e-ISSN 2300-3065 p-ISSN 2300-12402025, volume 14, issue 2 Copernican Journal of Finance & Accounting Date of submission: June 25, 2025; date of acceptance: August 25, 2025. * Contact information: sanjay.suresh20eph@iimranchi.ac.in, Indian Institute of Management, Prabandhan Nagar, Nayasarai Road, Ranchi, Jharkhand 835303, India, phone: +918408027817; ORCID ID: https://orcid.org/0009-0009-2809-1999. ** Contact information: kamran.quddus@iimranchi.ac.in, Indian Institute of Man- agement, Prabandhan Nagar, Nayasarai Road, Ranchi, Jharkhand 835303, India, phone: +919007973996; ORCID ID: https://orcid.org/0000-0003-3365-381X. Shanbhag, S., & Quddus, K. (2025). Cross-sectional Predictability of Indian Stock Returns: A Fac- tor Analytical Approach. Copernican Journal of Finance & Accounting, 14(2), 59–76. http://dx.doi. org/10.12775/CJFA.2025.009 sanjay shanbhag* Indian Institute of Management, Ranchi Kamran QuDDus** Indian Institute of Management, Ranchi CROSS-SECTIONAL PREDICTABILITY OF INDIAN STOCK RETURNS: A FACTOR ANALYTICAL APPROACH Keywords: asset pricing, return predictability, Fama-MacBeth regression, arbitrage pricing, principal components. J E L Classification: C51, G0, G12. Abstract: The core objective of this article is to analyze how firm characteristics col- lectively affect the risk-adjusted returns of Indian stocks. It aims to understand the si- multaneous explanatory power of multiple variables that have been shown to predict the cross-sectional returns in prior studies. We include eight firm characteristics as de- terminants of expected returns: size, book-to-market equity, reciprocity of share price, volume traded, dividend yield, and three lagged returns. The data consists of monthly returns and firm characteristics for a sample of listed securities that constitute the Na- tional Stock Exchange’s (NSE) NIFTY 100 Index. We use Arbitrage Pricing Theory, with Connor and Korajczyk’s (1988) benchmark factors for risk-adjusting returns on indi- vidual securities. We conduct Fama-MacBeth regressions to determine the statistical Sanjay Shanbhag, Kamran Quddus6060 significance of the firm characteristics. Furthremore, we find that lags of size, book-to- market, dividend yield, and momentum have strong residual pricing power and in-sam- ple predictability of risk-adjusted returns. We also find that the intercepts are positive and highly significant. Thus, the average stock in the sample underperforms the risk model by a substantial amount. The results lead us to categorically reject the Arbitrage Pricing Model with Connor and Korajczyk’s factors as a risk model for Indian stock re- turns.  Introduction Introduction The understanding and measurement of the sources of fundamental, non-di- versifiable macroeconomic risks underlying asset prices largely remain un- answered. The CAPM (Sharpe, 1964; Lintner, 1965; Black, Jensen & Scholes, 1972), a cross-sectional model, shows that expected excess security returns are a linear function of market beta only with an intercept of zero. However, over the past decades, numerous empirical asset pricing studies contradicting the CAPM have been documented. These CAPM “anomalies” that reject the zero intercept hypothesis have steadily increased. Some of the more prominent anomaly research findings demonstrate the inability of CAPM to price portfolios formed by grouping securities based on firm characteristics. Basu (1983) finds that, on average, securities with low P/E earn higher risk-adjusted returns than securities with high P/E. Banz (1981) discovers the “size” effect, with small capitalization stocks earning higher risk- adjusted returns than large capitalization stocks. Rosenberg, Reid and Lan- stein (1985) discover the “value” effect with high B/M (value) stocks earning higher risk-adjusted returns than low B/M (growth) stocks. Finally, Jegadeesh and Titman (2001) identify the momentum factor. As the number of documented violations of CAPM grew, so did the research efforts to find possible explanations. Prominent among them were explana- tions based on deviations from perfect markets due to transaction and liquid- ity effects (Amihud & Mendelson, 1986; Pastor & Stambaugh, 2001); irrational investor behavior (such as overreaction) or market inefficiencies (Lakonishok, Shleifer & Vishny, 1994); momentum anomaly arising from investors behavio- ral and cognitive biases (Jegadeesh & Titman, 1993; Chan, Jegadeesh & Lakon- ishok, 1995; Daniel, Hirshleifer & Subrahmanyam, 1998; Hong & Stein, 1999); fundamental non-diversifiable risks such as missing risk factor(s) or improper proxy for market portfolio (Roll, 1977); and the biases in the empirical method- ology (such as data-snooping). CROSS-SECTIONAL PREDICTABILITY OF INDIAN STOCK RETURNS… 6161 Many theoretical equilibrium-based models (unrelated to the Linear Fac- tor Model (LFM)) in literature offer non-CAPM-based explanations of asset re- turns. For example, Kraus and Litzenberger (1976) and Harvey and Siddique (2000) use co-skewness as a risk measure, Hwang and Satchell (1999) use co- kurtosis, while Bawa and Lindenberg (1977) propose a semi-variance, down- side beta-based equilibrium model. Theoretically motivated LFMs, such as Intertemporal CAPM (Merton, 1973) and Arbitrage Pricing Theory (APT) (Ross, 1976), assume rational investors and perfect markets. However, these models are quiet when it comes to which factors and how many of them should be included in the LFMs, making it largely an empirical issue. This “fishing license” (Fama, 1991) that apparently allows researchers to use just about any factor led to a rise in the number of potential factors. Harvey, Liu and Zhu (2015) document over 300 factors identified in em- pirical studies to explain asset cross-sectional returns. Cochrane (2011) calls this situation “a zoo of new factors”. The large number of factors in literature is contrary to earlier empirical APT studies that have suggested the existence of not more than 10 factors. The findings of a statistically significant non-zero CAPM intercept also led to the empirical testing of multiple beta asset pricing models. Connor (1995) lists 3 types of multiple beta models: macroeconomic, statistical, and funda- mental factor models. Chen, Roll, and Ross (1986) find empirical