Checking Risk Models with the Mosaic Permutation Test

Financial companies use fundamental factor models to understand how asset returns are connected and to manage risk. But after big events like COVID-19, analysts might wonder if their risk models still fit well. Specifically, they want to know if, after accounting for known factors, the leftover parts of asset returns are independent.

To help with this, we've created the mosaic permutation test. It's a nonparametric goodness-of-fit test for factor models already in use. This test uses modern machine learning techniques to spot when models aren't working right. The best part? It controls the false positive rate without relying on big assumptions or approximations. This means analysts won't waste time and resources fixing models that are actually okay. Let's look at an example. We tested the BlackRock Fundamental Equity Risk (BFRE) model. Generally, it explains the biggest correlations among assets. But we found some real estate stocks that didn't fit the model. Adding new factors improved the model's fit. We've made our methods available in a Python package called mosaicperm.

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