Algorithms and rule-based systematic trading systems have gone from representing near 30% of the market to now dominating where only 10% of those influencing the supply and demand balance decisions are “fundamental discretionary traders,” JPMorgan (JPM) head of quantitative and derivatives research Marko Kolanovic pronounced recently. In a June 2017 research note to clients, he said such trading is undoubtedly influencing the price of given securities. In fact, he attributed the June 9 and 12 sell-off in technology stocks to computer-based algorithms receiving sell signals.
How a computer algorithm views stocks is perhaps one of the most important factors driving a stock price today, but few people have any clue how it works, what algorithms think about their stocks, and why a stock may be moving up or down in price absent fundamental news.
That is about to change.
The goal of this series of articles is to illuminate to various degrees how certain algorithms might view individually named equities. We not only consider technical market factors but also connect dots with fundamental economic forces that influence algorithms more than is generally recognized.
Accomplishing the goal of providing a concise analysis of how literally billions of lines of code might think is no easy task to be sure. An argument can be made that each algorithm has its own set of characteristics, market proclivities, and idiosyncratic execution triggers that make condensing an outlook more than challenging, some might say impossible.
While the argument that each algorithm is unique in its own right has significant merit, I tend to disagree that a general consensus view cannot be developed. While it is a difficult task, it is not impossible.
As someone who has studied various systematic trading strategies, developed professional trading programs for use in a hedge fund setting, written or contributed to four books, and taught a Northwestern University Executive Education course on the topic, it is my opinion that to a large degree, computer-based trading and investing systems can be understood by fundamental portfolio managers once the proper perspective is explained. In particular, this means correlating a strategy or formula component to its macro “beta market environment.”
While the computer code and mathematics behind each unique trading or investing algorithm is almost always unique and complex, a thesis driving this philosophy is that there are core fundamentals, innate performance drivers that relate to a larger macro market environment that drive the success of most algorithmic systems regardless of their complexity.
In the series of articles, we will analyze the algorithmic factors potentially influencing a stock's performance in an easy to read format.
When analyzing an algorithm, starting the framing to understand how it works from this beta market environment perspective can be immensely valuable. With this understanding, you can not only recognize how or why a stock might be influenced by a systematic program, but that is not all. Sophisticated institutional allocators can use the system to develop noncorrelated investment portfolios, make quantitative hedge fund evaluation and selection decisions, and manage alternative investments going forward with a beta market understanding.
It should be clear, however, that what is discussed is not simple. Claims are not being made that algorithms are easy to build or fully understand. The claim is that when starting an understanding of these algorithms from a macro perspective based on beta market environment, we can best understand what is driving supply and demand factors in a given stock, market, or hedge fund trading strategy.
In this series of articles for Seeking Alpha, I will attempt to take the complexity of various algorithms, break them down into understandable nuggets. I am not teaching people how to do this; that would be infinitely more complex. What I am suggesting is that if investors recognize the basic beta market environments influencing algorithmic trading, they can obtain a sense of what might be driving the price direction of their individual stocks and/or recognize how various hedge fund trading systems might work.
One key to success is to break down the complexity, the first point of this is to recognize the number of market environments that dominate.
I primarily consider three technical beta market environments: Price persistence, used in a trend following/momentum strategy; mean divergence and convergence of related asset prices used in relative value; price volatility used in algorithmic systems that are impacted by sudden and large price movements. These are not the only market environments by any means. I use these three as a primary point of understanding because this was my method when a practitioner for building noncorrelated portfolios and relates to research conducted. (See the “beta market environment” section below.)
Much like factor investing, where there are now some 300+ economic factors are driving various beta-based systems, there are numerous sub-category market environment considerations, such as mean reversion and various breakout theories that are applied. Lance Humphrey, a USAA Portfolio Manager who manages over $5 billion, pointed out to me in this podcast, there are too many factors being “discovered.” Rather than get lost in the complexity, he understands markets by first recognizing the most meaningful and useful factors and expanding wisdom from that point.
I take the same approach with technical beta market environment price factors.
Below that are additional technical details surrounding the major beta market environments typically considered in this analysis along with some academic support when available.
