In the Beginning there was Trend Following – A Primer – Part 3

Trend Following Primer Series  – Divergence, Convergence and Noise- Part 3

Primer Series Contents

Divergence, Convergence and Noise

So far in this Primer Series we have discussed that when considering market trends, it is wise to not get too attached to the notion of trend form. We have also introduced you to the notion of ‘real trends’ or ‘fake trends’, however there is another powerful way to also consider how price action can be applied to trading which offers considerable insight.

A divergent or convergent time series provides a quantitative way to classify any trading strategy seeking to exploit serial correlation and each definition lies at the spectral ends of price action. This therefore includes our trend following approach and a host of other trading techniques that seek serial correlation in a time series.

In simplest terms convergence means coming together, while divergence means moving apart and these definitions provide a very powerful way to classify trading styles into two broad camps that relate to the region of the distribution of market terms from which alpha is derived (more on this later however Chart 8 below introduces you to this concept).

Chart 8: Where an Edge is Derived from the Market Distribution of Returns

Chart 8 above highlights how convergent trading methods focus on the non-randomness that exists in the peak of the Distribution of Market Returns, whereas divergent methods focus on the non-randomness that exists in the left or right Tails of the Distribution of Market Returns.

An understanding of divergence and convergence is essential, as the methods we deploy to capture the elusive edge that exist in these zones of opportunity are, the antithesis of each other. By confusing the issue and treating both convergence and divergence in the same way within a diversified portfolio of trading solutions, you will quickly find that each method detracts from each other.  It is possible to trade both methods with different processes, but it is very unwise to include both in the same portfolio.

Now while a speculator seeks the arbitrage that exists within a convergent or divergent price series, a ‘noisy’ time series provides a problem for all traders. Unlike a convergent or divergent time series, a noisy time series lies in the middle of these spectral extremes of price action where there is no observed bias in the price series. As a result, a noisy time series is deemed to hold no arbitrage potential.

While we use the term random to express a noisy time series, this is not used in the same strict definition as that you may find in a physics textbook. Rather, a noisy or random time series in financial market terms is just a trading pattern that holds no arbitrage potential for the traders that call them ‘noisy’. There are different scales used to quantify and trade market data and what may be termed random or noisy in the longer term, may have arbitrage potential and be deemed non-random in the shorter term… don’t get too hung up on the term ‘noisy’. It is just a useful way to define a price series that holds no arbitrage potential for the quantitative trader throwing around the ‘name’.

Quantitative Techniques

Unlike many other forms of trading style that seek to understand the causative reasons for why price decides to move in a particular direction, trend followers choose to simply refer to the price action itself. This therefore places a diversified systematic trend follower into the definitional category of technical analysis and more specifically quantitative traders….. as while we trade based on signals generated from price action, we deploy statistical methods to interpret price data.

As discussed previously we do so to eliminate the propensity of our brains to ‘fool us’ and rely on the data itself to tell us an objective story that can be agreed on my all trend traders who adopt a quantitative method under the same assumptions. We can also return to our assumptions in a back-test and repeat these experiments with fidelity and thus use the back-test as a method to ‘objectively’ test these assumptions.

Many other forms of trading technique rely first on identifying the causal reasons for why price moves, then armed with this information, decide how best to capitalise on this causative driver. So for example fundamental investors first identify the causal factors for why price moves such as a particular market being overvalued or undervalued, and then they evaluate when those conditions are present. If these conditions are found, then a fundamental investor places a trade that takes advantage of the potential future price move associated with this assumed causal driver. The timing of this possible future move is however unknown. Furthermore, our ability to test these assumptions in a repeatable back-test is a fools errand as the process employed is highly discretionary.

Another example of a discretionary trading technique that first assigns causation to the move before striking are News Event Traders. This type of trader specialises in trading News Events where they closely monitor the news feeds and undertake scenario tests to evaluate their importance and possible impact on price behaviour. Having undertaken their analysis prior to the anticipated News Event they focus on the News release data and determine which scenario they will apply based on the analysis.

These prior popular trading methods (particularly abundant with discretionary processes) are examples of predictive methods that seek causal reasons for why price moves so they can predict a future outcome.

While we strongly agree that the primary causative driver for trends are economic fundamental factors, we avoid the need to speculate which of the drivers are being applied and the timing of those impacts to create business cycles and different trending conditions.  

We however as quantitative trend traders simply take all our trading clues from the statistics derived from historical price data action alone without any heed of any possible underlying causal factors. We understand that ‘all roads lead to Rome’ so rather than seeking to understand the possible causative reasons for price behaviour which can be vast and ‘fleeting in nature’, we focus on the primary (as opposed to the possibly derivative) information source for our technique……that magic clue called ‘price action itself’.

