Equity Market Anomalies,VIX and Asset Pricing: Trading Strategies for India

Abstract

In this article we examine five prominent equity anomalies, viz., size, value, profitability, investment and momentum for Indian capital market using data from July 2001 to June 2019. We test the sample anomalies through four prominent factor models and find that all the factor anomalies remain significant for India, however, size and value anomaly provide substantial risk adjusted returns to be exploited by portfolio managers. We further evaluate if the anomalies tend to reverse under different macro-economic uncertainty, which is proxied by VIX. We find barring Size effect none of the anomaly reverses under different macro-economic conditions. We further observe that Fama French three factor model subsumes the majority of the alpha effect, however, none of the factor models fully explain the alphas of sample anomalies. Finally, we find that few of the sample anomalies are countercyclical in nature and thus, provide time diversification opportunity. Profitability-size anomaly provides risk adjusted time diversification opportunity. Our results have significant implications for portfolio managers, policy makers and academia.

Keywords

Equity market anomalies asset pricing Indian economy portfolio strategies VIX time-diversified strategies

JEL Codes: C13, C22, G11, G12

I. Introduction

The central point of financial research is to explore the reason behind the variation in cross section of stock returns. Sharpe (1964), Lintner (1965) and Mossin (1969) provide an explanation of the variation by providing risk–return trade-off through the popular capital asset pricing model (CAPM). However, post CAPM, there have been significant deviations observed in the literature wherein researchers have shown that using certain firm characteristics, extra-normal returns can be generated which are called anomalies in the asset pricing literature. One of the earliest anomalies being found are size (Banz, 1981) and value (Stattman, 1980). Fama and French (1993) acknowledged the role of size and value effects in determining cross section of stock returns and provide an alternative multifactor asset pricing model, namely, Fama–French three-factor model (FF3), which posed serious challenge to CAPM. Jegadeesh and Titman (1993) observe another anomaly, that is, momentum anomaly, wherein past winners (stock returns in the past 3–12 months) remain winners in the next 3–12 months. Carhart (1997) augmented FF3 factors with an additional momentum factor and provide a four-factor asset pricing model for explaining stock returns.

In the recent literature, Cooper et al. (2008) find that growth in investments, also known as asset growth, is inversely related to stock returns and called it asset growth or investment anomaly. Another important anomaly observed in the academic literature is profitability anomaly, which claims a positive relationship between profitability and stock returns (Ball et al., 2016; Fama & French 2015; Haugen & Baker, 1996; Novy-Marx, 2013). Fama and French (2015, 2017) combined the profitability and investment rate anomalies and recommend two additional factors in addition to FF3 for explaining stock returns popularly known as Fama–French five-factor model (FF5).

Recently, several studies have been conducted to test the efficacy of the FF5 model. Zaremba and Czapkiewicz (2017) establish the superiority of FF5 in comparison to above-mentioned three other asset pricing models. Fama and French (2017) confirm the efficacy of FF5 for 23 developed markets, while Foye (2018) finds FF5 to be better predictor in Latin America and East European markets but observe it to be a poor model for explaining returns in Asian markets. Similarly, Balakrishnan et al. (2018) find FF3 to be the robust model in explaining stock returns for Indian market as compared to other models.

Apart from studying the prominent anomalies for the entire period, Copeland and Copeland (2016) provide a time-varying explanation of size anomaly. Size effect is mainly considered as a small firm effect, wherein due to various risks present in them (Pandey & Sehgal, 2016), small-size companies provide better returns as compared with large-size companies. They argue that when the macroeconomic uncertainty increases (which is measured by positive change in VIX), large-cap portfolio provides higher returns, and when the macroeconomic uncertainty decreases (as measured by negative change in VIX), small-cap portfolio provides higher returns. They consider VIX as a measure of fear psychosis and relate it to size anomaly. Hence, as per their argument size anomaly, that is, small-cap portfolios outperforming large-cap portfolios, works under low economic uncertainty and it reverses under high economic uncertainty, that is, large-cap portfolios beat small-cap portfolios. They recommend that according to economic conditions, investors should shift their portfolio between small-cap and large-cap stocks. The study has been conducted in the US context and should be evaluated in the context of other markets, including India. Besides, it would also be interesting to see how other sample anomalies behave under the macroeconomic uncertainty.

Novy-Marx (2012) recommends a time-diversified trading strategy to investors wherein the author combines the asset growth and profitability anomalies for US markets by showing that their bivariate strategy beats the portfolios formed on a univariate strategy. It would be interesting to test if such bivariate strategies could be formed by combining different anomalies from an emerging market perspective.

In the backdrop of the above literature, we conduct the present study to confirm the presence of five major equity anomalies, namely, size, value, profitability, investment and momentum, for the Indian equity markets. Mere confirmation of the presence of anomalies is not sufficient, so we also check if such anomalies can be explained by prominent asset pricing models. We use CAPM, FF3, Carhart and FF5 as our sample asset pricing models to check if the equity market anomalies sustain post asset pricing tests. We also examine if profitable trading strategies could be formed under different economic conditions and finally we evaluate if profitable time-diversified strategies could be formed by fund managers in Indian equity markets.

Our contribution to the literature is to provide an out-of-sample study for an emerging market, that is, India to test if the major equity market anomalies exist in India and also to examine their persistence using prominent asset pricing models. Though, in India, several studies have tested these anomalies (Agarwalla et al., 2013; Balakrishnan et al., 2018; Pandey & Sehgal, 2016; Tripathy & Aggarwal, 2018), profitability and investment anomalies have found limited attention in the existing literature for India. Therefore, we conduct this study to provide evidence on the presence of prominent equity anomalies for India.

