Quants can be Useful to Classic Trend Followers

Price in a financial market is a consolidated statement of all participant behaviour at a snapshot in time. A summary point estimate of the collective action of participants in the NOW.

In a complex adaptive system comprising many participants, the behaviour of each participant creates a perturbative effect on total price. A trader whose models adopt a mean reverting (convergent) premise will force price to move in the opposite direction to prevailing price movement. A trader whose models adopt a trend following (divergent) premise will force price to move in the prevailing direction of price movement. When you sum up all these perturbative behaviours we obtain a gross statement of all behaviours of a market during a snapshot which is ‘the current price’.

A Random Series of Market Data

If there is no bias in the underlying behaviour of the myriad of different divergent and convergent models operating in the market, then a noisy time series is produced where there is no prevailing tendency of price to move in a particular direction. The behaviour of each price bar can be re-stated as being independent of what the prevailing direction of price action has revealed from the past.

If participant behaviour is therefore not influenced by other participant’s behaviour (reflected by recent past behaviour) then we can state that price at any point in time is independent to price at any other point in time and displays a stochastic (aka random) nature.

When a time series is comprised of independent discreet price points, it can be defined as being random in nature. An independent price series has no causative impact on the price of the future. Much of the time, price action appears to display this ‘random behaviour’. A vast array of different participants behaviour creates a noisy time series when we summate impacts on price, where no particular behaviour dominates the participant landscape.

When trading a random price series, the trade outcomes and equity curve, which are a derivative result of this random price action, is also therefore by definition a random result. There is no causative bias in the price series that allows a speculator to benefit from any arbitrage potential that lies within the price series.

Let’s have a close look at how a ‘random price series’ visually appears against a ‘real price series’ in Figure 1.

If you closely look at Figure 1 you will be very hard pressed to notice any material difference in the visual representation of price. This is a major pitfall for traders that use discretionary visual techniques to trade a price series. A random series displays very similar form to a real price series.

So, there must be something within the price data itself that leads to the performance returns of a trader that possesses a definitive edge.

Now let’s have a look at the equity curves produced when we apply a trend following model to a random price series.

In Figure 2 we have created 15 different random series of market data and have traded these random series with a standard class of Classic Trend Following system. Each equity curve comprises approximately 1000 trades undertaken across a 50-year period.

We can see from the equity curves within the first 200 trades, that we have a few very favourable returns with our trend following models, where our equity significantly improved over this short duration. Most of the equity curves over this period however produced deteriorating returns. This short-term phenomenon however is short lived, as all equity curves experienced significant deterioration over the entire test period of 1000 trades.

The reason for this deterioration in the long term can be attributed to the frictional costs of slippage and holding costs applied to this random trade series which creates a negative drag (a negative bias) in the time series. This negative drag is amplified in a compounded series over time. This adverse compounding effect with negative drag is a path dependent feature associated with geometric returns.  

The same effect of negative drag can be seen in a coin toss experiment where we apply a slight bias to the coin. In the short term, the bias is not revealed, and we can have a diverse array of outcomes associated with the sequence of losses and wins in the time series. However, over a large sample size containing many coin tosses, we can see the bias exert a progressively dominant impact on the sequence of wins and losses in the long term. If we apply compounding to this coin toss experiment it will further amplify the impacts of this bias in a series of coin tosses.

So having an understanding of the impact of a random price series versus a biased price series on performance returns over large trade samples and the impacts of compounding, we can then better understand the mechanics of an equity curve produced in the long term track record of the Trend Following FM’s. 

Unlike the random series of equity curves, something strange is going on with the equity curves of Trend Followers (refer to Figure 3). Fortunately there is some non-random biasing feature present in the underlying data that is producing a rising equity curve over the long term.

When we closely peruse the equity curves of a number of Classic Trend Following Funds, we note that each fund supports a trade history of thousands of trades over a twenty year period. We note that there is not a classic deterioration of the equity curve evident in these examples. There is clearly a favorable bias that is non-random which is shaping the long term returns of these Funds.

All of these Funds are extensively diversified in terms of their geographic, cross asset, timeframe and system methods, but common to each of these Funds is their systematic application of cutting losses short and letting profits run…..so what gives? Why do they all possess common characteristics during certain coincidental market regimes?

So let’s dig a bit deeper with these equity curves and closely note how there are periods of time when the equity curves are uncorrelated, but there are also periods of time when these equity curves are clearly positively correlated.

When we closely look at the correlation between equity curves in Figure 4, we note that there are distinct periods of time where the equity curves are all moving in tandem (either up or down) and are positively correlated. I have highlighted these zones in white. There are quite a number of these positively correlated segments of a diversified trend followers equity curve. I have highlighted 12 of them.

