The shape of things to come -platykurtic

There is often talk about the distributions and deviations from normal for assets and macro variables. The discussion usually focuses on skew or whether there are fat tails, yet there can also other forms of peakedness or "tailness". 

The form that is not often discussed is platykurtic where there is a flatter peak and more probability mass in the midsection of the distribution. There may not be large tail events - the Fed may stop the extreme, but there may be more event probability that is away from the average. 

An interesting question is how an investor should change their allocations in a platykurtic environment versus a fat-tailed leptokurtic world. Perhaps when we think about macro fat-tailed events, we are really thinking about a flattening of the distribution and not a more peaked distribution.

Over-fitting and under-fitting and model building

Overfitting leads to a model that too closely follows a particular data set and will thus fail to fit new data or predict reliably new observations outside the initial or training set. You will feel good about modeling of the overfitted training set. You will be disappointed during testing out of sample. 

Overfitting can be thought of as fitting the model to noise, while under-fitting is not fitting a model to the signal. In your prediction with overfitting, you'll reproduce the noise, the under-fitting will just generate something close to the mean.

Overfitting: Training: good vs. Test: bad

Under-fitting: Training: bad vs. Test: bad

One will expect that there will be more shrinkage or difference between training and test results for an overfitted model.

Under-fitting - missing parameters that are important with explaining some relationship or making a prediction. Under-fitting can be in the form of choosing an inappropriate specification. For example, a linear model will always under-fit a non-linear relationship.

Training error will decrease as more features are added which is good, but like many things too much of a good thing will have adverse consequences. Validation error should also decline with more features, but there is a limit to this improvement. If validation error starts to increase while training error continues to decline, then there is overfitting. 

In the back of your mind, the modeler should always have the trade-off graph between complexity and error. More complexity and the training error goes down, but test error will be higher. For simple models, the training error is higher, but the test error may be  lower. The same can be shown in a variance-bias trade-off graph.

The simple trend-follower is willing to suffer from under-fitting rather than finding a model that does well in back-testing (overfit) through adding a significant number of features. The trend model may do worse in training yet may have better success out of sample.

Any fool can make a fortune, brains needed to hold onto it

 

Any fool can make a fortune, it takes a man of brains to hold onto it after it is made - Cornelius Vanderbilt 

This quote is sticking with me as all the passive long beta investors laugh at the low performing hedge funds. I am not trying to be an apologist for hedge funds. They have gotten their flows and fees. However, there is the current investor belief that holding long beta portfolios indicates astute investment skill. It could be, but the more likely case is that inertia kept investors from further action. The fortunes of the lucky? 

The question for 2022 is whether investment inertia will still be a winning strategy. Following momentum and maintaining a core allocation is still a good strategy, yet the issue is whether this is the best way to hold onto pandemic wealth. After the March 2020 crisis, the shift to pandemic-sensitive firms and a return to normalcy were the key trade themes. 

Is the same pandemic/normalcy portfolio the best way to hold onto the pandemic equity bump? With higher inflation, less stimulus and a different pandemic risk, the portfolio of yesterday may not fit the circumstances of today.

Science and investment ideas progress slowly... death, retirement, and failure

 

Science progresses not necessarily through bright new insights but "through the old professors dying off" - Eugen von Bohn-Bawerk

"Investment ideas progress not through new ideas but through management retiring...."  

"Investment ideas fall from favor through one major drawdown at a time only to return as the next style sees a major drawdown..."

This Bohn-Bawerk made his quote when referring to his precocious student Joseph Schumpeter, the other great economist from the first half of the 20th century, Keynes is the better-known name. 

I have taken liberties to apply the idea to investments. Embedded investment ideas will only change when the old guard retires. Management must understand an idea before it is accepted which means it usually has to be learned at an earlier age in some MBA or business class.

If not retirement, investment ideas will fall out of favor with the first significant drawdowns. Drawdowns are failure signals which have to be replaced with a new idea. Idea chasing is ongoing with most money management firms. Failure will beget change which will be replaced after another failure.  

Inflation narratives vary across groups - The reason for markets

Inflation forecasts vary because there are different implicit models used by the forecasters. Put differently, different groups have different inflation narratives or stories. This is what makes markets move. As narrative change, markets change. 

