Momentum Effect in Stocks
The momentum anomaly says that what was strongly going up in the past will probably continue to go up in the near future. Stocks which outperform peers on 3-12 month period tend to perform well also in the future. Countless studies show that this effect works in US stock market, stock markets in other developed countries and also in emerging markets. Momentum effect works in a small cap universe and also on large cap stocks, and it is one of the mostly academically investigated effect with strong persistence. Pure momentum portfolios are created as long stocks with the strongest momentum and short stocks with the lowest momentum. This pure momentum portfolio however recorded a disastrous year 2009 with more than 80% drawdown (data from Kenneth French library - http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/F-F_Momentum_Factor.zip). The momentum factor is however still a strong performance contributor in long only portfolios (formed as long stocks with the strongest momentum without shorting market or low momentum stocks).
Academic studies show strong support for momentum effects. The main reasons for anomaly persistence are behavioral biases like investor herding, investor over and underreaction and confirmation bias. Another natural interpretation of momentum profits is that stocks underreact to information. For example, if a firm releases good news and the stock price only reacts partially to the good news, then buying the stock after the initial release of the news will generate profits.
momentum, momentum in stocks, stock picking
Simple trading strategy
This investment strategy depends on investor needs as it is possible to create momentum portfolio consisting of 20 stocks or several hundreds of stocks. We present a complex strategy which is the underlying strategy for benchmarks calculated in Keneth French data library (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). Our investment universe consists of the largest 20% of stocks on NYSE, NASDAQ and AMEX. 20% of stocks with the best 12 month momentum (12 month performance) are then added to our portfolio and are weighted equally and the portfolio is rebalanced once in a month. Our benchmark is an equally weighted portfolio of the largest 20% of stocks on NYSE, NASDAQ and AMEX.
Jagadeesh, Titman: Momentum
There is substantial evidence that indicates that stocks that perform the best (worst) over a three- to 12-month period tend to continue to perform well (poorly) over the subsequent three to 12 months. Momentum trading strategies that exploit this phenomenon have been consistently profitable in the United States and in most developed markets. Similarly, stocks with high earnings momentum outperform stocks with low earnings momentum. This article reviews the evidence of price and earnings momentum and the potential explanations for the momentum effect.
Vogel, Gray: The Quantitative Momentum Investing Philosophy - Buy Stocks with the Highest Quality Momentum
Abstract: Our Quantitative Momentum (QM) system seeks to identify stocks with the highest quality “momentum.” We consider the term momentum to mean a continuation of past returns—past winners tend to be future winners, while past losers tend to be future losers. How can we exploit this phenomenon? At Alpha Architect, we have designed a system to identify the “quality” of momentum by examining how the momentum is formed.
Griffin, Ji, Martin: Global Momentum Strategies: A Portfolio Perspective
We provide practical perspectives on momentum investing in stocks internationally. First, momentum is generally more profitable on the long side than on the short side, making it accessible to a broad range of institutional capital. Second, both price and earnings momentum profits are significant globally. Third, internationally, earnings momentum is distinct from price momentum, and using price and earnings momentum in conjunction produces larger economic profits. Fourth, momentum profits have weaker co-movements across markets than market indices. Interestingly, while market correlations are much higher in down markets than in up markets, momentum correlations are low in both market conditions. Fifth, momentum strategies do not differ appreciably in profitability between up and down markets, which means timing is less important to momentum traders. Finally, momentum strategies are not riskless-historically there have often occurred periods of several months where they have netted low or negative returns.
Korajczyk, Sadka: Are Momentum Profits Robust to Trading Costs?
This paper tests whether momentum-based strategies remain profitable after considering market frictions. Alternative measures of price impact are estimated and applied to alternative momentum-based trading rules. The performance of traditional momentum strategies, in addition to strategies designed to reduce the cost of trades, is evaluated. We find that, after taking into account the price impact induced by trades, as much as 5 billion dollars may be invested in some momentum-based strategies before the apparent profit opportunities vanish. Other, extensively studied, momentum strategies are not implementable on a large scale.