evidence for 5 priced macroeconomic factors. Roll and Ross (1980) use a statistical proce- dure. Lehmann and Modest (1988) use maximum likelihood analysis to esti- mate the LFM. Connor and Korajczyk (1988) find empirical evidence for 5 to 10 principal component factors. The factors extracted through statistical pro- cedures or principal components are not observable, and their economic inter- pretation is unclear. Additionally, these factors are conditional to sample assets and time periods, and they are likely unstable. A different approach, not necessarily economically motivated, is based on creating factors from excess returns of portfolios formed from securities sort- ed on firm attributes such as size, B/M, etc., to explain assets’ returns and reas- sessing the zero intercept hypothesis. There are no specific theories identified with these risk factors, and they are hypothesized as either proxies correlat- ed to yet-to-be-known fundamental sources of risk, products of data snooping, or just redundant. Gibbons, Ross and Shanken (1989) posit that stock portfo- lios are used to test LFMs due to the limitations of the econometric techniques requiring a larger number of test periods than test assets. Fama and French Sanjay Shanbhag, Kamran Quddus6262 (1992) find that the three-factor model (FF3), with factor portfolios formed from excess market returns, size, and B/M, has an intercept not significant- ly different from zero. Besides the widely known FF3, other models in litera- ture are the four-factor model by Carhart (1997), three-factor model by Chen and Zhang (2009), four-factor model by Hou, Xue and Zhang (2014), five-factor model by Fama and French (2015) (FF5), and six-factor model by Barillas and Shanken (2018). Important considerations that are also present in literature include wheth- er FF3 firm-characteristic factors are priced (MacKinlay, 1995; Lakonishok et al., 1994; Liew & Vassalou, 2000; Petkova, 2006), whether the factor portfo- lios that correlate well with anomalies are related to fundamental sources of risk (Lewellen, Nagel and Shanken, 2010), and which factors best explain as- set returns. The ability of characteristic-sorted portfolios to explain CAPM anomalies is viewed with caution. The factor portfolio formation process itself may make it difficult to reject the model (Roll, 1977) or the CAPM anomaly (Lo & MacKin- lay, 1990; Ferson, Sarkissian & Simin, 1999; Berk, 2000) due to data snooping biases inherent in the characteristic-sorted test portfolios. Hwang and Satch- ell (2012) suggest an average F-test to get around this problem. Hou, Xue and Zhang (2018) and Chordia, Goyal and Saretto (2020) demonstrate that anom- alies fail to replicate when adjusted for multiple hypothesis testing. Kothari, Shanken and Sloan (1995) provide evidence of CRSP and Compustat database sample selection biases to demonstrate FF3’s ability to explain CAPM anoma- lies. Fama and French, however, provide evidence of the success of the FF3 mod- el in other international markets to demonstrate that not all characteristic-re- lated phenomena are spurious effects of data snooping or sample bias. Literature ReviewLiterature Review There is extensive literature focused on empirical testing of asset pricing models and uncovering anomalies in the Indian stock markets. Asset pricing models such as CAPM, Fama-French three-factor, APT, and Carhart four-fac- tor have been tested extensively on various indices such as BSE and NSE for different sets of portfolios and different time periods. While CAPM has gener- ally failed, the performance of Fama-French three-factor has been better and Carhart four-factor has been found to explain cross section of returns better CROSS-SECTIONAL PREDICTABILITY OF INDIAN STOCK RETURNS… 6363 than both these models. Basu and Chawla (2010), Ansari and Khan (2012), Se- hgal and Balakrishnan (2013), and Das (2015) document the failure of CAPM. Basu and Chawla (2012) find selected macroeconomic variables in multi-fac- tor APT to be good descriptors of asset returns. Zaremba (2015) demonstrates the January seasonal effect using several distinct value and momentum strat- egies on 78 markets and concludes that their findings are consistent with the tax loss selling and window dressing effects. Ansari and Khan (2012), Pandey and Sehgal (2015), Balakrishnan (2016), Vasishth, Sehgal and Sharma (2020), Sobti (2018), Harshita, Singh and Yadav (2018), Sharma, Subramaniam and Se- hgal (2019), Balakrishnan, Maiti and Panda (2018), and Tripathi and Aggar- wal (2020) confirm the existence of size, value, momentum, profitability, and investment effects. Das and Barai (2015) show the existence of time-varying portfolio beta. Sehgal and Balakrishnan (2013) and Das (2015) test the Fama- French three-factor model. Sehgal and Jain (2015) and Dutta (2019) find the Fama-French five-factor model more robust than the Fama-French three-factor model. Das and Barai (2016) test Carhart four-factor model. Roy’s (2021) find- ings reveal that the six-factor model performs better than Carhart four-factor and Fama–French five-factor models. Khudoykulov (2020) evaluates the CAPM, Fama-French three-factor model, and Fama-French five-factor model. Veeravel (2023) tests the short-term persistence of equity mutual fund returns in Indi- an stock markets and finds that the three-factor Fama-French model consist- ently explains the persistence better than four-factor Carhart model. Keswani, Puri and Jha (2024) find significantly positive association between returns and GDP, disposable income, foreign institutional investor flows, and negative rela- tionship with interest rates, government policies, exchange rates, and inflation. The literature in the area of predictability, however, is sparse. Narayan and Ahmed (2014) test sectoral stock return predictability on the Indian stock ex- change using P/B, dividend yield, and P/E and find evidence of predictability. Narayan and Bannigidadmath (2015) show predictability of B/M and size-sort- ed industry portfolios both in-sample and out-of-sample. ObjectivesObjectives In this article, our objective is to further study the cross-sectional predictabil- ity of returns for Indian stocks. We investigate whether the lags of firm charac- teristic variables