Beta Market Analysis Method and Recommended Reading:
The thesis that technical “beta market environments” influence algorithmic trading strategies was first seen in a book I wrote High Performance Managed Futures (Wiley, 2010). Meaningful in this book was the statistical look starting on page 239 where the three primary beta market environments outlined were profiled on a statistical basis using monthly returns data. Later different analysis using differing trade time frames and analytical techniques enhanced the view. Thoughts and research on the topic grew as did the underlying thesis, which was later expanded in a Northwestern University Continuing Education that addressed algorithmic strategy measurement, as well as in several articles and outlined in a chapter in the book from Bailey McCann, Tactical Portfolios: Strategies and Tactics For Investing in Hedge Funds (Wiley, 2014).
This section of the article gets more technical than most stock market analysis that will use beta market environments as a foundation but is less technical than a development documented used to create a CTA or algorithmic strategy.
The core concept surrounding beta market environment analysis
The success of the beta market environment analysis process is based on breaking down complexity found in a hedge fund strategy or algorithm by first understanding the fundamental components, the core performance drivers, that are direct causation for success.
It is a core truth, one not often discussed in public, that all trading algorithms, being formulas subject to if/then logic, are successful when they discover repeatable market events. These market events have identifiable technical features that can be best understood by first recognizing how they react to what I term a “beta market environment.” By definition, a strategy that falls under a particular beta market environment category is either positively or negatively impacted when the beta market environment condition is in place or absent. Beta market environments are statistically measured using consistent formulas. While most CTAs keep their algorithmic methods a secret unless they speak with consultants, there are some CTAs who have acknowledged to me for public consumption they identify market environmental factors in their analysis, including Natixis (in a podcast conversation) and Graham Capital Management, for instance. Bridgewater Associates, which does not use traditional CTA strategies, does engage in beta and volatility targeting, they disclosed in an exclusive interview.
Beta market environments are broken down into three primary categories with many sub categories:
- Price Persistence is a beta market environment where the force of a price trend is strong and the prices of a given asset continue to move in one direction. This market environment is conducive to many algorithmic strategies such as including trend following, momentum, and many of the sub-category strategies such as break-out theory. Mean reversion is placed under the price persistence category for specific portfolio development purposes and because it is influenced by the market environment of price persistence and force of trend, being negatively correlated. In the analysis of individual stocks, this work will be extensively referenced. Price persistence is a market environment that is commonly referenced by industry practitioners through a variety of publicly available measures. Price persistence often has fundamental and economic roots that have been best explained through a number of academic papers listed in the latter section addressing this topic as well as several excellent books on the topic of trend following and momentum trading and investing.
- Volatility is the movement of an asset’s price in rapid succession and sometimes surprising succession. The divergence from its price mean – and a separation from its beta, which measures relative volatility – are used in analysis to identify potential trade triggers. Volatility typically has a meaningful impact on the other two primary market environments, often igniting price persistence and creating a strong force of trend (most pronounced during the 2008 global financial crisis). Likewise, volatility often creates an opportunity for relative value strategies by creating mean divergence and, then after the volatility impact dissipates, mean convergence. Volatility analysis when combined with price persistence and relative value analysis will be frequently used to explain the algorithmic impact on individually named equities, as volatility triggers have a statistical correlation with force of trend that can be explained on a fundamental, economic basis. Volatility is most commonly measured through popular indexes such as the CBOE VIX, which bases its price on options volume. While options volume is significant – and recognizing signals from both options and single stock futures trading is meaningful – volatility analysis as it relates to individually named equities starts relative to its historic standard deviation of prices, specifically measured separately by upside and downside deviation.
- Mean Divergence/Convergence is the market environment that impacts relative value, spread, and arbitrage strategies and has much lesser known but equally powerful impact relative to individually named equities. Mean divergence occurs when the price of one asset materially changes relative to the price of another asset with a deep economic correlation. There are points when the mean divergence is technical in nature and then a convergence occurs, which completes the relative value/spread arbitrage cycle. But most materially for individual stock analysis is when a stock price diverts from its mean correlation with a deep economic correlation. In many systems, this sends a trade execution trigger and provides clues as to fundamental economic changes are occurring in a stock relative to its market beta. While mean divergence/convergence is not publicly measured to the same degree as price persistence or volatility, there are definitive, mathematical measures that quantify such activity and will be combined with a fundamental, economic overlay to understand price movements in individually named equities.
