LogNormalES {Dowd} | R Documentation |

## 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)
```

*Dowd*version 0.12 Index]