that have been attributed with the power to predict in prior Sanjay Shanbhag, Kamran Quddus6464 studies are cross-sectionally priced after adjusting for risk using the APT mod- el Connor and Korajczyk (1988) benchmarks. Our sample consists of securi- ties from the India’s National Stock Exchange (NSE) NIFTY 100 Index. The firm characteristics that we include have found importance in several prior empiri- cal studies and are backed by strong theoretical rationales (Lakonishok et al., 1994; Fama & French, 1988, 1992; Miller & Scholes, 1982; Pontiff & Schall, 1998; Goyal & Welch, 2003; Lewellen, 2004; Welch & Goyal, 2007). Theoretical FrameworkTheoretical Framework We base our analysis on Arbitrage Pricing Theory (Ross, 1976). For risk fac- tors, we use the Connor and Korajczyk’s (1988) (CK) approach to extract prin- cipal components risk factors from the covariance matrix of security returns. For a period spanning 1967–1991, Connor and Korajczyk (1993) document evi- dence for up to six factors underlying the returns on the NYSE and AMEX. The focus of our study is on testing the explanatory power or pricing lags of firm characteristics relative to CK benchmarks. Our model is based on risk adjust- ment of individual security returns. As discussed earlier, many studies show that characteristic-sorted test portfolios formed introduce data-snooping bi- ases. The approach of using individual securities permits the consideration of joint effects of many firm characteristics and also mitigates the data-snooping biases of the portfolio-based methodology. We include lags of eight firm level variables as determinants of expected returns: size (Banz, 1981), B/M (Fama & French, 1992), reciprocity of security price (Miller & Scholes, 1982), volume traded, dividend yield (Fama & French, 1988), and 3 lagged returns (Jegadeesh & Titman, 1993). We investigate the persistence of statistical significance of these firm char- acteristics after accounting for risk factors. Equation (1) is the condition- al K factor CK benchmark version of multifactor APT model of returns with M firm characteristics. Under the null hypothesis, cq (q = 1, ..., M) is zero, imply- ing that excess security returns are a linear function only of βi j ( j = 1, ..., K), the factor loadings. Thus, a violation of the null hypothesis would attribute predic- tive power to lagged values of firm characteristics. characteristics that we include have found importance in several prior empirical studies and are backed by strong theoretical rationales (Lakonishok et al., 1994; Fama & French, 1988, 1992; Miller & Scholes, 1982; Pontiff & Schall, 1998; Goyal & Welch, 2003; Lewellen, 2004; Welch & Goyal, 2007). Theoretical Framework We base our analysis on Arbitrage Pricing Theory (Ross, 1976). For risk factors, we use the Connor and Korajczyk’s (1988) (CK) approach to extract principal components risk factors from the covariance matrix of security returns. For a period spanning 1967–1991, Connor and Korajczyk (1993) document evidence for up to six factors underlying the returns on the NYSE and AMEX. The focus of our study is on testing the explanatory power or pricing lags of firm characteristics relative to CK benchmarks. Our model is based on risk adjustment of individual security returns. As discussed earlier, many studies show that characteristic-sorted test portfolios formed introduce data-snooping biases. The approach of using individual securities permits the consideration of joint effects of many firm characteristics and also mitigates the data-snooping biases of the portfolio-based methodology. We include lags of eight firm level variables as determinants of expected returns: size (Banz, 1981), B/M (Fama & French, 1992), reciprocity of security price (Miller & Scholes, 1982), volume traded, dividend yield (Fama & French, 1988), and 3 lagged returns (Jegadeesh & Titman, 1993). We investigate the persistence of statistical significance of these firm characteristics after accounting for risk factors. Equation (1) is the conditional K factor CK benchmark version of multifactor APT model of returns with M firm characteristics. Under the null hypothesis, 𝑐𝑐��� � 1, . . . ,𝑀𝑀� is zero, implying that excess security returns are a linear function only of 𝛽𝛽���� � 1, … ,𝐾𝐾�, the factor loadings. Thus, a violation of the null hypothesis would attribute predictive power to lagged values of firm characteristics. E�𝑅𝑅�� � 𝑅𝑅� � 𝑐𝑐� � ∑ 𝜆𝜆����� 𝛽𝛽�� � ∑ 𝑐𝑐����� 𝑍𝑍�� (1) RESEARCH METHODOLOGY The data consists of excess monthly returns and characteristics (as listed above) for a sample of listed securities which constitute the National Stock Exchange’s (NSE) NIFTY 100 Index. (1) CROSS-SECTIONAL PREDICTABILITY OF INDIAN STOCK RETURNS… 6565 Research MethodologyResearch Methodology The data consists of excess monthly returns and characteristics (as listed above) for a sample of listed securities which constitute the National Stock Ex- change’s (NSE) NIFTY 100 Index. 66 securities from the NIFTY 100 Index that had price data for all months for a period of 20 years from January 2004 to De- cember 2023 were selected. The firm level sample data has been obtained from Prowess database. The one month risk-free rate is derived from 91-days treas- ury bills yield from the Reserve Bank of India’s official website. Table 1 displays the predetermined firm characteristic variables used in the conditional APT model. Table 2 displays the summary statistics that represent the sample period average of cross-sectional means, medians, and standard de- viations of the firm characteristic variables for 66 securities over 240 months from January 2004 to December 2023 of the sample period. The variables dis- play minor skewness; we nevertheless use logarithmic transformations for all variables in our analysis. Table 3 displays the matrix of averages of monthly cross-correlation of all natural logarithm transformed variables for all securi- ties over the sample period. The largest correlation is between SIZE and VOL. The other correlations are fairly low. Using Connor and Korajczyk’s (1988) technique, the CK factors are estimat- ed for the 66 listed securities of the NSE exchanges on NIFTY 100 that had price data for all months from 2004–2023 of the sample