An Empirical Study on Small Firm Effect in Indian Stock Market

Introduction & Theoretical Background

Size effect in financial literature refers to a phenomenon, where stocks of small-sized firms outperform the stocks of large-sized firms over a long time. It is believed that market forces set the stocks of smaller firms at less price compared to stocks of larger firms due to the high risk involved in them even though all other things are the same. When both firms earn the same profit, smaller firm stock investor gets more profit because they pay less to acquire them.

The size effect was first observed by Banz (1981). He examined the relationship between the return and market value of a firm by observing NYSE stocks and found that the returns of small-sized firms are greater than that of the larger firms even after adjusting the risk. This effect has been in existence for at least 40 years and stated that the Capital Asset Pricing Model (CAPM) was misspecified. Further, he concluded that this effect was because of size itself or size may be one of the proxies for risk.

Some researchers identified autocorrelation, liquidity (see Amihud, 2002; Liu, 2006) and information uncertainty (Zhang, 2006) as a proxy for risk. As there is no clear understanding of the cause for such an effect, the factors underlying this phenomenon are not conclusive. As time varies further, studies documented the disappearance of the size effect after 1980 (see Barry et al., 2002; Fama & French, 2011). Mainly due to increased academic literature on the size effect after Banz (1981), an announcement of small firm effect along with the introduction of small-cap stock funds in the US made it easier for investors to buy these securities, and increased demand caused a rise in small stock prices.

Some studies documented seasonality in small firm effect returns, where the size effect observed in the U.S. majorly has its presence in the beginning of the year (January) and has little or no effect during the remaining months (see Easterday et al., 2009). Surprisingly, some studies reported no such seasonality effect in the UK (see Dimson). In the Indian context, various studies have been undertaken pertaining to the size effect, and most identified the presence of the size effect (Sharma & Jain, 2020; Vasishth et al., 2021). By observing the literature, it is obvious that there is no clarity on whether the size anomaly is a separate phenomenon or a manifestation of other known market anomalies.

Objectives of the Study & Methodology

Methodology: To achieve these objectives, setting portfolios based on individual market capitalisation involves a cumbersome procedure. Fortunately, well-constructed benchmark indices are readily available:

• Small-Cap Benchmark: Nifty Smallcap 100 Index.
• Large-Cap Benchmark: Nifty 100 Index.
• Time Horizon: 10-year period from January 1, 2011 to December 31, 2021 obtained from the National Stock Exchange (NSE) website.
• COVID-19 Outlier Exclusion: Returns from 1st January 2020 to 31st December 2020 were deliberately excluded due to extreme macroeconomic distortions and statistical outliers caused by the pandemic.
• Statistical Toolkit: Pearson correlation, Durbin-Watson autocorrelation tests, Amihud Illiquidity ratio, Student’s t-test for equality of means, and Fisher’s F-test for equality of variances.

Risk-Return Profile Across Holding Periods

The data is classified into different holding periods in order to verify the existence of an autocorrelation effect and analyse the risk-return trade-off. Autocorrelation measures the current stock price in relation to its past prices. A high autocorrelation indicates more influence of past prices on present prices, whereas low autocorrelation indicates price independence. It is believed that small firm stock prices exhibit higher autocorrelation due to infrequent trading. If small stocks are traded less frequently, risk measures from short-interval return data seriously understate the actual holding risk.

Table 1: Risk-Return Data on Small-Cap and Large-Cap Indices (2011–2021)

Table 2: Statistical Significance Tests (F-test for Variance & t-test for Means)

Autocorrelation & Illiquidity Analysis (Table 3)

The Durbin-Watson statistic tests for residual autocorrelation (value of 2 represents zero autocorrelation; values < 2 indicate positive autocorrelation). Illiquidity is measured through the Amihud Illiquidity measure:

Testing Seasonality: Monday / Weekend Effect (Tables 4 & 5)

The Monday (weekend) effect posits that stocks close lower on Mondays due to weekend investor negativity or Friday post-market bad news dumps.

Table 5: Statistical Analysis of Weekday Returns (2011–2021)

Testing January, April & Tax-Loss Selling Effects (Tables 6 & 7)

In western markets, the January Effect is linked to December tax-loss harvesting. In India, because the fiscal year closes on March 31, the equivalent tax-loss selling dynamic would manifest across March and April.

Table 6: Monthly Average Returns (2011–2021)

Table 7: Statistical Analysis of Monthly Returns (January/December & March/April)

In Table 7, it is statistically proven that there is no presence of the January effect in either index ($p > 0.25$). Small-Cap average returns in April (+0.20%) are statistically higher than other months ($t = 2.05, p = 0.0412$). However, because March returns were positive (+0.17%) rather than depressed, the April surge cannot be attributed to tax-loss selling recovery.

Conclusion

References

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• 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
• Barry, C. B., Goldreyer, E., Lockwood, L., & Rodriguez, M. (2002). Robustness of size and value effects in emerging equity markets, 1985–2000. Emerging Markets Review, 3, 1–30. https://linkinghub.elsevier.com/retrieve/pii/S1566014101000280
• Dimson, E., Marsh, P., & Staunton, M. (2011). Credit Suisse Global Investment Returns Sourcebook 2011.
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• Sharma, M., & Jain, A. (2020). Role of size and risk effects in value anomaly: Evidence from the Indian stock market. Cogent Economics & Finance, 8(1), 1838694. https://doi.org/10.1080/23322039.2020.1838694
• Vasishth, V., Sehgal, S., & Sharma, G. (2021). 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
• Zhang, X. F. (2006). Information uncertainty and stock returns. Journal of Finance, 61(1), 105–137. https://doi.org/10.1111/j.1540-6261.2006.00831.x