Abstract
Momentum is the most important investing factor today not only because it features in the market capitalized weighted Indexes, which are designed to make the big bigger but also as the king of the factor zoo that drives factor investing today. Momentum is understood as a statistical factor but it’s loosely defined like many other statistical factors. The author is not aware of published work seeking commonality in statistical factors. The search for one-size-fits-all factors though seems like a hypothetical study, but modern science thinking offers an opportunity to not only ask what is momentum. But also redefine the factor and see its commonality with a universal dynamic probability factor. The study delves into the history of the momentum factor to explore its evolution as a component of a probabilistic mechanism that explains how momentum does not work alone but transforms into an inverse momentum and other statistical factors. The paper studies historical momentum crashes to highlight the inseparability of factors if they are reviewed as part of a probabilistic mechanism.
The Importance of Momentum in Research and Literature
Investment momentum, a concept under scrutiny for more than two decades, stands as a pivotal element in financial markets. This phenomenon pertains to the inclination of stocks, whether they have exhibited strong or weak performance in the past, to persist in their respective trajectories in the future. The scope of momentum extends beyond equities and encompasses various asset classes, including stocks, currencies, commodities, and bonds.
Momentum has undergone extensive scrutiny in academic research and has consistently demonstrated the ability to generate superior returns across diverse asset classes. It is often considered a standalone factor for investment strategies or a critical component alongside other factors. While some literature has downplayed the significance of momentum in favor of value investing, recent research has affirmed that momentum can indeed serve as a valuable standalone factor or in synergy with other factors. Furthermore, studies have unveiled the association between momentum and industry performance, showcasing the potential for profitable momentum strategies grounded in industry returns.
Definition and Momentum Models
Momentum, in essence, signifies the atypical returns achieved by stocks with robust historical performance. In 1993, the pioneering work of Narasimhan Jegadeesh and Sheridan Titman initiated the comprehensive exploration of momentum. Their findings revealed that stocks that fared favorably over a 3 to 12-month period tended to continue their upward trajectory over the subsequent 3 to 12 months.
Diverse models have been proposed to elucidate the phenomenon of momentum. Among them are theories centered on investors' reactions to new information. The "underreaction" model posits that investors frequently underestimate the impact of fresh data, thereby contributing to the accrual of momentum-based profits. Conversely, the "overreaction" model asserts that investors tend to overemphasize new information, resulting in price overcorrections and subsequent reversals. Additionally, behavioral biases such as conservatism and self-attribution have been implicated as potential drivers of momentum.
Limitations of Behavioral Models
Behavioral explanations for momentum have faced opposition from certain quarters due to perceived model limitations. Richard Arnold and Rob Bauer, for instance, challenge the notion that the "anchoring-and-adjustment" heuristic, often invoked to explain momentum, invariably dominates other psychological factors such as overreaction to new information. They also cast doubt on the wholesale extrapolation of individual decision-making biases to broader market dynamics. Furthermore, Eugene Fama and Kenneth French argue that the efficacy of the momentum effect is most pronounced in smaller-cap stocks with limited liquidity, leading to elevated transaction costs.
Temporal Momentum
Temporal momentum introduces the cyclicality inherent in momentum profits over time. According to the research of Tarun Chordia and Lakshmanan Shivakumar, momentum profits are intrinsically linked to the business cycle. They posit that during economic upswings, momentum profits tend to be positive, whereas during downturns, they often turn negative. This underscores the temporal dependence of profitability in momentum strategies on varying expectations of returns.
Factors are statistical in nature
Factors in finance are statistical because they rely on empirical data and quantitative analysis. These factors, like momentum or value, are derived from historical observations and are measured using specific statistical metrics. They exhibit traits like persistence and are evaluated for risk-adjusted returns through statistical methods. Factor strategies undergo rigorous statistical testing to confirm their significance and impact on asset returns. They are also integrated into quantitative models and portfolio construction, enhancing diversification and risk management. In essence, factors are defined, analyzed, and applied in finance based on statistical principles and empirical evidence from historical market data.
