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TL;DR

Cauchy-Schwarz and Correlation Bounds: A canonical quantitative trading interview question at foundation difficulty. Commonly asked at Two Sigma, Citadel, DE Shaw, AQR.

By Valenke Exam Prep Team·Last updated 2026-06-01
foundationReal Analysis & Inequalities

Cauchy-Schwarz and Correlation Bounds

Asked at: Two Sigma, Citadel, DE Shaw, AQR

Problem
Prove the Cauchy-Schwarz inequality E[XY]E[X2]E[Y2]|E[XY]| \leq \sqrt{E[X^2]E[Y^2]} from first principles. Use it to prove that the correlation coefficient satisfies ρ(X,Y)1|\rho(X,Y)| \leq 1.

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