Our major contribution is to see if the equity market anomalies behave differently under different macroeconomic uncertainty conditions. Copeland and Copeland (2016) provide evidence of the reversal of size effect, under increasing macroeconomic sensitivity, for the US economy. We find it interesting to test if such size reversal happens in the Indian equity market. Moreover, we further carry out their argument to see such an effect for other sample anomalies as well. To the best of the author’s knowledge no such attempt has been made under the existing literature to test if prominent equity anomalies behave differently under different macroeconomic conditions, especially, for India.

Thus, taking the Copeland and Copeland (2016) argument further, apart from size anomaly, we also test the time-varying behaviour of our other sample anomalies. We examine if the sample anomalies reverse under periods of increasing macroeconomic uncertainty as measured by VIX.

Finally, we contribute to the literature by examining if the sample equity market anomalies are countercyclical in nature for India. If strategies based on some of the sample anomalies become countercyclical in nature, it may provide time diversification benefits (Novy-Marx, 2012). If it happens, we can create a bivariate strategy by combining two univariate strategies, which shall outperform univariate strategy on risk-adjusted basis.

Hence, our major contribution to the emerging market literature is to test the behaviour of prominent equity market anomalies under different macroeconomic conditions and to examine if profitable bivariate, time-diversified, trading strategies could be formed in the Indian context.

In the backdrop of above-mentioned research gaps, we conduct the present study for Indian stock market with the following objectives: (a) test the presence of five prominent equity market anomalies, (b) analyse the efficacy of asset pricing models in explaining these anomalies, (c) evaluate if different trading strategies can be formed under different macroeconomic uncertainty conditions and (d) examine if time-diversified investment strategies can be formed for sample anomalies.

Our study is divided into six sections, including the present one. In Section 2, we provide literature review, and data are discussed in Section 3. Methodology is described in Section 4, and in Section 5 we provide empirical results. Summary and conclusion are explained in the last section.

II. Literature Review

The various anomalies mentioned in the Introduction have been significantly tested in the past decade, especially for matured markets. It has been observed that, over time, size anomaly has been either diminished or disappeared in various capital markets (Crain, 2011; Michou et al., 2010; Nartea et al., 2009; Pandey & Sehgal, 2016). However, in the past couple of years, the debate on size effect has been ignited, and researchers have found it to be present in different global markets (Asness et al., 2018; Ciliberti et al., 2017; Leite et al., 2018; Muns, 2019). Copeland and Copeland (2016) have recommended different size-based strategies based on macroeconomic uncertainty for US markets.

Similarly, value effect has also been tested internationally over time and is found to be a significant anomaly (Leite et al., 2018; Nartea et al., 2009). Denis et al. (2016) confirm the presence of value anomaly for the Finnish stock market. Klaus and Topi (2019) observe the presence of value anomaly among small-cap stocks for the Nordic stock market.

Over time, different strategies based on momentum effect have been suggested by researchers (Alhenawi, 2015; Barroso & Santa-Clara, 2015; Blitz et al., 2018; Chang et al., 2018; Conrad & Yavuz, 2017; Daniel & Moskowitz, 2016; Moskowitz et al., 2012; Novy-Marx, 2012; Novy-Marx & Velikov, 2015; Pukthuanthong et al., 2019; Vu, 2012). Zaremba (2018) examines momentum effect among different anomalies in 78 countries and observes that half of the anomalies among sample countries have momentum effect. Yang and Zhang (2019) observe that portfolios having high volatility tend to lose their momentum strength. Liang et al. (2019) confirm explanatory powers of uncertainties in explaining momentum. Lin et al. (2020) observe no momentum effect for the Taiwanese market.

The two anomalies which have received attention in the recent past have been profitability anomaly and investment rate anomaly. The studies conducted in the past 10 years have confirmed the presence of profitability anomaly in various markets wherein portfolios of high profitable firms have outperformed portfolios of low profitable firms (Artmann et al., 2011; Ball et al. 2016; Chen et al., 2011; Novy-Marx, 2013). Linnainmaa and Roberts (2018) observe the presence of profitability and investment rate anomalies for one period while insignificant effect for the two anomalies in different time periods. Erhard and Sloan (2019) provide lack of investors and analysts anticipation about future dilution in less profitable firms as the reason for sustenance of profitability anomaly.

Similarly, recent literature has shown the presence of asset growth/investment rate anomaly, wherein portfolios based on low investment companies outperform portfolios based on high investment companies (Elliot et al., 2018; Grobys & Kolari, 2016; Nyberg & Pöyry, 2014;). Cao et al. (2018) document negative relationship between stock returns and investment. Chou et al. (2019) find strong connection between asset growth and style investing and propose style momentum strategy based on asset growth and size. Cia et al. (2019) provide investors overreaction as a reason for the presence of asset growth anomaly.

In India, several studies have also been conducted in the recent past to test these anomalies. Pandey and Sehgal (2016) have examined size anomaly through its rationale sources. Tripathy and Aggarwal (2018) have confirmed the presence of value anomaly in Indian markets. Balakrishnan (2016) confirms the presence of size, value and momentum anomaly testing them through the FF3 model. Gonenc and Ursu (2018) document the presence of asset growth anomaly among 26 emerging markets, including India. Sharma et al. (2019) revisit the size, value and momentum anomaly on data set of 2005 to 2016 and find weak persistence of these anomalies.

Thus, we find there several attempts have been made to test various anomalies in the Indian context in the recent past. However, we contribute to the literature by carrying out a comprehensive test of the five prominent anomalies over a longer time period. Secondly, all the recent studies for India have tested anomalies through FF3 or Carhart models. We check the efficacy of four prominent models including FF5 in explaining the anomalies. Third important contribution is to check the behaviour of sample anomalies under different macroeconomic conditions. Lastly, so far none of the studies has checked for time-diversified bivariate strategies based on prominent equity anomalies in India. We contribute to the literature for emerging markets by examining prominent anomalies for India and recommend risk-adjusted trading strategies to global investors.