The unique statistical characteristics of Momentum factor
The momentum factor in finance possesses distinctive statistical characteristics that set it apart in investment strategies. Momentum is all about the persistence of recent performance trends, a statistical trait that defines its essence. Assets that have shown strength in the recent past tend to continue performing well, while those with weak recent performance often persist in underperforming. This phenomenon is especially potent within a short to medium-term timeframe, typically ranging from weeks to several months. It is also relative in nature, as momentum ranks assets based on their recent performance relative to their peers, distinguishing it from absolute strategies.
Quantitative metrics lie at the core of momentum's statistical nature. Researchers employ statistical tools like rolling returns and moving averages over specific lookback periods, often three to twelve months, to measure and identify assets with strong momentum characteristics. This reliance on data-driven metrics contributes to the factor's unique statistical profile.
Behavioral biases play a pivotal role in shaping momentum's statistical patterns. Investor tendencies to underreact or overreact to new information underpin many of these trends. This behavioral aspect adds complexity to the statistical analysis of momentum.
The non-linear nature of momentum returns further distinguishes it. While momentum can yield strong positive returns during certain periods, it is not immune to abrupt reversals or "momentum crashes," where assets with high momentum suddenly decline. These non-linear patterns underscore the statistical intricacies of momentum.
Moreover, momentum's statistical evaluation includes a focus on risk-adjusted returns. Analysts assess the excess returns generated by a momentum-based strategy while accounting for market risk and other relevant factors. This rigorous risk-adjusted assessment ensures that momentum is not merely a result of random fluctuations.
Performance variability across different market conditions and asset classes is yet another statistical aspect of momentum. Its effectiveness may vary during economic upswings, downturns, or within different market segments, adding to the complexity of analyzing its statistical behavior.
Factor interaction is a critical statistical consideration in the world of momentum. It can interact with other factors, such as value or low volatility, in intricate ways. These interactions can either complement or counteract the effects of other factors, further emphasizing the dynamic and statistical nature of momentum in investment strategies.
Momentum is the king of the factor zoo
There isn't a fixed number of statistical factors in finance, and the list can evolve as researchers uncover new insights. Some well-established factors like market risk (beta), size, value, and momentum are widely recognized, while others are subject to ongoing research and debate. This diverse collection of factors is often colloquially referred to as a "factor zoo" in finance. This term emphasizes the complexity of financial markets, highlighting the multitude of factors that researchers and investors consider when analyzing asset returns. These factors play crucial roles in portfolio construction, risk management, and investment strategy development, contributing to the intricate landscape of finance.
Momentum reigns supreme in the factor zoo of finance due to its remarkable empirical effectiveness, broad applicability, and robust historical performance. It consistently delivers superior returns across diverse asset classes and markets, making it a formidable force in investment strategies. Its versatility extends beyond stocks to encompass currencies, commodities, and bonds, underscoring its dominance. Furthermore, momentum's ability to persistently outperform other factors under varying market conditions solidifies its status as the king of the factor jungle.
Failures of Momentum
Despite its track record as a profitable strategy, momentum can experience setbacks. The phenomenon known as a "momentum crash" occurs when high-momentum stocks suddenly reverse their performance. Such reversals can be triggered by substantial negative market shocks or by neglecting other influential factors, such as stock size and intrinsic value, in conjunction with momentum. It's important to note that negative momentum does not conform to the same patterns as positive momentum.
Commonality in statistical factors
To understand the failures of momentum and how the macrocosm of factor work, one can look at the commonality in statistical factors. While each of the statistical factors like market risk, size, value, momentum, volatility, liquidity, quality, yield, low beta, and credit risk represents distinct aspects of asset returns and market behavior, there are some common statistical behaviors and observations that can be associated with many of these factors.
Many of these factors exhibit persistence, meaning that assets or portfolios that have historically exhibited certain characteristics (e.g., high momentum, low volatility, high quality) tend to continue displaying those characteristics for some time in the future. This persistence is often measured over specific time horizons. In contrast to momentum, some factors exhibit mean reversion. This means that assets or portfolios that have deviated significantly from their historical averages or norms tend to revert toward those averages over time. Value investing, for instance, is often based on the expectation of mean reversion in stock prices. Some factors, like market risk (beta) and credit risk, are cyclical and tend to vary with economic cycles. For example, beta may increase during economic upswings and decrease during downturns.
