# tES: ES for t distributed P/L In Dowd: Functions Ported from 'MMR2' Toolbox Offered in Kevin Dowd's Book Measuring Market Risk

## Description

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

## Usage

 `1` ```tES(...) ```

## 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 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

## 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.

Dinesh Acharya

## References

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.

## Examples

 ```1 2 3 4 5 6``` ```# 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) ```

Dowd documentation built on May 30, 2017, 1:30 a.m.