III. Data

We take month end–adjusted closing prices for a 18-year period, that is, from July 2001 to June 2019, for NSE 500 companies. NSE 500 companies have been taken because these companies constitute over 94 per cent of the market capitalisation and 87 per cent of the traded volume (see Chundakkadan & Sasidharan, 2019). The stock prices have been converted into percentage returns for further estimations. The NSE 500 index has been taken as benchmark index to measure index returns. The 91-day treasury bills have been taken as proxy for risk-free rate from the RBI website. The March year-end information on market capitalisation, price to book value, return on equity and percentage change in total assets has been taken as a proxy to capture firm size, value, profitability and investment affect (or asset growth affect). Momentum effect has been estimated as the average of past six months’ returns. March-end values have been taken for company characteristics because the financial year in India ends in March. The data set has been taken from Capital Line Plus.

We use change in the volatility index, that is, VIX, to measure macroeconomic uncertainty in order to classify our study period. VIX data are available from January 2008 onwards and hence all the estimations with regard to VIX have been done from January 2008 to June 2019. The data with regard to VIX have been taken from Bloomberg.

IV. Methodology

We begin our examination by verifying the presence of five sample anomalies for India. We construct quintile univariate portfolios on excess stock returns based on different ranking criteria. We use size for market capitalisation; P/BV for value; M6 (6*6) for momentum; RoE for profitability and change in total assets as ranking criteria for investment anomaly. We create M6 by ranking sample stocks on the basis of past six months starting from July 2001 and holding them for next six months (i.e. from July to December). We rebalance the portfolios on a six-month basis and repeat the same process until the end of our sample period.

We construct our univariate portfolios based on market capitalisation by ranking stocks each year in June (t) on the basis of sample attributes, say market capitalisation. Next, the ranked securities are divided into quintile portfolios, and equally weighted returns of these portfolios are estimated for next 12 months (i.e. from July of t to June of t + 1), and these returns are called unadjusted returns. P1 becomes the smallest size portfolio (Winner) and P5 the largest size portfolio (loser portfolio). We rebalance the portfolios every year in June and hold them for next 12 months until the end of our sample period. We repeat the same process for constructing portfolios based on P/BV, RoE and change in total assets with an alteration that for RoE and change in total assets rankings are done on March of every year. P1 of portfolios formed on value (P/BV) and investment rate (change in total assets) are called as winner portfolios, whereas P5 of momentum and profitability (RoE) are called as winner portfolios. P5 for value and investment rate and P1 for momentum and profitability are called loser portfolios.

Next, in order to verify the behaviour of portfolio returns based on sample anomalies, under different macroeconomic uncertainties, we adopt the methodology of Copeland and Copeland (2016). We categorise each month of the time period as one exhibiting high (low) macroeconomic uncertainty based on whether the change in VIX values (delta VIX) is positive (negative). Copeland and Copeland (2016) defined positive delta VIX as a period of high macroeconomic uncertainty and observed that portfolios of large-cap stocks performed better than small-cap stocks under such periods. They further observed the contrary trend in periods of negative delta VIX periods.

Table 1

Factor Model Descriptions

Equation	Model	Equation	Remarks
1	CAPM	Rp_t − Rf_t = α + β (Rm_t − Rf_t) + e_t	Rp_t − Rf_t = excess return on sample portfolioRm_t − Rf_t = excess return on the market factorα and β = estimated parametersand e_t = error term
2	FF3	Rp_t − Rf_t = α + β (Rm_t − Rf_t) + s (SMBt) + l (LMHt) + e_t	SMB and LMH proxy size and value factors. s and l are coefficients of SMB and LMH factors, respectively. Other terms have the same meaning as in equation (1).
3	Carhart	Rp_t − Rf_t = α + β (Rm_t − Rf_t) + s (SMBt) + l (LMHt) + w (WMLt) + e_t	WML is proxy for price momentum and w is the sensitivity coefficient.
4	FF5	Rp_t − Rf_t = α + β (Rm_t − Rf_t) + s (SMBt) + l (LMHt) + r_i (RMWt) + c_i (CMAt ) + e_t	RMWt proxies for profitability factor measured as robust minus weak profitability, and CMAt proxies for investment factor measured as conservative minus aggressive investment. r_i and c_i are the sensitivity coefficients.

Source: Author’s own.

Taking their arguments further, we test, apart from size, if similar patterns are observed for other anomalies, namely, value, momentum, profitability and investment. If their argument is correct, then low P/BV, high momentum, high profitability and low investment should perform better when macroeconomic uncertainty is low while results should reverse under high economic uncertainty. Hence, we test the behaviour of portfolios formed based on all sample anomalies under different economic situations.

We start our examination by forming positive delta VIX and negative delta VIX size-based portfolios to observe their mean-unadjusted returns. We want to see if small-size effect persists under low economic uncertainty and if the trend reverses (as argued by Copeland) and large-size effect emerges under high economic uncertainty. We repeat the same process for our other sample anomalies and observe their unadjusted returns for further analysis and estimations.

Finally, we use alternative asset pricing models to test to meet the twin objectives of identifying profitable trading strategies as well to see which asset pricing model is the best descriptor of explaining anomalies in India. We start our analysis by testing each of the anomalies on single factor model, that is, CAPM, to see if the market factor is able to explain the extra-normal returns. Further, we test the efficacy of the different versions of multifactor models in explaining anomaly returns. Equations of factor models are given in Table 1.