At all other times over the equity curve there is no observed positive correlation between these equity curves and there is no common directional movement of the equity curves.

Outside of these positively correlated periods, we have significant dispersal of returns which seems to follow the principle of dispersion that exists in a random series of equity curves. However during periods of positive correlation, the same directional movement reduces any dispersal in return performance.

This is our first evidence, that we are not dealing with equity curves arising from random market data but rather equity curves that includes periods of market condition where a non-random feature of a markets returns are driving positive performance for the Trend Followers.

It is during these ‘clustered periods’ of positive correlation that we observe a non-random feature of the market returns called serial correlation that provides a directional bias to the market data (either long or short) in which Trend Following Funds through their system application capitalise on.

Given the diversified nature of these Funds, there is some ‘causative’ feature emerging somewhere in these diversified markets which is leading to this common feature across these Classic Trend Following Funds. Markets are exhibiting this same characteristic across asset classes, timeframes and systems.

Serial Correlation, Non Linearity and Compounding

So now that we understand that there is some non-random ‘market feature’ which is beneficially influencing the performance returns of Trend Following we can now introduce a quantitative feature into a random return series to observe the impact of Trend Following Performance.

We will refer to this feature as ‘serial correlation’ in the data series.

In a serially correlated price series we introduce the notion that price moves in a time series are not strictly independent to each other. We create an interrelationship between price at say T=0 with price at say T=3. This inter-relationship between the price intervals of a series creates a ‘causal’ bias on the price series. We refer to a price at T=0 as being correlated with a price at say T=3.

By inserting serial correlation in a time series we introduce a causal bias in the time series which drives price to move in a particular direction. Unlike a random price series where price at each interval in independent, there is some ‘causal driver’ backing the underlying price series that is enduring in nature. If we decide to trade in the direction of this underlying bias in the series, then this bias may extend into the future providing a causal definitive backing to our trade results.

Unlike a random price series where a derivative equity curve arising from applying a trading system to that random series is also a random equity curve, under a ‘non-random’ serially correlated series, a derivative equity curve arising from a system that correctly exploits that bias is also non random in nature.

So let us observe this effect with a hypothetical illustration in the following example.

In Figure 5 we have produced a random price series (green and red) and have plotted this against real market data (white).

In January 1995 we have introduced a 3-month period of serial correlation into the random data series to create a slight positive bias in the random market data. We can therefore see the positive bias in Figure 5 leading to an altered path of the random series over this 3-month period (blue and yellow).

We perform this process 5 times in a 30-year random time series to create varying degrees of positive or negative bias at discreet locations across the time series. This process clusters serial correlation at discreet locations throughout the time series.

Figure 6 visualises another section of serial correlation inserted into the serially correlated series (blue and yellow) in 2017 for a 6-month duration.

Figure 7 reflects the result of price at the end of the time series in 2021. Note that in this instance the random price series and the serially correlated price series end at similar process and lie above the price reached by the real price series in 2021.

The ultimate position of price is path dependent and influenced by the degree of random walk and the degree of serial correlation that resides in a price series.

So now that we have introduced these 5 discreet serially correlated periods into a random price series for a single market, let us see the impact this has on the equity curves produced by our Trend Following models.

Figure 8 above superimposes 5 distinct clusters of serial correlation into a single random market data series to produce the following equity curve for a Classic Trend Following model. I have highlighted on the equity curve where the serial correlation was inserted into this model.

Unlike the random equity curves of Figure 2, you can clearly see that this equity curve exhibits powerful compounded performance. All the positive performance seen in this equity curve resides in the serially correlated components of the price series. It is the serial correlation in the series that leads to these wonderful stepped equity curves that lift the returns of the entire series. This is quite an eye opener as it is hard to wrap the head around this phenomenon.

Most of the price action in the time series was indeed randomly constructed but the few serially correlated ‘patches’ in the time series are totally responsible for the excellent long term performance returns. This clearly demonstrates that there is a weak edge residing in most random market data which is sufficient to drive performance returns of Classic Trend Followers.

So what are the exact reasons for what is driving these performance returns?

If you drill down into the nuts and bolts. It is all about the nonlinearity that resides in serially correlated data and how we amplify this non-linear effect with our system application and our compounding treatment.

We only applied serial correlation in the series at 5 discreet points in the entire series for this single market but the bias that was created in the data in these zones were sufficient to extract non linear performance results during these critical periods of the time series.

