Understanding the Nature of Outliers...

Outliers are events that by definition are anomalies or aberrations in a data series. Their scale is of such magnitude yet their occurrence is unpredictable that they tend to be treated by statisticians seeking ‘order’ in the data as events that need to be excluded from their analysis as they are regarded as ‘one offs’ as opposed to repeating signals that can be exploited.

Unlike other complex adaptive systems, the financial markets are comprised of ‘human agents’ or their devised creations called algorithms whose behaviour is an expression of their ‘thinking’. Much of the research now arising regarding a different understanding of how the human brain works suggests that the brains role is not to describe a best match between what it senses and ‘what is out there to describe’. Rather a brains function has emerged through ‘distilling’ evolutionary processes as a response to how best a brain allows a living organism to ‘survive’. It has evolved to a different fitness function relating to ‘survival’ rather than a function that allows that organism to faithfully render an exact match to ‘what actually is ‘out there’.

A brain is therefore now thought of as a ‘prediction engine’ by many behavioural scientists as opposed to a faithful camera that simply renders an exact result from what it senses. There is just so much data that needs to be interpreted by a brain, that a faithful rendering of an external reality is just to energy inefficient and not sufficient to provide a suitably fast response to actually survive in the complex competetive and hostile environment out there. It is far more efficient to ‘predict’ what is out there so that we may be wrong many times in the ‘severity’ of the ‘actual’ signal, but we will actually still survive from our incorrect conclusion. A quick prediction allows for a far faster response than a very delayed response that is required to faithfully interpret all the data received by the senses.

The way we predict is to compare the signals we receive against similar patterns that have been stored in our memory. If we are right then we retain that signal in our memory as a reinforced memory….but if we are wrong, we then ‘error’ adjust and provide a new signal in our memory to refer to at a later time. This process is what we refer to as learning.

So, after this explanation that hopes to convince you that a human brain is a prediction engine, we can therefore see the limitations when immersed into a system that provides repetitive patterns versus a system that generates one off’ major impactful events’. Our brains innate tendency to predict will find meaning in the ‘repetitive patterns’ and ‘uncertainty’ when exposed to ‘Outlier events’.

Given that a financial market comprises ‘predictive human agents’ and that the financial markets is a zero sum game, we will find that by far the majority of participants will bias their focus to the tendency to ‘want to predict’…..however the real material risk events arise when ‘predictive agents’ get it wrong.

So, in this zero-sum game the majority of predictive agents will find that their ‘predictive models’ break down when Outliers arise and that wealth will be transferred en-mass to those participants whose trading models are counterintuitively positioned against the principles of the ‘predictive mindset. The predictive brain which specialises in ‘pattern recognition’ continuously understates the significance and the magnitude of these sporadic major price moves given their unpredictable nature and vast array of different forms taken.

The far fewer participants who adopt the principles of the Classic Trend Followers use a systematic rules-based process that target these anomalies which avoids the temptation at all times to predict and simply waits patiently for those times when ‘the predictive mindset gets it wrong’ and generates these anomalies from these internal market sources (aka endogenous sources).

Unlike the majority of predictive trading methods, Classic Trend Followers adopt a counterintuitive approach that embraces the Outlier as opposed to a predictive mindset that chooses to ignore them. After all these major anomalies to a predictive mindset are either anomalies that should be excluded from their analysis or they simply are too infrequent to worry about them as the predictable features of a market are what they feel they should be participating in. This building confidence that occurs when markets display predictable behaviour leads to increased leverage being applied to predictive trading models which can have catastrophic effects on a traders fortune.

Unfortunately, this mindset sets in place a major risk event waiting to happen by choosing to ignore or underestimate these major price moves.

As we understand these features better with modern research of complex adaptive systems, we can start to change our traditional narrative where we refer to our process as a method of ‘trend following’ to a process that can be referred to as a method that ‘Hunts for Outliers.

