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 conditional value at risk is used in portfolio optimization for effective risk management understanding conditional value at risk cvar generally speaking if an investment has shown stability over time then the value at risk may be sufficient for risk management in a portfolio containing that investment however the less stable the investment the greater the chance that var will not give a full picture of the risks as it is indifferent to anything beyond its own threshold conditional value at risk cvar attempts to address the shortcomings of the 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 conditional value at risk cvar formulasince 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 var has been calculated it is the average of the values that fall beyond the var cvar 11 c 1varxp x dxwhere 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 breakpointvar the agreed upon var level begin aligned cvar frac 1 1 c int var 1 xp x dx textbf where p x dx text the probability density of getting a return with qquad qquad text value x text c text the cut off point on the distribution where the analyst quad text sets the var text breakpoint var text the agreed upon var text level end aligned cvar 1 c1 1var xp x dxwhere 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 breakpointvar the agreed upon var level conditional value at risk and investment profilessafer investments like large cap u s stocks or investment grade bonds rarely exceed var by a significant amount 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 financially engineered investments often lean heavily on var because it doesn t get bogged down in outlier data in models however there have been times where engineered products or models may have been better constructed and more cautiously used if cvar had been favored history has many examples such as long term capital management which depended on var to measure its risk profile yet still managed to crush itself by not properly taking into account a loss larger than forecasted by the var model 1 cvar would in this case have focused the hedge fund on the true risk exposure rather than the var cutoff in financial modeling a debate is almost always going on about var versus cvar for efficient risk management 