Size, value, momentum, profitability and investment factors have been constructed using standard construction practice as followed in the asset pricing literature (Carhart, 1997; Fama & French, 2015; Nedumparambil & Bhandari, 2020). Any multicollinearity problem is sorted out before introducing these factors in the F–F framework. We run all regressions using Newey–West procedure to correct for heteroscedasticity and autocorrelation.

To examine countercyclical strategies, we form a dual attribute strategy (Novy-Marx, 2012) by combining two univariate portfolios and estimating their average returns over time. The two univariate portfolios have been selected based on the attributes which have time diversification possibilities. In order to create combine portfolios, we employ two filters. Firstly, we include only those univariate portfolios as the prospective portfolios whose monthly unadjusted returns are over 0.5 per cent to ensure that we can have reasonable time-diversified returns. Secondly, we consider only those portfolios, after passing the first filter test, which are significantly negatively correlated. After putting filters, we calculate the Sharpe ratio for the winners in univariate portfolios as well as of the combined bivariate portfolios to see if bivariate portfolios provide better risk-adjusted returns. Finally, we examine if bivariate portfolios provide extra-normal returns after passing through the test of sample asset pricing models used as performance benchmarks.

V. Empirical Results

Unadjusted Returns

We start our analysis by reporting mean monthly unadjusted returns of the portfolios ranked on our sample anomalies for total period and provide results in Table 2(A). We confirm the presence of all the prominent anomalies for our sample data in India. In consistence with literature, we find P1 outperforming P5 for size, value and investment anomalies, and P5 outperforming P1 for profitability and momentum anomalies. Size effect is found to be the strongest among all the anomalies, which provides an annual unadjusted return of 41.02 per cent. It is followed by value effect, which provides an annual unadjusted return of 31.42 per cent for our sample period. Investment, momentum and profitability anomalies also provide annual unadjusted returns in between 24 and 27 per cent. Thus, we confirm the presence of all the anomalies, based on unadjusted returns, for India. Such huge unadjusted returns are significant enough to attract the attention of global fund managers to explore investment opportunities in India.

Next, we report the mean unadjusted returns of the univariate portfolios under low and high economic uncertainties based on delta VIX. Negative delta VIX implies low economic uncertainty and we expect that the results should be in accordance with the established asset pricing literature. On the other hand, positive delta VIX implies high economic uncertainty and (as per Copeland argument) we should get reverse anomaly results under it. We report our results in Table 2 (B and C). Under a negative delta VIX period, the results are found to be in accordance with asset pricing literature as we find low size, value and investment effect and high profitability and momentum effect in the Indian equity market. In fact, the results are stronger than those of total period as the unadjusted annual returns vary in between 48.55 and 67.38 per cent. Size effect is found to be the strongest among all the anomalies.

Finally, we observe return patterns under high macroeconomic uncertainty and find low size effect, high momentum and profitability effect and negligible investment effect. We further observe that the returns of portfolios formed on value reverse under high economic uncertainty. Thus, we find that, unlike the Copeland argument, there is no large firm effect present in India under high economic uncertainty. We further observe that more profitable firms and high past performance firms continue to beat the less profitable and past losers under high delta VIX periods. The only exception is found to be value effect wherein growth stocks seem to outperform value stocks, which is in conformity to the Copeland argument. In sum, we observe that the Copeland argument is not found to be relevant for size, momentum and profitability anomaly in India. However, it appears to be working for value anomaly for India, and one of the reasons for such a reversal could be relative distress in value companies under periods of high economic uncertainty. This argument is also provided by Chan and Chen (1991), which states that value effect may differ under different macroeconomic conditions due to relative distress present in them.

Table 2

Mean Unadjusted Returns for Attribute Sorted Portfolios

Panel A: Mean Returns for Total Period
Attributes	P1	P2	P3	P4	P5	Long–short
Size	0.0342	0.0227	0.0170	0.0160	0.0109	0.0233
t-statistic	5.0593	3.5822	2.9383	2.8984	2.1148	5.4183
Value	0.0262	0.0249	0.0217	0.0184	0.0146	0.0116
t-statistic	3.4728	3.5415	3.4849	3.4604	2.9343	2.4890
Profitability	0.0217	0.0184	0.0176	0.0198	0.0201	0.0010
t-statistic	3.0476	3.0415	3.1859	3.7413	3.8433	0.4486
Investment rate	0.0228	0.0207	0.0166	0.0190	0.0165	0.0062
t-statistic	3.7170	3.5544	3.0975	3.3876	2.8509	2.7810
Momentum	0.0178	0.0176	0.0167	0.0182	0.0219	0.0041
t-statistic	2.6108	3.1401	3.0390	3.4187	3.8773	1.0836
Panel B: Mean Return for Low Economic Uncertainty (Negative VIX)
Attributes	P1	P2	P3	P4	P5	Long–short
Size	0.0562	0.0413	0.0345	0.0336	0.0275	0.0286
t-statistic	5.4066	4.2169	3.8689	3.9775	3.5353	4.9241
Value	0.0548	0.0409	0.0418	0.0370	0.0304	0.0244
t-statistic	4.5495	4.0073	4.3129	4.5737	4.0888	3.5070
Profitability	0.0425	0.0393	0.0370	0.0369	0.0364	−0.0061
t-statistic	4.0350	4.0781	4.1943	4.4967	4.7292	−1.3103
Investment rate	0.0437	0.0412	0.0347	0.0363	0.0361	0.0076
t-statistic	4.6578	4.5442	4.2293	4.2372	3.8878	2.8936
Momentum	0.0400	0.0380	0.0364	0.0355	0.0405	0.0005
t-statistic	3.5821	4.0851	4.1153	4.7657	5.1599	−0.0325
Panel B: Mean Return for High Economic Uncertainty (Positive VIX)
Attributes	P1	P2	P3	P4	P5	Long–short
Size	−0.0139	−0.0252	−0.0281	−0.0280	−0.0292	0.0153
t-statistic	−1.2607	−2.5178	−3.0865	−3.0765	−3.4738	2.7619
Value	−0.0340	−0.0265	−0.0271	−0.0221	−0.0221	−0.0119
t-statistic	−2.8255	−2.5246	−2.8473	−2.4815	−2.6217	−2.1098
Profitability	−0.0363	−0.0290	−0.0244	−0.0188	−0.0181	0.0182
t-statistic	−3.3341	−3.0714	−2.5594	−2.1553	−2.0506	−4.2154
Investment Rate	−0.0263	−0.0249	−0.0250	−0.0241	−0.0263	−0.0001
t-statistic	−2.6133	−2.6698	−2.9144	−2.6211	−2.5896	−0.0258
Momentum	−0.0287	−0.0250	−0.0258	−0.0255	−0.0203	0.0084
t-statistic	−2.5628	−2.7595	−2.8788	−2.8530	−2.1884	1.4978