Investors typically assess these factors in terms of risk-adjusted returns. They examine whether the excess returns (returns above a risk-free rate) associated with these factors are statistically significant and provide compensation for the associated risks.
Many of these factors can be used in portfolio construction to enhance diversification and manage risk. For example, combining assets with low correlations in terms of these factors can lead to more stable and efficient portfolios. Factors often interact with each other. For example, size and value factors can complement each other in portfolio construction. These factors are commonly used in factor models to explain the cross-sectional variation in asset returns. Factor models aim to capture the systematic risks and patterns associated with these factors.
Many of these factors are used to assess specific types of risk (e.g., credit risk, liquidity risk, volatility risk) in portfolios. They help investors manage and control risk exposure. Investment professionals use these factors for performance attribution analysis. They assess how much of a portfolio's performance can be attributed to exposure to these factors.
It's important to note that while these common statistical behaviors can be observed, it is believed that there is no one-size-fits-all rule for how these factors behave in all market conditions. Market dynamics, economic conditions, and investor sentiment can influence the behavior of these factors, and their performance can vary over time and across different asset classes and markets.
One size fits all factor
Let’s assume there was one "one-size-fits-all" factor in finance. This single factor would consistently explain the majority of asset returns across all markets and asset classes. Such a factor would exhibit several characteristics. The factor would demonstrate remarkable persistence, consistently influencing asset returns over long time horizons, regardless of market conditions or economic cycles.
It would apply universally to all types of assets, including stocks, bonds, real estate, commodities, and currencies, as well as various market segments and regions. This factor would be largely independent of other factors. In other words, mutually exclusive. Hence, it wouldn't be easily explained or overshadowed by existing factors like market risk (beta), size, value, or momentum. It would provide a consistent source of risk-adjusted excess returns, allowing investors to earn superior returns without taking on excessive risk. The factor would remain resilient to changes in market sentiment, economic conditions, and regulatory environments. Investors could easily implement investment strategies based on this factor, making it accessible to a wide range of market participants. The factor's underlying economic (or scientific) rationale would be intuitive and easily interpretable, allowing investors to understand why it generates returns. It would maintain its statistical characteristics and performance consistency over long periods, avoiding significant variations. The factor would have predictive power, enabling investors to anticipate its future behavior and adapt their strategies accordingly.
Momentum as part of a probabilistic mechanism
If there were a factor in finance that possessed all the characteristics mentioned earlier, it would indeed function like a probabilistic mechanism. Such a factor would would provide investors with a systematic way to understand and potentially manage market dynamics and generate alpha (outperformance above market). This mechanism would not only allow factors to interact but also transform into each other. Factors would complement each other in a portfolio. For example, a value factor (stocks with low valuations) and a momentum factor (stocks with recent positive performance) can be used together in a portfolio to capture different aspects of market behavior. Factors may interact in complex ways. For instance, economic conditions can influence multiple factors simultaneously. A change in economic conditions might affect both value and growth factors differently.
Factors would also exhibit correlations with each other. Some factors might be positively correlated, meaning they tend to move in the same direction, while others may be negatively correlated, moving in opposite directions. The relationships between factors would change over time. For example, a factor that was historically negatively correlated with another factor might become positively correlated in different market conditions.
If we entertain the hypothetical scenario further, these factors could transform into each other in the context of financial markets, it would represent a fundamentally different and complex model of market behavior. Such a scenario would introduce a dynamic and fluid system where factors are not static but rather exhibit the capability to change their attributes or characteristics over time. The financial markets would be characterized by a dynamic and ever-changing landscape, where factors continuously evolve, merge, or transform into different factors. Factors would change their statistical properties, risk-return profiles, and underlying economic drivers. This transformation might occur in response to changing economic conditions, market sentiment, or other external factors.