There are statistical proclivities that definitively define each of these strategies that are explained in the individual strategy analysis below, with particular emphasis on win percentage relative to win size and worst drawdown. These measures will be combined with other meaningful algorithmic indicators to overlay on top of individual stocks to understand the algorithmic force behind or against a particular strategy. The win percentage of a particular execution trigger often increases with the number of properly correlated algorithmic overlays. When conducting individual stock analysis, readers will notice that a confluence of signals is given significant weighting over an individual signal.
But before we get even further into the weeds relative to beta market environment analysis, let’s consider its history.
The history of beta market environment analysis
Having a history consulting with various exchanges and market participants in the derivatives industry, I noticed that strategies used on the exchange floor (back when humans had a meaningful role) were varied. Trend following received the most popular public attention and was documented to be the most popular by far, with many practitioners and academics arguing this was the only valid managed futures CTA strategy. I diverged from the consensus, which, in my opinion, was not examining all the data. I advocated for a diverse strategy set approach that leveraged multiple market environments, not just one. I professionally traded a volatility strategy along the yield curve and while running a managed futures CTA division for a small brokerage/trading firm built noncorrelated CTA portfolios based on the market environment concept. This business was later negatively impacted to differing degrees by the failure of MF Global and Peregrine Financial Group.
Research into beta market environment analysis started while studying hedge funds that failed. The BarclayHedge “Graveyard” CTA database was at first very challenging to analyze, a topic partially discussed in my 2010 book High Performance Managed Futures and later in the book Tactical Portfolios. But ultimately, I turned the fund returns data around, looking at it from the point of failure backward, and discovered a few statistical provincialities as hedge funds were failing – moving into a “death spiral” - that could be explained on a fundamental basis. This was used in developing not only a method to monitor hedge fund performance but also provided insight into strategy stability of algorithmic triggers. My thinking has advanced in the past eight years and looking back the three most significant discoveries made through this research were: 1) Systematic hedge funds that failed had a statistical tendency to deliver performance inconsistent with their stated beta market environment and core performance drivers; 2) Hedge funds that significantly outperformed market peers based on specific upside and downside deviation benchmarks were most likely to fail in the long run; 3) Recognizing the statistical propensity of each strategy, with a focus on upside and downside deviation and correlation analysis, can provide unique insight into what moves markets and stock prices, particularly given the increased influence of algorithmic strategies of late. The entirety of the study findings has not been released as many of the findings are used on a commercial basis. Algorithm effectiveness has been known to have a diminishing information value that is negatively correlated with exposure. However, certain strategies are more elastic than others.
For further details on how macro market environments impact markets and portfolio building in general, as well as recommended reading of public academic documentation also see:
Bilello, Charles V. and Gayed, Michael A., An Intermarket Approach to Beta Rotation: The Strategy, Signal, and Power of Utilities (January 31, 2014). 2014 Charles H. Dow Award Winner. Available at SSRN: An Intermarket Approach to Beta Rotation: The Strategy, Signal, and Power of Utilities by Charles V. Bilello, Michael A. Gayed: SSRN or An Intermarket Approach to Beta Rotation: The Strategy, Signal, and Power of Utilities by Charles V. Bilello, Michael A. Gayed: SSRN
Faber, Meb, A Quantitative Approach to Tactical Asset Allocation (February 1, 2013). The Journal of Wealth Management, Spring 2007. Available at SSRN: A Quantitative Approach to Tactical Asset Allocation by Meb Faber: SSRN
Meucci, Attilio, Managing Diversification (April 1, 2010). Risk, pp. 74-79, May 2009; Bloomberg Education & Quantitative Research and Education Paper. Available at SSRN: Managing Diversification by Attilio Meucci: SSRN
Choueifaty, Yves and Froidure, Tristan and Reynier, Julien, Properties of the Most Diversified Portfolio (July 6, 2011). Journal of Investment Strategies, Vol.2(2), Spring 2013, pp.49-70. Available at SSRN: Properties of the Most Diversified Portfolio by Yves Choueifaty, Tristan Froidure, Julien Reynier: SSRN or Properties of the Most Diversified Portfolio by Yves Choueifaty, Tristan Froidure, Julien Reynier: SSRN
Li, Lingfeng, Macroeconomic Factors and the Correlation of Stock and Bond Returns (November 2002). Yale ICF Working Paper No. 02-46; AFA 2004 San Diego Meetings. Available at SSRN: Macroeconomic Factors and the Correlation of Stock and Bond Returns by Lingfeng Li: SSRN
With an overview of the beta market environment philosophy in hand, consider how each of the primary strategies statistically differs – altering their execution algorithms – and what this means towards understanding the impact of systematic trading on market and individual stock prices.
