### What is Conditional Value At Risk - CVaR

Conditional Value at Risk (CVaR) also known as the expected shortfall is a risk assessment measure that quantifies the amount of tail risk an investment portfolio has. CVaR is derived by taking a weighted average of the “extreme” losses in the tail of the distribution of possible returns, beyond the value at risk (VaR) cutoff point. It is used in portfolio optimization.

### BREAKING DOWN Conditional Value At Risk - CVaR

Conditional Value at Risk (CVaR) attempts to address the shortcomings of VaR model, which is a statistical technique used to measure the level of financial risk within a firm or an investment portfolio over a specific time frame. While VaR represents a worst-case loss associated with a probability and a time horizon, CVaR is the expected loss if that worst case threshold is ever crossed. CVaR, in other words, quantifies the expected losses that occur beyond the VaR breakpoint.

Safer investments like large-cap U.S. stocks or investment grade bonds rarely exceed VaR by a significant amount. But more volatile asset classes, like small-cap U.S. stocks, emerging markets stocks or derivatives, can exhibit CVaRs many times greater than VaRs. Ideally, investors are looking for small CVaRs. However, investments with the most upside potential often have large CVaRs.

### Conditional Value at Risk Formula

Because CVaR values are derived from the calculation of VaR itself, the assumptions that VaR is based on, such as the shape of the distribution of returns, the cut-off level used, the periodicity of the data, and the assumptions about stochastic volatility, will all affect the value of CVaR. Calculating CVaR is simple, once the VaR has been calculated. It is the average of the values that fall beyond the VaR:

p(x)dx = the probability density of getting a return with value “x”

c = the cut-off point on the distribution where the analyst sets the VaR breakpoint

VaR = the agreed-upon VaR level