1. What is Value at Risk (VaR)?

Value at Risk (VaR) is a statistical measure that quantifies the level of financial risk within a firm, portfolio, or position over a specific time frame. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period.

2. Understanding Conditional VaR (CVaR)

Conditional Value at Risk (CVaR), also known as Expected Shortfall, is a risk assessment measure that quantifies the amount of tail risk in an investment portfolio. Unlike VaR which gives the worst-case loss for a given confidence level, CVaR gives the expected loss given that the loss has exceeded the VaR threshold.

Where:

• \( \alpha \) — Confidence level (e.g., 95%)
• \( F^{-1} \) — Inverse cumulative distribution function
• \( E[X | X \leq VaR_\alpha] \) — Expected value of losses exceeding VaR

3. Importance of Risk Measurement

Details: VaR and CVaR are crucial for risk management, portfolio optimization, regulatory compliance, and capital allocation decisions in financial institutions.

4. Using the Calculator

Tips: Enter confidence level (typically 95-99%), time horizon in days, portfolio value in USD, and annualized volatility percentage. The calculator uses parametric (variance-covariance) method.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between VaR and CVaR?
A: VaR tells you the maximum loss at a certain confidence level, while CVaR tells you the average loss beyond the VaR threshold.

Q2: What are common confidence levels?
A: 95% (1.645σ), 97.5% (1.96σ), and 99% (2.326σ) are most common in practice.

Q3: What are VaR calculation methods?
A: Parametric (variance-covariance), historical simulation, and Monte Carlo simulation are the three main approaches.

Q4: What are VaR limitations?
A: VaR doesn't measure worst-case loss, assumes normal distributions, and can underestimate tail risk.

Q5: Why use CVaR?
A: CVaR is coherent risk measure (unlike VaR) and better captures tail risk, making it preferred for risk management.