CVaR

Syntax

CVaR(returns, method, [confidenceLevel=0.95])

Arguments

returns is a numeric vector representing the returns. The element must be greater than -1 and cannot be empty.

method is a string indicating the CVaR calculation method, which can be:

• 'normal': parametric method with normal distribution
• 'logNormal': parametric method with log-normal distribution
• 'historical': historical method
• 'monteCarlo': Monte Carlo simulation

confidenceLevel (optional) is a numeric scalar representing the confidence level, with a valid range of (0,1). The default value is 0.95.

Details

Calculate Conditional Value at Risk (CVaR), or expected shortfall (ES) to estimate the average losses incurred beyond the VaR level.

Return value: a DOUBLE value indicating the absolute value of the average losses that exceed the VaR. The value of VaR is returned if there is no return beyond the level.

Examples

Calculate CVaR using historical method at a confidence level of 0.9 based on given returns:

returns = [0.0, -0.0023816107391389394, -0.0028351258634076834, 0.00789570628538656, 0.0022056267475062397, -0.004515475812603498, 0.0031189325339843646, 0.010774648811452205, 0.0030816164453268957, 0.02172541561228001, 0.011106185767699728, -0.005369098699244845, -0.0096490689793588, 0.0025152212699484314, 0.017822140037111668, -0.02837536728283525, 0.018373545076599204, -0.0026401111537113003, 0.019524374522517898, -0.010800546314337627, 0.014073362622486131, -0.00398277532382243, 0.008398647051501285, 0.0024056749358184904, 0.007093080335863512, -0.005332549248384733, -0.008471915938733665, -0.0038788486165083342, -0.01308504169086584, 0.00350496242864784, 0.009036118926745962, 0.0013358223875250545, 0.0036426642608267563, 0.003974568474545581, -0.003944066366522669, -0.011969668605022311, 0.015116930499066374, 0.006931427295653037, -0.0032650627551519267, 0.003407880132851648]
CVaR(returns, 'historical', 0.9);
//output: 0.016057655973