Jagadeesh, Titman: Momentum (2011 version)
There is substantial evidence that indicates that stocks that perform the best (worst) over a three to 12 month period tend to continue to perform well (poorly) over the subsequent three to 12 months. Up until recently, trading strategies that exploit this phenomenon were consistently profitable in the United States and in most developed markets. Similarly, stocks with high earnings momentum outperform stocks with low earnings momentum. This article reviews the momentum literature and discusses some of the explanations for this phenomenon.
Israel, Moskowitz: How Tax Efficient are Equity Styles?
We examine the tax efficiency and after-tax performance of long only equity styles. On an after-tax basis, value and momentum portfolios outperform, and growth underperforms, the market. We find that momentum, despite its higher turnover, is often more tax efficient than value, because it generates substantial short-term losses and lower dividend income. Tax optimization improves the returns to all equity styles, with the biggest improvements accruing to value and momentum styles. However, only momentum allows significant tax minimization without incurring significant style drift. This is because managing gain and loss realization incurs less tracking error than avoiding dividend income and momentum's tax exposure is primarily capital gains, while value and growth's tax exposures are more sensitive to dividends.
Boynton, Jordan: Are momentum premia robust to trade frictions? Tests of large-stock portfolios
We test how market frictions might limit momentum profits. While most papers assume that investors can self-finance, in practice, investors must invest capital or borrow for long stock positions. No self-financing can occur. Traders can borrow to buy longs, short losers, and earn the rebate interest on the short sale proceeds. We find that the difference between the margin and rebates rates is 139 bp for 1946-2002. We test on large stocks where trade and costs are lower and price impact costs are minimal. Net of trade and borrowing costs, large stock momentum earns, on a raw return basis, 5% per unit of borrowed capital annually. Risk-adjusted tests show larger premia.
Lewis: Relative Strength and Portfolio Management
This paper presents the results of several relative strength strategies tested in a real world portfolio management setting. Monte Carlo simulations are used to determine the possible range of outcomes if a portfolio manager selects a subset of high relative strength securities over time. A testing protocol that rebalances the portfolio on a continuous basis is also used to simulate real world portfolio management practices.
Barroso, Santa-Clara: Managing the Risk of Momentum
Compared to the market, value or size risk factors, momentum has offered investors the highest Sharpe ratio. However, momentum has also had the worst crashes, making the strategy unappealing to investors with reasonable risk aversion. We find that the risk of momentum is highly variable over time and quite predictable. The major source of predictability does not come from systematic risk but from specific risk. Managing this time-varying risk virtually eliminates crashes and nearly doubles the Sharpe ratio of the momentum strategy. Risk-managed momentum is a much greater puzzle than the original version.
Rachwalski, Wen: Momentum, Risk and Underreaction
Momentum profits can be explained by exposure to risks omitted from common factor models and underreaction to innovations in these omitted risks. Consistent with risk as a partial explanation of momentum profits, long formation period momentum strategies earn higher returns and are more highly correlated with factors designed to measure risk than short formation period momentum strategies.
Landis, Skouras: Momentum is Higher Than We Think
This paper evaluates Momentum on international markets based on data from Thompson Datastream. Using a complete ltered and corrected daily database from 52 International markets, and more than 50.000 common stocks, from TDS, we re-examine previous empirical work on International Momentum and document consistently higher momentum returns for the majority of markets and regions of our sample. We find evidence that data outliers create a "Pseudo-Reversal effect" in international Winner minus Loser profits, reflecting in the overestimation of premiums of loser portfolios and the underestimation of the pro ts of the momentum strategies. Moreover, we revise International Momentum premiums from 1964 to 2010, for all markets and regions of our sample and document that momentum continues to be strong in the majority of individual markets and all in regions except Japan.
