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TL;DR

The maximum loss at a given confidence level over a specified time horizon: \( P(L > VaR) = \alpha \). For example, 1-day 99% VaR of $1M means a 1% probability of losing more than $1M in one day.

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

Value at Risk

The maximum loss at a given confidence level over a specified time horizon: \( P(L > VaR) = \alpha \). For example, 1-day 99% VaR of $1M means a 1% probability of losing more than $1M in one day.

Why it matters for interviews

VaR is the standard regulatory risk measure (Basel accords). Understanding its computation (historical, parametric, Monte Carlo), limitations (not subadditive), and alternatives (CVaR/Expected Shortfall) is essential.

Definition and Mathematical Foundation

The maximum loss at a given confidence level over a specified time horizon: \( P(L > VaR) = \alpha \). For example, 1-day 99% VaR of $1M means a 1% probability of losing more than $1M in one day.

Application in Quantitative Finance

VaR is the standard regulatory risk measure (Basel accords). Understanding its computation (historical, parametric, Monte Carlo), limitations (not subadditive), and alternatives (CVaR/Expected Shortfall) is essential.

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Frequently Asked Questions

What are the three methods for computing VaR?▼
Historical simulation (non-parametric, uses actual return distribution), parametric (assumes normal returns, \( VaR = \mu - z_\alpha \sigma \)), and Monte Carlo (simulates from a fitted model). Each has different assumptions and computational costs.
Why is VaR not a coherent risk measure?▼
VaR violates subadditivity: the VaR of a portfolio can exceed the sum of individual VaRs. This means diversification can appear to increase risk under VaR -- a serious theoretical flaw. Expected Shortfall (CVaR) is subadditive.
What is Expected Shortfall (CVaR)?▼
The average loss given that the loss exceeds VaR: \( ES = E[L | L > VaR] \). It is a coherent risk measure, captures tail risk better than VaR, and is now preferred by Basel III/IV regulations.