Price Persistence: Trend Following/Momentum/Breakout Theory:
The most popular CTA algorithmic trading strategy with the largest quantity of both professional adoption and documentation surrounding its methods is trend following. Historically, this involved the use of simple or exponential moving averages (or a combination) through a “moving average cross” of two time frames to issue a buy or sell signal. For example, the Societe Generale Trend Indicator, a popular method to benchmark trend following beta, uses a 20-day/120-day moving average cross to benchmark a price trend in 55 markets across four asset classes. This is considered a mid-term time horizon by many practitioners, and time horizon is a key factor when evaluating such systems and trend behavior in a given market. More advanced models apply a time series momentum lens, adaptive models or use the Nyquist criterion or Kalman filter models to reduce statistical noise which also improves win percentage but, at times, results in catching a trend at a different point in time than the more sensitive execution triggers.
Here is the key point: While all trend, momentum and breakout models have important nuanced differences, they benchmark the existence of the same thing - a trend or momentum in a given market. While they often identify the same trend with execution triggers that operate on slightly different time frames, it is the general beta market environment strength that by definition determines success.
A premise of the beta market environment analysis philosophy is that when a positive market environment is present - price persistence in a given asset, for instance – this results in positive performance and vice versa. This results in a determination of the strength of a trend, which can, in part, be seen in measures such as the “Trend Barometer” developed and managed by Dunn Capital’s Niels Kaastrup-Larsen, which is one variation of a benchmark for the level of trend strength in markets.
Strategy win percentage is often negatively correlated with win size
Win percentage is material relative to analysis of individual stocks. Relative to win percentage, over time, the trend strategies developed new overlays that improved win percentage, but also delayed the timing of a trade signal if not eliminating many valid trades. When evaluating individual stocks, momentum signals are given relative to a range based on the signals sensitivity. Likewise, win percentage is considered, particularly relative to the use of other indicators, as certain overlays have a statistical correlation with increased signal accuracy but at times also lower win size. As you will see, in these strategies, win percentage and win size are often negatively correlated. Another important metric for trend/momentum signals is how over time the increasing popularity of algorithmic strategies creates a re-enforcing market mechanism to various degrees. Once certain systematic execution triggers are hit an amplification of the trend occurs over given time frames, most noticeable in the short term.
What I found most interesting while studying various market environments is that trend following has a different statistical profile when considering the entire portfolio of assets than it does when evaluated on a trade by trade basis. In my initial study of the BarclayHedge database, which at the time had the largest percentage of CTA and systematic fund managers reporting, the trend following strategy had monthly fund returns win percentage of 57.89% and an average win size of 4.52%. Compare this to the volatility strategy average, which at that time had a win percentage of 74.25% but a smaller monthly win size of 3.75%. This can be a slightly nuanced number to consider when juxtaposed to the average statistical analysis on an individual trade basis that did not consider a monthly reporting time frame but rather the length of the trend (not published in the book.) Proprietary studies I have since seen from various CTAs, as well as my limited research, suggested that on an individual trade basis, win percentage was rather low – near 20% in many studies – while win size was significantly higher. Strategies typically exhibit a relatively inverse relationship between win percentage and win size. While there is much noise around algorithmic trading, these are key statistics to focus on and often define strategies to certain degrees. Short volatility strategies have corresponding high win percentages with low win size but high maximum drawdown levels, for instance. Understanding the meaning of this is valuable when evaluating individual stocks, and it is one reason why recognizing different beta market performance drivers such as relative volatility and mean divergence come into play.
