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Czekanowski Index-Based Similarity as Alternative Correlation Measure in N-Asset Portfolio Analysis

Excerpt

In quantitative finance we are used to measuring direct linear correlations or non-linear cross-bicorrelations among various time-series. For the former, by default, one adopts the calculation of Pearson product-moment correlation coefficients to quantify a linear relationship between two vectors. This is true if the the data follow Gaussian distribution. In other case, the rank correlation methods need to be applied (e.g. Spearman’s or Kendall’s). A good diversification of assets kept in the investment portfolio often benefits from correlation measures. We want to limit the risk of losing too much due to highly correlated (co-moving in the same direction) assets. While correlation measures of any kind are powerful tools in finance, can it be something better than that?

Remarkably, this is a quantitative biology that delivers new weapon to the table. Biologists love in-depth data analyses and devoted lots of time to the studies of biological samples. The samples can be far different in their origin or composition, however when it comes to counting, comparing and classifying, the language of mathematics standing behind has, luckily, the same denominator with the analysis of financial data samples.

In biology people are more inclined towards talking about similarities, thus similarity metrics. Similarity metrics — also referred to as correlation metrics — are applied to two or more objects (e.g. DNA sequences, etc.). The similarity metric will quantify an association the objects have with each other. This quantification could be a variety of measurements, such as how often the objects are involved in a similar process, how likely the objects are to appear in the same location, etc. The value representing the quantified correlation is often referred to as the similarity coefficient, or the correlation coefficient. This similarity coefficient is a real-valued number that describes to what extent the objects are related.

Visit Quant at Risk to learn about the theory of Pearson’s and Spearman’s correlation coefficients, and to download sample Python code illustrating the functionality based on 39-Crypto-Asset Portfolio during micro flash-crash in May 2021:
https://quantatrisk.com/2021/10/27/czekanowski-index-similarity-correlation-asset-portfolio-analysis-python/.

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