Under a random time series, performance results are effectively linear in nature. We get consecutive strings of minor wins and minor losses. Just like tossing a coin many times. Each win and each loss is effectively equivalent and the strings in the series lead to significant dispersion in returns.

For example, consider the following sequence of random wins and losses of approximate equal magnitude.

-1,-1,+1,+1,+1,-1,-1,-1,-1,-1,+1  = -3

And now let’s reorder the sequence

+1,+1,+1,+1,+1,-1,+1,-1,-1,+1,+1  = +5

….and again

-1,-1,+1,+1,-1,-1,-1,+1,+1,-1,+1  = -1

As you can see from the prior 3 examples when we randomise a linear sequence we get considerable dispersion in the final consolidated result that range between -3 and +5.

But now let’s introduce the first non linear event in the series. In this example we take the first example of a random sequence above and introduce a nonlinear event at the end of this series.

-1,-1,+1,+1,+1,-1,-1,-1,-1,-1,+1+20  = +17

As you can see, the non linear magnitude of this single event totally changes the result of the entire prior random sequence. We lift the final result from -3 to a handsome +17 through the introduction of this single non linear event.

This example is used to illustrate what is doing the heavy lifting in the serially correlated series of trade results. It is the nonlinear impact of the serially correlated components of the price series that does the initial heavy lifting of the equity curve.

Now that we understand this aspect of non linearity, let us look at another which resides in our Trend Following Method.

Through the application of multiple trade systems that are ‘turned on’ during periods of extreme price movement, we further enhance this nonlinear impact on our return streams.

So for example, let us take the past hypothetical example and update this example to reflect how we deploy multiple Trend Following systems when trends become material in nature. It produces the following observed effect on our equity curves.

-1,-1,+1,+1,+1,-1,-1,-1,-1,-1,+1+20+15+10+5  = +47

Simply by having multiple systems deployed when trends become material in nature we amplify the non linear result through additional important contributors to our trade history. In this case 3 additional TF systems added to our diversified portfolio lifted the consolidated result from +17 to +47.

Finally, another important non-linear contributor to our performance lies in the compounded nature of our trade returns. The impact of beneficial outliers that reside in our trade history accelerate the compounding effect of that time series. This is to be contrasted with the adverse impact that drawdowns exert on compounded wealth.

Compounding acts as a two edged sword that is beneficial with positive volatility in an equity curve and detrimental to adverse volatility in an equity curve.

If we return to the equity curve produced in Figure 8 you will notice the beneficial impact that compounding has on an equity curve with significant step-ups reflective of positive volatility. A Trend Following Fund regularly revisits high watermarks over its trade history which is beneficial for geometric returns.

So now we can return to the equity curve produced by Classic Trend Following Funds  of Figure 4 to better understand their collective performance.

We can state with more confidence that those times where the TF funds are positively correlated are during those regimes where markets are displaying non-random behaviour and returns are being driven by the nonlinear nature of serial correlation in the market data. The very high degree of diversification of these models allows for most Trend Following Funds to benefit from a patch of serially correlated data that exists in the market data….somewhere and somewhence.

If these FM’s were not highly diversified and focussed on specific market sectors, models or timeframes, then we would not find this degree of positive correlation in their performance. In fact the performance of non-diversified TF funds would be highly dispersed in nature across the entire series.

Broad diversification allows a TF fund to hunt for Outliers wherever they exist and it increases the chances of being the beneficiary of these very positive beneficial events.

Of course for those Trend Following funds that fail to capture the Outlier, their returns are largely going to be a feature of ‘random performance’ but given that a TF fund always cuts losses short these unfortunate funds are able to defend their capital base but simply not enjoy the fruits that Outliers bring under extensive diversification.

So How do we Explain this Serial Correlation in the Data?

Now we don’t hear much in finance circles about the beneficial impacts of serial correlation that produce non linearity in performance returns, and there is a reason for this. Most trading methods do not exploit this phenomenon as they operate within the Gaussian envelope of normal market data. In the tail environments, we see this serial correlation and non-linearity unfold. To better understand it, we need to step outside traditional finance speak and observe how other complex adaptive systems work. When we examine all complex adaptive systems, we find a common theme relating to feedback loops which we can use to explain how serial correlation works.

Under a complex adaptive system where we have a multitude of agents displaying different behaviours, we can explain this behaviour as arising from the behaviour of the individual agent itself and the behaviour of an agent that is influenced by the behaviour of others.

So, in a financial market we can substitute the term ‘agent with participant’ and then observe the nature of participant behaviour of a system. We can attribute this behaviour to either an participant’s individual behaviour in isolation, or indeed the collective influence of a systems participants on a single agents behaviour.