The stories matter with determining the forecast. These forecasts are rational because they are based on a set of rational explanations, yet all forecasts cannot be right at some end date. You can have rational beliefs but still be wrong. 

A recent study (Inflation Narratives) looks at inflation forecasts and finds that there are significant difference in views especially between households and experts. experts place more value on demand factors and less on non-market factors. 

These differences show up in one and five-year inflation forecasts. Households have higher forecasts than managers and experts. This issue is not trivial because it shows a dislocation between the real and financial economy. Some group will be wrong, and mistakes will create market adjustments - real and financial.

Money matters, but credit counts - Follow credit and not just central banks

 

Money matters, but credit counts - Henry Kaufman 

There is significant focus on Fed monetary policy - quantitative easing, tapering, the balance sheet, rate increases, forward guidance, and objectives like FAIT, but these all should tie back to credit. 

How much credit will be extended, what will borrowers need, and what will be the risks to creditors? These are all the questions that must be addressed when thinking about the real economic impact of monetary policy. Simply put, does monetary policy facilitate the extension of credit for productive growth?

There is a wealth effect, but the credit effect, the use of borrowed funds to provide future growth, moves economies. Right now, whether total outstanding debt or C&I loans, there is not demand for credit and not of loans being made relative to the growth in the Fed balance sheet.

We forgive humans but not machines - Bias against algos

 “People judge humans by their intentions and machines by their outcomes.” - César A. Hidalgo

Why aren't we more accepting of systematic models and algos for our investment decisions? We have talked about the interesting research on algo anxiety - even if a model is a better predictor many are willing to go with the discretionary forecast. Discretion always adds choice and flexibility if there is new information or situations, even if modeler may get it wrong. Users feel constrained and don't want to be limited by a model. 

Philosophical and ethic thinking concerning machine decisions have focused on the chasm between how we accept algo decisions versus those by humans. For example, humans can do a good job of appreciating the nuances between broad terms like good and bad. For example, was the weather bad today? Nevertheless, more AI is being used to make decisions about who is extended credit or who should be given parole. Judgment by machines is encroaching on what used to be human decisions. This encroachment can be for the better given a machine can make consistent decision albeit there is still the issue of biases in the modeling process. 

This can be a big investment problem - should you prefer machine decisions or human decisions? Many will not care - the proof is always in the returns, yet those who have studied human and machine decisions find that the criteria for judgment are different. See "Why We Forgive Humans More Readily Than Machines"

Research has found that humans judge on three criteria, wrongness, harm, and intentions. In the graph below, humans judge machines differently from machines. The researcher looks at the trade-off plane from humans judging humans and humans judging machines. When judging machines, the harm is the key criteria - what is the results of the decision. For humans judging other humans, there is a clear bias toward the intentions of the decision maker. There is a forgiving of harm based on a judgment of the intentions. 

In the portfolio management space, humans may be forgiving of the discretionary trader who fails if his intentions were good. He tried to make money and had a good narrative of what he was trying to do. Unfortunately, that is a poor way to judge trading - the focus should always be what are the results. Knowing the process is critical but not an excuse for poor performance. 

See our posts: 

"Algorithm aversion" and managed futures 

Algorithm aversion or just a desire for low cost optionality

More on algorithm aversion - it can be eliminated if given some choice

Performance curves - Still says that simple works relative to complex

 

Machine learning is taking over the modeling process in many fields including asset management. Out with the old modeling and in with the new modeling. With cheap computing, there has been a bias to adding more complexity to models, but over-parameterization does not mean that performance will improve. More is not better. Using extensive testing of different model types (random forests, XGBoost, and deep neural nets) and a wide set of parameters, a recent paper, "The Shape of Performance Curve in Financial Time Series", looks closely at financial time series tests.

The paper's overall conclusion is that there is a flat lining of estimators for mean squared error and accuracy. However, it is always the case that MSE and accuracy are lower during training periods over test periods. Adding more is not always better but rest assured models will do worse outside the training period.

It is always the case that modelers should follow the KISS method, Keep It Sophisticated Simple. Adding complexity is not a substitute for a good simple model.