period. Connor and Korajc- zyk (1993) show evidence for 1 to 6 factors. We use 5 factors in our model. The regression in Equation (2) is Fama-MacBeth estimation: 66 securities from the NIFTY 100 Index that had price data for all months for a period of 20 years from January 2004 to December 2023 were selected. The firm level sample data has been obtained from Prowess database. The one month risk-free rate is derived from 91-days treasury bills yield from the Reserve Bank of India’s official website. Table 1 displays the predetermined firm characteristic variables used in the conditional APT model. Table 2 displays the summary statistics that represent the sample period average of cross-sectional means, medians, and standard deviations of the firm characteristic variables for 66 securities over 240 months from January 2004 to December 2023 of the sample period. The variables display minor skewness; we nevertheless use logarithmic transformations for all variables in our analysis. Table 3 displays the matrix of averages of monthly cross-correlation of all natural logarithm transformed variables for all securities over the sample period. The largest correlation is between SIZE and VOL. The other correlations are fairly low. Using Connor and Korajczyk’s (1988) technique, the CK factors are estimated for the 66 listed securities of the NSE exchanges on NIFTY 100 that had price data for all months from 2004–2023 of the sample period. Connor and Korajczyk (1993) show evidence for 1 to 6 factors. We use 5 factors in our model. The regression in Equation (2) is Fama-MacBeth estimation: �̃�𝑅�� � 𝑅𝑅�� � 𝑐𝑐� � ∑  ���� 𝛽𝛽��𝐶𝐶�̃�𝐶�� � ∑  ���� 𝑐𝑐�𝑍𝑍��� � �̃�� (2) Table 1. Predetermined Firm Characteristic Variables Variable Definition SIZE The natural logarithm of the firm’s market capitalization ending month before the previous month. BM The natural logarithm B/M as of the previous month. VOL The natural logarithm of the rupee trading volume ending month before the previous month. PRICE The natural logarithm of the reciprocal of the security price ending month before the previous month. YLD The natural logarithm of the previous 12 month cumulative dividends divided by the security price as of month before the previous month. RET 2-3 The natural logarithm of the two months cumulative return ending two months before the current month. RET 4-6 The natural logarithm of the three months cumulative return ending three months before the current month. RET 7-12 The natural logarithm of the 6 months cumulative return ending six months before the current month. (2) Table 1. Predetermined Firm Characteristic Variables Variable Definition SIZE The natural logarithm of the firm’s market capitalization ending month before the previous month. BM The natural logarithm B/M as of the previous month. VOL The natural logarithm of the rupee trading volume ending month before the previous month. Sanjay Shanbhag, Kamran Quddus6666 Variable Definition PRICE The natural logarithm of the reciprocal of the security price ending month before the previous month. YLD The natural logarithm of the previous 12 month cumulative dividends divided by the security price as of month before the previous month. RET 2-3 The natural logarithm of the two months cumulative return ending two months before the current month. RET 4-6 The natural logarithm of the three months cumulative return ending three months before the current month. RET 7-12 The natural logarithm of the 6 months cumulative return ending six months before the cur- rent month. S o u r c e : authors hypothesis of the eight firm level variables as determinants of expected re- turns, based on existing literature size (Banz, 1981), B/M (Fama & French, 1992), reciproityc of security price (Miller & Scholes, 1982), volume traded, dividend yield (Fama & French, 1988), and 3 lagged returns (Jegadeesh & Titman, 1993). Table 2. Summary Statistics Variable Mean Median Standard Deviation Size (₹ billion) 0.791 0.643 0.569 BM 0.386 0.362 0.098 Trading Volume (₹ billion) 0.034 0.021 0.029 Share Price (₹ ) 1,374.937 1,340.738 586.043 Dividend Yield (%) 1.148% 1.100% 0.331% S o u r c e : authors’ analysis and calculations with data sourced from Prowess dx. Table 3. Correlation Matrix for Firm Characteristics RETURN SIZE BM VOL PRICE YLD RET 2-3 RET 4-6 RET 7-12 RETURN 1.00 SIZE -0.08 1.00 BM 0.03 -0.09 1.00 VOL -0.05 0.78 0.12 1.00 Table 1. Predetermined… CROSS-SECTIONAL PREDICTABILITY OF INDIAN STOCK RETURNS… 6767 RETURN SIZE BM VOL PRICE YLD RET 2-3 RET 4-6 RET 7-12 PRICE 0.05 -0.26 0.30 -0.13 1.00 YLD 0.02 -0.04 0.32 -0.01 0.32 1.00 RET 2-3 -0.05 0.01 -0.07 0.02 -0.10 -0.18 1.00 RET 4-6 -0.02 0.00 -0.08 0.01 -0.12 -0.18 -0.05 1.00 RET 7-12 0.00 0.01 -0.10 0.01 -0.16 -0.12 0.00 -0.03 1.00 S o u r c e : authors analysis and calculations with data sourced from Prowess dx. The null hypothesis is tested by estimating equation (2) using the Fama- MacBeth technique. Stationarity is a key assumption in the estimation of the CK factors (Connor & Korajczyk, 1988) based on an equilibrium APT model. The relationship between risk and return is expected to be stable over time, with sensitivities to the underlying factors or factor loadings () remaining un- changed. However, stationarity may not be the ideal description of real-world market conditions, with factors and factor sensitivities changing over time. We therefore estimate the CK factors on subsamples to simulate non-stationarity in the data. Results and DiscussionsResults and Discussions First, we conduct Fama-Macbeth regression (Equation (2)) of returns on a re- duced set of variables and lagged variables. Table 4 below displays the results of Fama-MacBeth regression. The sample includes 66 securities over a period of 240 months from January 2004 to December 2023. Of the variables, SIZE, BM, and the three lagged returns are well-known for their predictability of returns. The complete sample period is further partitioned into sub-samples of 5 years each: 2004–2008, 2008–2012, 2013–2017, and 2018–2023. For each sub-sam- ple, excess security returns and excess security returns risk-adjusted using the CK factors are calculated, respectively. The coefficients in the cross-sectional regressions are estimated using the Fama-MacBeth technique for the two sep- arate regressions: one with the excess security returns as the dependent vari- able and the other with risk-adjusted excess security returns. The numbers in the first and second columns of each subsample are the p-values. Table 3. Correlation… Ta bl e 4. F am a- M ac Be th R eg re ss io n Re su lts o f E qu at io n (2 ) 20 04 –2 00 8 20 09 –2 01 3 20 14 –2 01 8 20 19 –2 02 3 20 04 –2 02 3 Fi rm Ch ar ac te ri st ic Ex ce ss Re tu rn s Ri sk -A dj us te d Re tu rn s Ex ce ss Re tu rn s Ri sk -A dj us te d Re tu rn s Ex ce ss Re tu rn s Ri sk -A dj us te d Re tu rn s Ex ce ss Re tu rn s Ri sk -A dj us te d Re tu rn s Ex ce ss Re tu rn s Ri sk -A dj us te d Re tu rn s IN TE RC EP T 0. 