But being aberrations in the data series of major ‘one off events’ that are significantly different to the predictable market mechanics that most traders love to exploit, how do we ‘hunt for them’. This implies that Classic Trend Followers have a ‘non-predictive method’ which can be used to gain a greater representation of these anomalous features of liquid market data in our trade results. Well, we spend a lot of our effort attempting to best describe how we achieve just that….but new research is really helping to distill our narrative to bolster the reasons for the systematic rules-based process that we follow.

So, what is this new research that supports our narrative?

The following precis summarises pertinent findings from Jean-Phillipe Bouchard that helps add to our Trend Following Narrative. Forgive the use of dot points as I wanted to avoid a Tolstoy epic and focus on the major implications.

The Theme of this Discussion today which looks at the research and its implications is titled ‘Drilling into the Nature of Outliers’ as us Trend Followers love to ‘Hunt them’.

Overview

Recently in Episode 8 of TTU’s Volatility Series we had an excellent discussion with Jean-Phillippe Bouchard (JPB) about findings from his research about what ‘causes’ these Major Price Moves in a liquid financial market.

This triggered some discussion on Twitter and really helps us to distil a narrative for our TF philosophy.

So, we want to dig into the implications of this research as it provides us with important information that helps to distil our narrative about ‘why and how we focus our attention on these Major directional Price Moves (aka Outliers’)

From research undertaken by JPB a number of traditional viewpoints about the theory of market behaviour can be challenged. Let’s burrow down into some of these implications as ‘major price moves’, (which trend followers refer to as Outliers) are the bread and butter of our technique. It therefore is important that we attempt to understand them better.

Assumptions

In this review we need to be careful about our assumptions as the findings relate to ‘Major Price Moves only’ and do not necessarily relate to ‘ALL price moves’.

We are specifically referring to ‘Major Price Moves’ that exhibit nonlinear directional moves and are confined to the ‘Tail Region’ of the distribution of market returns (refer below). We are not assuming that the ‘mechanics’ of these large price moves are the same as that which drive the bulk of the market distribution of returns.

So, our Trend Following (TF) method is deliberately positioned to take advantage of these specific form of price moves that reside in the Tail of the distribution (on the edge of chaos). They are not positioned to take advantage of other forms of price move found in the balance of the distribution of market returns which adopt patterns associated with their repetitive oscillation about an equilibrium condition.

In fact, to take advantage of these ‘tail features’ we need to be almost perfectly anti-correlated to the techniques deployed by ‘Convergent trading styles. We refer to our style as being ‘counterintuitive to the convergent mindset’.

Research Findings and Implications

1. The MAJORITY of extreme market shock events are not driven by EXOGENOUS NEWS EVENTS that provide new information to a financial market, but rather 'ENDOGENOUS FACTORS’. Namely feedback effects generated from within the financial market itself. This begins to challenge the notion that markets are efficiently priced and are representative of fundamental value AT ALL TIMES.
   
   This means that during major price moves….the traditional risk premia that many like to use as ‘causative drivers’ of price may only be loosely correlated to the ‘real reason’ that drives these major price moves.
   
   Findings from JPB’s research support the excess volatility puzzle of R. Shiller whereby volatility (in this respect price jumps) cannot be fully explained by fundamental causative drivers.
   
2. A way to understand ‘Endogenous price moves’ is not to think about cause and effect where a linear input leads to a linear output…….but to think of a Market as comprising numerous agents whose collective attributes comprise a ‘market state’ in a state of flux. This market state comprises the impacts of both independent agent behaviours and collective agent behaviours but the agents in complex systems are not linearly related to each other ‘one to one’. An efficient system comprises ‘one to many’ dependencies.
   
   Sometimes a small change in these important ‘interdependencies creates massive change. So, when we refer to ‘endogenous’ shocks derived from the system itself we are referring to ‘self-induced’ impacts that have major impacts on the market state by impacting the interconnected architecture.
   
   We understand endogenous market shocks as a ‘self-excitation phase’ where price effects are progressively amplified with positive feedback effects to a critical point before price then relaxes into a less excited state. Such endogenous effects produce a symmetric profile that builds to a peak and then decays over time.
   
