Conditional Value at Risk seeks to measure what occurs when the VaR breakpoint is exceeded.

While VaR provides a loss limit that a manager is rarely expected to exceed, when that limit is exceeded VaR provides little information about the size of the expected loss. One way to address this concern is to instead consider the average value of all possible losses that exceed VaR, weighted by the probability of each loss occurring. This is defined as Conditional Value at Risk (CVaR).

Based on a probability distribution, Value at Risk (VaR) quantifies the expected loss under extreme market conditions. It measures the potential loss in value of a risky asset or portfolio over a specified period for a given confidence interval, typically 95% or 99%.

If we assume that returns are independent and identically distributed, then VaR is a quantile of the return distribution. Mathematically, this means that VaR solves the following equation: