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TL;DR

A measure of dispersion: \( \text{Var}(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2 \). The square root of variance is the standard deviation.

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

Variance

A measure of dispersion: \( \text{Var}(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2 \). The square root of variance is the standard deviation.

Why it matters for interviews

Variance quantifies risk in portfolio theory (Markowitz), appears in volatility modeling, and is central to hypothesis testing. The computational formula \( E[X^2] - (E[X])^2 \) is heavily tested in interviews.

Definition and Mathematical Foundation

A measure of dispersion: \( \text{Var}(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2 \). The square root of variance is the standard deviation.

Application in Quantitative Finance

Variance quantifies risk in portfolio theory (Markowitz), appears in volatility modeling, and is central to hypothesis testing. The computational formula \( E[X^2] - (E[X])^2 \) is heavily tested in interviews.

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Frequently Asked Questions

What is the variance of a sum of random variables?▼
\( \text{Var}(X+Y) = \text{Var}(X) + \text{Var}(Y) + 2\text{Cov}(X,Y) \). For independent variables, the covariance term vanishes.
Why do we use variance instead of absolute deviation?▼
Variance is analytically tractable -- it decomposes nicely for sums, connects to the normal distribution, and has elegant properties under linear transformations. Absolute deviation lacks these algebraic conveniences.
How does variance relate to portfolio risk?▼
Portfolio variance is \( \mathbf{w}^T \Sigma \mathbf{w} \) where \( \Sigma \) is the covariance matrix. Diversification reduces variance when assets are not perfectly correlated.