Trusting the rating agencies - A global problem

 

For debt investors, 2021 is year of nervousness - what don't we know about the debt we hold? More specifically. what are the risks in China fixed income? What is underneath the Evergrande iceberg?

Evergrande was declared in default by S&P on December 16th, a week after Fitch. Moody's gave Evergrande a C rating in September which is typically applied to default firms and is its lowest rating. Chinese rating agencies have kept Evergrande at much higher ratings than the big three international agencies. There really was no choice but the real question is why rating agencies took so long to see the problems of Evergrande 

There is a home bias that works against international bond investors and the bankruptcy process now falls into the political. Two of the most important elements of an efficient capital market are trust and certainty with the rules of the game. 

There needs to be trust in accounting numbers. Auditors have to be a frontline defense for investors. There needs to be trust in those who evaluate firms, yet we know that brokerage firms can have biases withe their evaluations. We look to third party firms to provide unbiased advice, the rating agencies, yet these firms also may have biases. Regulators must ensure that firms follow the rules and push for maximum transparency. Still, we always must ask the simple question, "Cui bono, who benefits?".

Certainty is needed to know that the rules of the game are stable. This applies to contract and bankruptcy law. It is a fluid concept based on the interests of the powerful.

There is no question that every investor should do their own analysis, but rating agencies should provide a useful signal weight of relative credit worthiness versus the set of all possible credits. 

Unfortunately, only under stress do we find out that there are clear biases, and the system has biases. Only under bad times are the flaws of the system evident but by then it is too late. 

Monetary policy, inflation, and FAIT

Flexible Average Inflation Targeting (FAIT) is the name of the Fed game, but that does not give us much guidance on what will be the activity of the Fed nor are markets playing as expected.  

Inflation is higher than expected - There is no transitory inflation albeit the trimmed core PCE is still close to target at 2.6%, but there are some statistical gymnastics to get to this number. Top-line PCE inflation is at 5%, CPI is higher, and PPI is even higher.

The taper has been increased to double in December and another doubling in January 2022. The taper will be pushed forward to end in March and three hikes are planned for 2022. The dramatic change is present in the dot-plot changes from September.  

Flexible is not supposed to lead to a policy about-face. The fundamental approach to central bank is to provide clear guidance of gradual change with swift action in a crisis. This December announcement is not gradual and does suggest an inflation crisis. Yet, the markets have taken this in stride and acts as though this action was completely expected, so as we move to the last two weeks of the year, we are left with markets expecting front-end Treasury yields higher and long-dated bonds acting as though an economic slowdown which will dampen inflation as a given. Our FAIT will be in the hands of central bankers that do not have clarity on inflation, full employment or the link between policy and the real economy.

Tail risk - shocks and systemic failure

 

All systemic risks will be tail risks, but all tail risks may not be systemic. There is a sequencing of events before there is a systemic failure, so investors may have some warning albeit the speed to systemic failure may be very quick. 

Can you see it coming? It is unlikely you can predict a tail event but they will usually have specific characteristics. They can be firm-specific or macro in nature, but will have to be a surprise to existing expectations. Tail events will not be a confirmation of existing views. The news event must be strong enough to change consensus judgment and consensus will most likely have large, levered capital positions. An exogenous event can lead to endogenous trading events like the February 2018 volatility debacle. We will note that some tail events cannot be directly associated with specific news event. The October 1987 crash comes to mind. 

What is the speed of failure from a tail event to a systemic risk event? Ex post, there will be clear warning signs that could have been seen, but these will usually not be the focus of the market. There will usually be heightened volatility before a systemic risk shock, but the time to a systemic failure risk can be measured at most in days not weeks. The failure in March 2020 was within days of pandemic news fears albeit pandemic warnings were already building in February. 

How do you protect against systemic risk? Beyond being diversified, the simplest answer is measuring the time to cash liquidation. If you must convert all positions to cash, how long will it take? Can you risk bucket all assets by liquidity? Have you identified safe assets? Where are the exits in case there is a fire? Are their secondary primes, brokers, and liquidity providers that can be called upon in a crisis? Of course, having secondary liquidity providers requires regular usage otherwise they will not take your business when asked. Have all liquidity provider operations been reviewed for crisis conditions? if you don't ask now, you will not get any answers during a systemic failure. 

