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).

CVaR is the mean value of p(x) conditioned on the fact that x < VaR. This can be written as the mean value of p(x│x<VaR) or:

Where:
p(x)dx= the probability that the next return will fall between x and x + dx
c = confidence level

To compute a Cornish-Fisher CVaR, we calculate:



For more in-depth details on the derivation of this equation, please read The Zephyr Implementation of Value at Risk and Conditional Value at Risk by David Kirkman, Ph.D., Mathematician.

Learn more about Conditional Value at Risk by reading Understanding Value at Risk and Conditional Value at Risk by Marc Odo, CFA, CAIA, CFP, Director of Applied Research.