/jofi.12504 Lalwani, V., & Chakraborty, M. (2020). Multi-factor asset pricing models in emerging and developed markets. ManagerialFinance,46(3), 360–380. 10.1108/MF-12-2018-0607 Lettau, M., Ludvigson, S. C., & Ma, S. (2019). Capital share risk in U.S. asset pricing. The Journal of Finance,74(4), 1753–1792. https://doi.org/10.1111/jofi.12772 Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. The Review of Economics and Statistics,47(1), 13–37. https://doi.org/10.2307/1924119 Maharani, A., & Narsa, I. M. (2023). Six-factor plus intellectual capital in the capital asset pricing model and excess stock return: Empirical evidence in emerging stock markets. Cogent Economics & Finance,11(2), 1-17. https://doi. org/10.1080/23322039.2023.2252652 Maiti, M., & Balakrishnan, A. (2018). Is human capital the sixth factor? Journal of Economic Studies,45(4), 710–737. https://doi.org/10.1108/JES-05-2017-0132 Malkiel, B. G. (1995). Returns from investing in equity mutual funds 1971 to 1991. The Journal of Finance,50(2), 549– 572. https://doi.org/10.1111/j.1540-6261.1995.tb04795.x Mayers, D. (1972). Nonmarketable assets and capital market equilibrium under uncertainty. In M. C. Jensen (Ed.), Studies in the theory of capital markets. (pp. 223–e248). Praeger Publishers. Miller, M. H., & Modigliani, F. (1961). Dividend policy, growth, and the valuation of shares. The Journal of Business, 34(4), 411–433. https://doi.org/10.1086/294442 Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica,55(3), 703 10.2307/1913610 Olea, J. L. M., & Pflueger, C. (2013). A robust test for weak instruments. Journal of Business & Economic Statistics, 31(3), 358–369. https://doi.org/10.1080/00401706.2013.806694 Park, D., Kang, Y. J., & Eom, Y. H. (2024). Asset pricing tests for pandemic risk. International Review of Economics & Finance,89, 1314–1334. https://doi.org/10.1016/j.iref.2023.08.014 Prasad, S. S., & Verma, A. (2013). Size and returns: A study of the Indian stock market. Indian Journal of Finance,7(5), 5–13. Racicot, F.  E., Rentz, W. F., Tessier, D., & Th eoret, R. (2019). The conditional Fama-French model and endogenous illiquidity: A robust instrumental variables test. PLOS One,14(9), e0221599. https://doi.org/10.1371/journal.pone. 0221599 Roy, R. (2020). A six-factor asset pricing model: The Japanese evidence. Financial Planning Review,4(1), 1-18. https:// doi.org/10.1002/cfp2.1109 Roy, R., & Shijin, S. (2018). A six-factor asset pricing model. Borsa Istanbul Review,18(3), 205–217. https://doi.org/10. 1016/j.bir.2018.02.001 Santoni, A., & Salerno, F. (2023). Financial assets valuation. How to Value a Bank. Springer Texts in Business and Economics. Springer. number 978-3-031-43872-1 https://doi.org/10.1007/978-3-031-43872-1_8 Sharpe, W. F. (1965). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance,19(3), 425–442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x Shijin, S., Gopalaswamy, A. K., & Acharya, D. (2012). Dynamic risk-return relation with human capital: A study on Indian markets. International Journal of Emerging Markets,7(2), 146–159. https://doi.org/10.1108/17468801211209929 Stattman, D. (1980). Book Values and Stock Returns. The Chicago MBA: A Journal of Selected Papers,4,25–45. 14 S.S. PRASAD ET AL.