For further details about general trend following/momentum and recommended reading of public academic documentation also see following:
Benhamou, Eric, Trend Without Hiccups - A Kalman Filter Approach (April 12, 2016). Available at SSRN: Trend Without Hiccups - A Kalman Filter Approach by Eric Benhamou: SSRN or Trend Without Hiccups - A Kalman Filter Approach by Eric Benhamou: SSRN
Hurst, Brian and Ooi, Yao Hua and Pedersen, Lasse Heje, A Century of Evidence on Trend-Following Investing (June 27, 2017). Available at SSRN: A Century of Evidence on Trend-Following Investing by Brian Hurst, Yao Hua Ooi, Lasse Heje Pedersen: SSRN
Moskowitz, Tobias J. and Ooi, Yao Hua and Pedersen, Lasse Heje, Time Series Momentum (September 1, 2011). Chicago Booth Research Paper No. 12-21; Fama-Miller Working Paper. Available at SSRN: Time Series Momentum by Tobias J. Moskowitz, Yao Hua Ooi, Lasse Heje Pedersen: SSRN or Time Series Momentum by Tobias J. Moskowitz, Yao Hua Ooi, Lasse Heje Pedersen: SSRN
Bergstresser, Daniel and Cohen, Lauren and Cohen, Randolph B. and Malloy, Christopher J., AQR's Momentum Funds (October 8, 2010). Harvard Business School Finance Case No. 211-025. Available at SSRN: AQR's Momentum Funds by Daniel Bergstresser, Lauren Cohen, Randolph B. Cohen, Christopher J. Malloy: SSRN
Baltas, Nick and Kosowski, Robert, Momentum Strategies in Futures Markets and Trend-following Funds (January 5, 2013). Paris December 2012 Finance Meeting EUROFIDAI-AFFI Paper. Available at SSRN: Momentum Strategies in Futures Markets and Trend-following Funds by Nick Baltas, Robert Kosowski: SSRN or Momentum Strategies in Futures Markets and Trend-following Funds by Nick Baltas, Robert Kosowski: SSRN
Glabadanidis, Paskalis, Market Timing with Moving Averages (November 9, 2012). Available at SSRN: Market Timing with Moving Averages by Paskalis Glabadanidis: SSRN or Market Timing with Moving Averages by Paskalis Glabadanidis: SSRN
Baltas, Nick, Trend-Following, Risk-Parity and the Influence of Correlations (October 12, 2015). "Risk-Based and Factor Investing", Elsevier & ISTE Press, 2015 (Forthcoming). Available at SSRN: Trend-Following, Risk-Parity and the Influence of Correlations by Nick Baltas: SSRN
Bruder, Benjamin and Dao, Tung-Lam and Richard, Jean-Charles and Roncalli, Thierry, Trend Filtering Methods for Momentum Strategies (December 1, 2011). Available at SSRN: Trend Filtering Methods for Momentum Strategies by Benjamin Bruder, Tung-Lam Dao, Jean-Charles Richard, Thierry Roncalli: SSRN or Trend Filtering Methods for Momentum Strategies by Benjamin Bruder, Tung-Lam Dao, Jean-Charles Richard, Thierry Roncalli: SSRN
Volatility/Price Dispersion:
Price volatility, like market price trends, are definitively measured in a public setting. The CBOE volatility products, most notably the S&P 500 VIX index, document market volatility by measuring the volume of options transactions. For the purposes of this stock market analysis, volatility is also measured through the average standard deviation in an asset’s price and is used in numerous risk/reward measures, such as the Sharpe Ratio, which gives equal weighting to upside and downside deviation. While there are many public observations regarding volatility impacting stock market performance – Crestmont Research, for instance, documented the relationship between higher volatility and lower stock prices and lower volatility and higher stock prices – there is also private research on volatility that notes correlations with trend strength. These concepts are used in the development of CTA strategies as well as high frequency trading models. The most notable example of volatility leading to market trend strength occurred in 2008, when the initial “Lehman moment” led to the VIX index spiking to 42.16. This resulted in significant market trends and led to one of the best periods of CTA system performance in history, particularly trend following systems calibrated towards a mid-term time horizon.