Central banks and government regulatory may be looking at macro-prudential policies but there are no guarantees that any government can provide appropriate policies at all times. Safety is still the burden of the individual investor.

Fed's current tapering by the numbers - A long way to go to normalcy

 

I have looked at the current Fed tapering in the context of the Fed balance sheet past and present. The current tapering is for $15 billion a month ($10 billion in Treasuries and $5 billion in MBS) for eight months.

The Fed balance sheet will increase by over $420 billion during these eight months and will take fed assets to over $9 trillion. 

There is no provision for reduction based on bond maturity, so the Fed will still be buying Treasury and MBS to replacing pay-down of principal and interest. 

$15 billion per month is only .17% of the current balance sheet. $120 billion will be less than 1.5% of total Fed assets. 

Fed assets will be $1.5 trillion higher in 2021 from a starting level of $7.3 trillion. The Fed balance sheet will be $2 trillion greater than July 2020 levels which is after the recession ended.

The Fed assets were $890 billion before the GFC. Fed assets were at $2 trillion after the GFC and reached a peak of $4.5 trillion during QE3. At the end of the tapering Fed assets will be over 10 times greater than pre-GFC levels, more than 2 times greater than pre-panic levels, 2 times greater than the QE3 peak, and 4.5 times greater than levels after the post-GFC in 2010. 

The tapering is just not that important relative the overall balance sheet. If the tapering quickens, the impact relative to the overall balance sheet will be small. Of course, the marginal effect may be different and the signaling impact is also different. However, investors are just not fully realizing the size of the Fed balance sheet versus the past.  

Looking beyond risk factors and focusing on basics like economic profit growth

Economic profit, the total profits of a company after subtracting the cost of capital, is the key metric for shareholders. This is not the traditional way finance professions will look at firms, but it gets to the heart of the issue - focusing on the return to invested capital and revenue growth. 

McKinsey researchers focused on over 2000 large firms to find the metrics that really matter for the total return to shareholders. It is all about revenue growth, growth in profits, and the firm's margin delta. Not growth at any cost but growth that can sustain a profit on invested capital and not on earnings per share which can be engineered without value creation. Their grid tells the relevant story.  If you want to beat other investors you have to think about alternative metrics for shareholder value. 

Blending traditional research and ML processes - There is a lot of overlap

Systematic investing is process driven and not just implementing a single model. There is a quant investment pipeline which starts with data, modeling of decisions for alpha generation, portfolio optimization, execution, and performance review. This same model pipeline is used with any machine learning investment process. There is commonality between old and new quant processes. Yes, machine learning is different, but the process is the same.

• There is first data analysis and feature extraction - What are the inputs for any model? Features can be simple price-based systems or include exogenous variables like fundamental macro or firm specific data.
• From the feature selected there is alpha modeling, the method of stacking or ranking the set of opportunities. Alpha modeling can look at times series or cross-sectional data to assess each investment or pick high and low performance deciles.
• The set of alpha choices then have to be placed through a portfolio optimization process which determines size and distribution of allocations. The optimization process finds the mix of alpha choices from which to target return and risk.
• Output then has to be converted into executable orders. A model has to be deployed through specific order processes that signal what is to be bought and sold.
• Performance has to be assessed and learning generated to adapt or change models. An effective system has to include a feedback loop to learn from mistakes.

The process of alpha generation is the core difference between traditional and ML approaches. This difference may not be trivial but preparing data, optimizing, executing, and feedback are the same.

Explainable and Interpretable AI - Looking inside black boxes

Machine learning is the darling of data science and rightly so. It has truly advanced our ability to make accurate predictions but there is still an issue of how ML procedure make their predictions. There is more complexity than traditional tools such as linear regression. For asset management, ML creates two problems: (1) understanding how result were generated and (2) explain how decisions were made for both compliance and investors. 

There are solutions to these problems through advances in interpretable and explainable AI. One of the key findings of the work in these two areas of ML is that accuracy does not have to be forsaken by choosing processes and models that may be less complex. 

Interpretable AI, also called symbolic AI (SAI) employs less complex ML procedures which are easier to read interpret. Interpretable AI will focus on traditional techniques like rules-based learning in the form of decision trees. Because there are rules, it is easier to provide some story about how forecasts are made. Each rule can be examined, and rules can be added or dropped to find the marginal value of any change. 

