The weak-form efficiency of the Indian stock market: Fresh Evidence
Research Synopsis & Key Empirical Discovery
The primary goal of the present research initiative is to determine if the Indian stock market follows a random walk or not. The data on eight NIFTY sectoral indices’ daily opening, closing, high and low values are investigated from 3 January 2012 to 31 December 2021. The Augmented Dickey–Fuller (ADF) test and the Phillips–Perron (PP) test are used to assess the stationarity of the selected eight sectoral indices. The Variance ratio test is used to check for auto-correlation between the returns and the Runs test is performed to examine if the stock market followed a random walk or not.
The unit root tests show that the returns from the eight selected sectoral indices are integrated of order 1. According to the variance ratio test, future stock prices can be forecasted by prior stock prices in the Indian stock market. The Runs test results indicate that the returns are not random throughout the studied time frame—confirming that the Indian stock market is weak-form inefficient.
1. Introduction & The Efficient Market Hypothesis (EMH)
Numerous types of research have been done ever since the efficient market hypothesis notion was created to support or, in some cases, refute the theory. It is practically hard to predict future prices and turn a profit from them when it is clear that prices move randomly or drunkenly. On the other hand, if the outcome is the opposite, there is a potential to profit simply by looking at a security price’s historical behaviour. Because of this, economists and the general investing community are particularly interested in this topic.
The Efficient Market Hypothesis (EMH) was first proposed in financial literature by Samuelson (1965) and Fama (1965). According to EMH, share prices adjust swiftly in reaction to new information; therefore, current prices should fully reflect all available information and follow a random walk, which means that subsequent stock price changes (returns) should be distributed independently and equally. EMH described an efficient market as one in which prices always entirely reflect available information.
Fama’s (1970) Three Levels of Financial Market Efficiency:
Dynamic Transformation of the Indian Financial Market (2012–2021):
- GDP Expansion: India’s GDP surged from USD 1.83 trillion to USD 2.66 trillion (World Bank, 2022).
- Market Appreciation: The Nifty Broad Index expanded by more than three times during the study period.
- Exponential Retail Investor Demat Growth: Demat accounts climbed from 16.8 million in 2009 to 39.3 million in 2019.
- Digital & Information Democratization: Rapid expansion of low-cost internet and ubiquitous online trading systems allowed anyone to trade shares seamlessly from anywhere in the world.
2. Comprehensive Literature Review
Empirical literature on weak-form market efficiency presents contradictory findings across global and Indian markets, motivating this granular sectoral inquiry:
Studies Supporting Weak-Form Efficiency:
- Hong (1978): Analyzed daily data (1973–1976) across Australia, Japan, Hong Kong, and Singapore; discovered Japanese stocks were more efficient and larger stock exchanges exhibited higher efficiency.
- Chan et al. (1992): Investigated 18 national stock markets individually and collectively, supporting weak-form efficiency alongside a contagion effect.
- Indian Context: Chavannavar and Patel (2016), Jain and Jain (2013), and Asiri and Asiri (2008) documented weak-form efficiency in Indian equities.
Studies Refuting Weak-Form Efficiency (Inefficient):
- Panas (1990): Athens stock market rejected weak-form efficiency using autocorrelation, Kolmogorov-Smirnov, runs, and Von Neumann tests.
- Worthington & Higgs (2003): In European markets, only Hungary (emerging) and the UK (developed) satisfied strict random walk criteria; Germany, Ireland, Portugal, and Sweden failed.
- Hamid et al. (2010): Examined 14 Asia-Pacific nations (2004–2009); none followed a random walk.
- Rahman et al. (2021): DSE General and Broad Indices in Bangladesh rejected the random walk hypothesis.
- Li & Li (2016): Examined India, China, Malaysia, and Korea; Runs tests showed random walk, but variance ratio tests proved weak-form inefficiency across all four.
