Trading with signal and price impact uncertainty

 

When you want to make your model practical, you have to look at signal uncertainty and price impact. If you use any model, your one-step-ahead forecast may have some uncertainty because the average coefficient may not accurately represent the true coefficient sensitivity at a given time. Similarly, for any model there is going to be a prcie impact from trading. If the signla is weak then iapct uncertainy is not that important but as the siganl strengthens, the effect price imapct will become more important. See “Trading with uncertainty about signals and price impact.” These real-world effects are important if you want to trade a model.  

The morning volatility uncertainty effect

 

There has been an increase in research on what happens between the close and the open, and from the open to the close, in asset markets. In the equity market, significant differences have been found between overnight returns and daytime returns. 

In the paper, “Early Birds Get the Vol; Morning Volatility Uncertainty and Variance Risk Premium”, the authors find that the volatility of the VIX or VVIX at 10 AM EST can strongly predict the next day’s asset return's variance. The authors mine the day to show that there is a significant risk premium that can be exploited. I have reservations about the results, but I’m interested in the finding that volatility shocks have a spillover effect on volatility the next day. 

Volatility shocks will have spillover effects that can be exploited. 

Can market forecasts front run information? The answer is yes

 

The foundation of market rational expectations is that a scheduled report cannot affect the firm’s stock price until it is reported. You can’t act on information you do not have. Yet, the paper “How markets forecast and ‘front run’ Information: Bayesian Market Efficiency” tells a plausible story that can explain some key market behavior.

The argument for this front-running is based on Bayesian statistics. Assume there is a Bayesian investor who, rather than waiting, infers what will be in a report before the release. Given this inference, the Bayesian investors will reprice the stock before the announcement. Yet there remains uncertainty about the content of any news that could lead to a rise in premiums, particularly regarding the precision and quality of the firm’s financial reporting. The premium can be either positive or negative. Hence, the stock price and the cost of capital will be impacted by how well investors can form expectations about a given financial report. 

It seems this already happens in markets. Investors form expectations about what a financial report will say, and those views are incorporated into the price. The Bayesian approach provides more structure to how expectations are formed. We are all Bayesians, so saying that we form rational expectations does not really tell us much about how expectations are formed in real life. Using Bayesian updating provides structure around our behavior.

False discovery rate in finance - Thinking out of the box

 

Aha! I found another risk premium. This has been the mantra of finance for well over the last decade, yet perhaps we should comment, "not so fast." While on the one hand, there has been an explosion of research finding new factors, what has been called the factor zoo, there has also been pushback by other researchers who have pointed out the issue of data mining. The argument of data mining is that conventional inferential frameworks are inappropriate when there are endless tests of different model specifications before the right one is reported. We will mine the data until we find the right result. Other researchers have pushed back against the data miner, with analyses showing that the posterior-expected alphas still exist even after the initial results were reported.

A new paper. "The False Discovery Rate in Finance: Identification failure and search-adjusted estimation" outlines how this problem can be solved. There should be a search-and-selection process for identifying factors. Knowing that process will help detect the false discovery rate, but if this search mechanism is unknown, there will be a greater likelihood of underestimating the true false discovery rate. 

Using some lower bounds calculated from their work, the authors suggest that most reported discoveries in finance are likely false. Ouch, that is a strong indictment and has strong implications for academic research and the work of quants who use that research to develop profitable trading strategies.  

Signal filtering for mean reversion trading

 

If you aren't a trend follower within the quant price space universe, then you are a mean reverter. A paper discusses how to filter these reversion signals, "Advanced signal filtering for mean reversion trading." Mean reversion is based on the simple concept that an asste's price will converge to some fair value. This fair value could be as simple as a moving average. The spot price may fall above or below this fair value price. To solve this problem, the authors develop what they call the local average filtering objective (LAFO), a low-pass filter that operates across different frequencies. LAFO examines the average residuals over a moving window to capture moving-average characteristics. This information can be used to measure or describe mean reversion. LAFO is an extension of the mean squared error. Machine learning can help process data to identify the method of reversion to the mean and mispricing in a time series. 

Can there still be dislocations that will cause mean-reversion not to occur? Yes, but by examining different rolling windows of residuals, there is a good chance of finding revision opportunities.  

Unified framework for anomalies - all in the past month of return behavior

 

The daily return information factor (DRIF) is a new concept that helps explain many of the anomalies we see in financial markets. Instead of imposing or seeking a new risk premium, the authors of this paper, “A unified framework for anomalies based on daily returns”, examine the overall mapping of returns over the last month to make predictions about next month’s returns. The authors examine both the time ordering and the magnitude of returns to develop a forecasting framework.

