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Small Capitalization Stocks Premium Anomaly

The small capitalization stocks premium is one of the few effects which is accepted by nearly the whole academic community. It says that low capitalization stocks earn substantial premiums against stocks with large capitalization (without additional risk). This anomaly is the best described in the classical Fama and French research paper (1993). Additional details are calculated from data which are present in the Kenneth French data library (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). Pure small cap effect portfolios are created as long stocks with lowest capitalization and short stocks with largest capitalization. However, this pure small cap effect had disastrous drawdowns with nearly 80% drawdown in 90s. The small cap factor is however still a strong performance contributor in long only portfolios (formed as long stocks with smallest capitalization without shorting large caps).

Fundamental reason

The size effect can be explained by the illiquidity of small companies, particularly as a result of higher trading costs. The effect could be also caused by bigger space to grow for smaller companies, their greater flexibility during the business cycle and greater inside innovation which give small caps an advantage against large cap stocks. Another explanation for this effect is simply higher risk involved in small cap companies.

Markets traded
equities
Confidence in anomaly's validity
Moderately strong
Notes to Confidence in anomaly's validity
Period of rebalancing
Yearly
Notes to Period of rebalancing
Number of traded instruments
1000
Notes to Number of traded instruments
more or less, it depends on investor's need for diversification
Complexity evaluation
Complex strategy
Notes to Complexity evaluation
Strategy complexity depends on number of stocks investor wishes to include into his/her portfolio, as strategy could be much simpler for execution if investor picks less stocks.
Financial instruments
stocks
Backtest period from source paper
1927-2010
Indicative performance
12.08%
Notes to Indicative performance
per annum, benchmark performance 9,79%
Estimated volatility
32.00%
Notes to Estimated volatility
benchmark volatility 20,10%
Maximum drawdown
-91.52%
Notes to Maximum drawdown
benchmark drawdown -85,67%
Sharpe Ratio
0.25

Keywords:

small cap, stock picking

Simple trading strategy

The investment universe contains all NYSE, AMEX, and NASDAQ stocks. Quintile portfolios are then formed based on market capitalization of stocks and the lowest quintile (stocks weighted based on market cap.) is held for one year after which the portfolio is rebalanced.

Source Paper

Fama, French: The Cross-Section of Expected Stock Returns
http://www.bengrahaminvesting.ca/Research/Papers/French/The_Cross-Section_of_Expected_Stock_Returns.pdf
Abstract:
Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market beta, size, leverage, book-to-market equity and earnings price ratios. Moreover, when the tests allow for variation in beta that is unrelated to size, the relation between market beta and average return is flat, even when beta is the only explanatory variable.

Other Papers

Israel, Moskowitz: The Role of Shorting, Firm Size, and Time on Market Anomalies
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2089466
Abstract:
We examine the role of shorting, firm size, and time on the profitability of size, value, and momentum strategies. We find that long positions comprise almost all of size, 60% of value, and half of momentum profits. Shorting becomes less important for momentum and more important for value as firm size decreases. The value premium decreases with firm size and is weak among the largest stocks. Momentum profits, however, exhibit no reliable relation with size. These effects are robust over 86 years of U.S. equity data and almost 40 years of data across four international equity markets and five asset classes. Variation over time and across markets of these effects is consistent with random chance. We find little evidence that size, value, and momentum returns are significantly affected by changes in trading costs or institutional and hedge fund ownership over time.

Frazzini, Israel, Moskowitz: Trading Costs of Asset Pricing Anomalies
http://www.gsb.stanford.edu/sites/default/files/documents/fin_12_12_moskowitz.pdf
Abstract:
Using nearly a trillion dollars of live trading data from a large institutional money manager across 19 developed equity markets over the period 1998 to 2011, we measure the real-world transactions costs and price impact function facing an arbitrageur and apply them to size, value, momentum, and short-term reversal strategies. We find that actual trading costs are less than a tenth as large as, and therefore the potential scale of these strategies is more than an order of magnitude larger than, previous studies suggest. Furthermore, strategies designed to reduce transactions costs can increase net returns and capacity substantially, without incurring significant style drift. Results vary across styles, with value and momentum being more scalable than size, and short-term reversals being the most constrained by trading costs. We conclude that the main anomalies to standard asset pricing models are robust, implementable, and sizeable.

Asness, Frazzini, Israel, Moskowitz, Pedersen: Size Matters, If You Control Your Junk
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2553889
Abstract:
The size premium has been challenged along many fronts: it has a weak historical record, varies significantly over time, in particular weakening after its discovery in the early 1980s, is concentrated among microcap stocks, predominantly resides in January, is not present for measures of size that do not rely on market prices, is weak internationally, and is subsumed by proxies for illiquidity. We find, however, that these challenges are dismantled when controlling for the quality, or the inverse “junk”, of a firm. A significant size premium emerges, which is stable through time, robust to the specification, more consistent across seasons and markets, not concentrated in microcaps, robust to non-price based measures of size, and not captured by an illiquidity premium. Controlling for quality/junk also explains interactions between size and other return characteristics such as value and momentum.

