#### The Many Different Flavors of Trend Definition – Who is Right and What Really Matters?

Trends come in many forms but in any definition, you need to benchmark your interpretation of a trend relative to a price benchmark. In fact as general relativity concludes, any measurement you take in this universe needs to be put into a relative context as different perspectives matter. So when you say a market is trending, you really need to say the market is trending ‘relative to some chosen benchmark’. We however rarely mention the latter….hence it gets quite confusing and subjective.

In simplest terms a trend can be defined in terms of the relative movement of a data series from a stationery point such as a price point or price level taken at a particular time (t=0) where the average movement of price from that reference point at time t has an overall positive or negative trajectory defined in terms of momentum (where momentum is vertical distance moved/time). Your definition only is valid from the perspective of your chosen reference frame. If you change your reference frame then your definition ceases to have validity.

You can become more prescriptive in your definition to help further categorize your description, but this is more an arbitrary choice than a mandate.

So here is a trend in accordance to the prior simple definition. The benchmark used to anchor the trend definition is price 0 at t=0 and you can see that the overall tendency of price movement is away from 0 with a positive general slope. This particular trend however was derived from random data and is based on a series of random price movements that represent one possible outcome in a normal ‘Gaussian’ distribution. The definition makes no mention of the requirement for a trending data-set to be either random or non-random…..however as a trend trader, you could profit from this particular series of price movements. In fact this would be a profitable random outcome that would also be represented in your equity curve.

Now here is another trending series of data that has auto-correlation present in the series by virtue of a small bias being added to the prior random series of 2% throughout the date-set.

Once again, a trend trader is likely to profit from this price series and the result represented in his/her equity curve.

They key point here is that the overall profitable equity curve of a successful trend trader comprises** both random trends with no auto-correlation present and trends of forecasting potential with auto-correlation presen**t. The latter actually comprises a small piece of the total profit pie but this is the component that is necessary to account for your edge and provide the necessary surplus to pay for ‘noise’ and frictional costs.

But where is the edge in the market data above (aka the ‘true trend’)? You can only visually discriminate the edge if you superimpose both data series together. Unfortunately while you can see the ‘edge’ visually in this example (being the vertical separation between the two equity curves), in the real world we don’t have this luxury on the fly when trading real time.

Now what a trend trader needs to understand is that **the slight auto-correlation that may be present in the data is what translates to an edge over the very long term.** Notice how the very small bias in the data early on in the series leads to progressively larger amplifications of bias later on in the series provided that auto-correlation is persistent. This effect is just like compound interest and relates to the non-linear power laws that serve to amplify price variations over the longer term. For example a small bias that is repeated (serial correlation) progressively leads to larger and larger longer term price variations.

You can never actually visually determine whether a price movement is actually a random movement or an auto-correlated one ….**so that is why a trend trader needs to apply continued patience to catching all trends according to their subjective definition as they will never know if that trend they are riding is simply a random result with no future potential momentum or an auto-correlated one with future substance.**

**Cherry picking based on visual cues on the right hand side of the chart into a blank uncertain future is a fools errand**. You can apply statistical tests such as Fuller-Dickey tests etc **after the event**, to assess the likely levels of auto-correlation present, but on visual cues alone and while riding these momentum signatures you will never be able to tell which is which.

The bread and butter made by the trend follower is based on the ‘non-gaussian’ nature of market returns. Namely, that for speculation to be successful over the long term, the market return distributions must **not be** normally distributed. The auto-correlation that may exist in an otherwise random data series is what creates these **non-linear** extreme variations to return distributions resulting in their leptokurtic nature and associated ‘fat tails’.

The basics of trend following is that your system seeks to bias the return streams in your favour **by preventing you from ever venturing out too far on the left tail of the distribution.** You do this by ‘cutting losses short’ every time and never allowing a position to extend too far on the left of the distribution. Once this rule has been embedded, you then leave your profits ‘unlimited’ in nature. **You need to keep the right side of the distribution ‘unbounded’ to allow for the very occasional ‘extreme positive return’ which happen occasionally but you can never predict with certainty**. Profit targets actually prevent your ability from riding those market conditions that are the necessary accompaniment to the grueling slog of keeping your head above water. Those that apply profit targets have a sense of psychological and short term success but the most important factor is to allow for the occasional white swan (or abnormality) that ‘pays for em all’ through the strategies unbounded open ended profit nature.

As the markets appear to be efficient and mostly random, you should find that most of your trades will end up in the center of the distribution and the negative and positive returns around this central plot should effectively cancel out. Your overall success therefore is generated by ‘extreme price movements’ aka the ‘fat tails’. For example the trade frequency distribution of returns in the chart below demonstrates the positive skew associated with typical trend following strategies. These extreme positive returns are referred to as ‘anomalies’, as they are the exception as opposed to the rule. You must be diversified to get as much access to these anomalies as possible as they are rare beasts.

But in addition to the application of general rules such as ‘cutting losses short and letting profits run’, the simple application of this premise is not sufficient **‘these days with more efficient markets’** to guarantee long term results with trend following. Other variables that play a strong role in the success of trend following models include:

- Market volatility (more volatile markets improve the overall results of trend following systems). Trend following models tend to reveal better results across major currency blocks with high market volatility. It appears that under high vol regimes, markets tend to become non-Gaussian in nature.
- A high trade frequency has a negative impact on trend model performance. What this infers is that you need to avoid the normal everyday churn. Your trend models are better placed to be active only during more ‘extreme’ times and you should avoid trading activity during more ‘efficient market conditions’.

So how do you catch auto-correlation, market volatility and also avoid the everyday churn? The key ingredient here is to be diversified and to impose rules that only come into effect when price movement is approaching ‘extreme’ levels. In these more exotic extreme conditions, there is a greater probability that participant behaviour will become more coordinated and predictable as many are ‘rushing for the exits’ with only a handful remaining to take advantage of the less competitive environment.

So trend following in a nutshell is **not about striving for profits through prediction**, but in **how you diversify and restrict your trading activities to more exotic market conditions in tandem with strictly managing your risk and leaving your self open for potential unlimited upside**. We talk about ‘following price’ as opposed to predicting price as you simply let your rules dictate when to enter any possible trend which is more often a loser than a winner….However if the markets are non-Gaussian in nature, which we as speculators believe, then your profitability is simply a consequence of abnormal positive outliers associated with this market nature…rather than your predictive ability.

In this context you can have many types of trends that meet the conditions of your rules with an array of different morphologies…**so the exactness of an approach to trend following is a bit of a misnomer**. The techniques applied by technical analysis are not a great help here such as the requirements for a minimum of 2 consecutive higher highs and 2 consecutive lower lows to define a trend by the purists etc. It might look pretty….but that is about as useful as it is.

Once you have developed your broad rules to activate your strategy during extreme conditions, you then** cannot afford to be selective in which trends you decide to take (whether real or not)**. You need to “take them all” as a true trend of substance can only ever be deciphered after the fact (a hind-site measure).

In fact, let the mighty Ed Seykota give you some instant edification to how you need to approach this game of trend following.

Trade well and prosper

Rich B

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[…] a previous blog post we discussed “what is a trend?”, and during the course of that discussion settled on a […]