04 99 0. 16 88 0. 10 11 0. 10 70 0. 08 52 0. 14 75 0. 09 74 0. 15 94 0. 08 52 0. 14 44 (1 .6 7) (1 2. 22 ) (4 .0 6) (8 .0 8) (2 .7 0) (9 .5 0) (3 .6 3) (1 1. 56 ) (6 .0 2) (1 9. 98 ) SI ZE -0 .0 03 6 -0 .0 05 3 -0 .0 07 4 -0 .0 01 9 -0 .0 06 7 -0 .0 05 2 -0 .0 06 4 -0 .0 06 0 -0 .0 06 1 -0 .0 04 6 -(1 .6 7) -( 5. 15 ) -( 3. 84 ) -(1 .6 7) -( 2. 98 ) -(4 .5 0) -( 3. 62 ) -( 5. 90 ) -( 6. 08 ) -( 8. 24 ) BM 0. 00 20 0. 01 16 0. 00 07 0. 00 73 -0 .0 02 8 0. 00 80 0. 00 02 0. 00 70 -0 .0 00 1 0. 00 83 (0 .5 3) (4 .9 4) (0 .1 7) (4 .9 5) -( 0. 91 ) (6 .7 2) (0 .0 7) (6 .3 7) -( 0. 05 ) (1 0. 90 ) RE T 2- 3 0. 00 36 0. 02 44 -0 .0 32 2 0. 00 54 -0 .0 16 6 0. 01 75 -0 .0 26 4 0. 03 26 -0 .0 19 0 0. 01 97 (0 .1 8) (2 .0 4) -(1 .9 8) (0 .6 1) -( 0. 98 ) (1 .8 8) -(1 .3 4) (3 .3 0) -( 2. 09 ) (3 .9 8) RE T 4- 6 -0 .0 14 3 0. 02 61 -0 .0 01 5 0. 00 05 -0 .0 02 5 0. 01 08 0. 01 15 0. 02 83 -0 .0 01 0 0. 01 59 -( 0. 96 ) (3 .5 0) -( 0. 11 ) (0 .0 8) -( 0. 29 ) (1 .5 5) (0 .8 2) (3 .6 2) -( 0. 16 ) (4 .3 2) RE T 7- 12 0. 00 99 0. 02 25 -0 .0 11 3 0. 00 29 0. 00 44 0. 00 54 0. 01 23 0. 00 70 0. 00 35 0. 00 88 (1 .2 9) (4 .5 7) -(1 .3 2) (0 .7 1) (0 .7 3) (0 .9 6) (1 .4 5) (1 .7 7) (0 .8 9) (3 .6 9) S o u rc e : a ut ho rs ’ a na ly si s a nd c al cu la tio ns w it h da ta so ur ce d fr om P ro w es s d x. CROSS-SECTIONAL PREDICTABILITY OF INDIAN STOCK RETURNS… 6969 We present the results for the full sample as well as for four subsamples of 5 years each. For regressions of excess returns, we observe that the coefficient of SIZE is negative and statistically significant in all periods, consistent with Fama and French (1992), whereas the coefficient of BM is statistically insignifi- cant. The coefficients of all 3 lags are statistically insignificant. The intercept of the regression is highly significant. Next, we repeat the regressions for excess risk-adjusted returns using CK factors. We compare the results and find the coefficient of SIZE now to be negative, the coefficient of BM to be positive, and both statistically more significant for all periods. The lagged returns are now statistically significant for two periods – 2004–2008 and 2019–2023 – and for the full sample. Moreover, the sign of these lags changes after risk adjustment. An overarching observation is that regardless of the statistical significance, all coefficients except for that of the intercept are small and thus can be consid- ered to be economically insignificant. Next, we conduct Fama-MacBeth regressions using a complete set of vari- ables and lagged variables. Table 5 displays the results of Fama-MacBeth re- gression (Equation (2)) of excess returns and risk-adjusted excess returns for all securities in the sample space on characteristics. As seen in Table 5, for ex- cess returns and for the period of 2019–2023, coefficients of SIZE and YLD are negative and statistically significant, and PRICE is positive and statistically sig- nificant. For all other periods, all other variables are statistically insignificant. There is a distinct departure from these results, however, for regressions of excess returns risk-adjusted using CK factors. Coefficients of SIZE and YLD are negative, and BM and VOL are positive, and all four are now statistically more significant for all periods. With the introduction of PRICE, VOL, YLD, the coeffi- cient of SIZE is more pronounced, and that of BM is slightly attenuated. The co- efficient of PRICE is no longer significant. The lags show statistical importance in some periods, notably 2004–2008 and 2019–2023, as before. Moreover, the sign of these lags changes after risk adjustment, and lags become less signifi- cant after PRICE, VOL, and YLD are introduced. The intercept remains highly significant for all periods. But for the intercept, the economic significance of all coefficients remains small. Ta bl e 5. F am a- M ac Be th R eg re ss io n Re su lts o f E qu at io n (2 ) 20 04 -2 00 8 20 09 -2 01 3 20 14 -2 01 8 20 19 -2 02 3 20 04 -2 02 3 Fi rm Ch ar ac te ri st ic Ex ce ss Re tu rn s Ri sk A dj us te d Re tu rn s Ex ce ss Re tu rn s Ri sk A dj us te d Re tu rn s Ex ce ss Re tu rn s Ri sk A dj us te d Re tu rn s Ex ce ss Re tu rn s Ri sk A dj us te d Re tu rn s Ex ce ss Re tu rn s Ri sk A dj us te d Re tu rn s IN TE RC EP T 0. 05 74 0. 19 82 0. 12 43 0. 13 07 0. 05 63 0. 14 72 0. 10 00 0. 15 68 0. 08 59 0. 15 61 (1 .6 1) (9 .8 2) (4 .0 7) (9 .0 5) (1 .6 5) (8 .4 6) (3 .8 8) (1 0. 11 ) (5 .4 5) (1 8. 44 ) SI ZE -0 .0 00 7 -0 .0 14 3 -0 .0 06 0 -0 .0 11 5 -0 .0 01 7 -0 .0 11 1 -0 .0 07 8 -0 .0 12 7 -0 .0 04 2 -0 .0 12 3 -( 0. 21 ) -( 6. 21 ) -(1 .6 9) -( 5. 93 ) -( 0. 50 ) -( 6. 46 ) -( 3. 02 ) -( 8. 36 ) -( 2. 60 ) -(1 3. 30 ) BM 0. 00 10 0. 00 97 -0 .0 01 1 0. 00 66 -0 .0 02 7 0. 00 73 -0 .0 01 2 0. 00 54 -0 .0 01 1 0. 00 71 (0 .2 4) (4 .0 0) -( 0. 28 ) (4 .3 4) -( 0. 94 ) (5 .6 4) -( 0. 41 ) (4 .5 3) -( 0. 64 ) (8 .9 3) PR IC E 0. 00 39 -0 .0 01 0 0. 00 26 0. 00 15 0. 00 11 -0 .0 01 7 0. 00 37 0. 00 13 0. 00 28 0. 00 01 (1 .0 8) -( 0. 50 ) (1 .5 6) (1 .2 8) (0 .5 7) -(1 .4 4) (2 .1 0) (1 .5 2) (2 .5 1) (0 .1 1) VO L -0 .0 00 5 0. 00 72 -0 .0 00 6 0. 00 81 -0 .0 04 0 0. 00 58 0. 00 21 0. 00 82 -0 .0 00 8 0. 00 73 -( 0. 24 ) (4 .4 7) -( 0. 28 ) (6 .6 7) -(1 .6 3) (4 .4 6) (0 .8 8) (6 .4 9) -( 0. 67 ) (1 1. 01 ) YL D 0. 00 36 -0 .0 02 3 0. 00 48 -0 .0 08 0 -0 .0 01 5 -0 .0 02 3 -0 .0 04 2 -0 .0 03 2 0. 00 05 -0 .0 04 0 (0 .6 8) -( 0. 85 ) (1 .6 3) -( 5. 32 ) -( 0. 65 ) -(1 .7 4) -( 2. 38 ) -( 2. 79 ) (0 .3 3) -(4 .7 9) RE T 2- 3 0. 00 33 0. 01 72 -0 .0 20 1 0. 00 06 -0 .0 15 2 0. 