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.
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.
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