LogNormalES {Dowd}

ES for normally distributed geometric returns

Description

Estimates the ES of a portfolio assuming that geometric returns are normally distributed, for specified confidence level and holding period.

Usage

LogNormalES(...)

Arguments

...

The input arguments contain either return data or else mean and standard deviation data. Accordingly, number of input arguments is either 4 or 5. In case there 4 input arguments, the mean and standard deviation of data is computed from return data. See examples for details.

returns Vector of daily geometric return data

mu Mean of daily geometric return data

sigma Standard deviation of daily geometric return data

investment Size of investment

cl VaR confidence level

hp VaR holding period in days

Value

Matrix of ES whose dimension depends on dimension of hp and cl. If cl and hp are both scalars, the matrix is 1 by 1. If cl is a vector and hp is a scalar, the matrix is row matrix, if cl is a scalar and hp is a vector, the matrix is column matrix and if both cl and hp are vectors, the matrix has dimension length of cl * length of hp.

Author(s)

Dinesh Acharya

References

Dowd, K. Measuring Market Risk, Wiley, 2007.

Examples

# Computes ES given geometric return data
   data <- runif(5, min = 0, max = .2)
   LogNormalES(returns = data, investment = 5, cl = .95, hp = 90)

   # Computes ES given mean and standard deviation of return data
   LogNormalES(mu = .012, sigma = .03, investment = 5, cl = .95, hp = 90)