Explainable AI, also called XAI, will use more complex ML but attempt to explain it. More complex ML systems that are not rules-based have to rely on explainable AI where there is a focus on the value of features and outputs used in a black box. With XAI, tools like Shapley Additive exPlanations (SHAP) values are used to associate the importance of features with the explanation of a forecast. See "Machine Learning: Explain It or Bust" for more details.

Interpretable and explainable AI represent an age-old problem for all systematic managers. Even simple models have to be explained and provide context. For example, trend-followers can have very different return and risk profiles. The burden is on the managers to explain why they differ from others and when they will or will not make money. There is always interpretation and explanation issues.

See also:

Explainable AI - A solution that will not offset hard work

Shipping - Markets excesses gone or something different?

 

Shipping costs have risen, and it is not just for containers. The cost of dry bulk as measured by an index created for the BDRY shipping ETF has increased by close to 400 percent this year at the high only to fall by 50 in a month with the poorer economic news from some large bulk importers. Clearly this is a China play since it represents over 40 percent of dry bulk imports. Fifty percent of dry bulk shipping is associated with coal and iron ore. The market has retraced some the decline although it is now facing the Omicron-COVID threat. 

Dry bulk rates represent a high beta reflection of global trade and China demand for raw materials. Container rates represent a high beta trade on finished goods. Of course, shipping rates are closely tied with the ship building cycle, but this cycle is just a delayed representation of the trade cycle. While history suggests 2021 moves are exceptional and will not continue, the trade disruptions are unlikely to clear until a post-pandemic normality returns.

P-hacking - maybe our concerns are overdone

P-hacking is an important concept for understanding the value or failure of financial research. Whether called data mining or data snooping, the process of searching for significance can lead to results that are spurious and will not follow in out of sample analysis and trading. What was significant for a back-tested sample will not be replicated out of sample or in real life. There is now a zoo of factors that have showed significance in financial research which begs the question of whether there really are so many unique factors in an efficient market. There is also the question of what are the drivers for these significant factors.

P-hackling is real, but the question is whether it applies to all factor tests. A recently published paper "The Limits of p-hacking; some thought experiments" takes a step back and focuses on the likelihood of a p-hacking problem for all of the research results in the factor zoo. He focuses on the likelihood of p-hacking with factors that have t-stats close to 6. 

This p-hacking problem may be especially present on the margins for t-stats around 2. While there are hundreds of studies on unique risk premium, the field of studies that show high levels of significant are limited. The author of this study states that the likelihood of p-hacking for high t-stat factors is low. There would have to be millions of tests to find these levels of significant. 

P-hacking is real and should be feared, but data snooping cannot be the explanation for all the results on pricing anomalies. There is a continuum of market efficiency. The bar for finding unique factors, risk premium, and anomalies is high, and the null should be that markets are likely to be significant, but that does not mean that markets will always be efficient. Mispricing, pricing anomalies, structural opportunities, and limits to arbitrage do exist. Be a skeptic, but sometimes the results from testing are real.

Prospect theory can explain many stock anomalies

 

One of the problems of behavioral finance research is that there is no unified approach or model that can explain all the anomalies that exist in the stock market. Some behavioral models can explain one or two anomalies, yet they may contradict other anomalies. I accept that this is a part of the scientific process, but it limits the usefulness of this research. 

It looks like we have a model based on prospect theory that can explain many stock anomalies. See "Prospect Theory and Stock Market Anomalies". This exhaustive paper means that prospect theory should be at the forefront of thinking about how investors behave.

Prospect theory was developed by Kahneman and Tversky to explain decision-making under risk. Prospect theory states that investors will evaluate risks based on gains and losses with a kink at the origin. Investors will be more sensitive to losses than to gains. The sensitivity is concave over gains and convex over losses; risk aversion for gains and risk seeking over losses. There is loss aversion and narrow framing.

The price of an asset in a prospect theory world will be dependent on (1) asset return volatility, (2) skewness, and (3) the average prior gain or loss since purchase, the capital gain overhang. Investors require (1) higher average return for higher volatility, (2) lower average return for positive skew, and (3) higher average return for assets with larger prior gains. 