3. The research identified that both Exogenous News Events and Endogenous market events both have the ability to produce major price moves….BUT that Endogenous prove moves were far more frequent in nature and their impact profile was considerably different to ‘News Events’.
   
   Exogenous News Events have an immediate volatility expansion AND faster decay rate in terms of 'effect' than endogenous factors which typically take time to build (expand) and accommodate far greater uncertainty for extended periods of time. This uncertainty is driven by the lack of any guidance provided by the causal impetus of this price move.
   
   Given this principle of ‘enduring’ impact dissipation or ‘signal decay’ means that markets do not instantaneously reflect fundamental value at all times particularly during these impactful price events. The markets therefore at best are only 'semi-efficient'.
   
4. We all understand how news events such as a pandemic, tidal wave, nuclear explosion, oil embargo decision etc. can instantaneously impact the financial markets…..but we are left scratching our heads wondering what caused these much more frequent endogenous events.
   
   Where did the impetus for such ‘endogenous’ events come from? If we assume markets operate in equilibrium, then it shouldn't 'come at all.'….but if we accept that markets operate far from equilibrium then we can see how this latent energy is stored (warehoused) in the system and can be released by sudden system phase shifts brought about by very small changes that quickly ‘cascade’ into major system phase shifts.
   
5. It is pointless trying to predict the causative driver of these endogenous events. It could be ‘any reason’ that impacts the interconnected system architecture to cause these tipping points. For example, a major institution failure (such as MF Global, Lehman Brothers etc.) that connects with many participants could be caused’ by a vast number of different reasons, but the impact on the system architecture is profound.
   
   It is easy to associate a causal driver with a news event….but it is far more difficult assigning a causal reason for an endogenous event. For example, you could imagine snow on a mountainside that appears stable for extended periods of time, but the system state is incredibly fragile and a single sound like a rifle short can ‘tip this system’ through endogenous factors into a cascading amplifying mechanical event.
   
6. Now because TF focus their attention using long lookbacks on these ‘tail regions’ of the distribution and not the causative reasons for the bulk of the distribution, then we need to ‘forget about ‘predicting’ and simply focus on risk mitigation to defend ourselves against adverse major price moves from both Exogenous and endogenous causes.
   
   Risk mitigation is something that needs to happen ALL the time when TF decide to participate in a risk event to defend the trader against adverse 'exogenous and endogenous shocks'. Our models specifically apply risk constraints to all adverse price moves (major or minor) but leave ourselves open to the bounty that these nonlinear universal features of market mechanics can bring to our asymmetrical models.
   
7. The key point here when trying to understand what causes major price jumps is that the mechanics of a major price move follows a Power Law not a linear law. A small change in one variable is associated with a large change in another, because it reflects variables multiplied with each other rather than added to each other, as in the normal distribution. Traditional statistical models do not pick up this principle of system mechanics but ‘agent-based modelling’ of systems does. The more interconnected the system becomes, the more pronounced the Power Law behaviour.
   
8. In terms of the causal reasons for this major price move, the actual ‘trigger’ could be any factor that sets in train a cascading correlated train of trading behaviour. But given that agents are human participants, or their fiendish contraptions called algorithms that have been designed by a human mind we can use behavioural studies to observe this effect in action.
   Under normal market conditions trading behaviour is diverse (more independent) which constrain price movement….but during extreme uncertainty, traders abandon their different models allowing their predictive brains take over to produce ‘coordinated’ behaviour under positive feedback.
   
   As a predictive species the human brain always seek to understand cause and effect, but complex adaptive systems do not oblige that way. Small changes can and do create large system effects. The linear sequence of causative events is lost in a minefield of dependent (correlated relationships) across both space and time that exist in a complex system. That is why we understand the impact of ‘news events’ but do not understand the impact of ‘endogenous events generated from within the system itself.
   
   Impacts of trading behaviour (as opposed to fundamental causative drivers) have a far greater impact than traditional theory suggests when it comes to major price moves.
   