Li, Brooks, Miffre: Low-Cost Momentum Strategies
The article analyses the impact of trading costs on the profitability of momentum strategies in the UK and concludes that losers are more expensive to trade than winners. The observed asymmetry in the costs of trading winners and losers crucially relates to the high cost of selling loser stocks with small size and low trading volume. Since transaction costs severely impact net momentum profits, the paper defines a new low-cost relative-strength strategy by shortlisting from all winner and loser stocks those with the lowest total transaction costs. While the study severely questions the profitability of standard momentum strategies, it concludes that there is still room for momentum-based return enhancement.
Henker, Martens, Huynh: The Vanishing Abnormal Returns of Momentum Strategies and 'Front-Running' Momentum Strategies
We find large variations in returns from momentum strategies. Momentum strategies did not earn significant returns during the period of 1993-2004 which was due to their poor performance over the period from 2001-2004. We find that the previously documented large firm momentum effect is sensitive to the momentum strategy examined, and is in our sample driven by the abnormal returns of large Nasdaq stocks. We also evaluate momentum strategies that do not adhere to the end of month portfolio formation universally used in the academic literature. To this end we form portfolios one week prior to the end of month and call them 'front-running' momentum portfolios. Consistent with institutional momentum trading affecting end of month returns and volatility, we find that 'front-running' a momentum strategy generates similar, but less volatile returns than the month-end strategy.
Israel, Moskowitz: The Role of Shorting, Firm Size, and Time on Market Anomalies
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.
Cheema: Three Essays on Momentum Returns
This dissertation consists of three essays on momentum returns. The first essay is entitled ‘Momentum Returns, Market States and the Global Financial Crisis’. This essay investigates the profitability of the momentum trading strategy in the stock exchanges of Shanghai, Shenzhen and Hong Kong over the period 1994 to 2010. In the second essay, entitled ‘Momentum Returns and Information Uncertainty’, I study the impact of information uncertainty on the profitability of the momentum trading strategy. In the third and final essay, entitled ‘Momentum Returns, Long-Term Reversal and Idiosyncratic Volatility’, I study the impact of idiosyncratic volatility (IV) on the profitability of momentum and long-term reversal trading strategies in China over the period 1994 to 2010.
Cakici, Tan: Size, Value, and Momentum in Developed Country Equity Returns: Macroeconomic and Liquidity Exposures
The paper investigates value and momentum factors in 23 developed international stock markets. We find that typically value and momentum premia are smaller and more negatively correlated for large market capitalization stocks relative to small. Momentum factors are more highly correlated internationally relative to value. We provide international evidence on three sets of risk exposures of value and momentum returns: macroeconomic risk, funding liquidity risk, and stock market liquidity risk. We find that value returns are typically lower prior to a recession while momentum returns often exhibit little sensitivity. Value returns are typically lower in times of poor funding liquidity, whereas, with notable exceptions, momentum returns are typically unaffected. Lastly, for almost all countries, value returns are high in poor stock market liquidity conditions. The same result appears to be true for momentum in Asia Pacific, North America, and largely in Europe.
Jensen-Gaard: Equity Investment Styles - Recent evidence on the existence and cyclicality of investment styles
Over the past two decades, financial academics and investment professionals have documented several anomalies on the global financial markets. A subset of these anomalies, known as equity style strategies, has been shown to yield substantial excess returns, which cannot be explained by traditional finance theory. However, in the light of the financial turmoil during the 2000s, several studies have shown considerable changes in the magnitude of the style-based strategy premiums. The purpose of this thesis is to investigate whether recent data support the continued existence of these premiums and evaluate how these premiums fluctuate in relation to the economic cycle.