The interactions between factors would become more intricate. Factors would interact in ways that lead to the emergence of new factors or the extinction of existing ones. Investors and portfolio managers would need to develop adaptive investment strategies capable of adjusting to changing factor dynamics. Traditional static factor models may need to be replaced with more dynamic approaches. As complex and speculative concept as this may sound, simple rules, simple statistical states of mean reversion, and persistence that change in time can simulate such a mechanism.
Momentum crashes transform momentum into another factor
Momentum can be recharacterized as a pure probabilistic factor. During or after a momentum crash, there is more than a small chance that the respective momentum factor would transform into another probabilistic factor. A momentum crash is an event where assets with strong positive momentum suddenly experience a sharp decline in performance. During such a crash, the typical probabilistic pattern associated with momentum is disrupted. During a momentum crash, the behavior of assets within the momentum factor temporarily transforms. Instead of continuing their recent positive trends, they may exhibit negative or volatile performance. This transformed behavior resembles a different probabilistic factor, possibly one associated with high volatility or mean reversion.
Importantly, this transformation is often temporary. Once the momentum crash subsides, assets within the momentum factor may or may not return to exhibiting more typical momentum behavior, consistent with their historical probabilistic pattern. So, while a momentum crash doesn't permanently transform momentum into another probabilistic factor, it does represent a temporary alteration in the behavior of assets within the momentum factor. This transformation is often characterized by increased volatility, reversals in performance, and deviations from the typical momentum pattern. Once the crash period concludes, the momentum factor can revert to its characteristic probabilistic behavior. In a probabilistic mechanism, a momentum crash could be called an “Inverse Momentum” factor which behaves dramatically differently than momentum in persistence mode, in the sense that recent winners become losers.
However, it's important to note that though this behavior is temporary and typically does not represent a systematic, long-term factor, there is always a chance that only a part of what was considered momentum might reemerge as momentum components. An "inverse momentum" factor where recent winners suddenly become losers has a strong chance to see an overlap with characteristics of the value factor. Value investing involves selecting assets that are undervalued or have low price-to-fundamental ratios. When momentum assets crash, they may resemble undervalued assets, leading to an overlap with the value factor. It's important to acknowledge that factors like momentum, inverse momentum, and value do not exist in isolation. They interact with each other and respond to changes in market conditions, investor sentiment, and economic factors in complex ways. Investors and portfolio managers may adapt their strategies to factor rotations, switching between momentum, value, and other factors based on changing market conditions, but without the systematic science of a probability mechanism, the odds of successful timing are high.
Historical Momentum Crashes
I have looked at the more than 20% decline since 1929 and listed popular reasons associated with the fall. Not only the periods of recovery were varying, but even the period till the next 20% fall also varied. The range of periods was so large that it was impossible to assume (or predict) that what started as a momentum factor with a set of components got reinstated at its previous integrity without change. Momentum is a probabilistic state, which moves like an elevator in a multi-storied building. It is impossible to predict the set of components expressing momentum (people in the elevator) over a certain period of time. The mere act of observation won’t lead to prediction. The odds will always be stacked against the forecaster. This is why factor failures are a reality and factor prediction an impossibility.
Momentum crashes more than 20%
* Why 1987 does not make the list? The reason why 1987 is not in the table of the S&P 500’s 20% declines since 1929 is because the crash of 1987 did not meet the criteria of a 20% decline from its previous peak on a closing basis. The S&P 500 peaked at 336.77 on August 25, 1987, and then fell by 20.4% to 225.06 on October 19, 1987, which is known as Black Monday. However, this was not the closing price of the index, as it recovered slightly to close at 224.84 on that day. The closing price of the index on October 16, 1987, the last trading day before Black Monday, was 282.702. Therefore, the percentage drop from the previous peak to the closing price on Black Monday was only 18.6% ([(336.77 - 224.84) / 336.77] x 100), which is less than 20%. The index did not close below 269.42 (which is 20% lower than the previous peak) until November 4, 1987, when it closed at 251.792. By then, the index had already rebounded from its lowest point on Black Monday, so it was not considered a continuous decline of 20% or more.