You see many alternative methods of trading are based on a philosophy that may or may not have a bearing on price ‘in the moment’. As a result, many alternative forms of technique that use derivative causative drivers of price may be appropriate “for a period of time”, but may not necessarily “stand the test of all time”.

However, unlike these derivative methods, by trading the primary agent (namely price action itself), such a canvas will never alter. So long as financial markets offer potential for arbitrage, then that record will be recorded in price itself. We actually do not need to know the ‘why’ at all in trading it.

Quantitative Camps

Fortunately, despite there being a plethora of different trading styles, quantitative techniques can be bundled into two discreet camps. Those who target convergent opportunities (such as mean reversion or counter-trend methods also referred to colloquially as short volatility methods) and those who target divergent opportunities (such as trend following and momentum methods referred to as long volatility methods).

It is possible for a trader to adopt both broad styles in their trading repertoire, but each method is the antithesis of each other and requires diametrically opposed treatment.

In attempting to understand why trend traders don’t consider that they ‘predict’ future price moves, it is useful to think of the reasons in ‘divergent or convergent’ terms.

A convergent trader is regarded as backwards looking. They use historic price action as a basis to evaluate a price level which is regarded as ‘an intrinsic’ level that price historically has converged towards. Once this ‘intrinsic price level’ has been calculated, then a predictive stance is assigned to all future price action on the understanding that a trading opportunity exists when price takes an excursion far from this intrinsic level and is therefore ‘predicted’ to eventually revert back to this intrinsic level.

A divergent trader on the other hand is regarded as forwards looking. They use historic price action simply as a basis to understand where price is ‘unlikely’ to be in the future if prices diverge away from their historic state. Now while a trend follower is one such divergent trader, we simply do not know where this future price will diverge to or the possible direction of this divergent move. We just understand that divergence implies that change is ubiquitous. The lack of any historic benchmarks to use in this philosophy of divergence makes trend followers ‘risk managers’ as opposed to ‘profit seekers’ as the only means they have to possibly take a controlling state in the uncertain future state of price is to mitigate risk events but leave the possibilities open for unbounded divergence. We consequently do not use back-tests as a basis to predict future returns but rather, we use back-tests as a basis to test the sensitivity of our risk management assumptions. 

Given the vast disparity between the two different schools of application we avoid convergent methods like the plague as they can undermine our ambition of wealth building if not applied judiciously. This is despite the attractive ‘ephemeral’ lure of what convergent markets can deliver from time to time. We will spend a great deal of time in this Primer Series explaining the ‘why’ for this particular stance taken on avoiding convergent methods.


Trend followers like to categorise their opportunities as arising from financial markets that are in disequilibrium (or a state of transition). This tendency towards transition can lead to tail events when the transitions are large. We tend to think that trending markets exhibit this state when previous equilibrium levels are no longer respected. During this period of transition, price takes a directional journey either higher or lower to ultimately settle on a new equilibrium level for a period of unknown duration. The extent of the journey between equilibrium levels varies and periods of transition can be of any arbitrary duration and extent.

Given the tendency during transition for price to diverge away from previous equilibrium levels, we refer to this price action as being divergent in nature.  For those traders that capitalise on divergence (eg. trend followers and momentum traders), we refer to them as ‘divergent traders’. Divergent traders can never predict when and for how long market conditions remain in transition and they simply work off the principle that during these uncertain market regimes, it is a wise tactic to simply float with the market and participate in the journey.

Given their non-predictive stance and uncertainty regarding the possible extent of the directional move, these traders simply cut their losses short and let their profits run without any profit targets deployed. They also do not pay a great deal of attention to their trade entries, but they do have a lot of them as provided that an existing trend is in place, they simply jump on board for the ride. By having a variety of different entry techniques to catch a trend, this provides much needed diversification that ensures that no trends of substance are missed. Furthermore, diversification of entry is a much-needed method to reduce correlations between return streams at the global portfolio level.

Trend followers need to wait until a trend is formed before they are attracted to participate in the price action. As a result, they never catch the beginnings of the trend and are always late to the party. Furthermore, the stance taken of letting profits run mean that trend followers always leave the trend when it ‘bends’ and as a result never are able to exit the trade at the optimal point of the trending condition. Given the late entry and late exit, trend followers acknowledge that they never can exploit the full length of the trend and they therefore focus their attention on catching the ‘meat of the trend’. The infrequent nature of trending events combined with their potentially unbounded nature in duration and extent naturally leads to trend following strategies having low trade sample sizes per system deployed. It is through diversification at the global portfolio level where we up the ante in trade frequency but is never a case at the level of the individual return stream.