A chronological vector preserves time ordering and captures short-term reversal dynamics, while a ranked vector accounts for magnitude effects. The DRI variable will combine these two vectors so that next month's returns are based on the beta of the time and magnitude vectors. A chronology dimension captures price pressure and liquidity effects, while ranking reflects investors' focus on extreme outcomes. These effects remain after controlling for other risk factors. 

Dual role of prices - endogenous and exogenous events

 

...dual role of prices. By “dual role”, we mean that prices not only reflect the underlying economic fundamentals, they are also an imperative to action. That is, prices induce actions on the part of the economic agents. If some actions are the consequence of binding constraints and exert harmful spillover effects on others, then price changes can bring about amplifying spillover effects that disrupt the smooth working of the market, and sometimes shut down the market completely.

Endogenous Extreme Events and the Dual Role of Prices

It is important to appreciate the dual role of prices, although this is a subtle concept. Prices first reflect exogenous events as markets reflect new information that impacts expectations. If inflation increases, for example, there will be a reaction in prices as investors adjust their expectations. However, investor will not just react to new information and adjust their portfolios. They will also adjust or take action when they see prices change. 

The reaction to price movements may be independent of the change in exogenous information. The reaction could be due to uncertainty about what information is being displayed in the price. A reaction to price behavior independent of exogenous information is an endogenous reaction. Investors react to prices rather than to any other information. This can lead to extremes and explain most of the price movement during the day. One of the most important tasks for an investor is understanding the difference between these price moves and appreciating the action that stems from the distinction between exogenous and endogenous moves. 

Peter Lynch on economics

 “If you spend 14 minutes a year on economics, you just wasted 12 minutes.”

— Peter Lynch

Of course, he means macroeconomics, and that may have been the case when stock-picking was supreme and generated strong alpha. You still need to know the economics of the firm and industries. Still, with the focus on beta and risk premia, there is also a need for understanding the business cycle, the credit cycle, and monetary policy. Can investors predict the macroeconomy? That is a tricky question, but understanding where you are in the macro cycle may make all the difference between success and failure.

Perhaps analysts need ot spend 28 minutes on economics per day and learn not to waste any of them. 

Causal neglect and finance

 

Finance has been dominated by factor investing, and the set of factors identified is ever-expanding. These excesses in factor premia could be related to p-hacking and overfitting with past data; however, there is a more fundamental issue: our reliance on association rather than causal inference. When there is poor causal inference, the likelihood of misinterpretation and false inference increases. We create factor mirages. In the simplest terms, building models before theory can lead to post-test narratives. We identify relationships and then develop a narrative that can explain the findings. The line of reasoning should be from theory to testing.

How can this problem be solved? Of course, a better theory will help, but there is also a way of thinking associated with causal inference that has not been effectively used in finance. The problem starts with the econometrics of finance, which is often based on Granger causality. Finance needs to map out the network of relationships and acknowledge and account for confounders - variables that can impact both independent and dependent variables. We often discuss omitted variables, but researchers need to think more deeply about the causal links with omitted variables. Researchers must also look for colliders or variables that causally downstream from both independent and dependent variables. Greater focus needs to be placed on how the world works, rather than on how the econometrics are conducted. Choose varibales wisely before testing.

The paper "Causality and Factor Investing: A Primer" effectively describes the problem and provides guidance on how to address it. This process is not easy, but it leads to better predictive models. Do not engage in causal neglect.

Private equity payoffs - Set of options

 

The return profile for private equity is one of the critical investment issues for many institutional investors. This will also become a crucial issue for retail investors if many of the large PE firms have it their way. We need to go back to basics and look at the pay-off structure for private equity, and the graph below provides valuable insight. This chart is from the new paper "Analytic Valuation of Private Equity Investments". 

Notice that four distinct pay-offs form a real option. If you cannot pay the borrowing costs, the investor makes nothing. Once the costs are covered, the investors make money until the invested capital is returned, and the GP then receives his fees. Afterward, the investor receives the excess. You have to clear hurdles to receive the next set of cash flows. There are failures which impact this pay-off, and the investments are illiquid and take, on average, 5-7 years to return capital. This is a long-term option on the quality of management to provide a return above the cost of capital. 

Conditional betas solve a classic problem

Beta is time-varying. There is no dispute about this. The traditional approach to addressing this problem is to utilize a rolling window to adjust beta over time; however, this method does not account for the changing environment. It just increases the use of new information.

A new paper, "Conditional Betas: A Non-Standard Approach," attempts to find a new method to account for changing beta. It compares the quality of beta forecasts with one of the leading alternatives of windsorizing the data for beta. The overall effect of a simple machine learning approach is very positive. Results are strong and only based on past price data. This is worth further exploration. 

