VaR and CVaR risk measurement

Value at Risk (VaR) and Conditional Value at Risk (CVaR) are critical tools in modern financial risk management, designed to quantify potential losses in investment portfolios under adverse market conditions. VaR measures the maximum loss that a portfolio could incur over a specified time horizon with a given confidence level, while CVaR extends this concept by calculating the expected loss in the worst-case scenarios. These metrics are widely adopted in portfolio management, regulatory reporting, and risk assessment frameworks, reflecting their role in balancing computational efficiency with precision.

Key Differences Between VaR and CVaR
VaR is typically calculated using historical data and assumes a normal distribution of returns, making it computationally efficient. It provides a threshold for the maximum loss at a specific confidence level, such as 95% or 99%. In contrast, CVaR accounts for tail risks by averaging the losses beyond the VaR threshold, offering a more nuanced understanding of potential losses in extreme market events. While VaR is often criticized for its inability to capture non-normal