#### Let’s go Non Linear with Outliers – A NonLinear^2 Case Example

As classic trend followers, aside from managing risk at all times to protect ourselves from adverse Outliers, we focus our attention with our diversification in capturing Beneficial Outliers that exist in the market data. These Outliers are non linear events in the market data, which our asymmetrical trading systems are designed to capture.

What we mean by the ‘non linearity’ in this statement is that we differentiate between standard wins which we regard as linear wins, versus exceptional wins which we regard as non linear wins.

So we experience standard wins and standard losses (as all our losses are standard losses by cutting losses short) during normal market regimes where Outliers are absent. These wins and losses are all of fairly equal magnitude and their cumulative result translates into an effective random distribution of trade returns. However when we successfully capture an outlier, the magnitude of these unexpected anomalies are many many multiples of the average size of a winning trade. By capturing a small number of these exceptional events, our random equity curve suddenly becomes a highly positively skewed equity curve that reaches for the stars.

So, we could imagine our trade distributions during normal market regimes as representing a string of fairly equally sized losses and wins…of say….-1,-1,+1,+1,+1,-1,-1,-1,-1,-1,+1  = -3 .

But now let’s introduce the non-linear Outlier to this series….-1,-1,+1,+1,+1,-1,-1,-1,-1,-1,+1+20  = +17.

You can see how the single favourable non-linear Outlier in a single stroke, dwarfed the results of the prior linear sequence of wins and losses.

However, while we can now understand the non-linearity that exists in the market data itself, what is less well known is that….through our system diversification, Classic Trend Followers compound the story of Outliers even more by magnifying the bounty we receive from the market by deploying multiple systems that capture aspects of the elusive Outlier.

So, in a sense we not only capture a market outlier by our method but we compound the magnitude of the market anomaly through our diversified suite of TF systems that are used to target an outlier.

So, we have a non-linear process applied to a non-linear market condition. In a sense we square the power of non-linearity with our technique. (non-linearity^2)

So, let’s understand what we mean by this.

If we take the prior sequence of trades that includes an Outlier….then by allowing for multiple systems to ‘switch on’ when Outliers are being experienced….we can further magnify the non-linearity of the trade history to achieve this……-1,-1,+1,+1,+1,-1,-1,-1,-1,-1,+1+20+15+10+5  = +47.

You may have heard the expression that a classic trend follower adds to winning trades….but many might misinterpret this to mean that we pyramid into a position.

The nuance is this….Yes, we add to winning trades through our system diversification, yet we do not pyramid along the course of a single trajectory of a possible Outlier.

An Outlier frequently takes the form of many different paths. By committing our efforts to a single possible trajectory through pyramiding, we significantly reduce our ability to take advantage of the many possible forms of outlier. Furthermore, a pyramiding method concentrates our bets towards a particular trajectory, so if we are wrong in our assessment of that future trajectory, we can experience significant risk exposure with this assumption.

An Outlier needs to be distinguished from that of a simple trend.

As classic trend followers, we use simple trends as a basis to identify when to jump on board a possible Outlier. These can never be predicted in advance. We use trends as a launching platform where we hope that our entry decision is backed up by serial correlation in that underlying trend that extends the directional price series into a many multiple sigma event.

We are specifically looking at a trending price series and waiting for the signs that the trend is material in nature. In other words, we are waiting for signs that the trend is starting to go non-linear in its extension.

The Outliers that a Trend Follower catches needs to be distinguished from a ‘normal everyday trend’. In terms of magnitude, a normal trend is a fairly representative directional price series that resides in the average range of a normal market. It’s magnitude is linear when compared to other common trends in this ‘normal market regime’. However the magnitude of an Outlier is many orders of magnitude greater than a normal linear trend. It’s magnitude is non linear when compared to these more normal trends.

When we observe a liquid market data series, we can quite quickly observe these directional anomalies. They really stand out, but they can be of many different forms.

• It could be an exponential move of such magnitude that it meets the definition of an anomaly when compared to the balance of most other visual trends observed in the market data. This would be applicable to Tesla or Bitcoin’s recent market behaviour;
• It could be a protracted linear move of such magnitude that it also meets the definition of an anomaly when compared to the balance of most other visual trends in the series. This would be applicable to the move of the Nasdaq or S&P500 which has enjoyed epic linear trends post March 2020;
• Or an outlier may be a combination of many different forms of price extension comprising exponential moves and linear moves such as that described by Soybeans alone (refer to the chart below).

The Outlier region described in the chart above is highlighted in the green rectangle. This region comprises multiple forms such as exponential price extensions (highlighted in blue) inter-dispersed with more linear price extensions. Note that this Outlier region (in green) extends from a linear trending condition that emerges from the yellow rectangle. The yellow rectangle defines more normal day to day price action.

So under a breakout method of entry, we jump on board an existing trending condition that is starting to shape up as being possibly more *material* in nature. Of course, we do not know at this point whether this material trend will become a significant Outlier, and it may be a false flag. However by delaying our trend entry, we are increasing our probability that this trend we are about to jump on board might just have enduring momentum impregnated within it.

If we are fortunate and find that we are entering the Outlier zone….we will progressively deploy more and more different TF systems that ‘switch on’ as the Outlier continues.

These systems are not all the same. In fact they need to be different. Outliers can be of many different ‘explicate forms’. For example in the example above, we see multiple different forms of trend in the Outlier region. We see exponential trends defined by the blue ellipses and more linear price extensions outside these regions in the Outlier zone.

The reason for the various forms is not important as this may just be a random effect on an underlying bias….but what is important is that we have many different types of system to tackle the many possible forms an outlier can take. Our multiple systems therefore might catch aspects of the Outlier or the complete Outlier itself dependent on how they are configured.

So let us have a look at a current Outlier that is in front of us and the way a multiple TF system approach is tackling it. In this example we will use the Nasdaq Index as an example.

In hind-site we can state that this Outlier has been in progress since 12 Mar 2021 following a rebound from the March 2020 hiccup. Initially a single system was deployed when the rules for that system were triggered as a trend started becoming material in nature.

Subsequently as the trend evolved into an Outlier, more and more separately configured systems with different entries, stops and trailing stops were progressively deployed. Each with a different trajectory to capture many facets of a possible Outlier.

So now with this single Outlier we find that we have 7 separate systems deployed.

Rather than a single trade event with significant unrealised equity….we now have multiple trade events with significant unrealised equity. The trailing stops of each solution have been progressively ‘ratcheting up behind the long bias of this particular Outlier’.

So this is our intent. We throw our different TF models at the Outliers in the hopes that some of them stick….and sometimes…..only sometimes….you wake up one morning and find that your fortune has been made.

These events are what our game is all about. We ensure the pain of the 95% of patience required to participate in these events are more than worth it through the bounty that the 5% of these extraordinary events can deliver….and then some with our multiple guns firing.

We compound the Market Outliers with our systems to turn Non Linearity into Non Linearity^2.