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Asset Management

Erratic correlation: an illustration through Chord diagrams

T. Fuertes


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Let’s start with a simple question: what is the first thing to think about when you create a portfolio? I’m sure several ideas spring to mind, but let’s go to the heart of the matter: what is the relationship between the assets in a portfolio? That is one of the greatest managers’ concerns. They want to be sure that if some assets fall, the others could make up for losses.

That is, baskets with assets that behave in opposite ways might outperform baskets made up of assets with similar behaviour. This is based on the idea that the gains of the assets that rise cancels out the losses of the assets that drop.

It’s difficult to determine if assets have different behaviour, but the most common way to set it is the correlation. In this blog, there’re many posts related to that: we’ve seen how to calculate correlation and dynamic correlation, the relationship between correlation and other measurements, the influence of correlation in a strategy, and many others.

Multi-assets are usually low correlated, that is why a way to find balance in portfolios is to create a multi-asset portfolio. Moreover, it’s supposed that this kind of portfolios is well-balanced in behaviour, as fixed income and equity usually move in different ways.

Here it goes an example. The curve “same behave” is a portfolio made up of some equities with high correlation between them; the curve “diff behave & same assets” is composed of equities with low correlation; and finally, the curve “multi-asset” is a portfolio that consists of fixed income and equity. As you see, the “multi-asset” version outperforms the other versions.

equities by behaviour

Time consistency of correlation

Unfortunately, this is all well and good on paper, but what if it doesn’t always work? I mean, the correlation between assets is not constant and it depends on market moments. In general, a type of assets cancels out the others when their correlation is low; however, this isn’t a rule and it can change when you least expect it.

In particular, fixed income and equity usually behave in opposite way, although some assets in the same family risk can behave differently from the rest. This helps managers to manage portfolios.

Let’s see an example. I’ve plotted a Chord diagram divided by risk family: fixed income in blue and equity in pink. Then I’ve marked the correlation above 0.5 between assets with lines. Notice that the lines’ thickness denotes the value of the correlation, that is, the higher the value is, the thicker the line is.

In 2008 the correlation in fixed income markets was high, and the same happened to equity. There were also some equity assets related to some fixed-income assets, but it wasn’t a prevailing trend. (Notice that I don’t show correlations below 0.5 in the following graphs).

Chord diagram with correlation in 2008

On the contrary, nowadays we are in an unusual market environment where most assets are dropping and, moreover, at the same time. The correlation has increased and performance is poor, and that is the worst for portfolios’ performance.

Next graph shows that in 2018 (until September) there is no high correlation between assets in the same family risk, and both fixed income and equity are moving in the same way.

Chord diagram with correlation in 2018

How can we manage a portfolio in that situation? I must confess that it’s hard and we go on facing it.

Chord diagram

Let me add a further comment on this. The graphs shown are Chord diagrams that display the inter-relationships between data in a matrix. In our case, this matrix contains the correlation between assets (over 0.5). To plot diagrams, I’ve also used Bézier curves, which a French engineer used first to design automobile bodies, although they were known earlier.

There is no package in Python to show Chord diagrams, so I’ve relied on a very useful tutorial.

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