Source: Author’s own.

Note: The table provides the mean unadjusted returns of quintile portfolios and long-short portfolio based on various anomalies along with their t-statistic. P1 denotes small size, low price-to-book value, low profitability, high asset growth and low momentum. P5, on the other hand, denotes big size, high price-to-book value, high profitability, low asset growth and high momentum. Mean excess returns are shown for both total period and two subperiods, which are divided based on economic uncertainty as represented by negative and positive VIX.

Table 3

CAPM Results

Size portfolios
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0237	1.1199	5.5896	18.4798	0.6130
P5	0.0009	1.0667	0.8788	71.9421	0.9601
Value portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0143	1.2720	3.1086	19.3697	0.6351
P5	0.0052	1.0084	3.5657	48.5162	0.9163
Profitability portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0094	1.3080	2.6651	25.8909	0.7569
P5	0.0104	1.0351	5.6291	39.1964	0.8772
Investment portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0119	1.1622	4.3624	29.8565	0.8055
P5	0.0059	1.1357	2.6683	35.8199	0.8564
Momentum portfolio
Portfolio	α	β	tα	tβ	Adj. R²
M1	0.0059	1.2679	1.8169	27.3075	0.7760
M5	0.0118	1.0771	4.7980	30.5927	0.8130
Panel B: Results for Delta VIX-negative Period
Size portfolios
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0238	1.3044	3.9015	13.4998	0.7073
P5	-0.0006	1.1361	-0.3738	42.3907	0.9599
Value portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0170	1.5260	2.4515	13.9288	0.7202
P5	0.0045	1.0482	1.6825	24.9658	0.8924
Profitability portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0065	1.4516	1.4946	20.9419	0.8537
P5	0.0099	1.0671	3.2467	22.0517	0.8661
Investment portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0120	1.2776	2.9008	19.4935	0.8348
P5	0.0036	1.3122	1.1177	25.8914	0.8992
Momentum portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0019	1.5667	0.3960	21.1765	0.8564
P5	0.0148	1.0361	3.7360	16.5517	0.7845
Panel C: Results for Delta VIX-positive Period
Size portfolios
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0196	1.2307	3.0986	14.2607	0.7655
P5	−0.0006	1.0508	−0.3326	40.3286	0.9633
Value portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0031	1.3644	0.4814	15.3641	0.7913
P5	0.0058	1.0263	1.9419	25.2283	0.9111
Profitability portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	−0.0017	1.2750	−0.3234	18.2496	0.8427
P5	0.0105	1.0504	2.7926	20.5246	0.8714
Investment portfolio
Portfolio	α	β	tα	tβ	Adj. R²
P1	0.0059	1.1851	1.2872	18.9097	0.8519
P5	0.0067	1.2109	1.6038	21.2612	0.8792
Momentum portfolio
Portfolio	α	β	tα	tβ	Adj. R²
M1	0.0062	1.2845	1.0741	16.2168	0.8086
M5	0.0087	1.0677	1.8525	16.5613	0.8151

Source: Author’s own.

Note: The table reports results based on the single-factor model, that is, CAPM containing alpha values and market factor denoted by β and their t-statistic values. The results are reported for total period as well as two subperiods representing macroeconomic uncertainty.

Table 4

Fama–French Three-factor Model Results

Panel A: Total Period Results
Size portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P1	0.0134	1.1005	1.0518	0.4558	3.8417	28.3405	10.3510	7.7446	0.8394
Value portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P1	0.0094	1.1944	0.5711	0.6649	2.1687	18.7533	4.3708	6.3111	0.7505
P5	0.0030	1.0305	0.1934	−0.0761	2.2746	29.7462	4.6440	−2.7615	0.9294
Profitability portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P1	0.0047	1.2815	0.5042	0.3258	1.4358	21.0666	5.7964	2.8458	0.8135
P5	0.0070	1.0582	0.3108	−0.0440	3.8752	31.9563	5.8672	−1.1675	0.9040
Investment portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P1	0.0067	1.1447	0.5345	0.2797	2.6929	34.1623	7.2379	4.1435	0.8823
P5	0.0021	1.1424	0.3704	0.0763	1.0345	19.4319	5.6366	1.5461	0.8881
Momentum portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
M5	0.0070	1.0888	0.4640	0.0756	3.0909	21.8615	6.6795	1.6874	0.8650
Panel B: Results for Delta VIX-negative Period
Size portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P1	0.0078	1.1447	1.3109	0.4634	2.6217	20.7346	12.6488	5.9722	0.9396
Value portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P1	0.0049	1.2392	1.0014	0.7921	0.8127	12.4642	4.9735	5.4007	0.8716
Profitability portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P5	0.0050	1.1094	0.4015	−0.1004	1.6711	10.9620	5.9486	−1.8436	0.9118
Investment portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P1	0.0026	1.1378	0.7752	0.3946	0.9933	22.1179	7.8025	7.1143	0.9460
Momentum portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P5	0.0071	0.9964	0.6284	0.1243	2.1243	10.1755	6.9938	1.6795	0.8705
Panel C: Results for Delta VIX-positive Period
Size portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P1	0.0060	1.0496	1.3433	0.5919	1.7704	21.9365	13.4844	7.3396	0.9475
Profitability portfolio
Portfolio	α	β	β_SMB	β_LMH	tα	tβ	t _SMB	t _LMH	Adj. R²
P5	0.0024	1.0282	0.6452	−0.0478	0.6922	18.3345	9.9831	−0.8030	0.9271