From the standpoint of this individual stock research, volatility is a key market trigger that certain algorithmic strategies utilize and thus is relevant towards analysis. Further, volatility analysis will be used in relation to trend and relative value analysis as an overlay filter with the goal to improve win percentage regarding force of trend.
For details and recommended reading of public documentation see the following:
Zhang, Frank, High-Frequency Trading, Stock Volatility, and Price Discovery (December 2010). Available at SSRN: High-Frequency Trading, Stock Volatility, and Price Discovery by Frank Zhang: SSRN or High-Frequency Trading, Stock Volatility, and Price Discovery by Frank Zhang: SSRN
Menkveld, Albert J., High Frequency Trading and the New-Market Makers (May 13, 2013). Journal of Financial Markets, Vol. 16, 2013. Available at SSRN: High Frequency Trading and the New-Market Makers by Albert J. Menkveld: SSRN or High Frequency Trading and the New-Market Makers by Albert J. Menkveld: SSRN
Gomber, Peter and Arndt, Björn and Lutat, Marco and Uhle, Tim, High-Frequency Trading (2011). Available at SSRN: High-Frequency Trading by Peter Gomber, Björn Arndt, Marco Lutat, Tim Uhle: SSRN or High-Frequency Trading by Peter Gomber, Björn Arndt, Marco Lutat, Tim Uhle: SSRN
Whaley, Robert E., Understanding VIX (November 6, 2008). Available at SSRN: Understanding VIX by Robert E. Whaley: SSRN or Understanding VIX by Robert E. Whaley: SSRN
Cartea, Álvaro and Jaimungal, Sebastian, Modeling Asset Prices for Algorithmic and High Frequency Trading (December 8, 2010). Applied Mathematical Finance, Vol. 20, No. 6, 2013. Available at SSRN: Modeling Asset Prices for Algorithmic and High Frequency Trading by Álvaro Cartea, Sebastian Jaimungal: SSRN or Modeling Asset Prices for Algorithmic and High Frequency Trading by Álvaro Cartea, Sebastian Jaimungal: SSRN
Griffioen, Gerwin A. W., Technical Analysis in Financial Markets (March 3, 2003). Available at SSRN: Technical Analysis in Financial Markets by Gerwin A. W. Griffioen: SSRN or Technical Analysis in Financial Markets by Gerwin A. W. Griffioen: SSRN
Gabaix, Xavier and Gopikrishnan, Parameswaran and Plerou, Vasiliki and Stanley, H. Eugene, Institutional Investors and Stock Market Volatility (October 2, 2005). MIT Department of Economics Working Paper No. 03-30. Available at SSRN: Institutional Investors and Stock Market Volatility by Xavier Gabaix, Parameswaran Gopikrishnan, Vasiliki Plerou, H. Eugene Stanley: SSRN or Institutional Investors and Stock Market Volatility by Xavier Gabaix, Parameswaran Gopikrishnan, Vasiliki Plerou, H. Eugene Stanley: SSRN
Relative Value/Mean Divergence/Pairs Trading
Unlike market price trends and volatility, there are not the same public benchmarks for relative value beta benchmarking despite the concept being widely used in commodity and stock trading. As outlined in multiple books, the core concept is to measure the relative value of one asset to another asset with a similar profile, one with a “deep economic link,” as one Quantopian seminar outlined, consistent with many books and research on the topic.
The beta is most often measured by a statistical average between two asset prices. In trading algorithms a “fair value” is represented to certain degrees, often validated by outside factors that influence price disparities such as a price earnings ratio in a stock or economic supply and demand factors in a commodity. When the price of one asset diverges from this mean to a significant level, it represents an opportunity in certain investment methodologies so long as the fundamental economic drivers that correlated the two assets have not materially changed. Quantitative formulas look for “mean divergence” and then “mean convergence” to make a relative value strategy work, often technically measured by what is known as a “Z score” and many times involves a linear regression analysis. Quantopian acknowledged the use of moving average crosses in helping determine relative value analysis, and this is actually much further advanced in private CTA formulas than has been publicly discussed.