I cannot tell you how frustrating it is to see a hedge balanced trade fall apart because the beta estimate is wrong. Market neutral is no longer market neutral. This may not seem like a significant issue for long-only managers, but for a long/short portfolio, it is a substantial problem.

Sophisticated investors and market efficiency

 

Market efficiency will vary by the type of investor. There are different levels of efficiency based on your structural advantage. Market efficiency is based on the behavior of a given market and not on the profitability of a given trader. Hence, you can declare a market as efficient, yet there could still be profitable investors. Similarly, market efficiency could be rejected, yet that does not ensure an investor can make money in that market. 

For retail investors, the market is very efficient. You cannot get an edge if you are slow to react, have less information than other investors, process the information poorly, and have high transaction costs. If you are an institutional trader, your sense of efficiency is different. You may have a slight edge on reaction time, trading efficiency, and information processing. If you are a hedge fund, you may have an even greater edge; however, being declared a hedge fund does not necessarily confer a lower efficiency level. 

The old argument by Friedman on the efficiency of speculation is that reasonable speculation will drive out poor speculators and thus make the market efficient. The counterargument is that noise traders are more prevalent than shrewd speculators and can keep the markets inefficient. A corollary to the Friedman argument is that there are different classes of investors with varying levels of capital that can exploit opportunities, so while efficiency may exist on average, that is not the same as saying the markets are efficient for everyone.

A sophisticated investor has an edge and creates an opportunity to exploit inefficiencies. Hence, the job of any due diligence is to identify sophistication and the chance for the edge that can be exploited. 

Bond and equity expectations are different

 

A recent paper by AQR, "Why are bond investors contrarian while equity investors extrapolate," makes an interesting observation. I have always thought that bond investors were mena reverting based on their conservative nature. There are limits to where yields can go. Equity investors are optimists, which means that returns can always move higher based on unlimited possibilities. Overoptimism will lead to the extrapolation of good news. Of course, this does not explain what happens to markets when they start to move negatively. The pessimism of bond investors forms beliefs about limitations and the notion that good news cannot last.

AQR states that the cause is information salience, the attention -grabbing qualities of certain information. This, however, does not focus on why there is salience that is different across markets and why it may persist. Nonetheless, it is essential to think about differences in how expectations are formed in major asset classes. 

Get your financial stylized facts right - The Bayesian foundation for empricial finance

Economists and financial professionals often use the term "stylized facts" as an alternative to a set of descriptive statistics or just data. Formally,  a stylized fact can be a simplified representation or an empirical regularity that serves as the foundation for building theory. It may not be a simple piece of information, but a formal empirical regularity. In a recent paper, "International Financial Markets Through 150 Years: Evaluating Stylized Facts", the authors test a set of well-known stylized facts across a broad set of markets and a long time. This is the most exhaustive analysis of well-known stylized facts ever undertaken. We will not present all of the findings, but will show the summary table of what was tested.

Why is this so important? The stylized facts should be thought of as the Bayesian prior for any future analysis. Start with the stylized facts of what should appear in the data. You should not find something different, but you should argue that this is the basis for any future work. Before you pass judgment on a theory or set of data, look for the stylzied facts that already exist.

 

Evaluating trading strategies - Harder than you think

Most investors often rely on a simple search and ranking across managers to find the best trading strategies. For example, sort by the highest Sharpe ratio and choose the manager with the highest number; then you have a winner. Alternatively, search for a manager with a minimum Sharpe ratio and then conduct due diligence as a two-step process. 

Unfortunately, life is more complicated. There is a distribution of Sharpe ratios across managers and over time, based on the strategy type and analysis used. If there is an average Sharpe for a strategy, then outliers on the high side may not be following the strategy named, or they may be subject to mean-reversion. The Sharpe ratio for any period may differ, so the last three years may not be representative of the manager's performance over the long run.  There is a reversion to the mean when you sample the Sharpe ratio for a set of managers over a specific timeframe. Time and context matter.

If you look at enough managers, you will find some that are perceived to have an edge based on the sample data collected, yet this analysis may generate a false signal. For managers, you need to examine the sample set that has been analyzed. For quantitative strategies, you need to consider the backtesting performance and the length of time reviewed for the strategy. Again, sample size matters.

Additionally, evaluation is usually not concluded with the numbers but through extensive discussion with the manager to find their edge, yet the edge narrative or the manager's story-telling is inherently subjective. Is the choice of the manager a function of their skill at describing what they do or what they actually do? 

Perhaps a critical selection skill is reviewing why you chose a manager who failed as well as looking at the managers that you rejected who then went on to perform better than your existing portfolio. What your selection impacted by bad luck, and where the managers you rejected subject to good luck, or in either case did you miss something that is not in your due diligence analysis.