9. Furthermore, JPB talks about volatilities dependence on a Square Law (like Newtons gravitational law whose impact dissipates with the square of the distance between two massive bodies) which tells us that the impacts of trading behaviour take time to decay and that this force law is nonlinear in effect.
   
10. Markets therefore have a 'memory' which is another way of describing serially correlated dependencies in a time series.
    The extended decay of major price shocks coincides with the principle that these events carry with them 'serially correlated' impacts.
    
11. The research of JPB was conducted on extensive data sets of minute data, so this principle is embedded in all time series of any duration. It is a fundamental ‘universal principle’ of market mechanics and not simply a pattern arising from a unique state of a single liquid market.
    
12. Major price shocks are very similar to 'earthquake events' that have many recurring episodes of volatile behaviour before they subside…… but there are many different forms a major ‘shock’ can have on a system. They are not recurring ‘similar price’ features in a liquid market like a repeating pattern. They have a myriad of different forms and decay rates.

13. So as a TF we need simple but encompassing systems that can navigate these myriad of different possible forms. Prescriptive systems with many variables do not work well in these turbulent environments. We must sacrifice our desire to be precise in the ‘Tail Region’. We need to adopt ‘loose pants’ to extract an edge from this zone of market behaviour.
    
14. A TF method simply applies a risk mitigation principle to these Exogenous and Endogenous price moves that ‘cuts losses short and lets profits run’ which is a very simple ‘rule’ we can apply without having to understand the complex mechanics of the entire system in this zone. This rule works well for both Exogenous and Endogenous major price moves and is not concerned with the fundamental reasons ‘why’ these events occur in order to ‘predict’ the impact of these events.

Moving on from the Research towards the Process we Adopt to Hunt These Outliers

Now that we understand Outliers a bit better, let’s now discuss a common problem faced by many traders in understanding what we mean when Jerry refers to the requirement for a ‘large sample size’ when applied to these fairly infrequent universal phenomena of liquid market. If they are so few and far between, how do we obtain a large sample size?

1. These Outliers are serially correlated/positive feedback clusters in the data that are finite in number, but they are ‘relatively’ scale independent. In other words, their presence is felt across multiple timeframes due to their nonlinear nature (their magnitude and impact).
   
2. There are two steps a TF capitalizes on these major directional price moves to increase the RELATIVE FREQUENCY of their presence in our trade distribution when compared to the balance of linear trade results (random series of wins and losses) that arise from noise and mean reversion that are ‘unwanted’ side effects of our TF models.

Step 1 - We diversify widely across many liquid markets to increase our chances of including them in our trade results. So, this is easy to understand. Let’s say we have a trading career of 30 years. A single return stream may only deliver 5 significant Outlier events over a chosen time interval which spans numerous timescales.

150 return streams in a diversified TF portfolio over the same timespan of 30 years traded the same way by normalising the data using ATR might have 5 x 150 times the number of Outliers in the portfolio distribution.

In other words, far more Outliers in our Portfolio Distribution. Our use of ATR normalises the data for each return stream so we can trade them exactly the same way. We treat each data set as just another possible way that history could unfold and do not focus our attention on the individual characteristics of each data set.

However, while we obtain a far higher sample size of Outliers in our portfolio models this also means that we have 150 times as many unwanted side effects of random series of linear wins and losses….however the nonlinear scale of the Outlier when compared to the linear results dilutes the impacts of these unwanted side effects.

Step 2 - We adopt long lookbacks to reduce the impact of linear events (attributed to noise and mean reversion) that dilute the impact of these anomalous ‘Outlier’ events.
If we want to incur MORE linear impacts of noise and mean reversion in our trade distribution, then we reduce the 'scale' of our lookback. This means that the presence of these linear trade results is more abundant in relative terms.

So, by adopting a longer lookback this means that we are reducing the linear trade results without significantly compromising the nonlinear impacts of the Outliers in our trade distribution.