- Khoj & Akeel (2020): Saudi Tadawul All Share Index (TASI) was weak-form inefficient (2012–2019).
- Indian Context: Gupta and Basu (2007) [Sensex & Nifty], Mishra (2009) [BSE 18-year study], Sarkar (2019), Patel et al. (2018), and Elangovan et al. (2022) established Indian stock market inefficiency.
3. Data and Methodology
The empirical dataset spans 10 calendar years from 3 January 2012 to 31 December 2021 (2,475 daily observations) across eight key NIFTY sectoral indices:
Price Averaging Technique: Rather than relying solely on closing prices, this study utilizes the average of daily Open, High, Low, and Closing prices: $$ ext{Price}_t = frac{ ext{Open}_t + ext{High}_t + ext{Low}_t + ext{Close}_t}{4}$$ This average price is selected because it eliminates intra-day outlier variations and effectively controls for market volatility.
Econometric Equations & Test Specifications:
$$JB = frac{n}{6} left[ S^2 + frac{1}{4}(K - 3)^2 ight]$$
Where: n = number of observations / degrees of freedom; S = sample skewness; K = sample kurtosis. The statistic is non-negative; values departing from zero reject normal distribution.$$Z = frac{R - ar{R}}{sigma_R} quad ext{(Equation 2)}$$
$$ar{R} = frac{2n_1 n_2}{n_1 + n_2} + 1 quad ext{(Equation 3: Expected Runs)}$$
$$sigma_R = sqrt{frac{2n_1 n_2 (2n_1 n_2 - n_1 - n_2)}{(n_1 + n_2)^2 (n_1 + n_2 - 1)}} quad ext{(Equation 4: Standard Deviation)}$$
Where: R = observed runs; $ar{R}$ = expected runs; $sigma_R$ = standard deviation; $n_1, n_2$ = count of negative and positive values relative to the mean.
• ADF & PP Unit Root Tests: Evaluate stationarity under constant and constant + trend specifications. Optimal lag length selected via Schwarz Information Criterion (SIC).
• Lo and MacKinlay (1987) Variance Ratio Test: Assesses whether return variance scales linearly with holding interval $k in {2, 4, 8, 16}$. Statistically significant departures indicate serial autocorrelation.
H₀2: The indices have a unit root (non-stationary / random walk).
H₀3: The indices are generated in a random manner.
4. Empirical Findings and Statistical Results
Table 1: Summary Statistics of NIFTY Sectoral Indices Returns
| Statistic | NIFTY Auto | NIFTY Fin Serv | NIFTY FMCG | NIFTY IT | NIFTY Media | NIFTY Metal | NIFTY Pharma | NIFTY Realty |
|---|---|---|---|---|---|---|---|---|
| Mean | 4.605642 | 4.605830 | 4.605696 | 4.605912 | 4.605447 | 4.605491 | 4.605628 | 4.605562 |
| Maximum | 4.678504 | 4.695831 | 4.663530 | 4.671236 | 4.707923 | 4.681303 | 4.697768 | 4.692914 |
| Minimum | 4.504085 | 4.494494 | 4.533239 | 4.514328 | 4.513863 | 4.515734 | 4.534105 | 4.468306 |
| Skewness | -0.597523 | -0.314476 | -0.098561 | -0.791404 | -0.201148 | -0.278971 | 0.050117 | -0.542413 |
| Kurtosis | 10.94469 | 11.99347 | 11.01797 | 12.18418 | 8.740368 | 5.270998 | 9.124951 | 6.769017 |
| Jarque-Bera | 6656.334 | 8381.807 | 6633.693 | 8956.857 | 3414.846 | 563.9631 | 3869.773 | 1586.304 |
| Probability | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| Observations | 2475 | 2475 | 2475 | 2475 | 2475 | 2475 | 2475 | 2475 |
Source: Authors’ Calculation. Note: All indices except NIFTY Pharma exhibit negative skewness; kurtosis indicates non-normal distribution across all series.