The price paid by this form of trading style is that we can never know for how long a divergent condition will persist and there can be many false leads provided by trends that are randomly constructed without possessing any ‘causative’ bias in the trend construction. As a result, most of the time, traders that participate in apparent trending market conditions get it wrong and price action turns in the other direction as soon as you jump on board. It is only in the quite rare instance that a market will continue to trend given a causative bias embedded in the price series and therefore many researchers refer to a trending price series as being a market ‘anomaly’.

Typically, these methods stack up over a large trade sample size simply due to a handful of ‘outlier’ trades that have delivered sufficient profit to pay for all the losses along the way….and as a trading method, divergent trading methods can rarely deliver a sustainable cashflow over time. These methods are tailored for wealth building as opposed to cashflow generation.

Most retail traders simply do not possess the patience or required level of capital to participate in this form of wealth generation. 


At other times when markets are undergoing periods of stability, price can exhibit repeatable price behaviour patterns around an equilibrium level and during these periods of ‘stability’ trend followers need to avoid these conditions like the plague. These are the market conditions that suit methods that attack the tendency of price to move towards these equilibrium conditions. Traders that work off the principle that price will converge towards a historic equilibrium are therefore referred to as ‘convergent traders’.

Most retail traders who trade price action prefer to tackle this form of market behaviour as they can exercise control in predicting where price at any level is likely to land in the future. The relative frequency of this repeatable cyclic condition also leads to high trade frequencies that attempt to match the rhythm of the cycle and if done well, can lead to high win rates while the condition exists. Who wouldn’t be attracted to convergence? Well us trend followers for a start that are sceptical of a markets ability to retain a repeatable pattern over time.

During periods of market stability, predictable oscillations about an equilibrium can be very stable and endure for significant periods of time. Given the obvious nature of a repeatable market action this style of trading requires preciseness of entry and exit to take full advantage of the enduring repeatable pattern.

Convergent traders therefore place a great deal of emphasis on both the entry on the exit and apply profit targets that target the equilibrium levels around which these patterns oscillate.

Unlike their divergent cousins, convergent traders focus on the commencement and end of trend turning points. Having an understanding of the markets rhythmic oscillations allow this style of trader to be specific in pin-pointing areas that are most likely for price to commence their mean reverting move back towards equilibrium. These traders are not looking for diversified methods in targeting these opportunities. In fact, to be diversified using convergent methods significantly dilutes the premise that these traders can predate on a repeatable market condition. It pays to be precise when targeting convergence and a diversified approach is an obstacle for this required ‘preciseness’.

It is during predictable oscillating market conditions where convergent styles have particularly high win rates and can support many trades that are curve fit to the enduring pattern of price behaviour.

During extended periods of repeatable price behaviour, traders can participate in ‘easy money’ derived from the spoils of predictability and these methods are cash flow generating in nature and very appealing to retail traders. In fact, a repeatable market condition over an extended timeframe often leads to traders upping the ante and increasing their position size to capitalise on that opportunity and make hay while the sun shines. It is this temptation you need to strictly avoid when trading convergent methods as, unlike divergent methods that place their emphasis on managing risk by always cutting losses short, convergent traders often forget the fact that market conditions never persist. When market conditions change, the over-leveraged position sizes then lead to a string of very large losses that are sufficient to wipe out your trading capital in a quick series of unfavourable trades.

Unfortunately, the price paid by adopting ‘convergent trading principles’ is that you must attack the current condition while it lasts, and there is never any guarantee in the enduring nature of that condition. As the opportunity is exploited, markets then start to move to new equilibrium levels and the repeatable pattern no longer exists.

Convergent traders continuously need to monitor their performance and be prepared to jump ship when drawdowns arrive. It is exceedingly difficult to evaluate whether the drawdown is a temporary phenomenon where market behaviour will once again resume its predictable oscillation, or whether that predictable market condition will ever occur again.

So, while cashflow is easily obtained during periods of market stability, when markets alter their behaviour once the condition has been exploited, convergent traders need to be on the ball and quickly stop their trading systems before they encounter large string of unfavourable losses that destroy the small pool of cash flow that has been previously generated.

Convergent traders need to ‘strategy hop’ as market conditions change continuously searching for the next exploitable pattern of stability and repeatability.

What many retail traders do not understand is that a sustainable trading life is as much about being able to endure unfavourable market conditions as it is about being able to exploit a single market condition. While many new entrants enjoy the spoils of an enduring market condition, these spoils are frequently totally lost when market conditions become unfavourable.

The attraction of a high win rate, high trade frequency and the prospects of a regular cashflow is what typically attracts retail traders to the trading game. Unfortunately, the lure is a false promise given the non-stationery nature of financial markets. While you may have luck on your side for a short period or you are able to effectively exploit a ‘convergent market condition’, there is no guarantee that you will be able to survive during those times when markets offer unfavourable market conditions.