01 02 -0 .0 28 6 0. 02 82 -0 .0 16 1 0. 01 39 (0 .1 7) (1 .4 0) -(1 .2 6) (0 .0 7) -( 0. 92 ) (1 .1 3) -(1 .6 1) (2 .9 5) -(1 .8 7) (2 .8 7) RE T 4- 6 -0 .0 13 7 0. 02 38 0. 00 37 0. 00 02 -0 .0 07 4 0. 00 65 0. 00 90 0. 02 47 -0 .0 01 5 0. 01 33 -( 0. 94 ) (3 .1 4) (0 .2 7) (0 .0 3) -( 0. 86 ) (0 .8 6) (0 .6 3) (3 .2 1) -( 0. 23 ) (3 .5 6) RE T 7- 12 0. 01 05 0. 02 20 -0 .0 09 2 0. 00 17 0. 00 54 0. 00 17 0. 00 76 0. 00 23 0. 00 32 0. 00 61 (1 .3 9) (4 .1 0) -(1 .0 9) (0 .4 1) (0 .8 8) (0 .3 2) (0 .7 8) (0 .5 8) (0 .7 9) (2 .5 7) S o u rc e : a ut ho rs ’ a na ly si s a nd c al cu la tio ns w it h da ta so ur ce d fr om P ro w es s d x. CROSS-SECTIONAL PREDICTABILITY OF INDIAN STOCK RETURNS… 7171  Conclusions Conclusions In this article, we test the principal components approach of the APT mod- el (Connor & Korajczyk, 1988) against firm characteristic variables such as SIZE, BM, YLD, VOL, PRICE, and several return lags using data on individual securities. We find strong evidence of risk-adjusted excess returns to be more strongly related to SIZE, BM, and lagged returns or momentum than unadjust- ed excess returns. The presence of YLD, PRICE, and VOL makes SIZE even more significant and BM less significant. YLD and VOL are significant in the overall sample, whereas PRICE is insignificant. All characteristics, except for PRICE, become highly statistically significant after risk adjustment. It is also worth noting that in both sets of regressions of risk-adjusted returns (Table 4 and Table 5), the intercepts are positive and highly significant. Thus, the average stock in the sample underperforms the risk model by a substantial amount. The results lead us to categorically reject the null hypothesis that returns are determined by the APT with CK factors as the risk model. The lags of SIZE, BM, YLD, and momentum have strong residual pricing power and in-sample pre- dictability of risk-adjusted returns. The statistically and economically signifi- cant intercept suggests the presence of omitted risk factors.  References References Amihud, Y., & Mendelson, H. (1986). Asset pricing and the bid-ask spread. Journal of Finan- cial Economics, 17(2), 223–249. https://doi.org/10.1016/0304-405x(86)90065-6. Ansari, V.A., & Khan, S. (2012). Momentum anomaly: Evidence from India. Managerial Finance, 38(2), 206–223. https://doi.org/10.1108/03074351211193730. Balakrishnan, A. (2016). Size, value, and momentum effects in stock returns: Evi- dence from India. Vision: The Journal of Business Perspective, 20(1), 1–8. https://doi. org/10.1177/0972262916628929. Balakrishnan, A., Maiti, M., & Panda, P. (2018). Test of five-factor asset pricing mod- el in India. Vision: The Journal of Business Perspective, 22(2), 153–162. https://doi. org/10.1177/0972262918766133. Banz, R.W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9(1), 3–18. https://doi.org/10.1016/0304- 405x(81)90018-0. Barillas, F., & Shanken, J. (2018). Comparing asset pricing models. The Journal of Finance, 73(2), 715–754. https://doi.org/10.1111/jofi.12607. Basu, D., & Chawla, D. (2010). An empirical test of CAPM—The case of Indian stock market. Global Business Review, 11(2), 209–220. https://doi.org/10.1177/097215091001100206. https://doi.org/10.1016/0304-405x(86)90065-6 https://doi.org/10.1177/0972262918766133 https://doi.org/10.1177/0972262918766133 https://doi.org/10.1016/0304-405x(81)90018-0 https://doi.org/10.1016/0304-405x(81)90018-0 Sanjay Shanbhag, Kamran Quddus7272 Basu, D., & Chawla, D. (2012). An empirical test of the arbitrage pricing theory—The case of Indian stock market. Global Business Review, 13(3), 421–432. https://doi. org/10.1177/097215091201300305. Basu, S. (1983). The relationship between earnings’ yield, market value and return for NYSE common stocks. Journal of Financial Economics, 12(1), 129–156. https://doi. org/10.1016/0304-405x(83)90031-4. Bawa, V.S., & Lindenberg, E.B. (1977). Capital market equilibrium in a mean-lower par- tial moment framework. Journal of Financial Economics, 5(2), 189–200. https://doi. org/10.1016/0304-405x(77)90017-4. Berk, J. B. (2000). Sorting out sorts. The Journal of Finance, 55(1), 407–427. https://doi. org/10.1111/0022-1082.00210. Black, F., Jensen, M., & Scholes, M. (1972). The capital asset pricing model: some empir- ical tests. In M. Jensen. Studies in the Theory of Capital Markets. New York: Praeger Publishers. Carhart, M.M. (1997). On persistence in mutual fund performance. The Journal of Fi- nance, 52(1), 57–82. https://doi.org/10.1111/j.1540-6261.1997.tb03808.x. Chan, L.K., Jegadeesh, N., & Lakonishok, J. (1995). Momentum strategies. The Journal of Finance, 51, 1681–1713. https://doi.org/10.3386/w5375. Chen, L., & Zhang, L. (2009). A Better Three-Factor Model that Explains More Anoma- lies. Journal of Finance, 65(2), 563–594. Chen, N., Roll, R., & Ross, S.A. (1986). Economic forces and the stock market. The Journal of Business, 59(3), 383–403. https://doi.org/10.1086/296344. Chordia, T., Goyal, A., & Saretto, A. (2020). Anomalies and False Rejections. The Review of Financial Studies, 33(5), 2134–2179. https://doi.org/10.1093/rfs/hhaa018. Cochrane, J.H. (2011). Presidential Address: Discount Rates. The Journal of Fi- nance, 66(4), 1047–1108. https://doi.org/10.1111/j.1540-6261.2011.01671.x. Connor, G. (1995). The three types of factor models: A comparison of their explanato- ry power. Financial Analysts Journal, 51(3), 42–46. https://doi.org/10.2469/faj.v51. n3.1904. Connor, G., & Korajczyk, R.A. (1988). Risk and return in an equilibrium APT. Journal of Fi- nancial Economics, 21(2), 255–289. https://doi.org/10.1016/0304-405x(88)90062-1. Connor, G., & Korajczyk, R.A. (1993). A test for the number of factors in an ap- proximate factor model. The Journal of Finance, 48(4), 1263–1291. https://doi. org/10.2307/2329038. Daniel, K., Hirshleifer, D., & Subrahmanyam, A. (1998). Investor psychology and secu- rity market under- and overreactions. The Journal of Finance, 53(6), 1839–1885. https://doi.org/10.1111/0022-1082.00077. Das, S. (2015). Empirical evidence of conditional asset pricing in the Indian stock market. Economic Systems, 39(2), 225–239. https://doi.org/10.1016/j.ecosys.2014. 