In addition to this use of longer lookbacks, we also adopt a confirmatory measure that supports our hope that this major market move exhibits characteristics of a phase shift. We use volatility expansion as a confirmatory measure that tells us that the system behaviour is starting to change. A volatility expansion from either a short sharp news shock (aka exogenous event) or a building signal of volatility expansion associated with an endogenous event.

We can use ATR or accelerating momentum signal to provide this confirmatory measure in addition to our longer lookbacks.

3. While we cannot predict the ‘when and where’ of these Outliers (we are at the mercy of the market in this regard)…we certainly can exclude the trade signals that we do not want in our trade distribution. We use a process of exclusion to achieve this through our use of lookback.
   This way we can increase the 'relative frequency of these non-predictable anomalies' through a systematic rules-based process that diversifies far across uncorrelated markets PLUS uses long lookbacks to filter the ‘wheat from the chaff’.
   
4. Outliers are not patterns in a time series like repetitive price patterns that are market dependent features and dependent on linear inputs like oscillation cycles about an equilibrium. They are anomalous features like 'rogue waves' of a variety of different forms that require a multiplicative chain of events (serially correlated) to 'amplify' the signal. These events have memory yet there form radically changes and they dissipate over time.

To most traders Outliers are regarded as 'unforeseen risk events' which predictive traders seek to avoid….but for a TF….they are the bounty that we actually seek.

5. If we compare the trade distribution of a short-term trader with a long-term trader, Outliers are far more dispersed in the overall trade results for the short-term trader. The majority of the 'linear' trade results interfere with the 'nonlinear' benefits of Outliers. So, a short-term trader might have a large linear sequence of losses and small wins inter-dispersed with a few major Outliers whereas a medium to long term trader will retain the Outliers in their distribution but possess a far lower sequence of linear losses and small wins.
   
6. We ran this quick example today to demonstrate what we mean.
   Here are the results of 2 BO Traders applied to EURUSD between 1990 and Current day.
   • A Short-Term BO Trader; and
   • A Medium to Long Term BO Trader.
   Risk per trade is identical for both models as are all parameters except lookback.
   
   The average lookback for the short-term trader was 50 days….while the average lookback for the medium to long term trader was 125 days.
   
7. The performance results look similar, but the devil is in the detail and why we need to refer to the trade distribution of results to see what is going on.

• The Short-Term BO Trader had 539 trades
• The Med to Long Term Trader had 364 trades

8. When we peruse the histogram of trades the reason for the outperformance of the medium to long term BO trader is revealed. It is not the raw number of Outliers in the distribution that is important here….but the relative number of Outliers when compared to the linear results.
   
   We have far more linear trades 'RELATIVE TO' Outlier trades in the trade distribution of the short-term trader. The increase in the relative frequency of linear results to Outlier results not only 'dampens' the material impact of the Outliers in the trade distribution….BUT the increase in total trade results of the entire distribution includes with it additional transaction costs.

9. This is the secret to hunting Outliers. They are present on most timeframes BUT noise and mean reversion AND trading costs dampen their impact in the total trade distribution.
   We avoid this 'dampening impact' by stepping out our lookbacks AND we diversify widely to increase the population of Outliers in the trade distribution.
   
10. The key point of note is that Outliers are less scale dependent due to their magnitude and are universal market features found across multiple timeframes. Linear results are typically market dependent features and are often 'scale dependent’.
    
    We therefore accommodate the lower sample size produced by our longer lookback by diversifying across more markets by 'Normalising the data' using ATR to treat each market the same way to increase the "relative" proportion of Outliers in the portfolio trade distribution.
    
11. As you can see a Trend Follower is not concerned with the unique qualities of individual data sets. We are targeting non-linear tail events that are not repeating patterns. Our process is the antithesis to 'convergent trading styles' that seek to predate on predictable patterns. We are targeting universal features found in all liquid markets from time to time….that offer nonlinear windfalls to our PL.
    
12. As a good friend of ours Bruno Campos was mentioning on Twitter, you won’t pick this up with a ‘T-Test’.