Forcing Co-integration into your Portfolio through System Design

For the majority of those that inhabit the world of financial speculation, the chant of ‘correlation’ can be heard but it is the whisper of ‘co-integration’ that really makes you pick up your ears.

Here is an excellent article that will help you understand the difference.

Once this concept is understood, we as divergent traders can now foray into the different forms of diversification and spend time investing in system design as a method to lock in a more permanent causal relationship than what can be delivered by correlation alone..but before we discuss this, let’s back track to correlation.

Correlation describes best what can be achieved through diversifying into different markets and different timeframes. There will be certain times when assets are more correlated with each other or not….but there are no guarantees of this persistent relationship. In fact correlation when explored within non-linear market conditions needs to be very carefully considered. The adage ‘correlation does not necessarily imply causation’ needs to be kept front of mind in adaptive emerging market conditions. The interrelationship that exists within the nested systems of financial markets means at times causation can rear it’s ugly head leading to varying correlation relationships. A panic sell in one asset class frequently leads to liquidations in other asset classes to fund these shortfalls and before you know it, correlation goes to 1 across asset classes.

There is no better investment class to observe this feature as the equity markets. During long protracted bull runs, individual stocks tend over time to become uncorrelated, whereas during market crisis, this relationship evaporates where a sea of red across the entire market is attributed to a very high correlated relationship within the asset class itself and it’s impact is also felt across other asset classes. Now despite this moving feast of correlation, in general assessing the correlation between asset return streams is a useful measure that gives you that slight edge you need in that return stream which is then treated at the consolidated portfolio level, but is no guaranteed panacea.

In terms of diversification at the timeframe level, we all know that trending markets are not simple linear ascents or descents and tend to exhibit a fractal wave nature of persistent overshoots and undershoots in its overall trajectory. Diversifying into different timeframes therefore allows the divergent trader to benefit from trends up or down at any periodic level but more importantly allow you to benefit from the degree of anti-correlation or low correlation that exists between different return streams across timeframes when compiled at the portfolio level.

Now, despite the ‘no guarantees’, both market diversification and timeframe diversification are highly recommended in systematic divergent trading styles, but this is less attributed to benefits received through low correlation (though it certainly helps and we never turn down the slight edge achieved from the free lunch of risk adjusted returns) and more  attributed to the need to spread far and wide to catch those significant trends that ‘shout at you’.

Remember as trend followers we do not pick bottoms or tops and the meat of our gains lies within the mid-range of the trending condition. We simply follow price and when that price is clearly trending we jump on board the possible gravy train.  We are always late to the trend table reducing the chances of simply acting on an ephemeral signal of randomness as opposed to an auto-correlated time series of more enduring persistence.  Our patience is rewarded in our reduced trading costs by our lack of propensity to pull the trigger on everything that moves. So we diversify far and wide to only pull the trigger on those moves that matter.

While market and timeframe diversification is good but have their limitations at times, there is another way to more deliberately integrate cause and effect into the portfolio equation and ‘almost’ guarantee an uncorrelated relationship between return streams….and this is by forcing co-integration into the suite of systems deployed at the portfolio level by system design.

Let’s look at an example before we investigate ways to achieve this.

Think about what is achieved through a perfect hedge. For example we buy 1 lot of a particular instrument and we sell 1 lot of the same instrument at the same time and hold for a defined period of time. What we are actually doing here is using a system design principle to lock into a forced co-integrated relationship between the return streams of each position that never changes over the course of the trade event. Of course this example in real application is a fools errand as the frictional costs associated with taking these trades lead to a negative overall sum game….however it is the design principle that is important to consider here.

So let’s now assume we have a divergent trend following strategy that is not permanently ‘in the market’ but enters the market associated with a particular trade signal. The strategy in isolation demonstrates a small edge over say 20 years or more with a sufficient data sample to give confidence in the method…….but it has a 30% win rate with a risk/reward of say 1/3 to deliver positive expectancy.

The 30% win rate gives hope to a system designer that there “might” be an alternate strategy that enters at exactly the same moment but with the opposite sign with a divergent open profit condition that also possesses a positive expectancy over the same data series. Remember that a 30% win rate means that there is 70% of unsuccessful opportunities that might be available to an inverse strategy relationship.  But unlike the theoretical hedged position, you have not created a perfect hedged condition as the open profit conditions of both systems vary but you have created a co-integrated anchor point at the entry with oscillation about this. Imagine now how these two return streams co-vary together. There is a stronger causal connection between them and when one system is in drawdown the other will be reaching for the skies.

While the perfect symmetrical relationship is not theoretically possible with the inclusion of the frictional costs of trading, you will be surprised at what less than optimal solutions can achieve at the portfolio level.

It is through system design that you can go further in your quest to ‘force co-integration’ benefits into your portfolio with less emphasis applied to the vagaries that simple uncorrelated systems can produce.

Trade well and prosper

Rich B

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