Table 2: Unit Root Tests (ADF & Phillips-Perron)
| Variables | Augmented Dickey-Fuller (ADF) | Phillips-Perron (PP) | ||
|---|---|---|---|---|
| Constant (at level) | Constant + Trend (at level) | Constant (at level) | Constant + Trend (at level) | |
| NIFTY Auto | -31.7076* | -31.7271* | -36.5958* | -36.5864* |
| NIFTY Financial Services | -11.3633* | -11.3590* | -38.4550* | -38.4474* |
| NIFTY FMCG | -13.9775* | -14.0172* | -37.5352* | -37.5428* |
| NIFTY IT | -26.3877* | -26.4283* | -38.1131* | -38.1168* |
| NIFTY Media | -12.6184* | -12.6441* | -35.0492* | -35.0567* |
| NIFTY Metal | -14.3538* | -14.3995* | -36.6527* | -36.5838* |
| NIFTY Pharma | -24.7461* | -24.7501* | -35.2525* | -35.2497* |
| NIFTY Realty | -25.3372* | -25.3453* | -33.9717* | -34.3440* |
Source: Authors’ Calculation. Note: * represents statistical significance at the 1% level. All indices reject the unit root null hypothesis at level, confirming stationarity.
Table 3: Runs Test for Randomness of Sectoral Indices
| Sectoral Index | Mean | n₀ (< Mean) | n₁ (≥ Mean) | n₀ + n₁ | Observed Runs | Expected Runs | Z-Statistic |
|---|---|---|---|---|---|---|---|
| NIFTY Auto Index | 4.605642344 | 1199 | 1276 | 2475 | 955 | 1237.302 | -11.362* |
| NIFTY Financial Services Index | 4.605829977 | 1215 | 1260 | 2475 | 953 | 1238.090 | -11.467* |
| NIFTY FMCG Index | 4.605696286 | 1221 | 1254 | 2475 | 973 | 1238.280 | -10.668* |
| NIFTY IT Index | 4.605911804 | 1218 | 1257 | 2475 | 969 | 1238.192 | -10.826* |
| NIFTY Media Index | 4.605447334 | 1220 | 1255 | 2475 | 947 | 1238.252 | -11.713* |
| NIFTY Metal Index | 4.605491194 | 1223 | 1252 | 2475 | 939 | 1238.330 | -12.037* |
| NIFTY Pharma Index | 4.605627868 | 1196 | 1279 | 2475 | 937 | 1237.108 | -12.080* |
| NIFTY Realty Index | 4.605561983 | 1166 | 1309 | 2475 | 895 | 1234.368 | -13.691* |
Source: Authors’ Computation. * represents statistical significance at the 1% level. Across all sectors, actual runs are substantially lower than expected runs, firmly rejecting the null hypothesis of randomness (H₀3).
