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Hard · Linear Algebra & Machine Learning · Quant Trader interview question · random matrix theory, marchenko-pastur, eigenvalues, covariance matrix, linear algebra
You are analyzing a portfolio of assets and want to understand the statistical properties of its covariance matrix. You have a time series of returns for $N$ assets over $T$ time periods. You calculate the sample covariance matrix. Assuming that the asset returns are independent and identically distributed (i.i.d.) with zero mean and unit variance, and that $T$ and $N$ are large, what distribution does the empirical spectral distribution (ESD) of the sample covariance matrix converge to as $N, T