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TL;DR

The normalized measure of linear dependence: \( \rho_{XY} = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \in [-1, 1] \). Correlation 1 means perfect positive linear relationship; -1 means perfect negative.

By Valenke Exam Prep Team·Last updated 2026-06-03

Correlation

The normalized measure of linear dependence: \( \rho_{XY} = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \in [-1, 1] \). Correlation 1 means perfect positive linear relationship; -1 means perfect negative.

Why it matters for interviews

Correlation drives portfolio diversification, factor model construction, and risk management. Understanding its limitations (does not capture nonlinear dependence, unstable over time, correlation is not causation) is critical.

Definition and Mathematical Foundation

The normalized measure of linear dependence: \( \rho_{XY} = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \in [-1, 1] \). Correlation 1 means perfect positive linear relationship; -1 means perfect negative.

Application in Quantitative Finance

Correlation drives portfolio diversification, factor model construction, and risk management. Understanding its limitations (does not capture nonlinear dependence, unstable over time, correlation is not causation) is critical.

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Frequently Asked Questions

Why does correlation increase during market crashes?▼
Empirically, asset correlations spike during crises (correlation breakdown). This is partly mechanical (volatility increases), partly behavioral (panic selling), and partly structural (liquidity dries up uniformly). It undermines diversification precisely when it is needed most.
What is the difference between correlation and beta?▼
Beta measures sensitivity to a factor: \( \beta = \text{Cov}(R_i, R_m)/\text{Var}(R_m) = \rho \cdot \sigma_i/\sigma_m \). Correlation is symmetric and normalized; beta is asymmetric and depends on the volatility ratio.
Can perfectly correlated assets have different returns?▼
Yes. Correlation = 1 means \( Y = aX + b \) with \( a > 0 \). The assets can have different means and volatilities. Perfect correlation only constrains the linear relationship, not the levels.