07.003. Das, S., & Barai, P. (2015). Time-varying industry beta in Indian stock market and fore- casting errors. International Journal of Emerging Markets, 10(3), 521–534. https:// doi.org/10.1108/ijoem-02-2013-0035. https://doi.org/10.1177/097215091201300305 https://doi.org/10.1177/097215091201300305 https://doi.org/10.1016/0304-405x(83)90031-4 https://doi.org/10.1016/0304-405x(83)90031-4 https://doi.org/10.1016/0304-405x(77)90017-4 https://doi.org/10.1016/0304-405x(77)90017-4 https://doi.org/10.1111/0022-1082.00210 https://doi.org/10.1111/0022-1082.00210 https://doi.org/10.2469/faj.v51.n3.1904 https://doi.org/10.2469/faj.v51.n3.1904 https://doi.org/10.1016/0304-405x(88)90062-1 https://doi.org/10.2307/2329038 https://doi.org/10.2307/2329038 https://doi.org/10.1016/j.ecosys.2014.07.003 https://doi.org/10.1016/j.ecosys.2014.07.003 https://doi.org/10.1108/ijoem-02-2013-0035 https://doi.org/10.1108/ijoem-02-2013-0035 CROSS-SECTIONAL PREDICTABILITY OF INDIAN STOCK RETURNS… 7373 Das, S., & Barai, P. (2016). Size, value and momentum in stock returns: Evidence from India. Macroeconomics and Finance in Emerging Market Economies, 9(3), 284–302. https://doi.org/10.1080/17520843.2016.1148754. Dutta, A. (2019). Does the five-factor asset pricing model have sufficient power? Global Business Review, 20(3), 684–691. https://doi.org/10.1177/0972150919837060. Fama, E.F. (1991). Efficient capital markets: II. The Journal of Finance, 46(5), 1575–1617. https://doi.org/10.2307/2328565. Fama, E.F., & French, K.R. (1988). Dividend yields and expected stock returns. Journal of Financial Economics, 22(1), 3–25. https://doi.org/10.1016/0304-405x(88)90020-7. Fama, E.F., & French, K.R. (1992). The cross-section of expected stock returns. The Jour- nal of Finance, 47(2), 427–465. https://doi.org/10.2307/2329112. Fama, E.F., & French, K.R. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1–22. https://doi.org/10.1016/j.jfineco.2014.10.010. Ferson, W.E., Sarkissian, S., & Simin, T. (1999). The Alpha factor asset pricing model: A parable. Journal of Financial Markets, 2(1), 49–68. https://doi.org/10.1016/s1386- 4181(98)00005-6. Gibbons, M.R., Ross, S.A., & Shanken, J. (1989). A test of the efficiency of a given portfo- lio. Econometrica, 57(5), 1121–1152. https://doi.org/10.2307/1913625. Goyal, A., & Welch, I. (2003). Predicting the Equity Premium with Dividend Ratios. Man- agement Science, 49(5), 639–654. https://doi.org/10.1287/mnsc.49.5.639.15149. Harshita, Singh, S., & Yadav, S.S. (2018). Changing nature of the value premium in the Indian stock market. Vision: The Journal of Business Perspective, 22(2), 135–143. https://doi.org/10.1177/0972262918766135. Harvey, C.R., & Siddique, A. (2000). Conditional skewness in asset pricing tests. The Journal of Finance, 55(3), 1263–1295. https://doi.org/10.1111/0022-1082.00247. Harvey, C.R., Liu, Y., & Zhu, H. (2015). … and the cross-section of expected returns. Re- view of Financial Studies, 29(1), 5–68. https://doi.org/10.1093/rfs/hhv059. Hong, H., & Stein, J.C. (1999). A Unified Theory of Underreaction, Momentum Trad- ing, and Overreaction in Asset Markets. The Journal of Finance, 54(6), 2143–2184. https://doi.org/10.1111/0022-1082.00184. Hou, K., Xue, C., & Zhang, L. (2014). Digesting anomalies: An investment approach. Review of Financial Studies, 28(3), 650–705. https://doi.org/10.1093/rfs/hhu068. Hou, K., Xue, C., & Zhang, L. (2018). Replicating anomalies. The Review of Financial Stud- ies, 33(5), 2019–2133. https://doi.org/10.1093/rfs/hhy131. Hwang, S., & Satchell, S.E. (1999). Modelling emerging market risk premia using higher moments. International Journal of Finance & Economics, 4(4), 271–296. https://doi. org/10.1002/(SICI)1099-1158(199910)4:4%3C271::AID-IJFE110%3E3.0.CO;2-M. Hwang, S., & Satchell, S.E. (2012). Testing linear factor models on individual stocks us- ing the averagef-test. The European Journal of Finance, 20(5), 463–498. https://doi. org/10.1080/1351847x.2012.717097. Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Impli- cations for stock market efficiency. The Journal of Finance, 48(1), 65–91. https://doi. org/10.1111/j.1540-6261.1993.tb04702.x. https://doi.org/10.1016/s1386-4181(98)00005-6 https://doi.org/10.1016/s1386-4181(98)00005-6 https://doi.org/10.1002/(SICI)1099-1158(199910)4:4%3C271::AID-IJFE110%3E3.0.CO;2-M https://doi.org/10.1002/(SICI)1099-1158(199910)4:4%3C271::AID-IJFE110%3E3.0.CO;2-M https://doi.org/10.1080/1351847x.2012.717097 https://doi.org/10.1080/1351847x.2012.717097 https://doi.org/10.1111/j.1540-6261.1993.tb04702.x https://doi.org/10.1111/j.1540-6261.1993.tb04702.x Sanjay Shanbhag, Kamran Quddus7474 Jegadeesh, N., & Titman, S. (2001). Profitability of momentum strategies: An evalua- tion of alternative explanations. The Journal of Finance, 56(2), 699–720. https://doi. org/10.1111/0022-1082.00342. Keswani, S., Puri, V., & Jha, R. (2024). Relationship among macroeconomic factors and stock prices: Cointegration approach from the Indian stock market. Cogent Econom- ics & Finance, 12(1), 1–20. https://doi.org/10.1080/23322039.2024.2355017. Khudoykulov, K. (2020). Asset-pricing models: A case of Indian capital market. Cogent Economics & Finance, 8(1), 1–15. https://doi.org/10.1080/23322039.2020.1832732. Kothari, S.P., Shanken, J., & Sloan, R.G. (1995). Another look at the cross-section of expected stock returns. The Journal of Finance, 50(1), 185–224. https://doi. org/10.2307/2329243. Kraus, A., & Litzenberger, R.H. (1976). Skewness preference and the valuation of risk assets. The Journal of Finance, 31(4), 1085–1100. https://doi.org/10.2307/2326275. Lakonishok, J., Shleifer, A., & Vishny, R.W. (1994). Contrarian investment, extrapolation, and risk. The Journal of Finance, 49(5), 1541–1578. https://doi.org/10.2307/2329262. Lehmann, B.N., & Modest, D.M. (1988). The empirical foundations of the arbi- trage pricing theory. Journal of Financial Economics, 21(2), 213–254. https://doi. org/10.1016/0304-405x(88)90061-x. Lewellen, J. (2004). Predicting returns with financial ratios. Journal of Financial Eco- nomics, 74(2), 209–235. https://doi.org/10.1016/j.jfineco.2002.11.002. Lewellen, J., Nagel, S., & Shanken, J. (2010). A skeptical appraisal of asset pricing tests. Journal of Financial Economics, 96(2), 175–194. https://doi.org/10.1016/j.jfine- co.2009.09.001. Liew, J., & Vassalou, M. (2000). Can book-to-market, size and momentum be risk fac- tors that predict economic growth? Journal of Financial Economics, 57(2), 221–245. https://doi.org/10.1016/s0304-405x(00)00056-8. 