tES {Dowd} | R Documentation |

## ES for t distributed P/L

### Description

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

### Usage

```
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.

### Author(s)

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

```
# 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*version 0.12 Index]