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Hard · Linear Algebra & Machine Learning · Quant Trader interview question · linear-algebra, eigenvalues, matrix-updates, risk-management
A risk manager at a proprietary trading firm is analyzing the potential impact of a large trade on the firm's portfolio. The portfolio's covariance matrix is represented by the symmetric matrix $A$, with eigenvalues $ \lambda_1 \ge \lambda_2 \ge ... \ge \lambda_n $. The proposed trade is expected to add a rank-1 component, modeled as $vv^T$ where $v$ is a vector representing the trade's sensitivity to different assets. The updated covariance matrix is therefore $B = A + vv^T$. Let $ \mu_1 \ge \