Small Capitalization Stocks Premium Anomaly

The small-capitalization stocks premium (size effect) 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 that 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 the lowest capitalization and short stocks with the largest capitalization. However, this pure small-cap effect had disastrous drawdowns with nearly 80% drawdown in the 90s. The small-cap factor is however still a strong performance contributor in long-only portfolios (formed as long stocks with the smallest capitalization without shorting large caps).

Fundamental reason

The size effect can be explained by the illiquidity of small companies, mainly as a result of higher trading costs.

The effect could also be caused by bigger space to grow for smaller companies, their greater flexibility during the business cycle and higher inside innovation, which gives small-caps an advantage against large-cap stocks. Another explanation for this effect is simply higher risk involved in small-cap companies.

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Markets Traded
equities

Financial instruments
stocks

Confidence in anomaly's validity
Moderately Strong

Backtest period from source paper
1927-2010

Notes to Confidence in Anomaly's Validity

Indicative Performance
12%

Period of Rebalancing
Yearly

Notes to Indicative Performance

per annum, benchmark performance 9,79%


Notes to Period of Rebalancing

Estimated Volatility
32%

Number of Traded Instruments
1000

Notes to Estimated Volatility

benchmark volatility 20,10%


Notes to Number of Traded Instruments

more or less, it depends on investor’s need for diversification


Maximum Drawdown
-92%

Complexity Evaluation
Complex strategy

Notes to Maximum drawdown

benchmark drawdown -85,67%


Notes to Complexity Evaluation

Sharpe Ratio

Simple trading strategy

The investment universe contains all NYSE, AMEX, and NASDAQ stocks. Quintile portfolios are then formed based on the 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
- 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.

Strategy's implementation in QuantConnect's framework (chart+statistics+code)
Other papers
Israel, Moskowitz: The Role of Shorting, Firm Size, and Time on Market Anomalies
- 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
- 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
- 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
- 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
- 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
- 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
- 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?
- 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?
- 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
- 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.

McGee, Olmo: The Size Premium As a Lottery
- Abstract

We investigate empirically the dependence of the size effect on the top performing stocks in a cross-section of risky assets separated by industry. We propose a test for a lottery-style factor payoff based on a stochastic utility model for an under-diversified investor. The associated conditional logit model is used to rank different investment portfolios based on size and we assess the robustness of the ranking to the inclusion/exclusion of the best performing stocks in the cross-section. Our results show that the size effect has a lottery-style payoff and is spurious for most industries once we remove the single best returning stock in an industry from the sample each month. Analysis in an asset pricing framework shows that standard asset pricing models fail to correctly specify the size premium on risky assets when industry winners are excluded from the construction of the size factor. Our findings have implications for stock picking, investment management and risk factor analysis.

Grabowski: The Size Effect Continues to be Relevant When Estimating the Cost of Capital
- Abstract

In this paper, I will review the size effect, potential reasons why one observes the size effect, and correct common misconceptions and address criticisms of the Size Premia (SP). Throughout this paper, I will show that using a pure market factor as the sole risk factor in estimating the expected return provide an incomplete estimate. For the last four decades, research have shown that adjustments to the CAPM are required. I will address some of the criticism to the theoretical basis of the SP and to the application adopted through the CRSP Decile Size Premia and Risk Premium Report – Size Study. Specifically, I demonstrate that the size premium critique by Clifford Ang is not warranted and that the alternative methodology proposed by that author is misleading and cannot be considered as an alternative to the Duff & Phelps’ SP. The methodology the author is proposing picks up statistical errors that he was set to avoid by proposing a variation of Duff and Phelps’ methodology. Finally, I will provide some practical guidance on efficiently and correctly applying SP.

Huang, Song, Xiang: Fragile Factor Premia
- Abstract

We demonstrate that returns and volatilities of the Fama-French size and value factors are significantly determined by non-fundamental flow-induced trading from actively managed equity mutual funds. Mutual fund flows are largely ignorant about systematic risks. These non-fundamental shifts in demand induce large return heterogeneity within and across the Fama-French size and book-to-market portfolios. We show that aggregate mutual fund flow- induced trades across the size and book-to-market spectrum significantly influence the size and value premia, followed by large subsequent reversals. We also find that the expected volatilities of mutual funds’ flow-induced trades strongly predict future factor volatilities. Our results highlight the importance of non-fundamental demand shocks in determining factor premia and factor volatilities.

Alquist, Israel, Moskowitz: Fact, Fiction, and the Size Effect
- Abstract

In the earliest days of empirical work in academic finance, the size effect was the first market anomaly to challenge the standard asset pricing model and prompt debates about market efficiency. The notion that small stocks have higher average returns than large stocks, even after risk-adjustment, was a pathbreaking discovery, one that for decades has been taken as an unwavering fact of financial markets. In practice, the discovery of the size effect fueled a crowd of small cap indices and active funds to a point where the investment landscape is now segmented into large and small stock universes. Despite its long and illustrious history in academia and its commonplace acceptance in practice, there is still confusion and debate about the size effect. We examine many claims about the size effect and aim to clarify some of the misunderstanding surrounding it by performing simple tests using publicly available data.

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