While the market spends much of its time converging around an equilibrium and far less of its time in dis-equilibrium diverging away to a new area of stability, most of the time markets, in their efficient state, exhibit noisy market behaviour. During these market conditions, there is no arbitrage potential from any directional stance to exploit and gross price behaviour simply adopts random directional price moves. While many traders can achieve profits during these ‘noisy random conditions’ these spoils are derived from luck alone. These conditions are very like the conditions you face when playing games of chance at the casino. Your success is a factor of luck alone. There is no directional ‘bias’ in the market in which a trader with an actual edge can participate in.

In fact, when including the costs of trading which apply a slight frictional drag of bias to overall trading results, over the Law of Large numbers your luck is likely to slowly deteriorate to a point where you are left with no trading capital if you never are fortunate in finding an edge derived from a ‘real’ bias in the underlying market data.

Chart 9: Thirty Random Equity Curves resulting from trading a purely random price series – 500 Trades

Have a close look at Chart 9 above. This chart reflects 30 possible equity curves resulting from 500 trades undertaken by a trader when market conditions display no actual edge. Each trade adopted a position size of 2% of equity per trade. Starting with an initial equity position of $1,000 you will see that some lucky traders lifted their equity to $2,000 having undertaken 500 discreet trades.

Now luck swings both ways as well as you will also note that some ‘unlucky traders’ saw their equity rapidly diminish to a few hundred dollars at the end of the exercise.

Now you might find it hard to see, but there is a slight ‘frictional drag’ present in these equity curves arising from the impost of trading costs on the series.

So let’s see how the lucky traders fare when we extend the data sample with this frictional drag for say 10,000 trades.

Chart 10: Thirty Random Equity Curves resulting from trading a purely random price series  -10,000 trades

As Chart 10 above shows, it is a sad story for every participant in this story of randomness. The slight negative bias imposed by the trading costs ensures that over the ‘Law of Large’ numbers that small bias with compounding will diminish any trader’s account.

The Interplay between Divergence, Convergence and Noise

Now while the preceding definitions create an impression that these different market states of divergence, convergence and noise appear to represent distinctive market conditions, the reality is that the market state can exhibit various combinations of these price behaviours at any point in time. The result is that a complex market can exhibit a myriad of different market states.

For example, when we see a clear trending series representing a divergent market condition, we may also find a degree of convergence within that overall directional behaviour. This leads to the classic overshoots and undershoots along a trend cycle that frequently is interpreted as wave behaviour. We can also find that trending price series frequently stall in their trajectory within defined congestion zones where convergence and noise can dominate.

Sometimes the divergent condition is so pronounced that alternative market behaviour of noise and convergence is suppressed to such a degree that a trending condition never retraces and exponentially accelerates producing a parabolic time series.

Some traders who believe that they are trend followers will wait until a retracement of the trend to then jump on board the overall trend direction seeking a high reward to risk with a larger position size than more traditional ‘breakout’ trend traders. This style of trading is predictive in nature as the assumption surrounding this tactic is based on a prediction that a retracing price will ultimately revert back to the trending condition.

Given that more traditional trend traders adopt a non-predictive posture, they tend to operate off breakout entries that simply directly enter a trending move. The advantage of a ‘non-predictive’ breakout entry is that all trends are captured this way. Waiting for a retracement entry before entering a trend can result in a missed trending opportunity. While this predictive class of trend trader can achieve some great reward to risk results from their ‘sniper entries’ into a divergent trend that also possesses a convergent signature, they tend to miss the trends that never retrace….such as the noted parabolic moves seen with some cryptocurrencies and stocks such as Tesla. The parabolic move is a major windfall for the trend follower as these can lead to gargantuan trends, and you don’t want to miss any of them.

Now the plethora of different conditions a market can take based on the relative mix of divergent, convergent, and noisy states makes the trading game a very difficult one over the long term.

Many traders fall under the assumption that a particular market state is here to stay and while they may make hay while that sun shines, their prospects of wealth building returns over the very long term is an unlikely one.

We all are drawn to the lure of profits trading these markets, but to survive in this game we need to flip that mindset. This game is a game of survival and not a ticket to instant riches.

While the complex systems of our natural environment and the financial markets are different beasts, there is a common theme running through all complex systems. The winners are the participants that survive and can live to tell the tale to their offspring, and these are few and far between. The fossil record and the trading record have a very large graveyard of unsuccessful profiteers.

Stay tuned for our next instalment in this Primer Series.

Trade well and prosper

The ATS mob

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