Asness, Frazzini, Israel, Moskowitz: Fact, Fiction and Momentum Investing
It’s been over 20 years since the academic discovery of momentum investing, yet much confusion and debate remains regarding its efficacy and its use as a practical investment tool. In some cases “confusion and debate” is us attempting to be polite, as it is near impossible for informed practitioners and academics to still believe some of the myths uttered about momentum — but that impossibility is often belied by real world statements. In this article, we aim to clear up much of the confusion by documenting what we know about momentum and disproving many of the often-repeated myths. We highlight ten myths about momentum and refute them, using results from widely circulated academic papers and analysis from the simplest and best publicly available data.
Herberger, Kohlert: Trading inTurbulent Markets: Does Momentum Work? (page 53 - 65)
Identifying ways to successfully predict security returns based on past returns is a major objective ofinvestment research. One ofthe most impor-tant strategies, that of momentum, is employed in this chapter. Using NYSE datafrom December 1994 to May 2009, we analyze whether buying stocks that have performed well in the past and selling stocks that have performedpoorly in the past can generate signiﬁcant positive returns, even in a turbu-lent market phase. Our ﬁndings suggest that investors using momentumstrategies could have indeed generated superior returns during that timeperiod.
Foltice, Langer: Profitable Momentum Trading Strategies for Individual Investors
For nearly three decades, scientific studies have explored momentum investing strategies and observed stable excess returns in various financial markets. However, the trading strategies typically analyzed in such research are not accessible to individual investors due to short selling constraints, nor are they profitable due to high trading costs. Incorporating these constraints, we suggest and explore a simplified momentum trading strategy that only exploits excess returns from topside momentum for a small number of individual stocks. Building on US data from the NYSE from 1991-2010, we analyze whether such a simplified momentum strategy outperforms the benchmark after factoring in realistic transaction costs and risks. We find that it is indeed possible for individual investors with initial investment amounts of at least $5,000.
Sarwar: Sources of Momentum Returns: A Decomposition of the Explained and the Unexplained Risk Factors
In this paper, I examine the sources of momentum returns and uncover a list of intriguing features. I find that when the momentum returns are decomposed the contributions of the explained and the unexplained risk factors depend on the level of analysis, the risk factors used, and the lag structure of the risk factors. Further, I find that at the individual stock level, the total contribution of the lagged macroeconomic risk factors is 59 percent per month but that the total contribution of the contemporaneous macroeconomic risk factors at the portfolio level is only 9 percent per month. These new findings add important insights to the existing momentum theories.
Garcia-Feijoo, Jensen, Jensen: Momentum and Funding Conditions
We find strong evidence linking the momentum pattern in equity returns with a prominent measure of macroeconomic conditions, specifically the funding environment. We show that the size and consistency of the momentum premium varies systematically across funding states. Furthermore, we find evidence that the relationship between momentum returns and firm characteristics (documented in previous research) is conditional on the funding environment. After controlling for the funding state, we find that the importance of market states and return dispersion disappears. Additionally, funding conditions appear to contain incremental information about the momentum premium even after adjusting for the influence of market states and return dispersion. Overall our results are consistent with the conjecture that transitions in the funding environment encourage investors to revise their portfolio allocations; this reallocation produces inter-temporal variation in the momentum return pattern.
Geczy, Samonov: 215 Years of Global Multi-Asset Momentum: 1800-2014 (Equities, Sectors, Currencies, Bonds, Commodities and Stocks)
Extending price return momentum tests to the longest available histories of global financial asset returns, including country-specific sectors and stocks, fixed income, currencies, and commodities, as well as U.S. stocks, we create a 215-year history of multi-asset momentum, and we confirm the significance of the momentum premium inside and across asset classes. Consistent with stock-level results, we document a large variation of momentum portfolio betas, conditional on the direction and duration of the return of the asset class in which the momentum portfolio is built. A significant recent rise in pair-wise momentum portfolio correlations suggests features of the data important for empiricists, theoreticians and practitioners alike.
Goyal, Jegadeesh: Cross-Sectional and Time-Series Tests of Return Predictability: What Is the Difference?
