tES {Dowd}R Documentation

ES for t distributed P/L


Estimates the ES of a portfolio assuming that P/L are t-distributed, for specified confidence level and holding period.





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 P/L data

mu Mean of daily geometric return data

sigma Standard deviation of daily geometric return data

df Number of degrees of freedom in the t-distribution

cl ES confidence level

hp ES holding period in days


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.


Dinesh Acharya


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

Evans, M., Hastings, M. and Peacock, B. Statistical Distributions, 3rd edition, New York: John Wiley, ch. 38,39.


# Computes ES given P/L data
   data <- runif(5, min = 0, max = .2)
   tES(returns = data, df = 6, cl = .95, hp = 90)

   # Computes ES given mean and standard deviation of P/L data
   tES(mu = .012, sigma = .03, df = 6, cl = .95, hp = 90)

[Package Dowd version 0.12 Index]