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. Lo, A.W., & MacKinlay, A.C. (1990). Data-snooping biases in tests of financial asset pric- ing models. Review of Financial Studies, 3(3), 431–467. https://doi.org/10.1093/ rfs/3.3.431. MacKinlay, A. (1995). Multifactor models do not explain deviations from the CAPM. Journal of Financial Economics, 38(1), 3–28. https://doi.org/10.1016/0304-405x (94)00808-e. Merton, R.C. (1973). An Intertemporal capital asset pricing model. Econometrica, 41(5), 867–887. https://doi.org/10.2307/1913811. Miller, M.H., & Scholes, M.S. (1982). Dividends and taxes: Some empirical evidence. Jour- nal of Political Economy, 90(6), 1118–1141. https://doi.org/10.1086/261114. Narayan, P.K., & Ahmed, H.A. (2014). Importance of skewness in decision making: Evidence from the Indian stock exchange. Global Finance Journal, 25(3), 260–269. https://doi.org/10.1016/j.gfj.2014.10.006. https://doi.org/10.2307/2329243 https://doi.org/10.2307/2329243 https://doi.org/10.1016/0304-405x(88)90061-x https://doi.org/10.1016/0304-405x(88)90061-x https://doi.org/10.1016/j.jfineco.2009.09.001 https://doi.org/10.1016/j.jfineco.2009.09.001 https://doi.org/10.1093/rfs/3.3.431 https://doi.org/10.1093/rfs/3.3.431 https://doi.org/10.1016/0304-405x(94)00808-e https://doi.org/10.1016/0304-405x(94)00808-e https://doi.org/10.1086/261114 CROSS-SECTIONAL PREDICTABILITY OF INDIAN STOCK RETURNS… 7575 Narayan, P.K., & Bannigidadmath, D. (2015). Are Indian stock returns predicta- ble? Journal of Banking & Finance, 58, 506–531. https://doi.org/10.1016/j.jbank- fin.2015.05.001. Pandey, A., & Sehgal, S. (2015). Explaining size effect for Indian stock market. Asia-Pa- cific Financial Markets, 23(1), 45–68. https://doi.org/10.1007/s10690-015-9208-0. Pastor, L., & Stambaugh, R. (2001). Liquidity Risk and Expected Stock Returns. NBER Working Paper No. 8462. https://doi.org/10.3386/w8462. Petkova, R. (2006). Do the Fama–French factors proxy for innovations in predictive variables? The Journal of Finance, 61(2), 581–612. https://doi.org/10.1111/j.1540- 6261.2006.00849.x. Pontiff, J., & Schall, L.D. (1998). Book-to-market ratios as predictors of market re- turns. Journal of Financial Economics, 49(2), 141–160. https://doi.org/10.1016/ s0304-405x(98)00020-8. Roll, R. (1977). A critique of the asset pricing theory’s tests part I: On past and potential testability of the theory. Journal of Financial Economics, 4(2), 129–176. https://doi. org/10.1016/0304-405x(77)90009-5. Roll, R., & Ross, S. A. (1980). An empirical investigation of the arbitrage pricing theory. The Journal of Finance, 35(5), 1073–1103. https://doi.org/10.1111/j.1540-6261.1980. tb02197.x. Rosenberg, B., Reid, K., & Lanstein, R. (1985). Persuasive evidence of market ineffi- ciency. The Journal of Portfolio Management, 11(3), 9–16. https://doi.org/10.3905/ jpm.1985.409007. Ross, S.A. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13(3), 341–360. https://doi.org/10.1016/0022-0531(76)90046-6. Roy, R. (2021). Is the six-factor asset pricing model discounting the global returns? Mac- roeconomics and Finance in Emerging Market Economies, 16(1), 95–136. https://doi. org/10.1080/17520843.2021.1936110. Sehgal, S., & Balakrishnan, A. (2013). Robustness of Fama-French three factor model: Further evidence for Indian stock market. Vision: The Journal of Business Perspective, 17(2), 119–127. https://doi.org/10.1177/0972262912483526. Sehgal, S., & Jain, K. (2015). Dissecting sources of price momentum: Evidence from India. International Journal of Emerging Markets, 10(4), 801–819. https://doi.org/10.1108/ ijoem-04-2014-0046. Sharma, G., Subramaniam, S., & Sehgal, S. (2019). Are prominent equity market anom- alies in India fading away? Global Business Review, 22(1), 255–270. https://doi. org/10.1177/0972150918811248. Sharpe, W.F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442. https://doi.org/10.2307/2977928. Sobti, N. (2018). Does size, value and seasonal effects still persist in Indian equi- ty markets? Vision: The Journal of Business Perspective, 22(1), 11–21. https://doi. org/10.1177/0972262917750230. https://doi.org/10.1016/s0304-405x(98)00020-8 https://doi.org/10.1016/s0304-405x(98)00020-8 https://doi.org/10.1016/0304-405x(77)90009-5 https://doi.org/10.1016/0304-405x(77)90009-5 https://doi.org/10.1111/j.1540-6261.1980.tb02197.x https://doi.org/10.1111/j.1540-6261.1980.tb02197.x https://doi.org/10.3905/jpm.1985.409007 https://doi.org/10.3905/jpm.1985.409007 https://doi.org/10.1016/0022-0531(76)90046-6 https://doi.org/10.1080/17520843.2021.1936110 https://doi.org/10.1080/17520843.2021.1936110 https://doi.org/10.1108/ijoem-04-2014-0046 https://doi.org/10.1108/ijoem-04-2014-0046 https://doi.org/10.1177/0972150918811248 https://doi.org/10.1177/0972150918811248 https://doi.org/10.1177/0972262917750230 https://doi.org/10.1177/0972262917750230 Sanjay Shanbhag, Kamran Quddus7676 Tripathi, V., & Aggarwal, P. (2020). Is value premium sector-specific? Evidence from In- dia. Managerial Finance, 46(12), 1605–1628. https://doi.org/10.1108/mf-02-2020- 0049. Vasishth, V., Sehgal, S., & Sharma, G. (2020). Size effect in Indian equity market: Myth or reality? Asia-Pacific Financial Markets, 28(1), 101–119. https://doi.org/10.1007/ s10690-020-09318-0. Veeravel, V. (2023). Short-term persistence performance of equity mutual fund returns: Evidence from India. Copernican Journal of Finance & Accounting, 12(3), 79–92. https://doi.org/10.12775/cjfa.2023.017. Welch, I., & Goyal, A. (2007). A comprehensive look at the empirical performance of eq- uity premium prediction. Review of Financial Studies, 21(4), 1455–1508. https://doi. org/10.1093/rfs/hhm014. Zaremba, A. (2015). The January seasonality and the performance of country-level value and momentum strategies. Copernican Journal of Finance & Accounting, 4(2), 195–209. https://doi.org/10.12775/cjfa.2015.024. https://doi.org/10.1108/mf-02-2020-0049 https://doi.org/10.1108/mf-02-2020-0049 https://doi.org/10.1007/s10690-020-09318-0 https://doi.org/10.1007/s10690-020-09318-0 https://doi.org/10.1093/rfs/hhm014 https://doi.org/10.1093/rfs/hhm014