Analysts look to mean divergence as a sign that core fundamental economic variables in the stock have changed, which will be extensively explored when considering the algorithmic impact on individual stocks. There are specific time horizon triggers used in this analysis which will also be used frequently. In fact, there is a particular statistical “P Value” method of confidence analysis that tracks the stationarity of a reversion model to develop an economic thesis. In other words, a sustained deviation from the correlation mean provides an increased P Value confidence level as to the potential for an underlying economic event to be taking place, is one thesis.
While some of the relative value strategies have been publicly discussed, many strategies with meaningful nuances used by hedge funds, CTAs and high frequency trading firms remain private. Some of the meaningful differential in how relative value strategies are executed relative to stocks include selecting issues that not only have the same business orientation – in the same stock market sector – but some formulas also consider the differential between value and momentum and look at valuation methods such as price to earnings and other valuation formulas as a method to group correlated assets together. If one does begin to get deeper into algorithmic analysis, discussions of co-integration and the difference with correlation and stationarity is also considered.
For details and recommended reading of public documentation see the following:
Faber, Meb, Relative Strength Strategies for Investing (April 1, 2010). Available at SSRN: Relative Strength Strategies for Investing by Meb Faber: SSRN or Relative Strength Strategies for Investing by Meb Faber: SSRN
Till, Hilary and Eagleeye, Joseph, Commodity Futures Trading Strategies: Trend-Following and Calendar Spreads (January 17, 2017). Available at SSRN: Commodity Futures Trading Strategies: Trend-Following and Calendar Spreads by Hilary Till, Joseph Eagleeye: SSRN or Commodity Futures Trading Strategies: Trend-Following and Calendar Spreads by Hilary Till, Joseph Eagleeye: SSRN
Menkveld, Albert J., High Frequency Trading and the New-Market Makers (May 13, 2013). Journal of Financial Markets, Vol. 16, 2013. Available at SSRN: High Frequency Trading and the New-Market Makers by Albert J. Menkveld: SSRN or High Frequency Trading and the New-Market Makers by Albert J. Menkveld: SSRN
Cartea, Álvaro and Jaimungal, Sebastian, Modeling Asset Prices for Algorithmic and High Frequency Trading (December 8, 2010). Applied Mathematical Finance, Vol. 20, No. 6, 2013. Available at SSRN: Modeling Asset Prices for Algorithmic and High Frequency Trading by Álvaro Cartea, Sebastian Jaimungal: SSRN or Modeling Asset Prices for Algorithmic and High Frequency Trading by Álvaro Cartea, Sebastian Jaimungal: SSRN
Taliaferro, Ryan and Blyth, Stephen, Fixed Income Arbitrage in a Financial Crisis (C): TED Spread and Swap Spread in November 2008 (June 22, 2011). Harvard Business School Finance Case No. 211-051. Available at SSRN:
Fixed Income Arbitrage in a Financial Crisis (C): TED Spread and Swap Spread in November 2008 by Ryan Taliaferro, Stephen Blyth: SSRNKashyap, Ravi, Dynamic Multi-Factor Bid-Offer Adjustment Model (October 2, 2008). Institutional Investor Journals, Journal of Trading, Vol. 9, No. 3 (Summer 2014), pp. 42-55. Available at SSRN: Dynamic Multi-Factor Bid-Offer Adjustment Model by Ravi Kashyap: SSRN or Dynamic Multi-Factor Bid-Offer Adjustment Model by Ravi Kashyap: SSRN
Hanson, Thomas A. and Hall, Joshua R., Statistical Arbitrage Trading Strategies and High Frequency Trading (September 12, 2012). Available at SSRN: Statistical Arbitrage Trading Strategies and High Frequency Trading by Thomas A. Hanson, Joshua R. Hall: SSRN or Statistical Arbitrage Trading Strategies and High Frequency Trading by Thomas A. Hanson, Joshua R. Hall: SSRN
This has been a basic outline of the methods and systems used to understand how algorithms might be influencing individual stocks. Limited analysis such as this cannot cover all algorithmic impacts and potential influences. When the most fundamental market environments are considered, however, a useful picture can be painted for investors to further investigate.