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Estimate the Expected Shortfall (ES)

Source: R/risk_measures.R
est_es.Rd

The Expected Shortfall at level \(\alpha\) is defined as the expected value of the returns under the condition that the returns are smaller than the Value at Risk for the same \(\alpha\) level. Note that an absolutely continuous distribution of the returns is assumed. The three estimation methods are:

  • mean the mean of the samples that fall under the corresponding VaR.

  • median the median of the samples that fall under the corresponding VaR.

  • mc Calculation of the expected value using Monte Carlo integration over the \(\alpha\) levels. One draws mc_samples Monte Carlo samples .

Usage

est_es(sample, alpha, method = c("mean", "median", "mc"), mc_samples = 100)

Arguments

sample

Numeric vector representing the sample upon which the Expected Shortfall is calculated.

alpha

Numeric vector with entries in (0,1) specifying the levels at which the ES is calculated.

method

Method of estimation one of mean, median, mc. For more information see the Description section.

mc_samples

Number of Monte Carlo samples used for the mc method.

Value

Numeric vector with Expected Shortfall estimates (same length as alpha).

See also

est_var()

Examples

est_es(0:100, c(0.1, 0.2, 0.3))
#> [1]  5 10 15