Correlation is a statistical measure of the relationship between two variables. In trading, correlation is used to identify relationships between different securities. For example, a trader might want to know if two stocks move in the same direction. If they do, they are said to be positively correlated. If they move in different directions, they are said to be negatively correlated.

When managing a large portfolio, investors utilize a correlation matrix to help understand the relationships between all of the holdings. Correlation is a risk factor that should be considered when constructing a portfolio. By understanding the relationships between assets, investors can mitigate risks and optimize returns.

Reference [1] proposed a method based on Random Matrix Theory for identifying correlation risks of large portfolios,

*Using Random Matrix Theory, we have provided a universal and versatile tool to analyse the statistical significance and financial origin of risk over-realisation in large portfolios. The eigenvalues and eigenvectors of an appropriately constructed matrix mixing in-sample and out-of-sample data allows one to identify “fleeting modes”, i.e. portfolios that carry significant excess risk, signalling (ex-post) a change in the correlation structure in the underlying asset space. Our proposed test is furthermore independent of the “true” underlying correlation structure, which is obviously unknown to the modeler. We have shown empirically that such fleeting modes exist both in futures markets and in equity markets, and analyzed the directions in which excess risk manifests itself. We have proposed a metric to quantify the alignment between known factors and fleeting modes. As a case in point, momentum exposure clearly appears as a source of excess risk in equity portfolios that is not captured by low frequency correlation matrices.*

We think that this approach has its merits. It utilized in-sample and out-of-sample correlation matrices in order to identify portfolios that carry excessive risks. We note, however, that even using out-of-sample data, the analysis is still backward-looking.

What do you think? Let us know in the forum or comments below.

**References**

[1] Jean-Philippe Bouchaud, Iacopo Mastromatteo, Marc Potters, Konstantin Tikhonov, *Excess Out-of-Sample Risk and Fleeting Modes*, 2022, https://doi.org/10.48550/arXiv.2205.01012

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