Table 4: Lo & MacKinlay Variance Ratio Test Results (Periods 2, 4, 8, 16)
| Sectoral Index | Period (k) | Variance Ratio | Std. Error | z-Statistic | Probability |
|---|---|---|---|---|---|
| NIFTY Auto | 2 | 0.694805 | 0.050407 | -6.054591 | 0.0000 |
| 4 | 0.348964 | 0.087459 | -7.443935 | 0.0000 | |
| 8 | 0.167209 | 0.127321 | -6.540863 | 0.0000 | |
| 16 | 0.087152 | 0.179133 | -5.095925 | 0.0000 | |
| NIFTY Financial Services | 2 | 0.683415 | 0.053586 | -5.908031 | 0.0000 |
| 4 | 0.328281 | 0.092384 | -7.270909 | 0.0000 | |
| 8 | 0.156902 | 0.136190 | -6.190614 | 0.0000 | |
| 16 | 0.084363 | 0.192835 | -4.748295 | 0.0000 | |
| NIFTY FMCG | 2 | 0.674431 | 0.066712 | -4.880197 | 0.0000 |
| 4 | 0.333729 | 0.110485 | -6.030425 | 0.0000 | |
| 8 | 0.172468 | 0.149749 | -5.526113 | 0.0000 | |
| 16 | 0.089940 | 0.198970 | -4.573860 | 0.0000 | |
| NIFTY IT | 2 | 0.674004 | 0.056075 | -5.813550 | 0.0000 |
| 4 | 0.333777 | 0.093216 | -7.147091 | 0.0000 | |
| 8 | 0.170296 | 0.125491 | -6.611665 | 0.0000 | |
| 16 | 0.083725 | 0.166586 | -5.500301 | 0.0000 | |
| NIFTY Media | 2 | 0.674004 | 0.056075 | -5.813550 | 0.0000 |
| 4 | 0.333777 | 0.093216 | -7.147091 | 0.0000 | |
| 8 | 0.170296 | 0.125491 | -6.611665 | 0.0000 | |
| 16 | 0.083725 | 0.166586 | -5.500301 | 0.0000 | |
| NIFTY Metal | 2 | 0.741403 | 0.039309 | -6.578596 | 0.0000 |
| 4 | 0.373448 | 0.069291 | -9.042347 | 0.0000 | |
| 8 | 0.183463 | 0.101275 | -8.062605 | 0.0000 | |
| 16 | 0.094028 | 0.140654 | -6.441126 | 0.0000 | |
| NIFTY Pharma | 2 | 0.697493 | 0.038135 | -7.932508 | 0.0000 |
| 4 | 0.351637 | 0.065310 | -9.927541 | 0.0000 | |
| 8 | 0.168811 | 0.092991 | -8.938344 | 0.0000 | |
| 16 | 0.089111 | 0.130718 | -6.968339 | 0.0000 | |
| NIFTY Realty | 2 | 0.712179 | 0.045345 | -6.347315 | 0.0000 |
| 4 | 0.367637 | 0.078010 | -8.106157 | 0.0000 | |
| 8 | 0.182512 | 0.114054 | -7.167568 | 0.0000 | |
| 16 | 0.096686 | 0.159495 | -5.663569 | 0.0000 |
Source: Authors’ Computation. Note: Computed z-statistics are negative and significant at the 1% level across all intervals (p = 0.0000), conclusively demonstrating serial correlation in return series.
5. Discussion, Behavioral Explanations & Practical Implications
The empirical results across all econometric models lead to unambiguous conclusions:
- Rejection of H₀1: Jarque-Bera tests show that none of the return series are normally distributed; skewness and kurtosis deviate significantly from normal parameters, demonstrating asymmetric distribution.
- Rejection of H₀2: ADF and PP unit root tests indicate that returns are stationary at level (integrated of order 1 in price levels), meaning future returns can be forecasted based on past returns.
- Rejection of H₀3: Runs tests and Variance Ratio tests confirm the absence of randomness and presence of strong auto-correlation across all holding periods.
Why Does the Indian Stock Market Exhibit Weak-Form Inefficiency?
Behavioural finance asserts that market participants are guided more by psychology rather than textbook rationality and efficiency. The underlying drivers of weak-form inefficiency in India include:
Strategic Investment Takeaway: The Value of Technical Analysis
Because price returns do not follow a random walk and exhibit serial dependency, Technical Analysis—which examines previous stock price movements and volume patterns to predict future price trends—serves as an actionable, significant technique for Indian stock market investors and portfolio managers to generate consistent excess risk-adjusted returns (alpha).
Avenues for Future Research:
- Partitioning the decade into sub-periods (e.g. pre-COVID, crisis, post-COVID) to evaluate the time-varying nature of market efficiency.
- Deploying advanced mathematical methods, such as wavelet analysis, to isolate frequency-dependent market dynamics.
- Utilizing high-frequency intra-day tick data to examine microsecond price adjustment processes.
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