How to Calculate Shortfall?

Expected shortfall is calculated by averaging all of the returns in the distribution that are worse than the VAR of the portfolio at a given level of confidence. For instance, for a 95% confidence level, the expected shortfall is calculated by taking the average of returns in the worst 5% of cases.

How do you calculate expected shortfall in R?

intercept and slope can be used to compute the expected shortfall for the location-scale trans- formation Y = intercept + slope * X, where the distribution of X is as specified by the other parameters and Y is the variable of interest. The expected shortfall of X is calculated and then transformed to that of Y.

How do you calculate expected shortfall normal distribution?

Example: Expected Shortfall for a Normal Distribution

Can use (5) to compute expected shortfall of an N(µ, σ2) random variable. We find ESα = µ + σ φ (Φ−1(α)) 1 − α (6) where φ(·) is the PDF of the standard normal distribution.