Ensemble correlations - the eCORR index

August 1, 2018

When we first published our paper "Express Measurement of Market Volatility Using Ergodicity Concept" we received criticism for "assuming an uncorrelated market". Among some was Risk Magazine, that solicited a similar paper from us only to reject it, mentioning correlations as one of the problems. I noticed a correlation: the less someone trades, the more he is worried about correlations - that, to be accurate would be an anticorrelation. Well, risk managers don't trade, so no surprise.

 

The truth is that if a model is only partially correct, that does not invalidate it completely. Models working under quite strong assumptions can produce viable and useful results in real world, as long as they capture the features that they are supposed to capture. After all, in nuclear physics ±60% accuracy is quite common, yet, nuclear devices work and sometimes frighten the entire world. And we don't have an illusion that some OTC derivatives pricing models vary to ±40% among themselves, and then the S&T desk makes a deal at half the model price. Mathematicians and risk managers need to understand that.

 

On Feb 5, 2018 our eVOL and eVAR volatility indexes worked out just great. Trading professionals remember this recent flash crash that killed XIV. Those who paid attention to eVOL were able to avoid losses or seize an opportunity. We provided the plots for everyone to see in our article with Thomson Reuters: "Market Voice: Past Volatility, Future Volatility: What About Current Volatility?"

 

It now turns out that the same concept we used for eVOL and eVAR indices can be used to calculate market correlations. Thomson Reuters' Senior Data Scientist Joel Sebold shares the merit with us in this observation. All we need is again the prices at the beginning and the end of the period. Taking it through ensemble averaging procedure we come up with the index we call eCORR, that describes the overall level of market correlations. While the details will be provided in a later release, here are some preliminary results.

 

This is Dow Jones from March 20, 2008 up to last month (blue line) and its eCORR index (red line). Clearly, eCORR jumps up when DJI falls and relaxes afterwards. That's just what we expect from a correlation index. But the main thing to note is that there is no lag since eCORR takes only two points in time. Calculations using all traditional methods would involve many days (30, 60, 90, you name it). But who wants to be notified of changed market conditions in a month after the fact? Not winners.

Just like with eVOL, the speed of eCORR doesn't come free. To gain that speed we had to forsake individuality of each index component. eCORR describes just the overall level of correlations observed in the market and correlation of a specific pair of assets can be different.

 

This does not diminish the value of eCORR at all. Quite the opposite, eCORR solves an important problem: since correlations reduce ergodicity, eCORR can be seen as a measure of market non-ergodicity. We can say that when eCORR is low markets are more ergodic than when eCORR is high. A measure of market ergodicity is the order parameter, and eCORR is that order parameter. After many years of search, we finally have an order parameter that is relevant to the markets and one we can work with.

 

More updates to follow soon.

 

 

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August 1, 2018

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