Source: Author’s own.

Note: In this table, we report the alpha and coefficient values of the Fama–French three-factor model, that is, market, size and value. Size and value are represented by SMB and LMH. Values for total period as well as two subperiods are reported.

Asset Pricing Test Results

We first examine the efficacy of CAMP in explaining unadjusted returns of our sample portfolios and provide results in Table 3. Due to paucity of space, we provide results only of corner portfolios, that is, P1 and P5 from hereon under all asset pricing models. We find that for total period, CAPM is able to explain unadjusted returns of only two out of ten portfolios evaluated by us. Further, we observe that CAPM could not explain unadjusted returns for any of the sample anomalies. However, the market factor plays an effective role in explaining unadjusted returns as the annual risk-adjusted returns (given by alpha values) range in between 12.48 per cent (P5 of profitability) to 28.44 per cent (P1 of size), which is substantial reduction over the unadjusted returns.

Similarly, for the delta VIX negative period, it could not explain unadjusted returns of the winner portfolios. However, it is able to explain the unadjusted returns of all the five loser portfolios. Thus, CAPM is able to explain unadjusted returns of five out of ten portfolios under negative delta VIX period.

CAPM appears to be working better under high economic uncertainty, as barring winner portfolios of size and profitability, it is able to explain the rest of the eight portfolio returns. Thus, we find that CAPM is not able to fully explain any of the sample anomalies for India both for total and low economic uncertainty period.

Next, we move to multifactor models by first applying FF3 followed by Carhat and FF5 model and results are reported in Tables 4 –6. We examine only those portfolios that remained unexplained by CAPM. We observe that, like CAPM, FF3 is not able to explain any of the winner portfolio returns for total period. It is able to explain only two (loser portfolios) out of the remaining portfolios. However, we observe the role of size and value factors in explaining returns as the alpha value of winner portfolios further decreases and annual returns lie in between 8.05 and 16.03 per cent, which is again substantial reduction in comparison to CAPM alpha values. Size effect remains the strongest anomaly in the Indian context.

FF3 appears to be effective for explaining unadjusted returns under negative delta VIX period. Except size and profitability winner portfolios, FF3 is able to explain unadjusted returns of all the other portfolios. Similarly, it is able to explain both the remaining portfolios under delta VIX positive period. Thus, we observe that though FF3 is not able to explain any of the winner portfolios for total period, it appears to be an effective model for explaining returns of the majority of the portfolios under macroeconomic uncertainty period. Further, we also conclude, that after applying FF3, all the portfolios unadjusted returns got explained for high economic uncertainty period, including the size effect. Thus, the Copeland argument is totally negated for Indian equity markets, and it provides no risk-adjusted trading strategy for portfolio managers.

Table 5

Carhart Model Result

Panel A: Total Period Results
Size portfolio
Portfolio	α	β	βSMB	βLMH	βMom	tα	tβ	tSMB	tLMH	tMom	Adj. R2
P1	0.0138	1.0818	1.0757	0.4242	−0.1314	4.1452	33.6507	11.1859	7.5343	−2.4475	0.8436
Value portfolio
Portfolio	α	β	βSMB	βLMH	βMom	tα	tβ	tSMB	tLMH	tMom	Adj. R2
P1	0.0100	1.1708	0.6014	0.6249	−0.1659	2.2872	20.3233	4.5385	5.8130	−1.7165	0.7557
P5	0.0032	1.0235	0.2024	−0.0879	−0.0491	2.3218	38.3535	4.7364	−3.1394	−1.2088	0.9303
Profitability portfolio
Portfolio	α	β	βSMB	βLMH	βMom	tα	tβ	tSMB	tLMH	tMom	Adj. R2
P5	0.0072	1.0521	0.3186	−0.0542	−0.0423	3.9089	38.9282	6.0758	−1.3352	−0.9924	0.9044
Investment portfolio
Portfolio	α	β	βSMB	βLMH	βMom	tα	tβ	tSMB	tLMH	tMom	Adj. R2
P1	0.0072	1.1267	0.5576	0.2493	−0.1262	2.9528	38.4021	7.9380	3.6941	−2.8033	0.8874
Momentum portfolio
Portfolio	α	β	βSMB	βLMH	βMom	tα	tβ	tSMB	tLMH	tMom	Adj. R2
M5	0.0059	1.1352	0.4047	0.1540	0.3252	2.9273	42.6353	6.6493	2.9733	7.5453	0.9080
Panel B: Results for Delta VIX Negative Period
Size portfolio
Portfolio	α	β	βSMB	βLMH	βMom	tα	tβ	tSMB	tLMH	tMom	Adj. R2
P1	0.0087	1.1085	1.3328	0.4401	−0.0853	2.9826	21.8415	14.0469	5.3596	−1.8259	0.9408
Momentum portfolio
Portfolio	α	β	βSMB	βLMH	βMom	tα	tβ	tSMB	tLMH	tMom	Adj. R2
P5	0.0033	1.1626	0.5281	0.2312	0.3912	1.8063	36.9340	6.9830	4.0061	9.9071	0.9448

Source: Authors own.