If participant behaviour is influenced by other participant’s behaviour, where a participant’s behaviour changes to reinforce or counteract other participant behaviour, we obtain a feedback loop between the relationship that exists between a participant’s behaviour and that of its neighbours.

Feedback loops can be characterised as either positive feedback loops or negative feedback loops.

A positive feedback loop applies to reinforcing a particular behaviour by encouraging synchronous behaviour of participants. In a market that is trending, a positive feedback loop amplifies that trending condition. In a market that comprises many different forms of participant behaviour, a positive feedback loop leads to the progressive synchronising of the various behaviours into a single behaviour. It amplifies a single behaviour and leads to nonlinear price extensions of serially correlated  data. The overall impact on market data is akin to a phase shift where nonlinearity is associated with volatility explosions in the data. Within Tail regions of a markets distributions of returns, price movement becomes much less ‘sticky’ and less constrained leading to large extended price moves in a short period of time.  

You see there is no such effect as ‘overcrowding’ when we refer to divergent market conditions. More participants doing the same thing does not remove the arbitrage opportunity of divergence. It actually amplifies it. So the next time you hear a FM stating that the Trend Following space can become overcrowded….then shake a wagging finger at them and state…perhaps you have not heard of positive feedback effects.

A negative feedback loop however relates to behaviour that diminishes a particular behaviour by taking the opposite position to a dominant behaviour. In a market that is trending, a negative feedback loop suppresses the prior directional tendency of price and attempts to stabilise price movement. It makes price moves far more sticky and constrained about equilibrium levels. It seeks to force price towards an equilibrium tendency. A negative feedback loop leads to a multiplicity of various behaviours and diminishes the bias associated with a single behaviour.

Now overcrowding is a symptom that is pertinent to negative feedback. A signal generated by negative feedback such as a repeating oscillatory pattern about an equilibrium is diminished by the proliferation of multiple participant behaviours within periods of equilibrium. A convergent signal can quickly dissipate into a noisy signal with ‘overcrowding’.

So we can now understand different phases of market condition. Within the extreme Tails of the Distribution of returns we have a zone of elasticity defined by a dominant participant behaviour which promotes price transitions and within the normal range of market activity we have a constrained market regime around an equilibrium tendency characterised by a plethora of different trading behaviours. 

When feedback loops are present in a complex adaptive system, we see these feedback effects lag price. This lagging effect leads to price no longer representing an independent (aka random) series. Under feedback, price at any point in time becomes causally connected to price at another moment in time. Under feedback, price at any point in time can have a causative impact on price at a future moment in time.

It is these feedback loops that create serial correlation in the data. Where price at t=0 is influenced by price at t=1.

It is this correlated tendency between price NOW and price in the future that provides an edge for all forms of speculation. Without that ‘correlated tendency’ then markets are truly perfectly efficient in nature. Serial correlation in a data series demonstrates that markets are not ‘perfectly efficient’ at all times. During some market regimes, serial correlation leads to arbitrage opportunities for speculation and a definitive edge.

Now if you want to observe an example of positive feedback in action, then look closely at this metronome experiment. Treat each metronome as a participant. At the beginning of the example you will see each metronome applying their own models and doing their own thing. The model is noisy. You can hear the noise….but look what happens over time as positive feedback starts influencing the behaviour of the metronomes. You see over time that the behaviours all begin to correlate due to the inter-relationships that create feedback loops in the system. This example represents a noisy market that progressively becomes a divergent market. Keep your eye on the vibrations of the table. It starts out being overt (hidden) but under positive feedback the vibrations become obvious. Positive feedback creates synchronous behaviour that leads to a force that amplifies the collective behaviour leading to nonlinear price extensions in market data.

So there you have it. We now have a new explanation for how Trend Followers derive their edge in the long term. This story is a quantitative story that just looks at the data itself. It does not seek to draw further conclusions relating to a possible causal reason that may be driving this feature of a quantitative price series. It doesn’t need to. It just recognises that serial correlation under positive feedback leads to non linear price extensions that are colloquially referred to as our ‘Outliers’.

This story relates to serial correlation, non-linearity, Outliers, phase shifts and positive feedback loops. It is not a story you will hear frequently in trading circles but is a story that you may hear those quants talking about from time to time. So there is another layer to this trend following story that may help to add to the cause of trend following. A real geeky layer that demonstrates how trend following is just a natural feature of the mechanics of a complex adaptive system that exhibits power laws from time to time. 

Trade well and prosper

The ATS mob