According to the author's testing, prospect theory can explain: momentum, failure probability, idiosyncratic volatility, gross profitability, expected idiosyncratic skewness, return on assets, capital gain overhang, maximum daily return, z-score, external finance, composite equity issuance, net stock issuance, post-earnings announcement drift, and difference of opinion anomalies. 

Forming deciled portfolios for each of the tested anomalies, the authors find the same pattern, the extreme decile with lower returns has higher volatility, more positive skew, and a lower capital gain overhang relative to the other extreme decile. Prospect theory cannot explain the size and value anomalies.

The research provides powerful evidence for thinking about investor behavior in a prospect theory world. The null should be that investors will follow the expected behavior embedded in prospect theory - loss aversion, kinked behavior around the purchase price and capital overhang.

Price-based and fundamental systems - Trusting data structures

“Trusting a black box model means that you trust not only the model’s equations, but also the entire database that it was built from.” - Cynthia Rudin AI researcher 

This is an important concept to remember with any systematic model. Where are data coming from? What data are used? How are the data manipulated and adjusted before it enters a model? How are data cleaned? If there is fundamental data, are the taken from the original announcement? Are times series properly aligned with announcement times? 

It may not be garbage in and garbage out, but the quality of the ingredients will affect the cake that comes out of the oven. 

A price-based system has a lot of database trust - the source for decisions is well-defined and easy to manage. Yet, even in this case, there needs to be a review of database structure. There are differences between closing and settlement prices, and I have found differences in price between vendors for exchange traded prices. For equities there are issues with how to handle adjustment for dividends. For futures prices, there are issues with handling rolls. 

The problem of databases increases greatly when non-price data are added. Employment data are revised. Fed announcements may occur before the close. Earnings announcement usually have other information embedded with the accounting data. 

It is possible that small data differences can create a different return series for the same model. You are not investing in just a model. You are investing in a complete data management process. 

Stay, double down, double up, and walking away decisions

 

What you do after a trade has been added may be as important as when the trade was initiated. There are four choices: maintaining existing positions, adding, subtracting, and walking away. 

The choices are a matter of mark-to-marketing your ideas and trade conviction. Many systematic investors will view this as an easy decision. For. discretionary trader, this process will be more complex. 

If you run a trend model that uses daily data, the model will be marked for adjustment every day, yet variations on how you mark a trade for adjustment create a wide set of choices. The simplest choice is a digital marking, if above (below) trend go long (short). The digital choice is fully invested at a predetermined position size at all times; however, there can be other variations from a digital choice. Trades can be scaled by volatility so that there is price above (below) trend against volatility that change position sizes. If the return to risk falls, positions will fall.

In the case of discretionary trading or trading that uses exogenous information, investors can think of mark-to-marketing as mark-to-information. Positions sizes and risk will change as new information concerning the trade enters the market. Because information quality varies, the mapping between position and action will be less clear. Hence, positions are not switched on and off. 

Investors should think about how decision action is updated - what is the information or factors necessary for position changes.   

Hanke measures - Inflation is everywhere

The developed world is currently crazy about inflation but take a close look at some of the emerging and frontier market inflation numbers. Inflation is out of control as measured by free-market exchange rates from the Steve Hanke's website, Hanke's Inflation Satellite. 

Showing these numbers does not diminish the problem in the US or other DM markets, but it does show that prices can get out of control if there are not strong institutions and governments that have the desire to control inflation excesses.

China global financial stress elevated but not unusual

Implicit monetary policy is tied to financial stress along with growth and inflation. While it is not generally discussed in the central bank reaction function, there is a greater focus on macro-prudential policy and measurement. A good macro measure is to use some financial stress indicator index. These stress indicators will be correlated because stress is often global through a world-wide economic growth or financial market shock. 

China financial stress is elevated on a relative and absolute basis; however, it is still contained relative to the past and versus other countries as measured through a NYFED model. Generally, EM stress will be greater than in developed markets. 

The NYFED stress model includes equity returns, financial sector returns, equity volatility, short-term rates, the yield curve shape, interbank spreads, corporate bond spreads, sovereign bond spreads, and US bond convenience yields. It tracks closely with the Chicago Fed, KC Fed, ECB, and Bloomberg stress indices. 