Note: We provide the results of the Carhart model, where apart from the Fama–French three-factor model, we regress the quintile portfolio returns, based on sample anomalies, on an additional factor represented by momentum. Momentum factor is represented by Mom.

Table 6

Fama–French Five−factor Model Results

Panel A: Total Period Results

Size portfolio

Portfolio

βSMB

βLMH

βProfitability

βInvestment

tα

tβ

tSMB

tLMH

tProfitability

tInvestment

Adj. R2

0.0137

1.0292

0.9759

0.3203

−0.3185

0.0871

4.0396

22.6566

9.0580

4.6971

−3.9357

0.8602

0.8627

Value portfolio

Portfolio

βSMB

βLMH

βProfitability

βInvestment

tα

tβ

tSMB

tLMH

tProfitability

tInvestment

Adj. R2

0.0088

1.1000

0.4322

0.4383

−0.4193

0.3521

2.2979

14.3285

3.2394

3.9318

−3.5324

1.7827

0.8017

0.0032

1.0327

0.2027

−0.0634

0.0092

−0.0458

2.2813

29.3326

4.7991

−1.8552

0.1969

−0.7648

0.9292

Profitability portfolio

Portfolio

βSMB

βLMH

βProfitability

βInvestment

tα

tβ

tSMB

tLMH

tProfitability

tInvestment

Adj. R2

0.0064

1.0916

0.3288

−0.0022

0.1503

0.0678

3.5279

32.6049

6.1737

−0.0441

2.8496

0.9429

0.9093

Investment portfolio

Portfolio

βSMB

βLMH

βProfitability

βInvestment

tα

tβ

tSMB

tLMH

tProfitability

tInvestment

Adj. R2

0.0055

1.0863

0.4185

0.1025

−0.2572

0.4040

2.7858

28.9550

6.6663

2.4300

−5.0067

5.7101

0.9333

Momentum portfolio

Portfolio

βSMB

βLMH

βProfitability

βInvestment

tα

tβ

tSMB

tLMH

tProfitability

tInvestment

Adj. R2

0.0060

1.0811

0.4193

0.0159

−0.0318

0.2353

2.8047

25.3770

6.0184

0.3408

−0.5136

2.6575

0.8731

Panel B: Results for Delta VIX-negative Period

Size portfolio

Portfolio

βSMB

βLMH

βProfitability

βInvestment

tα

tβ

tSMB

tLMH

tProfitability

tInvestment

Adj. R2

0.0087

1.1147

1.3502

0.4817

−0.0486

−0.1425

2.2439

20.7965

15.4711

4.9073

−0.3520

−0.5658

0.9387

Source: Authors own.

Note: In this table, we report the results of our final multifactor model, that is, the Fama–French five-factor model, wherein apart from market, size and value, we regress portfolio returns on two additional factors represented by profitability and investment rate. Profitability and investment are the connotations used for these two additional factors respectively.

Table 7

Time Diversification Strategy Results

Panel A: Sharpe Ratio
Attributes	Mean				SD			Sharpe Ratio
Size	0.0342				0.0993			0.3442
Value	0.0262				0.1108			0.2363
Profitability	0.0201				0.0768			0.2615
Investment	0.0228				0.0900			0.2529
Momentum	0.0219				0.0830			0.2638
Value–momentum	0.0481				0.0554			0.8679
Profitability–investment	0.0428				0.0384			1.1162
Profitability–value	0.0463				0.0384			1.2064
Profitability–size	0.0543				0.0496			1.0934
Panel B: CAPM Results
Portfolio		α			β			tα			tβ			Adj. R2
Value–momentum		0.0261			2.3491			4.3837			27.3261			0.7733
Profitability–investment		0.0223			2.1974			5.4959			37.9196			0.8698
Profitability–value		0.0247			2.3071			4.4122			22.0536			0.8006
Profitability–size		0.0341			2.1550			6.2085			27.4512			0.7778
Panel C: FF3 Results
Portfolio	α			β			βSMB			βLMH			tα				tβ		tSMB		tLMH		Adj. R2
Value–momentum	0.0165			2.2832			1.0351			0.7405			3.0830				31.2715		6.3110		6.2762		0.8559
Profitability–investment	0.0137			2.2028			0.8454			0.2357			3.5855				41.3931		7.3146		2.7730		0.9172
Profitability–value	0.0164			2.2526			0.8819			0.6209			3.1783				26.5072		5.6300		5.5353		0.8639
Profitability–size	0.0204			2.1587			1.3626			0.4118			4.2844				34.8676		9.2657		4.9930		0.8949
Panel D: Carhart Results
Portfolio	α				β		βSMB		βLMH		βMom				tα	tβ			tSMB		tLMH		tMom		Adj. R2
Value–momentum	0.0147				2.3036		1.0371		0.7917		0.1879				2.9302	32.2467			8.8204		7.3559		2.1757		0.8584
Profitability–investment	0.0143				2.1963		0.8447		0.2194		−0.0600				3.6310	47.2789			7.0919		2.3503		−0.6070		0.9172
Profitability–value	0.0174				2.2410		0.8808		0.5919		−0.1067				3.1140	30.0431			5.5617		5.0117		−0.8064		0.8643
Profitability–size	0.0204				2.1582		1.3626		0.4105		−0.0049				4.5130	34.0876			9.2620		4.3098		−0.0404		0.8945
Panel E: FF5 Results
Portfolio	α		β			βSMB		βLMH		βProf		βInvst		tα			tβ	tSMB		tLMH		tProf		tInvst		Adj. R2
Value–momentum	0.0034		0.9587			0.4956		0.6082		1.2498		0.9206		0.8739			4.4170	2.8952		5.4257		6.7978		3.6223		0.9023
Profitability–investment	−0.0006		0.4569			0.2357		0.1878		1.6487		0.5920		−0.4119			7.7462	4.4146		3.8431		27.3515		7.4600		0.9849
Profitability–value	0.0016		0.4672			0.2517		0.5634		1.6859		0.6473		0.4656			2.5518	1.7062		5.0027		9.9551		2.7563		0.9238
Profitability–size	0.0063		0.2630			0.7535		0.4256		1.7908		0.3196		2.2807			2.8398	8.9442		7.7386		21.2185		2.7201		0.9598