We analyze the differences between past-return based strategies that differ in conditioning on past returns in excess of zero (time-series strategy, TS) and past returns in excess of the cross-sectional average (cross-sectional strategy, CS). We find that the return difference between these two strategies is mainly due to time-varying long positions that the TS strategy takes in the aggregate market and, consequently, do not have any implications for the behavior of individual asset prices. However, TS and CS strategies based on financial ratios as predictors are sometimes different due to asset selection.
Fan, Opsal, Yu: Equity Anomalies and Idiosyncratic Risk Around the World
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.
Berghorn, Otto: Mandelbrot Market-Model and Momentum
Mandelbrot has significantly contributed in many ways to the area of finance. He was one of the first who criticized the oversimplifications centered around the early stochastic process models of Bachelier utilizing normal distribution. In his view, markets were fractal and much wilder than classical theory suggests. Particularly, his work of fractional Brownian motion showed that the independence claim made by that hypothesis is not valid; in addition, he proposed a multi-fractal asset model to reconcile for effects observed in the market. However, it is also known that his vision of fractal markets used fractal trends. In this work, we will revisit Mandelbrot’s vision of fractal markets. We will show that the momentum effect discussed heavily in literature can be modeled by the so-called Mandelbrot Market-Model. Additionally, this model shows, from the risk side, that markets are wilder because of trend structures compared with classical models.
Moskowitz: Asset Pricing and Sports Betting
I use sports betting markets as a laboratory to test behavioral theories of cross-sectional asset pricing anomalies. Two unique features of these markets provide a distinguishing test of behavioral theories: 1) the bets are completely idiosyncratic and therefore not confounded by rational theories; 2) the contracts have a known and short termination date where uncertainty is resolved that allows any mispricing to be detected. Analyzing more than a hundred thousand contracts spanning two decades across four major professional sports (NBA, NFL, MLB, and NHL), I find momentum and value effects that move betting prices from the open to the close of betting, that are then completely reversed by the game outcome. These findings are consistent with delayed overreaction theories of asset pricing. In addition, a novel implication of overreaction uncovered in sports betting markets is shown to also predict momentum and value returns in financial markets.
Schmidt, Von Arx, Schrimpf, Wagner, Ziegler: Size and Momentum Profitability in International Stock Markets
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.
van Oord: Optimization of Equity Momentum: (How) Does it Work?
Standard mean-variance optimized momentum outperforms the traditional equally weighted momentum strategy if the expected return vector used reflects momentum's top and bottom only characteristic. This top and bottom only characteristic is the phenomenon that only the stocks in the top decile of momentum's ranking outperform and that only stocks in the bottom decile underperform, while all stocks in the intermediate deciles of the ranking have similar performance. If the optimization does not take this phenomenon into account the portfolio is also long the deciles 2 to 5 and short the deciles 6 to 9, while all these positions thus do not add anything to the return of the strategy. A new simplified bootstrapping methodology shows that the Sharpe-ratio of 52.8 percent of the optimized portfolio is significantly higher than the Sharpe-ratio of 29.3 percent for traditional equally weighted momentum. The optimized portfolio also exhibit less time-varying equity risk factor return exposures than traditional momentum and as such have more stable returns over the business cycle and have smaller drawdowns.
Goetzmann, Huang: Momentum in Imperial Russia
Some of the leading theories of momentum have different empirical predictions about its profitability conditional on market composition and structure. The institutional theory of Vayanos and Woolley predicts lower momentum profits in markets with less agency. In this paper we use a dataset from a major 19th century equity market to test these predictions. Over this period there was no evidence of delegated management in Imperial Russia. A regulatory change in 1893 made speculating on the St. Petersburg stock market more accessible to small investors. We find a momentum effect that is similar in magnitude to those in modern markets, and stronger during the post-1893 period than during the pre-1893 period, consistent with the overconfidence theory of momentum.