Conclusion
In the realm of investing, momentum emerges as a time-honored and crucial factor that has garnered in-depth attention over the years. It encapsulates the propensity of stocks with robust historical performance to sustain their excellence in the future. While various models, including those involving underreaction and overreaction, have been posited to explain momentum, it is essential to acknowledge the constraints inherent in behavioral explanations. Momentum profits are subject to temporal fluctuations and can encounter challenges, exemplified by momentum crashes. Momentum can be better understood as a probabilistic state of a mechanism, which is consistently evolving. In the end, the factors from the factor zoo can be categorized as forms of reversion and persistence that dynamically transform into each other in time.
Reversion factors are those that are associated with mean reversion or the tendency of assets to return to their historical averages over time. They include factors like the value factor, which is based on the idea that assets with low valuations (value stocks) may revert to higher valuations over time. Reversion factors tend to focus on assets that have temporarily fallen out of favor or have experienced recent underperformance.
Persistence factors, on the other hand, are based on the observation that assets with strong recent performance tend to continue performing well in the short to medium term. The momentum factor is a classic example of a persistence factor, where assets with positive momentum persist in their upward trajectory. What makes the factor zoo so intriguing is that factors within it can dynamically transform into each other over time. This transformation occurs in response to changing market conditions, economic cycles, and investor sentiment. During certain phases of the market cycle, reversion factors like value may transform into persistence factors as undervalued assets start to gain favor and their performance persists. Conversely, persistence factors like momentum can experience temporary disruptions or crashes, causing them to exhibit behavior resembling reversion factors. This transformation might happen during market corrections or shifts in investor sentiment.
Factors can also interact with each other, leading to dynamic transformations. For instance, a factor like low volatility, which focuses on stable assets, can interact with value or momentum factors during different market environments, influencing their behavior. Understanding these dynamics and how factors interact is essential for investors seeking to construct resilient and adaptable portfolios that can navigate the ever-changing landscape of financial markets. Probabilistic Factors can not only answer what is momentum but also provide a framework for capturing the ebb and flow of market behavior, allowing investors to capitalize on different opportunities as they arise.
Bibliography
French, Kenneth R., and Martin L. Weitzman. "The 'Smart Money' Indicator and Financial Markets." The Review of Economic Studies, 1988.
Jegadeesh, Narasimhan, and Sheridan Titman. "Momentum and Autocorrelation in Stock Returns." The Journal of Finance, 1993.
Thaler, Richard H. "The End of Behavioral Finance." Financial Analysts Journal, Vol. 55, No. 6, Behavioral Finance (Nov. - Dec. 1999), pp. 12-17.
Santa-Clara, Pedro, and Rossen Valkanov. "The Presidential Puzzle: Political Cycles and the Stock Market." The Journal of Finance, 2003.
Dahlquist, Magnus, Øystein Gjerde, and Sverre N. Herbjørnson. "Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole." The Journal of Banking and Finance, 2003.
Jegadeesh, Narasimhan, and Sheridan Titman. "Summary: Momentum Generalized (Screen)." 2001.
Chardia, Tarun, and Lakshamanan Shivakumar. "Momentum, Business Cycle, and Time-Varying Expected Return." 2002.
Lewellen, Jonathan, Stefan Nagel, and Jay Shanken. "Momentum in Stock Returns: Some New Evidence." The Review of Financial Studies, 2010.
Geczy, Christopher C., and Mikhail Samonov, CFA. "212 Years of Price Momentum." 2013.
Asness, Clifford S., Tobias J. Moskowitz, and Lasse H. Pedersen. "Value and Momentum Everywhere." Feb 2009.
Fama, Eugene F., and Kenneth R. French. "Size, Value, and Momentum in International Stock Returns." 2012.
Asness, Clifford S., Andrea Frazzini, Ronen Israel, and Tobias J. Moskowitz. "Fact, Fiction, and Momentum Investing." 2014.
Carhart, Mark M. "On Persistence in Mutual Fund Performance." The Journal of Finance, Volume 52, Issue 1, Pages 57-82, 1997.
Lewellen, Jonathan, Stefan Nagel, and Jay Shanken. "Momentum in Stock Returns: Some New Evidence." The Review of Financial Studies, 2010.