Clearly, junk bond spreads have exploded in China and volatility has increased, but the combined stress measure is nowhere near March 2020 pandemic levels. Nevertheless, given the size of the China market, stress measures should be tracked closely to determine portfolio risk allocations.

Rates versus absolute change - Mistakes that investors make that matter

Behavioral biases exist and they really do matter for both the individual investor and markets overall. A provocative paper attacks one of the more obvious problem in finance that should have been explored much earlier. The paper, "Can the Market Multiply and Divide? Non-proportional Thinking in Financial Markets" studies the problem that investors don't seem to understand the difference between a $10 price change and 10% or proportional change. 

We may be so used to hearing financial data presented in a certain way that we don't even notice the problem. A commentator will say stock x is up $5, or the benchmark index is up Y points without saying the percentage change is contributing to the bias. 

This problem becomes obvious when you scale values by price, a $x change in a stock that has a low price will have a very different meaning from a $x change in a higher priced stock. Proportionality matters. Ineffective juggling between dollar price and percentage changes is a problem for the individual, but when explored at the market level it can explain some of the odd anomalies or puzzles seen in the stock market. 

Investors usually think about dollar not percentage units which leads to more extreme responses to news for lower priced stocks. Higher price stocks will be less volatile - a doubling in price will lead to an approximate 25% decline in volatility. Consequently, volatility jumps after a stock split. Lower price stocks will respond more strongly to firm-specific news. This non-proportional thinking can explain size-volatility/beta relationships, the leverage effect and return drift.

Guard your thinking through always thinking about the proportional impact of prices. 

The "extreme precariousness of the basis of knowledge"

"The state of confidence, as they term it, is a matter to which practical men always pay the closest and most anxious attention. But economists have not analyzed it carefully.... Our conclusions must mainly depend upon the actual observation of markets and business psychology.... The outstanding fact is the extreme precariousness of the basis of knowledge on which our estimates of prospective yield have to be made. Our knowledge of the factors which will govern the yield of an investment some years hence is usually very slight and often negligible." 

- Chapter 12 "The State of Long-Term Expectation" from The General Theory of Employment, Interest and Money"  John Maynard Keynes 

I like the term "precariousness of the basis of knowledge". I had to help with a private company valuation in a fast-changing industry. The difference in valuation given some simple assumptions was enormous, and I was using some very standard valuation techniques. 

The same uncertainty problem applies to any forward estimate of rates, inflation, or the dollar. Perhaps we can speak to trend or views in the short run, but the range of potential estimates out to a year or more is so wide to be almost useless. Our only savior is the range of past behavior over a year horizon, but in a highly uncertain macro environment that conditional restriction may also work against an effective forecast. 

Holding bitcoin ETFs given the futures contango - A difficult game

 

Bitcoin futures ETFs have started to be traded with the excitement associated with an easy method for investors to access bitcoin price activity; however, these instruments are not linked to the cash market but rather to bitcoin futures. This feature has significant implications for investors because these ETFs will be subject to roll risk. If the underlying futures market is in backwardation, long trades will gain from the roll-up the futures curve, but if the market is in contango, there is a negative cost from holding the long futures. 

So, what is the cost from holding bitcoin futures ETFs? The bitcoin futures market is in contango which creates a return drag. If the cash price does not move, the investor will lose on the roll cost.  

The cost of this contango effect is significant. The drop from second to first month bitcoin futures is over 11% on an annual basis on November 22. The futures are listed monthly. The cost is over 7% for third to second futures and 6% for fourth to third futures. Unfortunately, the liquidity for the back months is significantly lower than the front month, so trading is concentrated in the front two contracts. Volume in the front month is averaging a few thousand contracts while five months out the volume is less than 30 contracts. 

To make money, the ETF investor has to overcome management fees that are close to 100 basis points, pay the transaction costs associated with the trading, pay brokerage on their transaction, and pay the roll costs which means that the hurdle necessary to make a positive return is well over 10% for trading the most liquid futures. 

There have been similar high costs associated with trading crude oil ETFs associated with the futures contract when the market is in contango; however, more liquid back months have allowed trading along the crude oil futures curve. Investors need to be aware of the market's structural costs before entering into these investments.