Heidari: Over or Under? Momentum, Idiosyncratic Volatility and Overreaction
Several studies have attributed the high excess returns of the momentum strategy in the equity market to investor behavioral biases. However, whether momentum effects occur because of investor underreaction or because of investor overreaction remains a question. Using a simple model to illustrate the linkage between idiosyncratic volatility and investor overreaction as well as the stock turnover as another measure of overreaction, I present evidence that supports the investor overreaction explanation as the source of momentum effects. Furthermore, I show that when investor overreaction is low, momentum effects are more due to industries (industry momentum) rather than stocks.
Dobrynskaya: Upside and Downside Risks in Momentum Returns
I show that the past winners and the past losers are differently exposed to the upside and downside market risks. Winners systematically have higher relative downside market betas and lower relative upside market betas than losers. As a result, the winner-minus-loser momentum portfolios are exposed to extra downside market risk, but hedge against the upside market risk. Such asymmetry in the upside and downside risks is a mechanical consequence of rebalancing momentum portfolios. But it is unattractive for an investor because both positive relative downside betas and negative relative upside betas carry positive risk premiums according to the Downside-Risk CAPM. Hence, the high returns to momentum strategies are a mere compensation for their upside and downside risks.
Cakici, Tang, Yan: Do the Size, Value, and Momentum Factors Drive Stock Returns in Emerging Markets?
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.
Schmidt: Trading Strategies Based on Past Returns - Evidence from Germany
Over the total time period from 1965 to 2014, the classical momentum strategy based on performance over the past two to twelve months earned an average return of 1.57% per month (excluding microcap stocks and value-weight returns). In the most recent ten-year time period, it has been even larger: 2.27%, which is much larger than in the U.S. However, the profitability net of transaction costs appears weak because the strategy involves trading in disproportionately small stocks with high transaction costs, especially observed for the loser portfolio. A strategy that only concentrates on the winner portfolio and thus avoids potential problems associated with (short) selling the costly loser portfolio appears to earn strong and persistently abnormal profits, even after transaction costs.
Bhattacharya, Li, Sonaer: Has Momentum Lost Its Momentum?
We evaluate the robustness of momentum returns in the US stock market over the period 1965 to 2012. We find that momentum profits have become insignificant since the late 1990s partially driven by pronounced increase in the volatility of momentum profits in the last 14 years. Investigations of momentum profits in high and low volatility months address the concerns about unprecedented levels of market volatility in this period rendering momentum strategy unprofitable. Past returns, can no longer explain the cross-sectional variation in stock returns, even following up markets. Investigation of post holding period returns of momentum portfolios and risk adjusted buy and hold returns of stocks in momentum suggests that investors possibly recognize that momentum strategy is profitable and trade in ways that arbitrage away such profits. In further analyses we find evidence that suggest three possible explanations for the declining momentum profits.
Dolvin, Foltice: Where Has the Trend Gone? An Update on Momentum Returns in the U.S. Stock Market
More recent studies note a declining benefit relative to that identified in seminal studies on momentum. Our results for the earlier part of our sample period (i.e., 1986 to 2006) fall in line with previous studies, as we find a monotonic relationship between decile portfolios formed based on prior six month performance and their subsequent twelve month holding period excess returns. In contrast, when we evaluate more recent periods (i.e., 2007-2015 and 2010-2015), we find dramatically different results. In particular, alphas for the “winner” portfolio are negative during both sub-periods and distribution follows a more inverted U-shaped curve.
de Carvalho, Xiao, Soupe, Dugnolle: Diversify and Purify Factor Premiums in Equity Markets
In this paper we consider the question of how to improve the efficacy of strategies designed to capture factor premiums in equity markets and, in particular, from the value, quality, low risk and momentum factors. We consider a number of portfolio construction approaches designed to capture factor premiums with the appropriate levels of risk controls aiming at increasing information ratios. We show that information ratios can be increased by targeting constant volatility over time, hedging market beta and hedging exposures to the size factor, i.e. neutralizing biases in the market capitalization of stocks used in factor strategies.
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