Multiple financial assets’ time-series data is stored in a matrix upon which we perform principal component analysis to find predominant factors in the market. Random matrix theory helps us to identify the number of factors present in the data, with the top eigenvalue-eigenvector pair bearing a strong resemblance to the market’s capitalization-weighted portfolio. This resemblance is consistent with fundamental concepts from portfolio theory, and can be extended to tensors of implied volatilities for which factors can be constructed using open interest as the analogue for capitalization. In our analyses we initially rely on the support of the Marchenko-Pastur distribution to serve as a cutoff for identification of outlying eigenvalues, but improved criteria can be developed using free probability.

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