Source: Authorss own.

Note: Panel A shows the winner portfolios of total period as well as bivariate portfolios based on our time-diversified strategy. Panels B–E show results based on the asset pricing tests of bivariate portfolios formed based on the time diversification strategy.

We find that the Carhart model has negligible additional explanatory power in explaining returns for India as it is not able to explain any of the winner portfolios for total period. It explains only the momentum anomaly under low economic uncertainty; however, size effect remains unexplained.

Finally, we find no additional role of profitability and investment factor under FF5 for explaining unadjusted returns of any of the remaining portfolios. There is negligible reduction in alpha values after applying the FF5 model as compared to FF3. Thus, we find Carhart and FF5 to be ineffective asset pricing models for India.

In nutshell, we find that none of the asset pricing models is able to fully explain any of the sample anomalies except, investment anomaly, in the Indian context. The results are similar to other emerging market findings in China (see Guo et al., 2017). All the major anomalies remain significant for India, and we observe annual risk-adjusted returns of 16.50, 10.55, 7.63 and 6.5 per cent for size, value, profitability and momentum anomalies, respectively. Size effect is found to be strongest followed by value and provide an opportunity to portfolio managers to form profitable trading strategies based on them. Though profitability and momentum effect are also found to be statistically significant, their economic significance has to be seen by fund managers before using them as a trading strategy. Finally, we confirm an additional role of multifactor models, especially FF3, in explaining sample anomaly returns in India.

Time Diversification Strategy Results

Our final examination is to test if we can form countercyclical strategies based on time diversification opportunity provided by our sample portfolios. The results are provided in Table 7. We check if the bivariate strategies, which are formed based on countercyclical univariate portfolios, outperform the winner univariate portfolios. We find value–momentum, profitability–investment, profitability–value and profitability–size as the significant bivariate strategies. Based on Sharpe ratios, we observe that all the bivariate strategies outperform the univariate strategies.

Next, we check if the bivariate strategies provide significant risk-adjusted returns by applying sample asset pricing models as used in the above section. We find that profitability–size is the only significant anomaly which remains unexplained by applying multifactor models. It provides an annual unadjusted return of 7.61 per cent, which can be exploited by portfolio managers to generate extra-normal returns for their investors.

VI. Summary and Conclusion

We conduct this study and contribute to the existing asset pricing literature as follow: (a) observe if the five prominent anomalies, viz., size, value, profitability, investment and momentum, are present in the Indian context; (b) check the efficacy of multifactor models, that is, CAPM, FF3, Carhart and FF5, in explaining sample anomalies; (c) examine if sample anomalies behave differently under high and low macroeconomic uncertainties in order to provide profitable trading strategies to portfolio managers; (d) provide an evidence of Copeland and Copeland (2016) argument for an out-of-sample study and extend their size argument to other anomalies; (e) check if univariate strategies based on firm attributes are countercyclical in nature and provide time diversification opportunities to portfolio managers; and (f) assess if bivariate strategies formed on countercyclical nature of univariate portfolios provide better risk-adjusted returns as compared to univariate portfolios.

We test our objectives by using 18 years’ data from July 2001 to June 2019, and observe that the annualised unadjusted returns for long portfolios of our sample anomalies range in between 24 and 41 per cent, which are substantial by any measure to attract attention of fund managers. Further, we find no reversal of anomalies, except value effect, in periods of high economic uncertainty as measured by delta VIX.

We further observe that CAPM has a limited role in explaining unadjusted returns for our sample anomalies. FF3 appears to be the relevant multifactor model for India as it sufficiently subsumes the alpha effect of all the sample anomalies. Carhart and FF5 factor do not appear to play any significant additional role in explaining returns in the context of India. On risk-adjusted basis, we find all the anomalies, except investment anomaly, to be relevant for India. However, size and value effect are the two prominent anomalies which provide double-digit annual risk-adjusted returns.

Based on time diversification strategies, we observe profitability–size to provide significant risk-adjusted returns, which can be exploited by portfolio managers for India.

We conclude by suggesting that size and value anomalies in India provide substantial risk-adjusted returns and should be looked upon for forming profitable trading strategies. We further observe that the Copeland argument is unfound in India for any of the anomalies. Hence, it should be tested for other markets before suggesting any universal application. Finally, bivariate time-diversified strategies could be formed in India based on profitability and size effect.

Our study has implications for academia, market regulators and portfolio managers. Using 18 years of data, we recommend that portfolio managers can form profitable univariate as well as bivariate trading strategies based on prominent equity market anomalies for India. Market regulators should try to bring in more transparency and efficiency in system as our results show that publicly available information can be used to generate extra-normal returns in India. For academia, we add to the existing asset pricing literature and provide an evidence of the persistence of prominent asset pricing anomalies for India.

Footnotes

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Asheesh Pandey

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