Narrative and crashes - there is a connection

When there is high uncertainty, there is more attention to the dynamic of the stock market which makes perfect sense. This is especially the case when there is a market downturn. That is, when faced with periods of significant change and uncertainty, investors will look to stories or narrative to help understand the cause of these big market moves. History plays a role when there are large market declines because investors will look for key past events to develop stories to explain the current market dynamics. When we have had stock market declines like 2008, there will be more attention given to past rare market disasters. Investors will reach back over their collective memory to offer some explanation for market downturns. These memories and stories are embedded in newspaper stories.

This work is explored in the paper, Crash Narratives by Goetzmann, Kim, and Shiller. Shiller has been developing thinking on narrative economics for over a decade. I think this is a fruitful are of research. There is an intersection between sentiment, market behavior and the stories that surround the market; nevertheless, it is unclear how narrative and market behavior are linked. Narratives inform or clarify beliefs which then impact choices. The stories that attempt to explain what is happening when faced with uncertainty helps direct decisions. Clearly there is a correlation between narrative and market moves, yet what is the impact of stories as a cause of market moves is murky. Clarifying the link between narrative, action, and market behavior is one the goals of this paper and narrative economics in general. 

The value of overnight trading

One of the more interesting anomalies is what we can call the overnight effect - the fact that most of the returns generated for the many stocks and indices occur between the close and open and not during normal trading hours between the open and close. This may seem obvious to many given that much of the important news about stocks is generated after the close and before the open. For example, most earnings announcements are made when the market is closed. Chart is from Elm Street. 

However, some have argued that this is a result of price manipulation, see Bruce Knuteson, who suggests that price pressure overnight leads to then declines during the day. This manipulation focuses on pushing prices higher during less liquid times and then offsetting the gains during the day. This is an interesting and compelling story and is consistent with the data; however, it is not clear who and how big is this activity. 

Surprisingly there has not been much research explaining this anomaly other than to document its existence. 

Market efficiency and financial crises

 

An older paper has come across my desk as a good review of the history of the efficient markets hypothesis (EMH) as well as   a novel view about how the EMH fit within a world with pricing bubbles, see Stephen Brown in the "The Efficient Markets Hypothesis: the Demise of the Demon of Choice".

Brown provides a good explanation of the foundations in the EMH along with the fact that most practitioners do not believe in the efficient markets hypothesis. Nevertheless, even though the EMH may. to be true, it may be important for many to believe that it is close to truth. Many will lose money attempting to prove the EMH to be false. Because there is this lack of belief in the EMH, many traders will take more risk and use more leverage than they should. Of course, when a crisis comes there will be greater loses and many traders are on the wrong side of the market.

Buy pro-cyclical stocks and get a higher return

 

A simple study finds a stock relationship that makes intuitive sense. The paper, "Procyclical Stocks Earn Higher Returns" shows that stocks that comove with the business cycle will earn higher average returns than those that are countercyclical. 

Using close to 75 years of data on real growth expectations, the factor loadings associated with growth show a strong pricing premium that is independent of size, value and momentum effects. This business cycle effect is stronger for large value stocks and momentum winners. It is notable that expectations not realizations are what is priced in the market. The concerns of a switch in the business cycle are relevant when pricing assets.  This paper shows again that have some macro focus even when building a long/short equity portfolio is important.

Narratives help explain stock returns

 

We can only explain a small portion of the variation in stock returns. We can tie returns with several key factors as displayed by the now classic three and four factor models of Fama-French. While these represent useful models for describing stock returns, their focus is on quantifiable measures of factors such as risk, size, value, and momentum. There is no factor that represents unscheduled news or sentiment in the market. However, there is a growing body of work that emphasizes narrative information such as Google search and sentiment. Popular stories, measured by search, can influence economic behavior that then impacts stock returns. Attention to news that is novel can help explain stock returns. 

I have highlighted the work of Nicholas Mangee who has not been given enough attention. This is not directly related to the exploding LLM work. Rather it is a simpler and thus more powerful as a foundational approach to explaining stock returns. News, especially unscheduled information, creates narrative to explain which then impact return. Simple stories attract attention which then translates into price moves. If there are more stories with the same narrative, there will be trends in price as these narratives take hold and embedded in the price. From narratives, there is a reason for price trends. 

Mangee is coming out with a new book on the novelty-narrative-hypothesis that can help advance our thinking about narratives and stock returns. I have seen a copy, and I am impressed. I will be writing more about this in the futures. It should have strong application for macro and commodity managers were there is less clear information to help with valuation.

Narrative drives return - even if stories do not generate measurable risk