Fan, Opsal, Yu: Equity Anomalies and Idiosyncratic Risk Around the World
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2611047
Abstract:
In this study, we examine how idiosyncratic risk is correlated with a wide array of anomalies, including asset growth, book-to-market, investment-to-assets, momentum, net stock issues, size, and total accruals, in international equity markets. We use zero-cost trading strategy and multifactor models to show that these anomalies produce significant abnormal returns. The abnormal returns vary dramatically among different countries and between developed and emerging countries. We provide strong evidence to support the limits of arbitrage theory across countries by documenting a positive correlation between idiosyncratic risk and abnormal return. It suggests that the existence of these well-known anomalies is due to idiosyncratic risk. In addition, we find that idiosyncratic risk has less impact on abnormal return in developed countries than emerging countries. Our results support the mispricing explanation of the existence of various anomalies across global markets.

Schmidt, Von Arx, Schrimpf, Wagner, Ziegler: Size and Momentum Profitability in International Stock Markets
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2642185
Abstract:
We study the link between the profitability of momentum strategies and firm size, drawing on an extensive dataset covering 23 stock markets across the globe. We first present evidence of an “extreme” size premium in a large number of countries. These size premia, however, are most likely not realizable due to low stock market depth. We also show that international momentum profitability declines sharply with market capitalization. Momentum premiums are also considerably diminished by trading costs, when taking into account the actual portfolio turnover incurred when implementing this strategy. In contrast to strategies based on size, we find that momentum premia especially for medium-sized stocks still remain economically and statistically significant in most equity markets worldwide after adjusting for transaction costs.

Lambert, Fays, Hubner: Size and Value Matter, But Not the Way You Thought
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2647298
Abstract:
Fama and French factors do not reliably estimate the size and book-to-market effects. We demonstrate inconsistent pricing of those factors in the US stock market. We replace Fama and French’s independent rankings with the conditional ones introduced by Lambert and Hübner (2013). Controlling ex-ante for noise in the estimation procedure, we have been able to highlight a much stronger book-to-market and size effects than have conventionally been documented similar to Asness et al. (2015). As a significant related outcome, the alternative risk factors have been found to deliver less specification errors when used to price investment portfolios.

Lambert, Hubner: Size Matters, Book Value Does Not! The Fama-French Empirical CAPM Revisited
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2506690
Abstract:
The Fama and French (F&F) factors do not reliably estimate the size and book-to-market effects. Our paper shows that the former has been underestimated in the US market while the latter overestimated. We do so by replacing F&F's independent rankings by the conditional ones introduced by Lambert and Hubner (2013), over which we improve the sorting procedure. This new specification better reflects the properties of the individual risk premiums. We emphasize a much stronger size effect than conventionally documented. As a major related outcome, the alternative risk factors deliver less specification errors when used to price passive investment indices.

Cakici, Tang, Yan: Do the Size, Value, and Momentum Factors Drive Stock Returns in Emerging Markets?
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2727257
Abstract:
This paper investigates the size, value and momentum effects in 18 emerging stock markets during the period 1990−2013. We find that size and momentum strategies generally fail to generate superior returns in emerging markets. The value effect exists in all markets except Brazil, and it is robust to different periods and market conditions. Value premiums tend to move positively together across different markets, and such inter-market co-movements increase overtime and during the global financial crisis.

Stefano, Serie, Simon, Lemperiere, Bouchaud: The 'Size Premium' in Equity Markets: Where Is the Risk?
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3018454
Abstract:
We find that when measured in terms of dollar-turnover, and once beta-neutralised and Low-Vol neutralised, the Size Effect is alive and well. With a long term t-stat of 5.1, the “Cold-Minus-Hot” (CMH) anomaly is certainly not less significant than other well-known factors such as Value or Quality. As compared to market-cap based SMB, CMH portfolios are much less anti-correlated to the Low-Vol anomaly. In contrast with standard risk premia, size-based portfolios are found to be virtually unskewed. In fact, the extreme risk of these portfolios is dominated by the large cap leg; small caps actually have a positive (rather than negative) skewness. The only argument that favours a risk premium interpretation at the individual stock level is that the extreme drawdowns are more frequent for small cap/turnover stocks, even after accounting for volatility. This idiosyncratic risk is however clearly diversifiable.

Herskovic, Kind, Kung: Size Premium Waves
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3220825
Abstract:
This paper examines the link between microeconomic uncertainty and the size premium across different frequencies in an investment model with heterogeneous firms. We document that the observed time-varying dispersion in firm-specific productivity can account for a large size premium in the 1960's and 1970's, the disappearance in the 1980's and 1990's, and reemergence in the 2000's. Periods with a large (small) size premium coincide with high (low) microeconomic uncertainty. During episodes of high productivity dispersion, small firms increase their exposure to macroeconomic risks. Our model can also explain the strong positive low-frequency co-movement between size and value factors, but a negative relation with the market factor.

Hypothetical future performance

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